I was fortunate to catch the rerun of an excellent Global Math Department presentation by Kyle Moyer and Zack Miller(@zmill415). They presented their approach to curriculum and instruction, which focuses on project based learning, and integration in the math classroom. They included a description of their “Booming Populations” project, designed to study and compare linear and exponential functions by examining population trends and predicting the population of a country in the year 2050. The materials they designed are well thought out and put together, and I decided to adapt the project for my Algebra 1 students in Cyprus. This was a rich experience for my students for many reasons.
I used a gallery walk format to build background knowledge and pique interest, and there was quick and solid engagement. Students were fascinated by the world population trends, and were especially hooked by the leaps in population size over the last century as compared to the rest of history. This example of exponential growth was both attention getting and highly understandable. There was built in choice. Students were allowed to choose a country – and I can’t overstate how much of a difference this makes for them. They picked a country that they had some interest in or connection to; a family connection or a place that they had visited or wanted to visit, or just a country that they wanted to learn more about. Choices ranged from China to Greenland to Peru to North Korea, allowing for deep comparisons of statistical trends, modelling validity, and evaluation of source data.
The work was easily and naturally differentiated. Students who were approaching mastery could plug numbers into a slope-intercept equation and into a standard exponential formula, and those who were ready could really push the nuances of their models. I even had a few students dabble with quadratic models (…and this was before we had covered quadratics in class). Advanced students could keep on adding complexity and depth to their predictions by taking into account more pieces of information – demographics, political stability, or even global climate change (will the Maldives still be around in 2050 or will the islands be underwater due to rising sea levels leading eventually to a zero population?). And this was naturally self-paced as well. Very few students reached a “stuck” point, where they needed to wait for the teacher to tell them where to go next. Over the four weeks that we worked on this, I used a combination of discovery-based lessons and some direct instruction to help students build skills to be successful in this project.
Students were asked to examine and compile population data for their country from 1960-1990, and to create linear and exponential models to study this data. They then created a model to predict the trends that they would expect from 1990-2015. After comparing this model to the actual population numbers, students committed to one type of model to predict the population of their country in the year 2050. They were required to complete a written analysis, and to present their analysis and predictions to an audience including a “panel of experts” at our “2015 Population Summit.” Knowing that they would be presenting this work publicly lent gravitas to most of what they did – they were invested in understanding and being able to explain the math that they used, and to justify the decisions that they made in creating their models. They learned to harness the power of spreadsheets to help them to organize their data and to create graphs – a really great skill for them to practice. The public nature of this work forced them to make accurate graphs, and to consider carefully decisions about scale, and how to best communicate data visually.
This was definitely some of the best learning that I have been able to orchestrate as a teacher. Every student achieved the basic learning targets, and most exceeded the standards. Students were comfortably using vocabulary like linear vs. exponential models, initial condition, growth factor vs. growth rate, and I heard many arguments between students who were invested in defending the mathematical choices that they had made. This project found that sweet spot between just enough structure to keep everyone on track, and enough freedom to allow students to make decisions and to own the work.
While I shamelessly use and reshuffle ideas from books and from the MTBoS, I nearly always have to tweak and remake the materials for my students. The language, design, or content have to be customized to meet them where they are, and to give them just enough information to succeed without giving them so much that they don’t have the chance to do their own thinking. The materials that Zack and Kyle have so openly shared (THANK YOU Zack and Kyle!!) are as close to ready-made as I have found. I made some minor tweaks to the guidelines and formatting, but used almost all of their work. Their approach to teaching math is very well articulated, and their Global Math presentation is very much worth watching in its entirety as well. Their use of “playlists” to help students self-direct is especially interesting.
I am hoping to develop this into a more interdisciplinary and comprehensive project for next year, and perhaps something that could be a staple of the 8th grade curriculum. My goals for our math program include building inquiry into the math class process, and creating connections between math and other content areas, and I am especially interested in feedback on ways to leverage these things. Please do throw your ideas in the comments. If you’d like to see some student work or reflections, just drop me a tweet or an email. While student presentations were strong this year, I will make sure to add in more rehearsal time for them to practice next time – especially when they request that the panel of experts ask hard questions.
“Hello and welcome to the 2015 AISC population summit. In our 8th grade Algebra class, we have been looking at world population trends, and thinking about what will happen going into the future. The UN experts disagree about what the future will hold, so we figured that if we wanted answers to our questions that we would need to become the experts.
Each of us chose one country to study. We examined our country’s population changes since 1960, and created graphs and mathematical models to help us predict what the population of our country will be in the year 2050.
We compared a linear model and an exponential model, and decided which one we thought would make a better prediction for our specific country. We did some basic research into our country’s history to give some context to our math models.
We hope that you enjoy yourselves, that you learn something, and that you are willing to ask us hard questions and give us critical feedback.”
BTW: The Desmos Penny Circle is of course a perfect companion/ follow up to this activity.