I’m sitting next to Matthew, a 12th grade student at High Tech High Chula Vista, and we have a problem. With only thirteen work days left before our first project exhibition that would see over two-hundred visitors, Matthew and his small team need a formula that they can use to estimate someone’s auto insurance. They need something that can take a few variables such as the age of a driver, the model of the car, and a driving record in order to compute an auto insurance quote within fifteen seconds – any longer than that and their group slows down our personal finance simulation. Progressive, Geico and Allstate have online estimators, but they take too long to calculate and they do not publish their formulas for us to recreate.
“I guess we could make a big spreadsheet and complete the online estimators for all of our profiles,” Matthew suggests, “then just record all the estimates.”
With 100 different profiles – doctor with three kids, unmarried janitor, rocket scientist with huge educational debt, etc.,- Matthew’s suggestion means going through Geico’s online estimator 100 times over the next week, which meant a lot of work and minimal thinking.
“No,” I say. “Let’s build our own formula.”
Matthew’s eyebrows shoot up. “How do we do that?”
“Well,” I say, “we’re going to need some data.
Matthew and his team start scouring the internet for data that could help us build our own formula. On one website, Matthew’s team finds the average car insurance for every age group from 16-85. On another, they find the average insurance for fifteen different kinds of cars, so we look up the costs of all those cars and build a data set that has cost of car compared with average insurance cost. Thankfully for our learning, these data sets weren’t linear (they weren’t just straight lines), which allowed us to build exponential models of the data and combine them into a really messy formula through regression analysis. In the end, Matthew and his team were able to compute auto insurance for visitors with their own formula in less than 15 seconds.
I teach at High Tech High Chula Vista, a charter school in California where teachers often use project-based learning to promote equity in the classroom. This semester, my partner teacher Caroline Chen and I engaged all 154 seniors in a personal finance project that lasted from the first week of January until the third week of March with two major exhibitions of learning where people from our community gathered to see our student work. The project culminated in a personal finance simulation where 12th graders from outside our school received a profile of a fictional person with a family, debts, and a credit history, and then shopped for all the necessities of life – a car with insurance, housing, internet, phones, childcare, fun money, retirement savings, further education, clothes, groceries, utilities – while trying to remain under budget in a budgeting spreadsheet so beautiful and functional it would have made a financial planner tear up. Note: The “coding group” built this interactive spreadsheet. In the upper left, there’s a dropdown menu that they programmed that would fill in every cell in the spreadsheet except for the red ones, which serve as inputs for the simulation.
In this article, I’ll explore a few bright spots that made this project successful, and I’ll also address some of the missed opportunities in our project. In addition, I’ll push on the idea that math curriculum – whatever the flavor – should have opportunities for students to connect with the content on a personal level – to see themselves in the math, to learn about themselves through the math, and to own the math by creating their own formulas.
Though we certainly made mistakes as designers of this project, and I’ll talk about these as well, there were a few things that we did really well which I feel are applicable to anyone interested in project-based learning. I will use these bright spots as a general outline for this article. Components that contributed to the success of this project include:
- We made sure that our students wanted to do this project.
- We co-planned every activity of the project.
- Our product was an exhibition.
First bright spot: We made sure that our students wanted to do this project
Before we started this project, Caroline and I wanted to make sure that our students actually wanted to spend a couple months doing a project. We pitched four project ideas to our students:
- A Calculus 2 project where we’d print 3-D prototypes of invented products and learn how to compute volumes of different types of solids using calculus.
- A unit where we prepared for college-level math in the style of open-ended problems, group work, and lively class discussion similar to the type of classroom you’d expect from teachers who love Jo Boaler’s work.
- A coding project where we’d make apps, games, etc. for potential clients.
- A personal finance project.
Over 80% of the kids either “liked” or “strongly liked” the personal finance option. We also solicited ideas about subtopics and other areas of interest. For example, some students really wanted to learn about taxes while others wanted to explore the cost of college. We shared these results with the students in hopes of providing transparency.
Personal Finance proved to be a very relevant topic for 12th graders, a point that should resonate with anybody who is trying to find ways for students to learn about themselves and to express themselves within a mathematics curriculum. According to Gutierrez:
The goal is not to replace traditional mathematics with a predefined ‘culturally relevant mathematics’ in an essentialistic way, but rather to strike a balance between opportunities to reflect on oneself and others as part of the mathematics learning experience (Gutierrez 2009, p. 5).
With regards to Gutierrez’s statement, it’s reasonable to approach all of your curriculum and find places where students can reflect on themselves as learners (e.g. How do you get started on a problem? How do you collaborate with peers? What are your thinking patterns?) even when the curriculum, like theoretical algebra, leaves less room for students to draw on personal experiences.
With personal finance, students drew on their identities in math class and, in doing so, brought different cultures to the forefront of the curriculum as students were able to plan for their futures based on their family values.
As part of my graduate work, I collaborate with three other high school teachers from other High Tech High schools. Every week, we ask our students to respond to the statement: “The skills or content from class was important to me this week.” The other three teachers run classrooms rich in Complex Instruction, open-ended problems, collaborative group work, yet students clearly see value in mathematical content that has a direct connection to the adult world that ALL of them will experience. When students worked on personal finance, we saw nearly perfect engagement, sometimes to a surprising extent as some students came alive in my class who, at other times, struggled to see relevance in curriculum that might be considered “math for the sake of math.”
Second bright spot: We co-planned every decision and activity
For my first six years of teaching, I planned nearly every day as an island. Sure, I solicited feedback from students through exit cards and formative assessments to inform my planning and often ran my lesson plans by other teachers asking for ideas or advice, but I was still doing this in relative isolation as a practitioner. This year, for the first time, and for the entire Project Life: A Chance to Finance, I co-planned every activity and decision with Caroline. If there is one practice that I think can make every classroom better, it’s co-planning.
Most design practices are centered around an iterative model – do a first draft, get feedback, do a second draft, gather information, do another draft, etc. and there’s a good reason for this: second drafts are better than first drafts. Yet we continue to plan on islands, doing our first draft in year one, hopefully making notes, planning our second drafts of lessons a year later. By the time we’ve taught something three or four times, we probably do a decent job of it, but why not have a great draft the first time we teach something?
For Caroline and I, we talk constantly about lesson plans. One of us gets an idea and we bounce it back and forth, working out the kinks, and by the time we present to the kids, our first drafts look more like my 2nd or 3rd drafts used to look: high quality, often still imperfect but with many more pitfalls avoided. By the time I get to my classroom, we’ve made plans for our students who are most difficult to engage, our students who need movement, our english language learners, and because Caroline and I are different types of learners, we bring different perspectives. We also learn teacher moves from each other because we compromise on lesson plans. Our go-to moves are different, so I’m often forced to try a structure that I wouldn’t normally use, which means that those structures become mine.
Our common planning requires that we share planning time, have adjacent desk space, and this requires administrative support. We also believe that working together is better for students than working alone because even when we disagree on an plan, we are able to present our sides and get to the heart of a classroom structure; we’re forced to clarify our intentions. We get one hour of planning per day together, but planning projects often requires dozens of hours of pre-planning that needs to be done. Caroline and I address this by finding time whenever we can to chip away at this large task – we meet during the summer, we occasionally meet on weekends, and we’re lucky enough that our schools professional development allots us time to project plan.
As a result of our co-planning, nearly every activity worked for the kids according to our end-of-the project anonymous student feedback surveys. The graph below is an example of an activity that seemed to work quite well for the kids where they calculated their future paychecks for two potential careers. For those interested, resources for doing the project can be found here with planning documents, student feedback, and student work examples.
Third bright spot: Our product was an exhibition
According to the students, the exhibition really worked. I am especially proud of this result since our 12th grade students have experienced between eight and sixteen major exhibitions as high school seniors at High Tech High Chula Vista.
And here is my major takeaway, which I thought was a significant bright spot in the project: our product was an exhibition. Here are more examples from High Tech High where the exhibition was the product: a live comedy show, a play, a public reading where all pieces were written for performance, a gallery of interactive multimedia, presentations to architects showing the building models kids made. In most cases, the best exhibitions aren’t add-ons to a project or afterthoughts, rather, they are built into the design of the product. I’m not saying that you can’t do a great project with a mediocre exhibition; I’m saying that the best exhibitions that I’ve experienced are ones where the product was an exhibition for an audience who cares or is invested in the project.
We spent approximately three out of eleven weeks building our simulation. For the first eight weeks, all students receive equal access to all ideas and mathematical concepts, but for the last three weeks, students had very different experiences as we built artifact cards, figured out logistics, planned for an exhibition, created graphics and artwork, launched an advertising campaign, built spreadsheets and calculators, and more. The groups listed above: coding, transportation, and further education had some complex and interesting math problems to solve to prepare for the exhibition, but many students, frankly, did not.
Math/Deliverables that all students did in the first eight weeks
- All students built formulas in google spreadsheets using =pmt, =fv, =sum, calling inputs from other cells.
- All students estimated monthly payments, total costs, and interest paid to attend a 4 year college.
- All students did their own taxes based on two preferred careers and preferred future families.
- All students constructed mathematical arguments for receiving future training in their preferred field (e.g. is college worth the money?)
- All students constructed Return on Investment (ROI) graphs comparing gains and costs for two different careers of interest.
- All students made their ROI graphs more complex by adding in an extra factor that could be expressed as a function of time (e.g. teachers get summer break, so they actually only work ¾ of what most careers work and a complex comparison would include this perk).
- All students learned about compounding interest and amortization schedules.
- All students wrote an annotated bibliography which included research of future jobs, adult interviews, and quotes from professionals in their future fields.
- All students made inspiration boards, detailing their life goals and priorities.
- All students attended a professionally run personal finance budgeting simulation.
- All students made high quality artifact cards for their respective group (housing, transportation, essential shopping, etc.).
Math/Deliverables that some students did in the final three weeks
- Coding students (11/154) built an algorithm that took into account tax tables when computing someone’s post-tax monthly income.
- Coding students built a dropdown menu in google spreadsheets.
- Coding students made an extremely user-friendly budgeting sheet with multiple inputs, outputs, with easily readable parts for over 100 different career profiles.
- Investment/Retirement students (9/154) built a calculator for retirement that output monthly retirement earnings and considered: starting money, time, and monthly payments into retirement.
- Investment/Retirement students used data sets and regression analysis to build an algorithm that calculates estimated social security.
- Investment/Retirement students used CalSTRS tables to build an algorithm that calculates retirement for teachers, police officers, and other California state employees.
- Transportation students (11/154) used data sets and regression analysis to build an algorithm which calculates monthly insurance premiums based on age of the driver and car bluebook value.
- Further Education students (7/154) calculated costs and gains for receiving further education for all fifty career profiles.
When putting together a real project, certain jobs just have to get done. For example, eleven students acted as “quality control” who evaluated student work-ethic and gave feedback to different groups. Twenty-two people served on a graphics committee that launched an advertising campaign, made all of the signage, interviewed students about math that they had done and made eye-catching posters based on those interviews to show our process. Fifteen students orchestrated an introduction and then a debrief for our exhibition when we presented this simulation to other twelfth graders. I found all of these jobs completely necessary for a successful project exhibition, but I wouldn’t consider all of these jobs as highly mathematical. I’ll call these missed opportunities, because in a perfect scenario, all of our groups would have done creative problem solving at all stages. Some of these groups were simply too large. We teach one-hundred and fifty-four students, but we could have easily pulled it off with fifty students and management would have been much easier.
Shifts in Identity
Paula was standing across from her partner, Trenece, the day after my students attended a personal finance simulation put on by a professional organization. The girls were deep in debate, arguing over who had it worse during the simulation.
“I was trying to buy a house but my loan didn’t get approved,” Trenece said, “so I had to rent a house and that made me mad.”
Paula smiled, eager to get her opinion in. “I had a realistic moment when I didn’t have any money on my card so I had a whole line of people behind me, and the machine kept saying that my card was declined.”
Trenece shook her head. “My husband was making twelve grand a year and I was like ‘what are you doing?’” As Trenece continued, she’s making a lot of rapid hand movements and her face turned slightly red, “I still had to pay for childcare. Like I had this kid, he’s only working part time, and he couldn’t watch the kid. Husband care! He didn’t do anything!”
Paula nodded vigorously. “Yeah, I had to buy my husband a car. I was like ‘what!?’”
It’s easy to push back against an eleven week project that doesn’t exactly prepare students for the SAT/ACT or college level math, but when I see a student come alive in math class because worked on something complex and relevant for their future, I get reminded that our country’s measures of “mathematical success” are often defined by profit-seeking companies and institutions. Rochelle Gutierrez, in her advice for teachers who want a new definition of success suggests that: rather than looking to external entities such as their students’ scores on state tests… [teachers] look to the mirror and ask themselves if they are doing what they set out to do in teaching, something I call The Mirror Test. Guided by their ethics, these teachers have learned to be creative in the ways they talk and act with others in their work environments so that they are successful in advocating for youth and not simply dismissed (Gutierrez 2016, p.53).
At the beginning of the year, Paula expressed a lot of anxiety about math and about being in math class. Before this project she had pretty bad attendance and would often ask to be excused in class during difficult math tasks to take breaks. During this project, she seemed herself. She debated mathematical ideas, even during days that were heavy with calculation. She involved herself deeply into the project, acted as a leader, and began greeting me every day with a big smile. When I see dramatic shifts in student engagement like this, I remember why we do projects in math class – because they allow us to see a whole new set of mathematical strengths, because this is the sort of curriculum and experience that people remember ten years later, and because it allows students to engage with the world in a mathematical way regardless of their culture and background. Then again, maybe we do projects in math class because we’re sick of answering that question “when will we need to know this?” within future math classes.
Gutiérrez, R. (2016). Strategies for Creative Insubordination in mathematics teaching. Teaching for Excellence and Equity in Mathematics, 7(1), 52-60.
Gutiérrez, R. (2009). Framing equity: Helping students “play the game” and “change the game.” Teaching for Excellence and Equity in Mathematics, 1(1), 4-8.
About the Author
Kyle Kirby currently works as a math teacher at the Denver School of Innovation and Sustainable Design. Kyle works to improve issues of social justice within mathematics curriculum by helping students bring their identities into the math classroom and teaching them to improve their agency as students who can both play the game and change the game. He has taught at a variety of schools, but the three years he spent as a math teacher and instructional coach at High Tech High Chula Vista, CA were instrumental at pushing him to become an advocate for student-centered mathematics curriculum and a warrior of social justice. He holds a Bachelor’s degree from Vanderbilt University, a Master of Science degree from The University of Colorado at Boulder, and a Master of Education degree from The High Tech High Graduate School of Education. You can email Kyle at firstname.lastname@example.org if you have any questions, or just want to start a conversation.