tag:blogger.com,1999:blog-72835843356357804282018-03-05T19:22:43.286-05:00Teaching TransformsEmily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.comBlogger69125tag:blogger.com,1999:blog-7283584335635780428.post-30261335911863968122015-04-27T22:20:00.002-04:002015-04-27T22:20:33.973-04:00All good things...*Today I did one of the harder things I've had to do over my four years of teaching. I told my IB 1 juniors that I wouldn't be returning next year. I told them, truthfully, that leaving them was the hardest part of this decision for me. Partially because they have been a joy to teach this year, and partially because I feel like I'm deserting them mid-stream, half-way through the Herculean task that is the two-year IB Physics course.<br /><br />I teared up a little, but did not start bawling. Victory?<br /><br />And thus, I become a statistic. One of those <a href="http://www.theatlantic.com/education/archive/2013/10/why-do-teachers-quit/280699/" target="_blank">40-50% of teachers who quit in their first five years</a>.<br /><br />So... why? As I told multiple people today, it's complicated. <br /><br />One way I've come to summarize it to myself and family and friends is, "I was too tired, too much of the time this year, to feel the love that until now has compensated for the lack of financial compensation." <br /><br />This year was, in many ways, too big a bite for me to chew. It was my first year with three preps, and all of them had high demands. The new IB 2 prep easily sucked up two hours of prep for every hour I was teaching it in the classroom, as I worked really hard to teach my students advanced physics topics I hadn't deeply considered since undergrad, and to faithfully implement the IB Internal Assessment labs in a way that wouldn't hurt all my students tremendously when I get moderated. The IB 1 prep required considerable rejiggering due to a revised IB curriculum and incorporating the Modeling Physics ideas I learned last summer. And the Physics I class was also considerably rejiggered thanks to the Modeling training, and due to a school-wide push to implement the IB Middle Years Program in our ninth and tenth grade classes. <br /><br />I tracked my time for most of January through March, and found that I was averaging 65 hours per week on high weeks and 55 hours per week on "low" weeks. The number of times I broke down crying in front of my 2 year-old daughter because I was just so tired and had more work to do that night was more than one (and therefore, unacceptably high). Every single vacation this year, I'd reach a point a few days before vacation and think, "There's so much to do on vacation, I might as well not bother going on vacation." (Over a week break in February, I "only" worked 20 hours!) The number of days I did absolutely no work between August and March could be counted on one hand, including Thanksgiving Day, Christmas Day, and a few days over winter break that I was very ill. <br /><br />I take full responsibility for my share of failing to somehow moderate that workload or manage it better. There are many successful teachers at my school who show that it can be done (although the other IB Science teachers were also running pretty ragged this year). But I just can't anymore. <br /><br />So, primarily, I'm tired. And, after four years of being continuously really tired during the school year, and then also working some over the summer to try to moderate the next school year (with little success), I've lost hope. We may be almost at the top of the mountain and about to slide down the other side to the easy living of repeated preps, but I've lost the energy and the emotional fire required to get the rest of the way there. I've rarely felt so literally "burned out" before.<br /><br />The article I linked to above has the following quote: <br /><blockquote class="tr_bq"><span style="background-color: white; font-family: 'Lyon Text', Georgia, Times, serif; font-size: 18px; line-height: 30.0000610351563px;">With the exception of retirement, </span><a href="http://www.urban.org/UploadedPDF/1001287_calderworkingpaper25.pdf" style="background-color: white; color: #458cd5; font-family: 'Lyon Text', Georgia, Times, serif; font-size: 18px; line-height: 30.0000610351563px; text-decoration: none;">studies suggest</a><span style="background-color: white; font-family: 'Lyon Text', Georgia, Times, serif; font-size: 18px; line-height: 30.0000610351563px;"> that there are only a handful of overarching factors that push teachers out the door—family or personal reasons, other career opportunities, salary, administrative support and overall job dissatisfaction. These are largely the same issues that arose in my interviews. Some were wholly unhappy or drained and left in pursuit of another career completely, some wanted more money; some wanted both.</span></blockquote>I cannot fault the administrative support at my school. My principals and head teacher have been, generally, excellent. And I also cannot fault my family for supporting me fully right up until the moment I broke, even though it meant my husband has been doing far more than an equal share of childcare and household management to enable my teaching habit. <br /><br />However, money is a part of it. I feel like saying this makes me an unworthy teacher and an unworthy Christian. Love is supposed to be enough. (And it was, until I got too tired.) But while I felt respected by my administration and my parents and students, I did not feel respected by the state legislature in the way it has chosen to fund K-12 education in this state for the past four years. And I reached a point where I said to myself and my husband (who was in full agreement), "If I'm going to work this much, I need to be paid much more." I worked similar hours as a business consultant, but was paid three times as much. That money made the time feel like an investment in my family's future -- in financial flexibility, in the ability to buy a new car when the old one died, in the ability to hire help to clean the house and pay for quality child care, in the ability to save for college. <br /><br />When I stopped working in business and became a teacher, I knew I would take a huge pay cut. However, I naively looked at the salary schedules posted on every school district's website and thought to myself, "well, at least there's reasonable growth over the first four years". I failed to pay enough attention to the political and economic climate. After four years of teaching, I am making almost exactly what I thought I would be making the first year (before I realized I had already taken a pay cut before even signing the contract). In that time, there has been a big pay cut, one compensatory raise back to where I started, and flat salaries since (accompanied by ever increasing special "teacher taxes" from the state for retiree benefits for which I, and 40-50% of my peers, will never qualify). This puts my salary about 20% lower than I thought I would be at this point. And the day I broke was the day that I found that there would probably be no raises for most teachers at my school again next year. <br /><br />I am developing a depressing theory: teachers are the new UAW workers. Which is to say, there are <a href="http://www.autoblog.com/2015/03/23/detroit-3-uaw-showdown-tiered-wages/" target="_blank">two classes of UAW workers</a> - more senior "Tier 1" workers who get much higher wages than more junior "Tier 2" workers who do the same work, side by side, on the assembly lines. This system is the logical result of a revenue crunch (created in the auto industry by the 2007 recession, created in education by the state legislature's fiscal priorities) in a collective bargaining environment where it is much easier to agree to sacrifices on behalf of future hires than current employees. This played out in my first district-level teaching contract re-negotiation as the addition of several new, shallower "steps" in the most junior years of the salary schedule, as well as a new lower overall maximum salary level that would only apply to junior employees. This plays out at the state level as the legislature has gradually reduced retiree benefits for new hires while increasing employee contributions and costs for those benefits (the days of cushy teacher pensions in Michigan are gone for new hires). And this plays out in news stories like <a href="http://www.mlive.com/news/ann-arbor/index.ssf/2015/04/ann_arbor_schools_anticipates.html" target="_blank">this one</a>, whose headline should be "Next Year's Budget balanced in the face of flat funding because well-paid senior teachers retire to be replaced by new, lower-paid junior teachers, everyone else's salary to be frozen." <br /><br />Business-consultant-me thinks she understands what's happening. Idealist-me is furious that the state seems to feel that the education of all our children is such a low priority that they refuse to invest in the amazing professionals who have dedicated so much time and energy to this work. And pragmatist-me knows I need to get out before my bitterness at the situation pollutes the work I do with students.<br /><blockquote class="tr_bq"><span style="background-color: white; font-family: 'Lyon Text', Georgia, Times, serif; font-size: 18px; line-height: 30.0000610351563px;">“Respected, well-paid lines of work do not have shortages”</span></blockquote>And, frankly, other career opportunities don't hurt. In the week I left school thinking "I'm done" a friend said, "I'll hire you!" (to do what you'd like to do... for approximately double the salary). It is a continual source of amazement to me that so little of the dialog around retaining high quality teachers (especially in STEM fields) involves comparing market rates (and market working conditions) for people of similar talents in other fields. (It probably does not help that I live with such a comparison -- my husband and I both have STEM Ph.D.s from the same prestigious research institution. He makes the same amount of money I do for literally half the hours.)<br /><br />A big part of me is going to dearly miss being in a classroom with students, thinking about science, helping them learn to question each other, build their understanding, identify weaknesses in their own and others' arguments, and together creating models of how the universe works. The rest of me wants to sleep for a month. And has heard rumors of this thing called a "40 hour work week" and would like to try it. If the Michigan State Legislature ever decides to fund teaching in a respectful way again, maybe in a way that lets work-loads approach sustainable levels with competitive salaries, please come re-recruit me. In the meantime, I think there are some databases and spreadsheets with my name on them. <br /><br />*<a href="http://en.memory-alpha.org/wiki/All_Good_Things..._%28episode%29" target="_blank">All good things...</a>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-43074139072410033542014-07-15T22:09:00.002-04:002014-07-15T22:09:21.966-04:00It's a bird, it's a plane, it's a projectile!<b>Model Summary: 2D Motion of a Particle</b><br /><b><br /></b><u>Scenario</u> - How can we tell whether a basketball will make the shot, given a motion map of its position at times early in the shot?<br /><br /><u>Force Diagram</u> - Unbalanced downward Force_{Earth_on_Object} ("Feo - the ugly force"), with no horizontal forces<br /><br /><u>Motion Graphs</u><br /><br /><ul><li>vertical position vs. time - downward facing parabola (assuming up is +)</li><li>horizontal position vs. time - linear with positive or negative slope depending on which direction object moves</li><li>vertical velocity vs. time - linear with negative slope (assuming up is +) equal to -10 m/s/s, similar to 1D free fall</li><li>horizontal velocity vs. time - constant</li></ul><div><u>Motion Map</u> - Position of dot shows change in both horizontal and vertical position, following parabolic path</div><div><ul><li>dots have even horizontal spacing and constant-length horizontal velocity vectors due to constant velocity horizontal motion (no horizontal unbalanced forces)</li><li>dots have changing vertical spacing and direction and length of vertical velocity vectors due to constant acceleration horizontal motion (unbalanced vertical Feo)</li></ul><div><u>Equations</u> - </div></div><div><ul><li>Basically just the CVM equations for horizontal motion and the CAM equations for vertical motion... except...</li><li>The two are linked by time -- the object has the same amount of time in air, for both the horizontal and vertical components of its motion. </li></ul><div><br /></div></div><div><b>Projectile Motion Implementation</b></div><div><b><br /></b></div><div>I have not done projectile motion with my ninth graders, and I don't intend to. I suppose the discussion of the independence of the components of the motion using video tracking might be a fun end-of-the-year / review activity if there were time. It does tie together a lot of good things about the constant velocity model, constant acceleration model, balanced forces, unbalanced forces, and vectors. On the other hand, without trig at least some of the typical projectile scenarios are, I think, out of their grasp. Maybe they could handle horizontally launched problems?</div><div><br /></div><div>I have done projectile motion with my eleventh graders, and I did it with a similar video tracking approach to the introduction. Like many workshop participants, I did it after 1-D motion and before forces, and I'll rethink that placement next year. My students relatively easily caught the independence and distinct behavior of the horizontal and vertical motion components, but had a harder time understanding the implicit clues about velocity and position in the wording of particular problems. Those <i>might</i> be easier to understand if they already had forces under their belts?</div><div><br /></div><div>As mentioned elsewhere, I found the practicum challenging, and I'll be looking for a way to do it that doesn't require the expensive projectile launchers and makes the math a little more approachable for more of my students.</div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-40177141044513719532014-07-15T21:48:00.000-04:002014-07-15T22:00:52.599-04:00Funballs!I seem to have fallen behind on my formal model summaries -- although it feels a bit more like they've accelerated away from me / blurred together a bit while I wasn't looking. So, forthwith I present a summary and implementation thoughts for the forces unit(s).<br /><br /><b>Force Model Summaries - Balanced and Unbalanced</b><br /><br /><u>Paradigm Lab / Scenario</u> - Whacking a bowling ball with a rubber mallet to make it go with a constant speed, speed up, slow down, make a 90 degree turn, and go in a circle. Hitting the ball makes it speed up, slow down, or turn (all forms of acceleration). Not hitting the ball makes it either stand still or go at a constant speed (if it's already moving).<br /><br /><u>Force Rules</u><br /><u><br /></u>First Rule of Forces: A force is defined as an interaction between two objects (and both objects must be included when naming a force with agent-victim notation).<br /><br />Second Rule of Forces: In all "non-spooky forces" (i.e. everything but "Earth force" (gravity), electromagnetism, and nuclear forces) the two objects must touch. <br /><br /><u>Force Diagrams</u><br />Forces on an object can be represented by force diagrams with<br /><br /><ul><li>a point that represents the object</li><li>arrows representing all the forces on that object</li><ul><li>all starting from / pointing away from the point, in the direction of the force</li><li>labelled F_{letter representing agent / letter representing object}</li><li>with lengths at least qualitatively showing relative strengths of the forces</li></ul><li>force arrows that are not aligned with the logical axes of a scenario (e.g. along a ramp) can be drawn with two parts -- one along each of those axes, that add up to the original vector; these are called components.</li><li>Adding the forces along each axes (taking direction into account) tells you whether the forces on an object are balanced or unbalanced (and how big the unbalanced force is) </li></ul><br /><u>Verbal model summary</u><br />"To have an acceleration, you need an unbalanced force."<br /><br /><u>Equation Summary</u><br />a = F_{unbal} / m<br />f_{surface_on_object} = mu{k or s} * F_{surface_on_object}<br /><br /><u>Additional Key Force Experiences / Investigations</u><br /><br /><ul><li><u>normal force</u> - conceptually bridged from an obviously deforming surface to much stiffer ones</li><li><u>weight vs. mass</u> - a relationship between weight and mass is experimentally derived (hey! W = mg, where g ~ 10 N/kg is the gravitational field strength)</li><li><u>Newton's Third Law</u> - try every possible combination of two objects acting on each other and figure out that: "The force that object A puts on object B is equal to the force that object B puts on object A, in the opposite direction" </li><li><u>Newton's Second Law</u> - measure how changing force and changing mass of a system change the acceleration, to experimentally derive a = Funball / m (the equation summary)</li><li><u>free fall</u> - measure the acceleration of some falling objects; realize that it's always near 10 m/s/s as long as the object isn't too big / light (beach ball)</li><li><u>friction</u> - how do many different factors affect the frictional force opposing a constant speed motion? Figure out that they key factors are the material and the normal force, which is encapsulated in f = mu * table force, where the static friction adjusts to the pulling force until the object starts sliding, at which point the kinetic friction is approximately constant.</li></ul><div><b>Force Model Implementation</b></div><div><b><br /></b></div><div>The study of forces, especially balanced forces, is the area of mechanics where I have least used the modeling materials prior to this workshop. The ninth grade FME curriculum I've been using spends several units building up a qualitative study of different types of static forces (weight, magnetic, friction), Newton's Third Law, pressure and buoyancy, and force vectors. It leads with the idea that an object at rest must have balanced forces and works with that for several units before getting to objects in motion and learning anything about kinematics. And then it has, as previously mentioned, a big gaping hole where acceleration and Newton's Second Law should be. (Which is why I've used much more of the modeling constant acceleration model materials.)</div><div><br /></div><div>There are some areas where what I've done manages to overlap pretty closely with what's described above. I did use the idea of defining a force as an interaction, classifying contact vs. non-contact forces, and the agent-victim notation (can't remember where I picked this up...). I have the Preconceptions in Mechanics book and have done a version of the normal force bridging discussion (old foam coach cushions work okay for the "foam" part). And my weight vs. mass lab and friction labs were very similar (although a bit less free-form) to the ones we did in this unit. However, there is very little formal discussion or use of force diagrams in my current curriculum, and since the mechanics instruction leads with forces rather than kinematics, we have to wait a while to get to the moving part of Newton's First Law and Newton's Second Law.</div><div><br /></div><div>I will give the modeling ordering a shot with my ninth graders this coming year, and I will also try being more rigorous about force diagrams. I have struggled to help ninth graders wrap their heads around vectors graphically, especially the components part, and I can't tell yet whether this approach will help with that or not. I strongly suspect I will follow Bryan's lead and cut the ramp problems out of my ninth grade problems. I have tended to qualitatively derive Newton's Second Law with kids pushing other kids on scooters, and while I might extended that to pushing carts with constant forces on tracks next year, I'm pretty sure I will NOT be dong the Modified Atwood Machine with them (unless they invent it themselves). I haven't done the force-probe version of Newton's Third Law, and I will definitely bring that in. And I think doing the free fall lab with the motion detectors seems easy and useful, and will bring that in.</div><div><br /></div><div>Overall, my prior instructional approach has generally failed to dislodge the "motion = unbalanced forces" preconception from a significant chunk of my students, and left an even bigger chunk of my students uncertain what a net force was and how one could relate it to a numerical acceleration. So there's definitely room for improvement! <br /><br />Did we do a practicum lab for forces? If not, does anyone have a favorite one?</div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-12451349611040149752014-07-14T22:11:00.000-04:002014-07-14T22:13:07.936-04:00What is this "Energy" stuff, anyway?After 12 days of discussing the awesomeness of "concept before name", operational definitions, and anchoring experiences, it was a bit jarring to start off the energy unit looking up definitions and formulas on the internet and then launching into a worksheet rather than any sort of concrete experience. Frankly, I think modeling can do better on at least the anchoring experience front. Kelly O'Shea's <a href="http://kellyoshea.wordpress.com/2012/02/05/building-the-energy-transfer-model/">"Building the Energy Transfer Model"</a> seems like a good place to start. <br /><br />This approach takes two different springs whose spring constants have already been determined by the class, and asks student to figure out how to make those springs have a similar "effect" on two identical carts. It took me more tries than I like to admit to fully internalize and communicate to my students that, "<span style="background-color: white; color: #333333; font-family: Helvetica, Arial, 'Lucida Grande', Verdana, sans-serif; font-size: 12px; line-height: 19.200000762939453px; text-align: justify;">...<u>we aren’t necessarily looking for the carts to get to the end of the track at the same time</u>. We are looking for the springs to give them the same effect, so <u>we’re looking for them to have the same speed once the springs aren’t stretched anymore</u>. So we should look carefully at their motion relative to each other (not for which one reaches the end of the track first)."</span> However, in the end it seemed reasonably effective and better than just a bit of hand waving saying, "hey kids, the area under the F-x graph MUST mean something, right? Let's call it energy!"<br /><br />Overall, the insistence in both the Swackhamer reading and Laura's introduction that "energy is a thing, it doesn't come in different types or flavors, it just sits in different containers that we observe different ways" is making it really hard for me to wrap my head around what energy really IS. I've embraced the idea of an operational definition, and the idea that gravitational mass and inertial mass are two different ideas, based on different observational properties of an object, which happen to have the same value. By analogy, we use different observational procedures (operational definitions, in my world) to detect the effects of kinetic, gravitational, and elastic energies. What makes the kinetic, gravitational, and elastic energies have an underlying one-ness that the two kinds of mass do not?<br /><br />Bryan (@BC_ocs) tweeted a link to <a href="http://www.feynmanlectures.caltech.edu/I_04.html">a discussion of energy from the Feyman Lectures</a> today. Feyman says: "<span style="background-color: white; color: #070707; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small; line-height: 23.202320098876953px; text-align: justify; text-indent: 32.00320053100586px;">there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. <u>It is not a description of a mechanism, or anything concrete</u>; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.</span><span style="background-color: white; color: #070707; font-family: Georgia, serif; font-size: 16px; line-height: 23.202320098876953px; text-align: justify; text-indent: 32.00320053100586px;">" </span>Is it too bleak to say that if Feyman couldn't come up with an operational definition of Energy then it's just not possible? If we go to an even more famous physicist, and consider Einstein's E = mc^2, does that give us a route to an operational definition for energy (albeit one that requires a particle accelerator... or at least a radioactive source)? Or is there one hidden in thermodynamics that I just haven't grokked despite taking thermo at least four times in my college / graduate education?<br /><br />Despite my conceptual unclarity, I enjoyed today's labs. It was fun to see what a difference the different snaky lengths could have in their spring constant -- it makes me want to think more about how the material properties of the substance in a spring interact with the geometry of the spring to make the spring constant. And I had contemplated doing the kinetic and gravitational energy labs with which we ended the day, and been too intimidated by the complexity of the materials required, the lab setup, and the procedure to try them. It was good to see those in action. I still think they're pretty tricky to ask students to figure out good procedures and collect good data for, but I can see that it might be worth the effort to try... I'm looking forward to seeing how the discussion of those gets wrapped up tomorrow.<br /><br />I'm also wondering what will be prioritized in the last two days of the workshop. We presumably need to wrap up the energy unit tomorrow morning with the lab discussions, and maybe one more deployment? There are two more units in the modeling binder -- uniform circular motion and momentum. I'm curious to see which parts of those seem important enough to the workshop facilitators to touch on in the remaining 1.5 days (minus last day paperwork). Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-47460889984480011222014-07-12T20:46:00.001-04:002014-07-12T20:46:21.581-04:00Backwards Design, Modeling StyleFriday was a fun and useful day. <br /><br />I learned that actual real life teachers (Bryan) do actually use system schema to help students figure out what objects are interacting as a pre-force diagram step, and I can see how it would be useful. (The way they were described in the Hestenes reading made me think maybe they were an idea that might not have actually panned out when attempted with real live students. Lesson: Don't Doubt The Hestenes.)<br /><br />I also wrote down a general modeling unit planning template that Bryan threw out:<br /><br /><ol><li>Figure out what <b>Prior Misconceptions</b> students are likely to have (<a href="http://www.amazon.com/Teaching-Introductory-Physics-Arnold-Arons/dp/0471137073">Arons</a>, <a href="http://diagnoser.com/">Diagnoser.com</a>, <a href="http://www.uncoveringstudentideas.org/">Paige Keeley books</a>, Laura's Pre-assessments, various articles we've read during this workshop... what resources am I missing?)</li><li>Decide your <b>Instructional Goals </b></li><li>Figure out how you're going to <b>Check for Understanding</b> (sounds so much gentler than Assessment, even if it means the same thing)</li><li>Determine your <b>Anchoring Experience(s) </b>(Paradigm labs, other useful demos and labs)</li><li>Be critical users of available curriculum materials (even the modeling ones) -- figure out <b>How will I use this? How might I modify it for my students and goals? How will we discuss this? What else could I ask students?</b> (This part came from Laura later in the day, not from Bryan.)</li></ol><div>I think this is fascinating, because it's core (#2 and #3) is the <a href="http://www.ascd.org/Publications/Books/Overview/Understanding-by-Design-Expanded-2nd-Edition.aspx?gclid=CPCXoqv8wL8CFUg2aQodJX0AOw">Wiggins and McTighe</a> Backward Design (TM) we all know and love from ed school, but it's got this additional layer of being much more explicit about students' less helpful prior knowledge (#1) and developing concrete experiences to help upgrade those conceptions to ones more aligned with scientific concepts of the world (#4) that seems more specific to science instruction and the modeling approach.</div><div><br /></div><div>I'm super-intrigued to try out Laura's Pre-assessments for each unit (and grateful that she's willing to share them rather than each of us going out and replicating her research into preconceptions that might be uncovered for each unit and good questions to bring those out). The class-wide "<a href="https://www.facinghistory.org/for-educators/educator-resources/teaching-strategies/four-corners">four corners</a>" style debate sounds entertaining in the moment, useful to inform the teacher of where her students are starting (without more student work to read!), and also like a great motivator for students to "figure out the real answer". Win, win, win! I wonder what happens if you go back and redo the voting at the end of the unit...</div><div><br /></div><div>I'm also intrigued to add the <a href="http://www.phystec.org/items/detail.cfm?ID=3686">Ranking Tasks</a> to the mix, as checks for the conceptual understanding that I hope will come with the mathematical and procedural understanding for my students. I also still like the idea of a Lab Practicum, but the version of "Shoot Bierber Bunny" that we did on Friday seemed way over the top for my ninth graders and most of my juniors (although a few could probably come up with something... but since my solution ended up using excel, graphing, and optimization with <a href="http://office.microsoft.com/en-us/excel-help/introduction-to-optimization-with-the-excel-solver-tool-HA001124595.aspx">solver</a> ...). I think I'll come up with a version that doesn't require a <a href="http://www.pasco.com/prodCatalog/ME/ME-6825_mini-launcher/">$180 piece of lab equipment</a> and doesn't ask students to solve simultaneous equations of a variable that only appears in those equations as a sine or cosine of that variable. Probably a ramp that dumps a ball off a table at a set angle, and the students have to catch it in a basket. </div><div><br /></div><div>Workshop colleagues gave me two ideas for DIY projects for those Anchoring Experiences in the Projectiles unit. First, I'm totally investing in some popsicle sticks and index cards so that my students can do <a href="https://drive.google.com/file/d/0BxejbqkJPAIXTERvMFhuWUZlYjZSdEtGRlVVSVQwWm90c3dN/edit?usp=sharing">Dave's Penny Flick</a> (repeatedly) to show themselves that the side-ways projected projectile and the vertically dropping projectile land at the same time. Second, I'm asking my husband for one of <a href="https://drive.google.com/a/wihi.org/file/d/0BxejbqkJPAIXLVpwNGdueHBXSk1fUXNXRGoyRlhSemtTMXVz/edit?usp=sharing">JP's homemade</a> <a href="http://www.pasco.com/prodCatalog/ME/ME-9486_ballistic-cart-accessory/index.cfm">vertical projectile launchers</a>. Our anniversary is coming up in a couple weeks... </div><div><br /></div><div><br /></div><br /><br /><br /><br />Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-81155938909150634922014-07-10T22:35:00.001-04:002014-07-10T22:38:45.868-04:00Invasion of the Pod PeopleNotes from facilitating this morning that I thought were important enough to highlight:<br /><br />Laura's Rules for Facilitation (TM) (Really, "Things to Consider for Facilitation"):<br /><br /><ul><li>What can you do to get students to ask questions of each other? ("Don't underestimate the value of student to student conversation.")</li><li>What will you point out if students don't?</li><li>What instructional points do you want to make?</li><li>What will you do to ensure a positive, questioning (not correcting) discussion culture?</li></ul><div>Strategies for Dead Silence during discussion:</div><div><ul><li>"Do you understand what I'm asking?"</li><li>"Check your partner" (and listen in, and figure out who you want to call on based on what you hear)</li><li>Do a quick boardwalk with the each student tasked with writing down at least one question for another group on a post-it or in their journal</li><li>Be super sensitive to student shut-down</li><li>Plan ahead -- prompt students to participate during board preparation ("I would love for you to share that during the class discussion; in fact, I'm going to ask you about it.")</li></ul><div>I'm probably not alone in being good at pointing thing out during discussion if my students don't, but not being nearly as good at getting them to talk to each other. I do frequently fall back on think-pair-shares whenever the silence gets too heavy. And I usually start a whiteboard discussion with a gallery walk, but not usually with the explicit instruction to develop at least one question for another group. I think I've been generally weak on having instructional goals for whiteboarding problems beyond, "have all the students see how to get a right answer", which is pretty lame, but fixable! </div></div><div><br /></div><div>Something I've been pondering in the back of my head is room arrangement. My Cooperating Teacher from student teaching sold me on the benefits of front-facing paired desks for seating. Students have an obvious think-pair-share partner (which can be usefully manipulated during my monthly seating-chart mix-ups). It's super-easy to make lab groups of 4 by having every other row turn around to work with the table-mates behind them. And for students who have trouble focusing, you don't add the additional challenge of having their natural focus be their peers rather than the front of the room. </div><div><br /></div><div>On the one hand, I'm super comfortable with this mode of teaching at this point. I like what it does for behavior management and supporting students who need help in focusing. On the other hand, it's really hard to make a whiteboarding circle, and I have the impression that a significant chunk of my challenge in getting a good whiteboard discussion going is due to the fact that the presenting group is up front and all the other students (and I) are facing them rather than the whole class facing each other. The obvious solution is to try pods (clusters of desks or tables, one per lab group) like we've been using in this workshop. However, whenever I've used those in the past it has seemed to make it much, much harder for my students to focus on the educational learning experiences of my course rather than socializing off-topic with their group-mates.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://www.newvideo.com/wp-content/themes/hybrid-newvideo/tools/timthumb.php?src=/wp-content/uploads/boxart/NNVG1644.jpg&h=360" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://www.newvideo.com/wp-content/themes/hybrid-newvideo/tools/timthumb.php?src=/wp-content/uploads/boxart/NNVG1644.jpg&h=360" height="320" width="213" /></a></div><div><br /></div><div><br /></div><div>I guess it comes down to the core question of where the students should be focusing. Deep seated in my teaching soul is, I think, a fundamental insecurity that students (especially the ninth graders who make up the vast majority of my students) will stay on task and engaged if their focus is not environmentally directed to the front of the room (where I usually stand to give directions and where a powerpoint is usually projected, not often with notes, but with reinforcing guidance for key discussion questions or the current activity). The part of me that wants my students to take control of their learning is all for being a facilitator / coach of their pod-centered learning experiences. That part of me hopes that if the students are in control of the learning activities, they'll find them engaging enough to stay on-task without environmental reinforcement. The control-freak part of me that wants to make sure students are making the most of their learning time in my room is having trouble letting go of her hatred of the pods. </div><div><br /></div><div>I suppose the hard question is: If my students are on-task when engaged in front-of-the-room focused learning activities that don't actually give them deep conceptual understanding or independent science meaning-making skills, is that better than them being sometimes off-task while working on more self-directed, meaningful learning activities? The rational part of my brain says I should give pods a chance, but the resistant part of me is pretty out of my comfort zone, emotionally nervous, and deeply rooted. That part of me wants to keep my seating as-is and just figure out a way to make a whole class discussion circle from it.</div><div><br /></div><div>If you're a pod person, I welcome tips, tricks, advice, and reassurance about that approach to seating! </div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-33028231648169530112014-07-09T23:09:00.000-04:002014-07-09T23:09:03.860-04:00The Constant Acceleration Particle Model - Summary and Implemetation<div class="p1"><b><u>Summary of the Constant Acceleration Particle Model</u></b></div><div class="p2"><br /></div><div class="p1"><b>Scenario: </b> A low-friction cart moving up or down a ramp, with increasing or decreasing change in position (displacement) for each unit of time.</div><div class="p2"><br /></div><div class="p1"><b>Motion Map: </b> Dots showing position have consistently increasing or decreasing spacing. Velocity arrows starting at each dot gradually increase or decrease in length, showing direction of motion and speeding up or slowing down. Acceleration arrows of constant length above or below each dot show the amount and direction the velocity arrow will change between this time snapshot. </div><div class="p2"><br /></div><div class="p1"><b>Graphs: </b></div><div class="p1"></div><ul><li><u>Quadratic (parabolic) position time graphs</u>, with vertical intercept at initial position, and steepening slope for speeding up or shallowing (flattening) slope for slowing down. </li><li><u>Linear velocity-time graphs</u>, with the vertical intercept representing initial velocity, slope representing the rate of change in velocity with time (acceleration), and sign (quadrant of the graph) representing direction (towards more positive positions or towards more negative positions). Adding up the area under this line between two times gives the displacement (change in position) that occurred during that time.</li><li><u>Constant acceleration-time graphs</u>, with the value of the constant acceleration showing the amount the velocity changes each second. When the sign of the acceleration is the same as the velocity, it represents speeding up in that direction. When the sign of the acceleration is opposite to that over the velocity, it represents slowing down. </li></ul><br /><div class="p1"><b>Equations: </b> </div><div class="p2"></div><ul><li>delta x = 1/2 a t^2 + v0 t -- relates displacement to acceleration, time elapsed, and initial velocity; corresponds to the area under the velocity-time graph.</li><li>v = at + v0 -- relates current velocity to acceleration, time elapsed, and initial velocity; corresponds to the equation for the line on the v-t graph.</li><li>vf^2 = v0^2 + 2 a delta x -- relates final velocity to intiial velocity, acceleration, and displacement; allows those quantities to be related to each other without using time elapsed. </li></ul><br /><div class="p2"><br /></div><br /><div class="p1"><b><u>How will I use this next year?</u></b></div><div class="p1"><b><u><br /></u></b></div><div class="p1">This unit is the first I ever tried to (imperfectly) nick from the modeling materials, because there's a big gaping hole in the FME curriculum I've been using where acceleration and Newton's Second Law should be. </div><div class="p1"><br /></div><div class="p1">For the paradigm lab, I don't have ticket tape timers, but I've experimented with using motion detectors and carts, first on the ramps of the hallways at my school (before I got my PASCO tracks), and this past year with the PASCO carts and tracks. I love the idea of hand marking the position according to the metronome every beat on a very shallow ramp -- I think it'll give my 9th graders (and also my 11th graders) a much more concrete connection to the acceleration motion maps and x-t graphs, before eventually bringing out the motion detectors. I will definitely be adopting the term "slope-o-meter" with my students. </div><div class="p1"><br /></div><div class="p1">I also loved part two of the lab, where students calculated the velocity at the midpoint of each x-t pair "by hand" (or by excel). I have definitely not been this careful about bridging from the position-time data to the calculated velocity-time data, and I think it's a lovely set-up for students as they prepare for thinking about derivatives and approximations of them with finite data in Calculus. It was also super satisfying to see how lovely the v0 terms coincided on our x-t and v-t fits, even though we had a weird overall fit. I think it's good to make the distinction between instantaneous velocity and average velocity and average speed, but I also think it was overly belabored in our in-workshop discussions. That would be vastly abbreviated for both of my classes, I think. </div><div class="p1"><br /></div><div class="p1">I very much appreciated seeing how the constant acceleration kinematic equations were developed from the data without just saying, "look here are these equations that match what you observed" (which is what I have tended to fall back on, especially when faced with imperfect data). I will do my best to copy this next year with the 11th graders. With the 9th graders, I haven't typically tried to get quantitative with the constant acceleration equations. I'll need to think about the time requirements and how I spend my time next year -- I think I can do it if I jettison my buoyancy unit, and probably my waves and sound units (which already were sacrified on the altar of snow days this year). But that means I'll need to make sure to be more careful about weight vs. mass when I get to forces unit, and think about whether / how to work in some thoughts about density and maybe pressure at some point. (Do those show up anywhere in the modeling curriculum, or are students supposed to be clear on them already when they come in?)</div><div class="p1"><br /></div><div class="p1">I loved the acceleration direction dance, and seeing all the work that went into developing it. Figuring out whether an acceleration means slowing down or speeding up is perpetually a source of confusion for all my students, and I'm hopeful that I'll do a better job of helping students clarify this for themselves next year using the Ramp Extension and Stacks of Kinematic Curves (which I have used before, but not to their fullest potential). </div><div class="p1"><br /></div><div class="p1">I haven't typically used the Unit 3 Worksheet 4 more standard "physics problems" before. With the ninth graders I've been rushed and not aiming for quantitative relationships between acceleration, velocity, time, and displacement. With the eleventh graders, I've typically reverted to textbook plug-n-chug problems at this point. It was fascinating, in student mode, to experience solving all of those problems graphically, rather than with the suvat plug-n-chug approach with which I was "raised". With the 11th graders, I will give this a shot, and hope to use it to help them connect all the different representations in a quantitative problem-solving mode. </div><div class="p1"><br /></div><div class="p1">I loved the practicum labs again, both for their sense of fun and challenge and open-ended problem solving and also because they so neatly extended the constant velocity practicums. I will be stealing these wholesale. </div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-73108417309821935932014-07-08T23:31:00.003-04:002014-07-08T23:31:57.039-04:00Schizophrenic Student ModeIt's been observed more than once in this workshop that I have a "schizophrenic student mode". I'm sure it's true... I have a hard time being one consistent student. (I'm also a terrible actor / role-player. I took music classes rather than drama, and I've never been very good at pretending to be anyone but me.) My student mode is me trying my darndest to channel a student mindset, but I definitely have multiple student personalities jumbled up in my head.<br /><br />Sometimes the "student" I'm feeling is one of my more concrete ninth graders. Sometimes the "student" who speaks with my mouth is one of my more precocious, deep-thinking eleventh graders. (It's worth noting that even as a K-12 student, I definitely had real learning experiences as both those students.) And occasionally it's current me grappling with bits of basic mechanics I learned by the "trained monkey" approach a long time ago and haven't gone back and conceptually "fixed" since then.<br /><br />I think the tension force and elements of force diagrams both fall in that last category. Which is humbling for someone with a <a href="http://www.whoi.edu/page.do?pid=97072&tid=3622&cid=19018">freakin' Ph.D.</a> from a well respected <a href="http://mit.whoi.edu/">doctoral program</a>. My favorite learning experiences from today were:<br /><br /><ol><li> The moment Bryan cut the string from which we were hanging an object and stuck a spring scale in the middle of it to measure what was going on with the tension force in the middle of the spring.</li><li>Working through the N3L force diagrams -- I've been thrown by the boxes side-by-side before, I think because I wasn't being careful enough about separating the force diagrams for the two different objects while simultaneously connecting them by making sure the N3L force pairs were the same length. </li></ol><div>Both of those moments touch on subjects where I've definitely had students stewing in confusion, but they were also moments that nibbled away at areas of my own personal less-than-total-physics-clarity. </div><div><br /></div><div>Favorite quotes from today: </div><div><ul><li>"What the physics?!?" (JP) </li><li> "When students are working on whiteboards is not time to check email. Check email during the discussion." (Bryan)</li><li>"You just have to shut up and let students talk." (Bryan)</li><li>"It's not about getting a touchdown every time; it's about moving the ball down the field." (Laura)</li></ul><div>I'm looking forward to seeing the N2L labs play out tomorrow. I've done a super qualitative version with my freshmen (scooters!) and the modified atwood versions with my juniors (kind of a mess), so I'm excited to see ways to make the lab experience and follow-up discussion more productive in both my classes.</div></div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-22011568362339644712014-07-07T23:14:00.000-04:002014-07-07T23:14:26.046-04:00Forcefully Losing My MarblesThe marble "discrepant events" today were interesting. My teacher brain predicted them correctly, but using energy rather than kinematics. It would have helped me wrap my head more around how to use them in the acceleration unit to see how the discussion at least started to play out in student mode. This will probably get mentally filed under "fun if I have time" or maybe "save for energy unit warm-up".<br /><br />The theme of today was forces (mostly static) and I think I've managed to pre-absorb more modeling ideas about this than I'd realized. My students know that a force is an interaction between two objects, and name it F^{type}_{actor}_on_{victim}. We've worked our way through a (slightly materials-limited) version of the bridging analogies for normal force (is there a reason we're not calling it the normal force yet? will we ever?). And we do a whole-class version of the Weight vs. Mass lab with which we ended the day. And I've picked up along the way the distinction between inertial and gravitational mass, and the distinction between the 9.8 N/kg gravitational field strength and the 9.8 m/s/s gravitational acceleration, and I try to help my students see the distinction.<br /><br />On the other hand, I've tended to be very loosey goosey about force diagrams, especially with my ninth graders. Which has, I think, made components I lot harder for them to grasp. It felt a bit like jumping in the deep end of a very cold pool to do Unit 4 WS 1 and start doing slanty, component-y force diagrams on only #4. I have tried to teach graphical addition of vectors and force components, and I think I've mixed it in with the force vectors in such a way that students' confusion ends up compounded. (At least based on my very high rates of retesting my components objective.) I'm curious to try the physical model of #8 to help with building students' concept of components -- my approach to components in the past has, I think, been was too abstract. I'd love to give each group of students two strings, a hooked mass or two, and have them work through the example Laura showed us for themselves.<br /><br />I've typically done the weight vs. mass lab very quick-and-dirty by having each table pair weigh one hooked mass and plot the observed force against the nominal listed mass on a projected graph that everyone used to recreate the graph for themselves in their own lab book and come up with a best fit line. We usually get something quite close to 10 N/kg, and then use that line to make the F^gravitational_earth_on_object = 10 N/kg * mass equation. The advantage of this approach is that it's fast (20-30 minutes for the whole thing), and each student pair gets to make one measurement for themselves. The disadvantage is that they don't experience for themselves a range of masses and notice the different spring compressions / extensions. On the other hand, they've already done that with a different Hooke's Law lab... Not sure if the extra time gives a big enough pedagogical payoff to do it the way we did today. Will see how the semester plays out.<br /><br /><br />Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-24511566848366336362014-07-06T19:53:00.001-04:002014-07-06T19:53:43.170-04:00You're in charge here (but I'm really in charge here)<div class="p1">Last Wednesday was an exciting day! The bowling ball force exploration is fabulous, and has renewed my zeal for the quest to acquire a set of 7 or 8 for myself (although it's worth noting that a local bowling alley let me borrow that many balls for a week, if acquiring them outright is too challenging an initial goal). I've only taught the bowling ball activity once, and I think (as with many of these learning activities) my debrief of what students figured out from it could have been a lot more meaningful and in depth, based on what Bryan started to do with it at the end of the day. I love the idea of working in some video analysis and timing multiple segments of 2 meters when bowling the ball down the hallway to verify and reinforce the constant speed motion. I'm interested to see if/when the phrase "Newton's First Law" comes up in the discussion on Monday.</div><div class="p2"><br /></div><div class="p1">The Ramp-n-Roll activity is something I've tried to do with students before and had a huge flop. The UI was confusing, my students didn't have a strong enough conceptual basis to get far with it beyond guess-and-checking, and I was trying to do it as an independent activity while I was consulting with subgroups on Cedar Point projects, which meant I wasn't available to help guide their efforts. It was eye-opening and fun to see that it was challenging even for two confident physics teachers in teacher-mode to get the details of the three models right. I think I'll try it again, but with more respect for its challenges to students and teachers, and with a stronger conceptual foundation, being more careful about where I place it in my lesson sequence.</div><div class="p2"><br /></div><div class="p1">I'm also super excited to dig into diagnoser.com more. My initial impression is that it's a fabulous tool for quickly checking more for myself what misconceptions students might have about a particular topic as I prepare for discussions. And I'm intrigued by the pre-test / post-test possibilities for working with students. (And more emergency sub plans are always good.)</div><div class="p2"><br /></div><div class="p1">Wednesday some of us also got to take our first try at facilitating a discussion in this workshop. I had the opportunity to take the lead when my group was facilitating, and it was fun! And easier with teachers in "student mode" than real students, in my experience. I, for one, was helped a lot by "Student Eric" spontaneously writing down ideas other students suggested on his whiteboard. My real students have done this exactly never. (Although maybe they will once I am a Super Modeler?) </div><div class="p2"><br /></div><div class="p1">The aspect of it I found most intriguing was how much I was accessing the "student mode" part of my brain as I was facilitating. My new slogan should be: "Student mode -- not just for playing a student". I have tried to whiteboard physics problems with my students in the past, and I am usually trying to draw students beyond the presenting group into the conversation (rarely as successfully as I'd like, at least in part because I'm usually rushing things and not consistently enough giving time and space for alternate approaches to the problems). The sensation of working in student mode to control the pacing of the presentation and put myself in the quiet students' shoes was new and super helpful. </div><div class="p2"><br /></div><div class="p1">There are obviously a ton of things to talk about in the Modeling reading we were assigned this weekend. (As a side note, I have read a lot of scientific papers and a fair number of education journal articles in my time, and this is strikingly the most elegiac of them.) The part of the article I think I'm having the most resistance to is this idea that a guide-on-the-side, facilitator-not-teacher "never acts as an authority or source of knowledge" but simultaneously "remains unobtrusively in control of the agenda". </div><div class="p2"><br /></div><div class="p1">It seems disingenuous to simultaneously tell students directly or indirectly, "I'm not in charge here -- you have to figure this out for yourself" and simultaneously tell them, "But here's the learning activity we're doing today, and I'm going to steer the discussion to get us where we need to go". I see why we need both the students to take control of their own learning and the teacher to make sure things don't go too far off the rails. But adolescents are expert, super-sensitive hypocrisy detectors. How do we get them on board with "you're in charge here (but I'm really in charge here)"? </div><div class="p2"><br /></div><div class="p1">Maybe I need to be clearer about what we're each in charge of? Another question I'm pondering after reading the article is: What's the difference between a "physics coach" and a "physics teacher"? I've never been a sports coach. But it seems like the coach's job is to help the players build skills and strategies so that they can go out and perform independently at a higher level. And the coach giving too much physical help with the conditioning or skill building exercises does no good to the student when they go to their competition and the coach is relegated to the sidelines. So maybe I need to think of it as, "the students are in charge of building their own physics questioning, experimental, reasoning, and conceptual skills; I'm in charge of providing them activities and guidance that will give them the opportunities to build those skills"? </div><div class="p2"><br /></div><div class="p1">How do y'all think about that dichotomy: we want the students to take charge of their learning… as long as it follows our agenda?</div><div class="p2"><br /></div><br /><div class="p2"><br /></div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-35805683676653461252014-07-02T13:16:00.000-04:002014-07-02T13:17:08.218-04:00"But what's the answer?!?" (I hear my students cry)<div class="p1">(Note: this blog is posted a day after it was written, as my internet connections as down last night. Also a really big tree came down in my neighbor's yard Monday night, and our willow tree has several fewer branches than it did Monday evening. These phenomena may or may not be related.)</div><div class="p2"><br /></div><div class="p1">I found myself resisting the open-ended, cycling, somewhat repetitious and jumbled nature of the modeling whiteboard discussions today (Tuesday). </div><div class="p2"><br /></div><div class="p1">At one point I thought, "I'm not sure I would have enjoyed being a student in this kind of class -- do students learn to enjoy it?". I was mostly reacting to the frustrating sensation that there is almost never just a simple answer or conclusion to any question. And the prompting facilitator questions sometimes feel like the "guess what the teacher's thinking" game.</div><div class="p2"><br /></div><div class="p1">I guess a follow-up question would be, "How important is it for learning to be enjoyable?" I suppose there's an argument to be made for building moral fiber by persisting in unpleasant tasks. On the other hand, I found it a lot easier to eat my spinach once I discovered forms of it that I find tasty. (Slimy nasty canned spinach of my childhood - no. Fresh spinach leaves in a salad, or sauteed with garlic, or made into saag paneer - yes, please.) </div><div class="p2"><br /></div><div class="p1">So, what makes the circular, repetitious, jumbled nature of these discussions palatable to students who are familiar with, comforted by, and good at the traditional approach to teaching and learning, where the teacher sometimes (often) provides answers? (Or are the discussions less circular, repetitious, and jumbled with real students? Doesn't seem likely, but may our student mode is failing?)</div><div class="p2"><br /></div><div class="p1">As we were deep in the weeds of whether motion maps show instantaneous or average velocity with their velocity vectors, I thought to myself, "I love physics and I am bored by motion maps right now. What will keep my students awake?" I suppose it will be somewhat a matter of tailoring the discussion to the level of my students. But are students really engaged by questions about whether the dot should have an arrow on it or not? Does it depend on how deeply we're tying it to the details of the actual, real-world, physical motion? (I did love the graphs Bryan put up at the end showing how the acceleration arrows could be pictured as the vertical side of the slope steps on the a v-t graph, adding to or taking away from the velocity lines at each position.)</div><div class="p2"><br /></div><div class="p1">I'm excited to have workshop participants try leading whiteboard discussions tomorrow. If I'm called on to do it, I think my biggest struggle is going to be restraining myself from "giving answers".</div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-12913617934011824582014-06-30T23:26:00.001-04:002014-07-01T09:33:11.904-04:00Constant Velocity Model -- Summary and Implementation ReflectionMy current impression is that the constant velocity model is a tool for describing and solving problems related to objects moving with a constant velocity. Two common examples of such motion would be much of our motion in cars between stop lights and falling objects that have reached a terminal velocity.<br /> It includes several complimentary representations of motion, from which the speed, direction, and (often) starting point of the motion can be determined:<br /><br /><ul><li> a verbal description of the motion (the object moves a constant distance in each unit of time, in a constant direction)</li><li>a diagram of the motion in the form of a motion map with equally spaced position dots at each "snapshot" of equal time intervals and equal length velocity arrows starting at each position dot and pointing in the direction of the motion</li><li>a graph of position vs. time, with the vertical-intercept representing the starting position of the object (relative to a designated reference point) and the slope representing the speed of the motion through its steepness and the direction of the motion through its sign</li><li>a graph of velocity vs. time, which by defintion of this being a "constant velocity model" will be a constant value whose magnitude and sign correspond to the slope of the position-time graph</li><li>an equation that comes from the position-time graph: x = vt + x0, where x is the position relative to the reference point, v is the velocity of the object, t is the time elapsed since the beginning of the motion, and x0 is the starting position of the motion.</li></ul><div>It can be developed by a inquiry activity in which students track the position of a <a href="http://www.amazon.com/The-Original-Lighting-Flipping-Spinning/dp/B004G0RWQK/">constant-velocity vehicle</a> from a variety of starting points as a function of elapsed time, graph that position-time data, consider the significance of various features of the graphs and equations. It is then, within the modeling instruction materials, additionally translated to the motion maps and velocity-time graph representations through Socratic small group and large group discussions. (Is this an operational definition of creating operational definitions?)</div><div><br /></div><div>I have previously done parts of this modeling-building process with both my ninth grade Physics I and my advanced 11th grade Physics course. In general, my students seem to get comfortable with the position-time graphs quite quickly but struggle much more with the velocity-time graphs and figuring out how to go backwards from the v-t to x-t graphs. And the idea that the area under the v-t graph tells the displacement, and the difference between average velocity and average speed are fairly fuzzy to many of them, at least in part because I'm not as careful about differentiating position, distance, and displacement up front as I could be. Based on my experience in this summer's modeling workshop, I will be strongly considering the following alterations next year:</div><div><ul><li>I will try my best to steal a (possibly shorter version of) Laura's discussion leading to operational definitions of position, reference point, distance, and displacement. </li><li>I've done the Buggy Lab with both my courses. However, each time I prescribed that everyone do two identical runs, one forward from the reference point (ish) and one back towards the reference point from high positions. I loved the combination of similar first runs with a broad variety of second runs for different groups (different starting positions, speeds, and directions, in various combinations) to bring interest and richness to the succeeding whiteboard discussion of the results. I will definitely do that next year. </li><li>I haven't really used Predicted Graphs before -- I like the idea of asking students try to think through the relationships between factors graphically. I have traditionally had them make "If, then, because" hypotheses verbally, and I wonder if you lose anything by not having students write out the verbal explanation of their thinking.</li><li>I also finally feel like I understand the 5% rule enough to try introducing it to my classes, although I remain concerned that it will creep into my IB students' externally moderated lab reports in places it doesn't belong.</li><li>I wonder about alternatives to reserving one of my school's two laptop carts every time we do a lab and the students want to be able to fit lines for 5 or 10 minutes per group. I think I should educate myself on how they can do it with the graphing calculators many of them bring, the Open Office distribution on the linux desktop in my room, and maybe the free Logger Pro Lite software I could have the students with laptops download. (Does the free version do curve fits? I'll have to check.)</li><li>It was very helpful to see the model development and summary through the unit. I will be more conscious about explicitly generalizing and publishing the consensus of the classes on the graph and the associated equation after the buggy lab discussion next year, and adding to it as we add further representations (motion maps, v-t graphs).</li><li>I've explained motion maps by first asking students to try to come up with their own system for diagraming motion, and then guiding them into invention something similar to motion maps, illustrated with the motion maps reading. I feel like my introduction of that was relatively effective this spring, although I love the blinking open-close kinesthetic experience. I asked my students to image a flash photo taken in the dark once per second, and that worked pretty well for them, but I think adding the blinking will help clarify it.</li><li>I loved "walking the graph" (and think it's also helpful for walking the motion map, and probably for walking the v-t curve, too) -- wish I'd thought of this sooner. I think it will really help make the graphs and motion maps more concrete for my students.</li><li>I've used most of the worksheets in Unit 1 with my students, but I've been very guilty of underutilizing their discussion and conception clarification potential. I think I often take for granted that my students are using language the way I hope they will, and don't ask for additional explanation often enough to realize where they're not as clear as they seem. I've also been super guilty of glossing over the highly useful ambiguities in the worksheets ("Is away from the detector always in the positive direction?", "What happens between the dots on a position - time graph we're given without actually seeing the motion for ourselves?").</li><li>I try to whiteboard most of the worksheets in some form, but I usually let student groups choose which problems they do, and usually each problem is done only by one group. I'm still getting used to the "assign two problems per group" strategy that seems to be much more common in the workshop, but I can see some advantages of it. I'm willing to try it, although it will require getting a lot more whiteboards than I have now.</li><li>I've already mentioned that I have a huge crush on the "Movie Shot" end of unit lab. I will be stealing this. </li></ul></div>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-46840981907035700282014-06-29T15:54:00.005-04:002014-06-29T15:56:47.368-04:00What is physics? (And who are you asking?)Mid-afternoon Friday, I tweeted: "<span style="background-color: white; color: #292f33; font-family: 'Helvetica Neue', Arial, sans-serif; font-size: 14px; line-height: 18px; white-space: pre-wrap;">What do you do with / for the student who zones out during discussion? The one always saying, "What did you say?" </span><a class="twitter-hashtag pretty-link js-nav" data-query-source="hashtag_click" dir="ltr" href="https://twitter.com/hashtag/semimodphys14?src=hash" style="background: rgb(255, 255, 255); color: #93a644; font-family: 'Helvetica Neue', Arial, sans-serif; font-size: 14px; line-height: 18px; text-decoration: none; white-space: pre-wrap;"><span style="color: #bec98e;">#</span><strong>semimodphys14</strong></a><span style="background-color: white; color: #292f33; font-family: 'Helvetica Neue', Arial, sans-serif; font-size: 14px; line-height: 18px; white-space: pre-wrap;"> </span><a class="twitter-hashtag pretty-link js-nav" data-query-source="hashtag_click" dir="ltr" href="https://twitter.com/hashtag/metoday?src=hash" style="background: rgb(255, 255, 255); color: #93a644; font-family: 'Helvetica Neue', Arial, sans-serif; font-size: 14px; line-height: 18px; text-decoration: none; white-space: pre-wrap;"><span style="color: #bec98e;">#</span>metoday</a>". I don't know if it's being short on sleep, the Friday-ness of it all, or a real problem with spending most of the day whiteboarding worksheets, but I did have a really hard time focusing on Friday. And I do have students who have an equally hard time focusing on a discussion that I and some of my students find engrossing. I wonder what happens to those students when whole-group whiteboard discussions become a primary mode of instruction. Maybe they make up for it in the small-group discussions and catch up with the model summary at the end of the discussion?<br /><br />Reading this weekend, I found the Hammer "Two Approaches to Learning Physics" article VERY useful. I hadn't previously thought to step back from individual physics concepts to the overall concept of what it means to learn physics and do physics. The two example students made it really concrete for me, and it gradually became clear to me that I, Dr. Jekyle and Mr. Hyde-like, teach two different conceptions of physics. With my ninth grade class, I have a lot of leeway on content coverage, I've deliberately and repeatedly chosen depth over breadth, and I think I do a reasonably good job of having students develop the qualitative concepts before the equations (especially fall semester, when I do <a href="http://www.phystec.org/items/detail.cfm?ID=4438">CASTLE</a> and we don't really get any equations until November or so). With my 11th grade class, which I taught for the first time this past year, I felt very pressured to cover a large syllabus of content to prepare my students for the IB Physics exam, and I think I've slipped into physics = formulas mode much more than I like to contemplate. The idea of pacing as a marker for how much time is allotted for independent reasoning and sense-making was a revelation to me.<br /><br />As I started the second article, Mestre on "Learning and Instruction in PreCollege Physical Science" I noticed the 1991 publication date. Then I went back and noticed the 1989 date on the Hammer article. I remarked to my husband how depressing it was that all these amazingly true and useful ideas about teaching and learning physics were published 25 years ago and yet haven't seem to have any impact on the mainstream approach to teaching physics at any level. My intuition is that this is at least in part because Mestre's list of science education reform stakeholders at the end of his article excludes some of the most important players. <br /><br />At the beginning of my education program and the University of Michigan, we pulled out the Michigan High School Content Expectations for our subject area and went through them. We were taught that the processing of designing instruction started with those standards. Most science teachers I know would love to take a deeper, more conceptual, more student-driven approach to learning, but feel that their primary responsibility, the job on which they are being evaluated, is to teach their students as much of the HSCEs as they can in the time available. And they feel that the traditional transmission method is the only chance they have to come anywhere close to that. <br /><br />You can argue that the traditional transmission method is actually less efficient at achieving real learning than a slower, more constructivist method. I think that probably depends very highly on what instrument you're using to measure the learning. If it's individual interviews or written explanations of scientific concepts, I believe that the constructivist approach is more productive. If it's a very facts-driven standardized test like the MEAP, I suspect that (much as the formula-driven student did better in her physics class) the transmission method instruction gets higher scores. But I'd love to see data that proves otherwise. <br /><br />Which leads me back to Mestre's list of stakeholders who should be involved in physics education reform. It includes teachers, scientists, and textbook publishers. It does NOT include the state or federal departments of education, the legislature, or parents. And yet, they are the ones who "pay the piper" through taxes and appropriations, and thereby "call the tune" by setting standards and evaluations of both student learning and teachers. Maybe the Next Generation Science Standards relax the breadth requirements and allow more breathing space for students to construct their own understandings. I haven't read them closely enough yet to have an opinion on that. But I also have doubts that they will be easily adopted by Michigan, given the resistance to adopting the Common Core and replacing the MEAP in the legislature over the past year or two. <br /><br />We're inviting our school administrators to come visit this workshop. That's important. But maybe we should also be inviting our local state senators and representatives? And the heads of our PTOs? Are we spreading the research-supported view of a better conception of what physics (and science) is to the right people?Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-39309011026311035652014-06-26T22:42:00.002-04:002014-06-26T22:42:52.255-04:00Lights, Camera, Action!I really enjoyed the last half hour of the workshop today, when we did the constant velocity "action movie shot" practicum lab. I've done a much less exciting "race prediction" version of this with my constant velocity buggies, and even that was fun, But the variation on the different scenarios and the dramatic window dressing made it a lot more fun and funny, as well as more challenging in applying the different concepts for this unit. I will definitely try to incorporate the "Chase Scene", "Get Away Crash", and "Blind Collision" scenarios and the "We have to get the perfect shot the first time -- if you get it, you're a Hero, if not you're a Bum who's never work in this town again!". <br /><br />Practicum labs in general seem like a cool, fun tool for application, extension, and assessment that I've underutilized. I hope we do more of them.Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-74056391973943922672014-06-25T20:44:00.000-04:002014-06-25T20:48:54.163-04:00Minecraft Babies and Concrete CanoesOne of the hardest concepts I currently tackle with my ninth graders is Buoyancy. It's the culmination of the mass vs. volume vs. weight vs. density vs. pressure unit. We learn to distinguish mass from weight (by thinking about what they are, how you measure them, and what they mean on the International Space Station). We find a relationship between mass and volume (by measuring them with a balance and a graduated cylinder and plotting them against each other to find the density of some aluminum rods). Then we think about a thumb tack and Newton's Third Law to define pressure and think about it in solid-solid interactions and fluid situations (swimming pools, airplanes). We measure the weight reduction of prisms of the same volume when submerged in water (it's the same! even if the prisms are different materials!). Then we roll all that together into two derivations that we work out together, both of which blow my students' minds (some in a good way, some in a bad): first the depth dependence of fluid pressure, then the fact that the difference in pressure on the top and bottom of a container reduces to be equal to the weight of the fluid displaced by the container.<br /><br />This unit does not immediately "work". I know, because I do Standards Based Grading, and the buoyancy concept is the one I do the most additional help and retesting on (although my Measured Uncertainty, Calculated Uncertainty, and Sig Fig concepts are close on its heels). Eventually, with further small group discussion and additional hard thinking on the part of my students, most of them internalize that for floating objects (e.g. concrete canoes) the buoyancy force must equal the gravitational force on the object. And some of them grok the connections between the volume of the displaced liquid, how the density of that liquid functions as a conversion factor between volume and mass, and how the gravitational field strength functions as a conversation factor between mass and weight. But it is painful. <br /><br />Every year I think about omitting buoyancy, and every year (so far) I've decided to mix things up instructionally and give it another shot, because it's such a beautiful combination of all these challenging, interrelated, but distinct concepts (volume, mass, density, pressure, force). This comes to mind both because one of yesterday's Hestenes readings bemoans the lack of a solid understanding of buoyancy in physics students, and because so many of those tricky fundamental concepts feature in tonights' Arons reading. <br /><br />All of which is to say, the weakness that Aron mentions are certainly ones I've seen in my students. I see how we've incorporated counting squares for area and displacement volume measurements in the Unit 1 labs. But do density and buoyancy come in anywhere? A casual flip through my binder of Modeling Mechanics units doesn't seem to include buoyancy. Is there a Modeling unit that deals with these basic ideas about different ways to describe how big something is or how much of it there is (length vs. area vs. volume vs. density)? And that addresses fluid forces? Is it off in some Physical Sciences set of materials?<br /><br />My favorite exercise for addressing the scaling issue is a warm-up I developed after the first time I read some of these sections. I call it my Minecraft Baby warm-up, as to figure out the right answer, I guide them through sketching a Minecraft baby and then increasing each of it's dimensions one at a time. It goes as follows: <br />"Consider an newborn who weighs 40 N. During a year she grows so that each dimension of her body (length, width, height) increases by 40%. How much will she then weigh? (Assume constant density.)"<br />It is accompanied by cute pictures of my daughter as a newborn and at almost-a-year. (This may be why it is one of my favorite warm-ups.)<br /><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-Svuh4qEXbN4/U6truaWQCtI/AAAAAAAAWH4/f-7ibjQ2tRs/s1600/Newborn+for+blog.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-Svuh4qEXbN4/U6truaWQCtI/AAAAAAAAWH4/f-7ibjQ2tRs/s1600/Newborn+for+blog.jpg" height="191" width="320" /></a><a href="http://2.bp.blogspot.com/-1Ie-cQAUmAA/U6truQXB9aI/AAAAAAAAWH0/KoBnkNVc4pA/s1600/Almost-a-year+for+blog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-1Ie-cQAUmAA/U6truQXB9aI/AAAAAAAAWH0/KoBnkNVc4pA/s1600/Almost-a-year+for+blog.jpg" height="320" width="185" /></a></div><br />Would anyone like to guess the most popular answer (by far)? And the second most popular answer? (Hint: the answer to at least the first is in the Arons section on Scaling!)<br /><br />Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-12744783823914592472014-06-24T23:15:00.000-04:002014-06-24T23:15:31.200-04:00What I want to get out of this Modeling Workshop (Quantitative Version)This morning, we were asked, "What do you want to get out of <a href="http://www.mimodelinginstruction.org/">this workshop</a>?". My basic answer was, "to be a better physics teacher". But I actually have numerical goals for that. <br /><br />For the last three years, ever since I audited a few afternoons of this workshop in 2011 and then was fortunate enough to be added to the modeling instruction list serv, I have given my ninth-grade students the (Simplified Language) FCI as a pre-test and a post-test at the beginning and end of my force and motion units (currently based mostly on Science Curriculum Inc's <a href="http://www.sci-ips.com/p_fme_txtbk.htm">Force, Motion, and Energy</a>). Each year, my ninth grade students' pre-test scores have averaged 27-28%, completely in line with the first year physics high school students in the Hestenes 1992 paper. And each year, my gains in percent correct answers have grown a bit, but from a non-awesome baseline -- 10% to 11% to 14%. I do much better with some students, but not with all of them. I want to be the kind of physics teacher who has average gains of 35-40%. (Figure: "Traditional" vs. "Interactive Engagement" FCI gains from Hake (1998) vs. my data for individual students this year and overall averages for the past three years.)<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-PYrZpYx_sAA/U6ozixBdcLI/AAAAAAAAWHI/jy6A-FhcwI4/s1600/FCI+for+blog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-PYrZpYx_sAA/U6ozixBdcLI/AAAAAAAAWHI/jy6A-FhcwI4/s1600/FCI+for+blog.jpg" height="320" width="290" /></a></div><br /><br />This year, based on some suggestions from the modeling listserv, I added the Lawson Classroom Test of Scientific Reasoning to the mix (Lawson, 1978; Lawson et al., 2000). Although I find the Information Processing discussing in the Hestenes 1979 article way too rational and mechanical to be a very useful view of my very human students, I do think the use of the Piagetian framework for student's reasoning skills should be helpful. When I analyzed my Lawson data, I had two pleasant surprises and one unpleasant one. Can you tell what they were?<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-cCt31EfIOQo/U6o09bDN8qI/AAAAAAAAWHU/bO2naJEmrXI/s1600/Lawson+2+for+blog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-cCt31EfIOQo/U6o09bDN8qI/AAAAAAAAWHU/bO2naJEmrXI/s1600/Lawson+2+for+blog.jpg" height="140" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-WuLrDB_4v7Q/U6o1BfwtO1I/AAAAAAAAWHY/9iSQPeqhBtM/s1600/Lawson+1+for+blog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-WuLrDB_4v7Q/U6o1BfwtO1I/AAAAAAAAWHY/9iSQPeqhBtM/s1600/Lawson+1+for+blog.jpg" height="227" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">On the plus side, my students come to me further along the concrete-formal transition than the average ninth graders collected by O'Donnell (2011). They also make good progress in moving along that transition over the course of the year. On the minus side, there's no correlation between their reasoning skills and their gains on the FCI. I am not, as a teacher, taking advantage of their scientific thinking abilities to help them do a better job of constructing solid Newtonian physics concepts. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">That's why I'm here. I want to do better. That first graph, while a bit depressing right now, offers hope that better is attainable. (Although I always wonder how valid the benchmark lines are for 9th grade physics.) And that Hestenes 1979 article tells me that, "The teacher can no more develop effective new curricula and teaching techniques on their own than he can discover <i>ab initio</i> the basic principles of the science he teaches. If the profession of teaching is ever to transcend the folklore state ... it must be guided and supported by a program of profound educational research." I'm hoping Modeling Instruction will be that guide and support for me.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><u>Works cited</u> (No, my blog posts don't usually have works cited lists, but this one is borrowed and modified from the student improvement data write-up I did last week, so I already had the references handy.)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="p1">Hake, R. R. (1998) Interactive-engagement vs traditional methods: A six-thousand- student survey of mechanics test data for introductory physics courses. <i>American Journal of Physics, 66 (64). </i><a href="http://dx.doi.org/10.1119/1.18809"><span class="s1">http://dx.doi.org/10.1119/1.18809</span></a><span class="s1">.</span></div><div class="p1"><span class="s1">Hestenes, D. (1979) Wherefore a science of teaching? <i>The Physics Teacher</i>, April 1979, 235-242.</span></div><div class="p1">Hestenes, D., Wells, M., and Swackhamer, G. (1992) Force Concept Inventory. <i>The Physics Teacher</i>, 3<b>0</b>, 141-158. </div><div class="p1"><span class="s2">Lawson, A. E. (1978). The development and validation of a Classroom Test of Formal Reasoning. Journal of Research in Science Teaching, 15(1):11–24.</span></div><div class="p1"><span class="s2">Lawson, A. E., Clark, B., Cramer-Meldrum, E., Falconer, K. A., Sequist, J., and Kwon, Y.-J. (2000). Development of scientific reasoning in college biology: Do two levels of general hypothesis-testing skills exist? Journal of Research in Science Teaching, 37(1):81–101.</span></div><div class="separator" style="clear: both; text-align: left;"> </div><div class="p1"><span class="s2">O'Donnell, J. R. (2011) <i>Creation of national norms for scientific thinking skills using the Classroom Test of Scientific Reasoning </i>(Unpublished masters thesis). Winona State University, Winona, Minnesota. Downloaded from modeling.asu.edu October 15, 2013.</span></div><br /><br /><br /><br /><br /> Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-80242759645029822132014-06-24T13:10:00.002-04:002014-06-24T13:10:41.762-04:00Also...I still think about <a href="http://teachingtransforms.blogspot.com/2010/07/project-runway-and-education-how-much.html">this old post</a> about Heidi, Tim, and teaching every time I watch Project Runway while "multitasking" and grading. That must make it my favorite post ever. Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-33700166534451714382014-06-24T13:03:00.000-04:002014-06-24T13:03:01.873-04:00Still Standing...Three years of teaching, one baby, one move, and three new courses developed later... I'm still teaching! Huzzah! (Although I'm deeply hoping that after I've developed one last completely-from-scratch-course next year, life will rebalance a bit away from work and towards sleep and time with my family and the occasional hobby. And maybe time to blog regularly.)<br /><br />And this year, I'm finally getting to attend a <a href="http://modeling.asu.edu/">Modeling</a> <a href="http://modelinginstruction.org/">Physics</a> workshop, which has been a goal since about the time of the last post I made on this blog. <br /><br />And they want us to reflect on the day each night on our blog. So, 15 guaranteed posts! How exciting!<br /><br /><br />Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-62684341239982992202011-07-20T18:53:00.000-04:002011-07-20T19:26:35.537-04:00Thoughts on Algebra 1After a five week mad sprint to teach my students everything they'll really need to know about Algebra 1 going forward, I have a few thoughts on the subject.<br /><br />First, as far as I can tell, there are two "Big Ideas" of Algebra 1:<br /><ul style="list-style-type: disc"><li>Everything students already know about arithmetical expressions (adding, subtracting, multiplying, exponents, radicals, fractions, simplifying, word problems) can be extended in a consistent way to situations involving variables.</li><li>Equations with variables give you the power to describe situations more generally than a single set of numbers allows.</li></ul>If you've taught Algebra 1, do you agree with those? Am I missing some? If I ever find myself teaching this class again, I'd like to try to present those up front and highlight them repeatedly as they come up, rather than gradually discovering them for myself and trying to make them clear to my students over the course of the class. <br /><br />I think one of the most problematic concepts of Algebra 1 is "Simplifying". It's so very easy to slip into "here are the rules for what constitutes simplified in this case, and this case, and this case..." (polynomials, exponents, rationals, radicals, ...) and so very difficult to access a big idea like, "We're trying to make our lives easier when we move on to the next step of solving or using a complicated equation that describes some situation in real life like particle physics or the stock market or the operation of an engine or the forces on a bridge." I can say that to students, but I have a hard time showing them or getting them to experience it...<br /><br />Second, I find that I have some startlingly clear memories of my own Algebra 1 class in eighth grade in 1990, probably because some of the subject matter I learned never got used again. It seems like there's a lot of manipulation and variations on a theme that we teach students but aren't actually critical to their ongoing life as mathematical practicioners.<br /><br />For example:<br /><ul style="list-style-type: disc"><li>I've used a lot of math in my life and graphed a lot of linear functions and data. All you really need is a deep and thorough understanding of y = mx + b. You do not need the point-slope form of a line. You might need the standard form when you get around to doing linear functions at a deeper level in Linear Algebra (and all of its applications in physics and economics and ...) in college, but could it wait until then? </li><li>I've used a lot of math in my life, and while being able to factor out the greatest common factor of a polynomial is a deeply practical skill for all the math it can make easier, and factoring x^2 + bx + c offers a sort of aesthetic pleasure and can be used to ensure that students understand FOIL at a deeper, backwards operation level, no one ever tries to factor ax^2 + bx + c . You pull out the quadratic formula, because it's so much more general and so much less guess and check. Why do we then waste time teaching an essentially guess-and-check approach to solving it? </li></ul>What's your perception of which parts of the standard Algebra 1 curriculum are actually essential and useful to practicing users of math in this modern, computational age, and which parts are historical cruft?<br />Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com1tag:blogger.com,1999:blog-7283584335635780428.post-12571056635079736922011-07-20T18:46:00.000-04:002011-07-20T19:29:00.797-04:00Standards-Based Grading, Take One (The Reflection)As I <span style="text-decoration: line-through;">procrastinate</span> take a break from making my final for the Algebra 1 summer school course I've been teaching for the past five weeks, I find myself reflecting on my first try at Standards Based Grading this summer.<br /><br />Things that are excellent:<br /><ol style="list-style-type: decimal"><li>I had a constant read on what my students did and didn't get, individually and as a whole class, which allowed a lot of course corrections, both major and minor, and would have allowed some awesome differentiation if I had more time for that kind of planning.</li><li>My students and their parents had a constant read on what they did and didn't get, which let motivated students target the areas on which they needed help and reassessment and let motivated parents push their less-motivated students into the same.</li><li>When I had a co-teacher for the last week of classes, I could send off the kids struggling to meet my goal of mastering at least half the concepts on my concept list, and she had instant access to where each student needed targeted help.</li></ol>Things that need work:<br /><ol style="list-style-type: decimal"><li>I stole my starting concept list pretty whole-sale from Dan Meyers (<a href="http://blog.mrmeyer.com/?p=346">here</a>). While it was great to have a starting place (thanks, Dan!), it needs some tweaking to serve the constraints of my class.<ul style="list-style-type: hyphen"><li>First: I only had 5 weeks (of 4 hours per day, 4 days / week) instead of a full year. While I had basically 80 instructional hours (so, theoretically almost a semester of time) and some pretty awesome kids, I still found myself slashing out some pretty critical concepts (solving systems of equations is the major one, but some other pretty important things also fell by the wayside). I ended up leaving out some core topics that we'll cover in the math class these students will take next year (solving systems, quadratic functions and graphs thereof, exponential growth and decay) and keeping some less central concepts that are at the back of most algebra books and many of many students hadn't seen yet (rational and radical expressions).</li><li>Second: I wanted to work a lot on my students' mathematical reasoning abilities with open-ended problems, and their comfort with dissecting and translating word problems into math. Yet I have a single concept on my final list for word problems, none for mathematical reasoning, and the word problem standard I have is by far the one the students still have the most trouble with. If I teach this class again, i want to think more about what I want students to be able to do beyond check off the key procedural and conceptual skills asked by a typical Algebra 1 textbook.</li></ul></li><li>Reassessment, Part 1- I tried stealing Sam Shah's <a href="http://samjshah.com/2011/06/15/to-reassess-or-how-to-make-more-work-for-me/">reassesment request form</a> but in a five-week class with limited other use of the class website and no paper copy available in my classroom, basically one student used it once. It was too cumbersome and / or too much overhead for students to use and for me to enforce. This may be somewhat different in a full year course, but at the very least I need to make sure I get a paper copy available in person the next time I do this.</li><li>Reassessment, Part 2 - I need a way to get the less motivated and more struggling students in for help and reassessment. Probably the most fundamental thing I need to do is to make my expectations about this crystal clear up front to both students and parents. Also, I should think about more creative ways of making the right choice the easy choice. This could constitute a mandatory 1 hour after-school session this week that you have to attend if you have less than a 4 on any concepts that I'm not assessing any more. Or it could constitute some part of a regular class period when the non-struggling students do a fairly independent activity (could use suggestions of these) and I focus on the struggling students. This summer I did it by setting my co-teacher loose on the most struggling students for the last three days of the course, but that's probably not a luxury I'll have in the regular year (but it may be worth brainstorming ways I could make that work).</li><li>Work load - grading 40 quizzes with 6-8 questions per day on top of planning 4 hours of new instruction a day almost killed me. This is probably partially because I'm a newbie teacher who started from scratch in terms of... everything... this summer, and it might be better in the future just because I'd be tweaking this year rather than making everything from scratch. But I wonder if I could get 80% of the results from either fewer daily quiz questions (3 instead of 6?) or every-other-day quizzes? Realistically, I could only do a good job of introducing two new concepts per day, but the need to give students multiple chances to assess past concepts drove up the number of questions. At the least, I think I need to give one "what do you already know?" assessment of every single standard at the beginning of the summer and then do my darndest not to waste the students' or my time by assessing a standard before I've had time to teach it, which happened multiple times this summer.</li></ol>More thoughts on Algebra 1 as a class in the next post...Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-78373483429376471172011-07-13T14:07:00.000-04:002011-07-13T18:08:00.800-04:00Lessons of the dayThings I learned in summer school today:<br /><br />0) Homemade Algebra Tiles are a lot cheaper than the $70 sets from Amazon, and work fine. (But if you have the funds, a more substantial set might be nice.) <br /><br />1) Algebra Tiles are pretty cool, and have a lot of potential, especially for making kids really consider what the meaning of integer addition, subtraction, and mutliplication are. I definitely saw some lightbulbs go off when we worked through "4*3 means four sets of 3".<br /><br />2) Trying to introduce Algebra Tiles from scratch and accelerate up to multiplying and factoring polynomials in 60 minutes is a recipe for disaster. (I should have known better.)<br /><br />If I were to teach this class next year, I would introduce the Algebra tiles the first week, and embed them as we reviewed integer arithmetic, solved simple equations for x, and worked our way up to polynomials. I think they'd be a useful addition to the boardwork / notes / practice / fun outside problems mix I've developed this summer. <br /><br />Live and learn.<br /><br />Useful algebra tiles resources on the web:<br /><ul style="list-style-type: disc"><br /><li>Good power point overview and a solid series of worksheets escalating from integer addition through polynomial division are <a href="http://hybridalgebra.wikispaces.com/Algebra+Tiles">here</a>.</li><br /><li>Good overview of a lesson flow for introducing the tiles is <a href="http://math.buffalostate.edu/~it/projects/dileas.pdf">here</a>.</li></ul>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-57894017796563433912011-06-30T12:19:00.000-04:002011-07-05T20:25:32.692-04:00Summer School MidtermI'm two mind-blowing weeks into the five weeks of my first summer school teaching experience. I gave the students a Teacher Evaluation as the exit ticket today, and I'm in a more reflective mood myself, so it seems like a good time to jot down some notes.<br /><br /><span style="text-decoration: underline;">Things that worked well</span><br /><br />Curriculum-wise (huge thanks to Dan Meyer for many of the items on this list):<br />* <a href="http://www.ammeinc.com/TnotesfortheseActivities.pdf">Algebra cups</a><br />* Graphical fractions (<a href="http://algebra.mrmeyer.com/">week 2</a>)<br />* Chewing gum measuring stick <br />* Origins of the word "Algebra" (modified for ninth-grade reading level from <a href="http://www.und.edu/instruct/lgeller/algebra.html">this</a>)<br />* <a href="http://www.thirteen.org/get-the-math/">Get the Math</a><br />* <a href="http://blog.mrmeyer.com/?p=692">Stacking cups</a><br />* Russian dolls (inspired by the comments on <a href="http://blog.mrmeyer.com/?p=10211">this post</a>, especially <a href="http://www.russianlegacy.com/catalog/images/matryoshka_music/NDM017.jpg">this image</a>)<br />* <a href="http://blog.mrmeyer.com/?p=213">Graphing stories</a><br />* "Leveling-up" linear functions worksheets (25LevelOne.pdf from Dan's algebra handouts - linked at the bottom of this <a href="http://algebra.mrmeyer.com/">page</a>)<br />* Daily warm-ups - the kids really do need to warm up their brains at 8 a.m. Trying to sneak in higher order thinking and group work will not work well at this point in the day.<br />* Judicious use of the powerpoints from the textbook to define the key concepts and walk through scaffolded examples<br /><br />Assessment-wise:<br />* Concept quizzes (once I scaled them to the topics I was really covering and a grading load I could handle)<br />* Concept checklist<br /><br />Classroom management / Relationships:<br />* Remembering that the students have reasons for acting in ways I find challenging, and I'll do better to find out what those root causes are and address them than to just try to force them into acting a different way.<br />* Asking students their opinion on the class atmosphere and environment and things they like and don't like about the class, incorporating that feedback where possible, explain why not when it's not possible, and being flexible and creative.<br />* My best example of being flexible and creative: some students want music when doing independent work and some want silence --> you can listen to your mp3 player during that time, as long as no one else is disturbed by it.<br /><br /><span style="text-decoration: underline;">Lessons Learned</span><br />* Still need to follow up Algebra cups with formal instruction on steps of solving equations<br /><br />* Don't pay for and pour hours into a new-ish online gradebook system when they just changed their whole infrastructure a few weeks ago, aren't expected to support summer school, and you're their unknowing beta tester<br /><br />* Find out on Day 1 what the students' self-assessment of their ability on your course material is. If they think they already took and mastered Algebra 1, and that's all you're planning to teach them, give them a version of your final ASAP so you can kick them up to a harder class, send them home for the summer, or show them (and even more critically, their parents) that they do need your class after all.<br /><br />* If it all possible, solidify the curriculum, schedule, and course resources before the second week of the class. (I did try, it's just that before trying to teach this and working out some of the kinks the first week, it wasn't clear to me what they should be. I got a lot more clarity this week, and I'm feeling good about this now, and like I'll be in a much better place if I do this again next year.)<br /><br />* Sometimes I really just need to give clear structured notes, and clear, basic opportunities to practice (even though it seems boring to me).<br /><br /><span style="text-decoration: underline;">Things to work on<br /></span>* Helping kids see how to follow up on non-mastery-level concepts<br />* More efficient planning<br /> Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com2tag:blogger.com,1999:blog-7283584335635780428.post-60171094985252968952011-05-04T15:52:00.000-04:002011-05-04T15:56:43.731-04:00Awesome pendulum videoBecause <A href="http://blog.matthen.com/post/5161315532/multiple-pendulums-of-varying-length-and-thus">Matt Hen</A> is a genius:<br /><br /><iframe width="425" height="349" src="http://www.youtube.com/embed/yVkdfJ9PkRQ" frameborder="0" allowfullscreen></iframe>Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-90886783296811273652011-03-20T11:28:00.000-04:002011-03-20T11:46:26.965-04:00Red Cross PedagogyYesterday I had the privilege of spending 8 hours in the hands of the Red Cross, freshening up my adult and child CPR and first aid and meeting AEDs for the first time. <br /><br />Here are the pedagogical approaches they used that I learned from in a way I might remember if an emergency actually hit: <br /><ul style="list-style-type: disc"><li>hands on practice in moving a choking friend back and forth between back blows and abdominal thrusts</li><li>hands on using the plastic torsos to practice CPR for a decent chunk of time - half an hour maybe? (I could also feel some muscle memory from the last time I did this in approximately 1998)</li><li>hands on using the plastic torsos to simulate using the AED</li><li>hands on tying a bandage on my friend and having him tie a sling on me.</li></ul>Here are the pedagogical approaches they used that I learned from for just long enough to pass their test end of they day multiple choice test:<br /><ul style="list-style-type: disc"><li>lecture</li><li>reading</li><li>demonstration of one student rolling another student</li><li>videos</li><li>last minute pre-test cramming of needed information into our head ("teaching to the test" in the purest form I've ever seen)</li></ul>It's always good to be forced to spend a day in a situation I'm not particularly intrinsically motivated for, just to see how most of my students feel most days. <br /><br />I think what surprises me the most is how little the demonstration did for me -- it was a purely visual flow of information that wasn't really much more engaging than a video. I tend to try to substitute demos for hands-on experiences in my lesson planning because it's so much more efficient in limited time, and I guess this says I need to try to squeeze my efficiencies out some other way -- like cutting down the lecture even more. <br /><br />Something that was surprisingly effective for me was the continual stream of verbal directions and reinforcement of critical information <span style="text-decoration: underline;"><em>as</em> </span>I was doing the hands-on work. Maybe that should be my main method of information transfer rather than lecture. <br /><br />I wish we'd done more writing in this class -- I'm wondering whether that would have fallen into the "doing something" category for me (resulting in some effective learning because I'd actually mentally had to process something and use it) or the "seeing / hearing something" category. Maybe it depends a lot on the kind of writing.<br /><br />Overall, I think I need to learn to be more zen about teaching. I know that "doing" is almost always better than "seeing" and "hearing", but I also know that giving my students time to "do" always (a) takes more time than I expect and (b) is the fastest way I know to spread out my fast learners from my slow learners (maybe because they're actually learning!). I need to learn to accept a slower overall pace and the need for basic / crticial and extension levels of any meaningful assignment. And more "doing".<br />Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com0tag:blogger.com,1999:blog-7283584335635780428.post-40683577972713485532011-03-17T18:16:00.000-04:002011-03-17T19:01:53.547-04:00Things I Learned at MACUL11So, today I got to go to the MACUL Conference, courtesy of our Teaching with Technology class. Here are some things I learned:<br /><br /><ol style="list-style-type: decimal"><li>You can do <a href="https://sites.google.com/site/uzelacshares/MACUL-2011/learning-our-way">really individualized, project-based, interdisciplinary learning that is driven by each student's interests, meets the state standards, and reaches kids who would otherwise drop out physically and / or mentally</a>. But you may have to blow up the traditional school structure to do it.</li><li>Using the <a href="http://www.youtube.com/t/annotations_about">annotate feature in YouTube</a> lets you and/or your students put commentary on videos and make interactive "choose your own adventure" video sequences. Also, youtube is fun, and making <a href="http://www.youtube.com/watch?v=T7TI-AJi2O8">youtube videos can make school more fun</a>. And <a href="http://welovelodge.blogspot.com/">sometimes it can be educational</a> too.</li><li><a href="http://www.cast.org/udl/index.html">Universal design for learning</a> (UDL) is about giving kids access to the topics in multiple ways, giving them multiple ways to demonstrate their learning, and giving them choices so they can use the ways to learn that work best for them. There are lots of <a href="http://www.cast.org/learningtools/index.html">resources on the CAST site</a>.</li><li>Project-based learning is cool, and there are lots of resources for it <a href="http://www.leadingpbl.org/w/page/15692082/FrontPage">here</a> and <a href="http://www.bie.org/tools/links/pbl_in_practice">here</a>.</li><li>You can use a combination of Google Sites and Google Docs to enable your students to collect their work over time in an e-portfolio and to enable you and your colleagues to share and collaborate on curriculum resources. There are resources and how-to's <a href="http://sites.google.com/site/skylinecpi/">here</a>, and it looks reasonably straightforward.</li></ol>If there was a theme to my day, it was how to use technology to engage students in individualized, self-motivated, creative, project-based learning, and thinking about what constraints need to be shifted within the traditional model of school to make it work. <br /><br />It seems like the most critical element is team-based teaching or some other way of solving the problem of "I want to study the Gulf of Mexico oil spill from a scientific, mathematical, political, literary, and foreign language points of view but my students all have five different teachers for each of those subjects, and that's a lot of <span style="text-decoration: line-through;">cats to herd</span> teachers to coordinate." <br /><br />Also helpful: One-to-one computers. So your students can access your UDL-based electronic texts and interactive assignments, collaborate with each other even when they're at home, and get to their project and e-portfolio sites whenever they need to, regardless of their family's economic resources.Emily Van Arkhttp://www.blogger.com/profile/10593903103254340877noreply@blogger.com2