The question in front of me now is “How do I teach a Physics First course to a student inadequately prepared in mathematics in a setting where most other students are so prepared?”
Middle School Math
I teach Physics First in a school with strong middle school math preparation. Our middle school teachers have modified their Algebra I courses in a few ways to prepare kids. Most notably, in Algebra 1, students apply trig ratios to solve right triangles and they see it again at the start of geometry in 9th grade. In contrast, the local public schools have put trig ratios in 10th grade mathematics.
If a kid went to our middle school, chances are high that they are competent with all the math needed in my physics class. Trig is the most obvious accommodation. Here’s all the mathematics topics I need physics students to have:
- Solve an equation for any unknown. The hardest equation in my course is for thin lenses and spherical mirrors:
. Solving for anything in the denominator is always problematic for the kids who struggle in math, so this one’s a doozy because it also always gets them on order of operations and fractions.
- Work out how two variables relate. For example, for F=ma, if I double m and hold F constant, what happens to a? The hardest ones are the quadratic relationships such as in
- Have solid Cartesian graphing skills. Some kids will scale axes weird (using data points as increments, so every line looks like slope of 1). I include in this computing the slope and y-intercept of a line.
- Estimate a best fit line from the graph of a messy data set (in freshman physics, we don’t use the fancy computational best fit methods) and then find the slope and y-intercept of that line
- Understand slope as a rate of change.
- Detecting a quadratic relationship from a data set using first differences (we spend a lot of time talking about the concept of an increasing slope on a f(x)=x2 graph)
- Solve a right triangle for either an unknown angle or an unknown side
Additional Reading: “Mathematics Underlying the Physics First Curriculum: Implications for 8th and 9th Grade Mathematics“
Unfortunately, students who transfer in for upper school here often don’t have this math. As we open up to more kids from wider socioeconomic and geographic areas, we must set them up for success in the upper school.
Helping transfer students succeed, then, is my task. I have three main ideas for supporting transfer students of mine. But really, I don’t have good answers or plans in place to support the unprepared. This post is more about getting the problem description out there.
Support #1: During Class
To get the most out of my class time, students need to be able to work together and with me. To me, the during class support is all about building a kick ass class culture. Ideally, my students are comfortable being open about their struggles, with me and each other.
My class culture isn’t where I’d like it to be. In the past, students worked with groups of their choice — which leaves out new kids more often than it includes them. Then I moved to working in table groups which I mostly selected. Still a no go. If you’re the only one not getting it at a table of three others who do, you’re just going to copy along rather than slow down the group to ask for explanations (and feel like you look dumb).
I can’t help but think several of the ideas Sara van der Werf presented at Global Math Department will be useful. The Pursuit of 100% Engagement: Practical ideas to get you closer. Specifically, she talked of how she models group work from the start of the year, including building norms and taking pictures. Also, she spoke of creating quality group or partner tasks. Where the former is about developing student habits, the latter is about changing up my game to get students working together. I like this balance.
How do you support students during class? Seriously, I feel like this is my weakest of the three supports here.
Support #2: During Office Hours
We have a half an hour per day set aside as office hours. Students drop in to any class they need and ask questions. In my room, I most often have students asking about a homework problem or retaking a quiz. Students who came through our middle school are already familiar with the setup and use it from day one.
Transfer students are often new to the idea of office hours. I need to get them in early in the year for office hours. It took me entirely too long this year to build a relationship with one of my students to where they’d ask for help. I’m leaning toward setting mandatory office hours, coordinated between the student, math teacher, me, and the grade chair.
Support #3: Building a Team
Every student has an advisor (aka homeroom teacher), a grade chair (who handles half their class’ students), a math teacher, and a physics teacher. That sounds like the basis of an excellent student team. What if I could do the following?
- Every new-to-our-school student gets a Team that includes the math teacher, the physics teacher, and the advisor. The team would meet once at the start of the year, possibly with counseling or whoever has the kids’ records from the last school. They then keep in touch throughout the year. This is pretty much happening informally after a kid gets into academic trouble, the change is being proactive with the team.
- Every new-to-us freshman gets mandatory office hours in math and physics for the first 9 weeks of school, at which time the SST determines if it needs to be continued.
- Everyone on a Team gets some training in researched-based interventions that might not be obvious. Maybe even instead of “sage on the stage” type training, we just hold a roundtable to decide what our own best practices are at our school. Might be received better by the teachers in a roundtable format.
Final Thoughts
I’m not saying that all transfer students struggle in my class. However, my data suggest that when a kid struggles, there’s a good chance they’re a transfer. How, then, do I give these kids the kickass experience they deserve?
What strategies have you seen work? Who should I be reading? Who should I be following on Twitter? C’mon friends, tell me what you know!
(oh and today’s T-minus-3 days till kids return on my 13th year teaching)
Megan Hayes-Golding 
Megan—I love this post. I think you’ve identified a number of math skills that challenge students trying to make the transition into 9th grade physics. I especially love your team idea, and it reminds me of the work Uri Triesman at UC Berkeley did back in the mid 80’s to try to reduce the failure rates of minority students in introductory calculus.
Triesman’s main finding was that remediation didn’t do much to help students who were struggling in calculus. His study followed URM students and a cohort of asian students who were seeing great success in the course. He found that the minority students often studied alone, and when they encountered difficulty or failure, they took it as a sign that they were not capable of succeeding in the course. Asian students most often studied in groups, and took failure as a sign that they needed to work harder in order to succeed.
To address this, Triesman formed enrichment groups for minority students, and provided enrichment opportunities outside of class to work on non-textbook, non-routine problems with the guidance of a TA or professor. This seems like something you could do in a required backwork session—have students work on novel problems, or extend their work on a lab, say by taking data to verify then thin lens equation, and then working out a conceptual explanation of the relationship between object and image distances for a given set of lenes, and then checking their calculations from the equations with this conceptual understanding they’ve developed.
Treisman’s work at UC Bekerely has continued to evolve, and most recently, have developed the following self evaluation rubric, which is pretty fantastic at specifically describing the skills students need to succeed in physics. This rubric might make for very productive conversations between the student, physics teacher and grade chair.
This is so cool. If I’m reading you correctly, the goal is to teach kids to study in groups. And the means is to model that with groups during backwork/office hours. But the twist is working non-trivial problems, new work, or lab extensions — ie, not just doing the stuff they’re already assigned.
Now you’ve got me thinking about how to get kids to buy in to this developmental work. Right? They’re busy and feel their time is precious. Why would anyone choose to go to physics where that batty teacher makes you do totally different stuff? My first reaction is to offer some kind of carrot. But that’s not right! I know it.
Office hours on a regular rotation will be required under the new team program (approved while I was drafting the post!), so the kids will be there. Maybe I need to think of that time less as answering physics questions time and more as metacognition time.
The self evaluation rubric from Treisman is really cool. I might try this on this year in my class. I am really excited for our school to engage in the third arm of Megan’s plan outlined above. I am hoping it brings greater awareness and conversation to some of these very issues. We also tend to leave a lot of the “burden” of office hours on the shoulders of the students (I suppose this teaches “independence.”). But, I like that your notes above point out that working in a collective, as a whole, part of a team, and with a collectivist mindset (study groups, sharing knowledge), is a better way to reach more students. Cool. Let the good work continue!