This fall, I and many of my colleagues decided not to give a cumulative final exam. Instead, I gave students a rubric for a math art project using Desmos. I’ve done this project before during spring semester, but never as an end of semester cumulative ‘assessment.’ In order to get an A, my Algebra 2 students needed to include functions we hadn’t learned about yet. They ran with it.
This was a genuine assessment, as I answered any question they asked, but got them to learn and take risks. This project allowed for instant feedback and was challenging and even frustrating at times for students, but they handled it and some even said it was addicting. Is that a bad thing?
“I really enjoy my math final art project. I got so kind of addicted to the process of doing it, even though it was a lot of trial and error. But it was a great opportunity for me to mix my passion with the ocean, sharks, etc… with something I’m learning in school. That’s one of the few opportunities you get to do in school. Mixing something that you’re really passionate about and put it into your daily life kind of. This was the highlight for me this semester during COVID and I really enjoyed it. Thank you Ms. Hailer.” – Caroline L.
Algebra 2 is a required course for University of California freshman applicants. Is it also a prep course for a career? It sure could be!!
I would love to never hear again, “When am I going to use this?” Or, at least, I want them to be able to answer that question themselves.
Personally, I really liked math and statistics and ended up getting my master’s in economics, specializing in econometrics. But, it wasn’t until grad school that I finally put all those early years of math to use. It was so cool to be doing applied math. If you like math and enjoy the ‘struggle’ of figuring things out, the traditional approach to learning Algebra 2 might be just fine for you. However, I will say, that once there was a real problem to solve with math, the math was even more exciting for me than it was before. Previously, I hadn’t made a connection to a real purpose for studying it, I just enjoyed doing and learning math for maths’ sake. But not everyone feels the same way. As a teacher, I really want students to be excited about what they are learning.
When I’ve taught my statistics students to download data and work with it for a presentation and let them choose their topics, I’ve been amazed to see students who had not been very engaged previously, become excited and start proactively asking about where to go next with their ideas. They took a real ownership of their learning. As a teacher, my job got really easy, too. Classroom management was not an issue and grading was easy because I knew where the students were. Most of my time was spent troubleshooting and circulating and talking to students about their projects. Students had a detailed rubric (but at the same time vague enough to allow for personalized outcomes) which we used as a talking tool to keep them moving towards covering all of the elements necessary for a high grade. I feel these projects prepare students for career and for college courses that require data analysis.
The images in this post are examples of a student, Audrey F., choosing to look at urban populations in different countries. Her rationale for which countries she chose for comparison are explained in her project. She describes what she found and then tries to find reasons for the differences in these groups. Some students need help narrowing down topics and they all need time to think critically. However, as more of this applied math is used, it gets easier for students and teachers.
Once I was working with data and looking for patterns and trying to put mathematical models to social, financial, health, and economic data, I was finally putting to use all that math I had learned in Algebra 2, Pre-calculus and Calculus. However, that was years after taking those courses. I wished I hadn’t had to wait so long to make those connections.
When I was learning, we didn’t have computers, iPads, Chromebooks, phones and easy to manipulate programs like Google Sheets or Excel or the free data analysis language R. So, it was easier to accept the traditional ‘pen and paper, no calculator’ approach. Plus, not everyone was taking those high level math classes. I think college pressures were lower and high school graduation requirements were just for Algebra 1 completion.
Now that data analysis tools are widely available, I really think we should be changing how we teach log functions, quadratics and other super cool math concepts. Teaching from a data science lens allows student to pick topics they’re interested in, create data displays, research the history of other countries or trends and create presentations that they can add to portfolio of work for when they move on to other courses or college and career.
Of course, that’s easy for me to say. I learned these applications and can easily share them with students. What about math teachers who haven’t had this exposure, though? There is a push right now from some pretty powerful minds – Jo Boaler and others – to get data science into the California math framework and it’s becoming more a part of standardized exams. I see it as a way to get students performing at high levels of analytic capacity on topics that matter to them. I see it as a way to integrate the curriculum with history, English, social science, science, technology and even art. I feel the disengaged student would become engaged – their strengths may show in ways that they didn’t even know they had under a traditional approach to teaching high level math.
Am I advocating that the entire course be project-based and applied? No, certainly not. However, some attention to application through data science would really help in terms of increasing engagement for all students, especially those who may not being served by our regular program, and in providing students some skills that are very much in demand today.
But, again, how to we get this professional training into the hands of our already hard-working, over stretched excellent teachers? I would love to come and do a workshop your teachers! Reach out via email at firstname.lastname@example.org.
When we hear that the unemployment rate is low and the economy is doing well, that’s not necessarily true in regional markets. The current 3.7% unemployment rate doesn’t really tell you what’s happening on the ground for many people and job markets. That’s a national average statistic. However, in some areas of California the rate is less that 2% and in other places it’s well above 6%. In Imperial County, it’s about 21%.
The above chart shows you the rates by county as of September 2019 in California. Most of the dark blue regions are between 5.8% and 7.6% percent. The only county higher than that is Imperial County at 20.7%. The next highest Rate is in the Central Valley county of Tulare, at 7.6%.
The lowest rates are in the San Francisco Bay Area, with San Mateo County at 1.7%, San Francisco at 1.8% and Marin at 1.9%. That’s one reason it’s hard to get people to work at low paying jobs in this area. Housing costs are extremely high, with wages that don’t support those high costs for many professionals.
If you look at a state like Mississippi, you see a different range of unemployment rates by County. The lowest unemployment rate in Mississippi is Rankin County at 4.1%, above the national average. The highest county unemployment rate is in Jefferson County, at 15.7%.
These unemployment rates are directly related to home costs. The more unemployment, the lower the housing prices. In low unemployment rates in some counties can drive up home prices, which push out lower income people and can make it hard to find employees for certain jobs, like teachers. Teachers work long hours and don’t want to add a long commute, especially if they also have a family.
Please feel free to leave a comment using the link at the top of the post, especially if you have some personal experience with these issues.
It wasn’t until they actually took a bite of the hot dog that they had an authentic experience. That bite transformed what was kind of a silly project meant to be fun into a life skill for cooking food when they are hungry and have no other resources. Like camping. Or, maybe lunch.
Two of my enthusiastic students were so happy with their results, they asked to have a couple more hot dogs, skewers and buns so they could cook more during lunch.
Yes, we made solar hot dog cookers.
I had thought about this for the past year or two. Prior to this year, I had asked students to answer some questions about designing a solar hot dog cooker after working on a unit on conic sections.
This year, I said, let’s make them. I didn’t really have a rubric and didn’t want to give them instructions. After all, this stuff is all over the internet (just Google it). I also didn’t want to make this so complicated that I would feel overwhelmed. And, I didn’t want to take away from the much more involved project one of my collegagues does with his Engineering student (we have a couple students overlapping our classes).
So, to me this is a great evolution of a project. Think about it, try it, formalize some things for next year. The kids said I should always do this, so I have to take that feedback at point value.
This year, I made it optional. Next year, everyone must do it. This year, I planned it for this week, which is right before spring break. I thought this was a fun thing to do during this week where lots of students are absent due to trips or have big tests or papers due in other classes. Next year, I’ll do the same. This was a good week for this, luckily.
This year, vague rubric written on board:
For a C, it must be parabolic and made from inexpensive materials, with the hot dog at about the right place.
For a B, document your process: how did you decide your shape, take some pictures while building, record problems and your solutions to the problems. Present in a power point, a paper, a movie or a poster board (or whatever other great idea you have).
For an A, all of the above and a calculation showing how you determined where your hot dog should go. And, maybe present it to the class. Actually, I have one student who wants to present, so he is.
Next year, I’ll type that up. I actually think it’s pretty good and the kids didn’t balk, complain or ask for clarification. Well, maybe some clarification. But, next year, I’ll have photos and example to show!! Yay!