Monday, April 27, 2015

All 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.

I teared up a little, but did not start bawling.  Victory?

And thus, I become a statistic.  One of those 40-50% of teachers who quit in their first five years.

So... why?  As I told multiple people today, it's complicated.  

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."

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.

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.

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.

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.

The article I linked to above has the following quote:
With the exception of retirement, studies suggest 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.
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.

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.  

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.

I am developing a depressing theory:  teachers are the new UAW workers.  Which is to say, there are two classes of UAW workers - 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 this one, 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."

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.
“Respected, well-paid lines of work do not have shortages”
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.)

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.

*All good things...

Tuesday, July 15, 2014

It's a bird, it's a plane, it's a projectile!

Model Summary:  2D Motion of a Particle

Scenario - How can we tell whether a basketball will make the shot, given a motion map of its position at times early in the shot?

Force Diagram - Unbalanced downward Force_{Earth_on_Object} ("Feo - the ugly force"), with no horizontal forces

Motion Graphs

  • vertical position vs. time - downward facing parabola (assuming up is +)
  • horizontal position vs. time - linear with positive or negative slope depending on which direction object moves
  • vertical velocity vs. time - linear with negative slope (assuming up is +) equal to -10 m/s/s, similar to 1D free fall
  • horizontal velocity vs. time - constant
Motion Map - Position of dot shows change in both horizontal and vertical position, following parabolic path
  • dots have even horizontal spacing and constant-length horizontal velocity vectors due to constant velocity horizontal motion (no horizontal unbalanced forces)
  • dots have changing vertical spacing and direction and length of vertical velocity vectors due to constant acceleration horizontal motion (unbalanced vertical Feo)
Equations - 
  • Basically just the CVM equations for horizontal motion and the CAM equations for vertical motion... except...
  • 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. 

Projectile Motion Implementation

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?

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 might be easier to understand if they already had forces under their belts?

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.


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).

Force Model Summaries - Balanced and Unbalanced

Paradigm Lab / Scenario - 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).

Force Rules

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).

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.

Force Diagrams
Forces on an object can be represented by force diagrams with

  • a point that represents the object
  • arrows representing all the forces on that object
    • all starting from / pointing away from the point, in the direction of the force
    • labelled F_{letter representing agent / letter representing object}
    • with lengths at least qualitatively showing relative strengths of the forces
  • 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.
  • 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) 

Verbal model summary
"To have an acceleration, you need an unbalanced force."

Equation Summary
a = F_{unbal} / m
f_{surface_on_object} = mu{k or s} * F_{surface_on_object}

Additional Key Force Experiences / Investigations

  • normal force - conceptually bridged from an obviously deforming surface to much stiffer ones
  • weight vs. mass - a relationship between weight and mass is experimentally derived (hey!  W = mg, where g ~ 10 N/kg is the gravitational field strength)
  • Newton's Third Law - 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" 
  • Newton's Second Law - measure how changing force and changing mass of a system change the acceleration, to experimentally derive a = Funball / m (the equation summary)
  • free fall - 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)
  • friction - 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.
Force Model Implementation

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.)

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.

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.

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!

Did we do a practicum lab for forces?  If not, does anyone have a favorite one?

Monday, July 14, 2014

What 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 "Building the Energy Transfer Model" seems like a good place to start.

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, "...we aren’t necessarily looking for the carts to get to the end of the track at the same time. We are looking for the springs to give them the same effect, so we’re looking for them to have the same speed once the springs aren’t stretched anymore. So we should look carefully at their motion relative to each other (not for which one reaches the end of the track first)."  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!"

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?

Bryan (@BC_ocs) tweeted a link to a discussion of energy from the Feyman Lectures today.  Feyman says:  "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. It is not a description of a mechanism, or anything concrete; 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."  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?

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.

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).

Saturday, July 12, 2014

Backwards Design, Modeling Style

Friday was a fun and useful day.

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.)

I also wrote down a general modeling unit planning template that Bryan threw out:

  1. Figure out what Prior Misconceptions students are likely to have (Arons,, Paige Keeley books, Laura's Pre-assessments, various articles we've read during this workshop... what resources am I missing?)
  2. Decide your Instructional Goals  
  3. Figure out how you're going to Check for Understanding (sounds so much gentler than Assessment, even if it means the same thing)
  4. Determine your Anchoring Experience(s) (Paradigm labs, other useful demos and labs)
  5. Be critical users of available curriculum materials (even the modeling ones) -- figure out 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?  (This part came from Laura later in the day, not from Bryan.)
I think this is fascinating, because it's core (#2 and #3) is the Wiggins and McTighe 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.

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 "four corners" 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...

I'm also intrigued to add the Ranking Tasks 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 solver ...).  I think I'll come up with a version that doesn't require a $180 piece of lab equipment 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.  

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 Dave's Penny Flick (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 JP's homemade vertical projectile launchers.  Our anniversary is coming up in a couple weeks... 

Thursday, July 10, 2014

Invasion of the Pod People

Notes from facilitating this morning that I thought were important enough to highlight:

Laura's Rules for Facilitation (TM) (Really, "Things to Consider for Facilitation"):

  • What can you do to get students to ask questions of each other?  ("Don't underestimate the value of student to student conversation.")
  • What will you point out if students don't?
  • What instructional points do you want to make?
  • What will you do to ensure a positive, questioning (not correcting) discussion culture?
Strategies for Dead Silence during discussion:
  • "Do you understand what I'm asking?"
  • "Check your partner" (and listen in, and figure out who you want to call on based on what you hear)
  • 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
  • Be super sensitive to student shut-down
  • 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.")
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!   

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.  

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.

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.  

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.

If you're a pod person, I welcome  tips, tricks, advice, and reassurance about that approach to seating! 

Wednesday, July 9, 2014

The Constant Acceleration Particle Model - Summary and Implemetation

Summary of the Constant Acceleration Particle Model

Scenario:  A low-friction cart moving up or down a ramp, with increasing or decreasing change in position (displacement) for each unit of time.

Motion Map:  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.  

  • Quadratic (parabolic) position time graphs, with vertical intercept at initial position, and steepening slope for speeding up or shallowing (flattening) slope for slowing down.  
  • Linear velocity-time graphs, 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.
  • Constant acceleration-time graphs, 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. 

  • 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.
  • 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.
  • 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. 

How will I use this next year?

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.  

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.  

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. 

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?)

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).  

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.  

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.