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.

In 2013, I wrote my master’s thesis on Algebra 2 as a gatekeeper course. I used performance data from the standardized test at the time, the STAR test. It tested every student every year in mathematics, by the course they took.

Since then, some things have changed including the standards we teach for each course and the frequency at which we test students. We administer a standardized test in high school mathematics only in the 11^{th} grade. There are some others, but this is the main one for monitoring proficiency levels on a wide-scale basis throughout California.

I was wondering if our proficiency scores had improved over time. At a glance, they haven’t. But, let’s dig deeper. In some ways, this is an apple to oranges comparison because now all students take the same exam in their junior year of high school, instead of taking an exam every year, based on which course they are currently taking. The exam is administered mostly online and is apparently interactive. You can get detailed information about how the exam works here. In fact, there is a lot of detail there and it may be overwhelming, so good luck!

I decided that the best approach for comparison would simply be to look at the Algebra 2 proficiency scores and compare them to the 11^{th} grade exam, since it is the recommended path that most students take Algebra 2 by their junior year, even though some take it sooner and some take it later.

You can see the results for 2012 Algebra 2 proficiency for each of the Counties in the 9-County San Francisco Bay Area and the State of California here. The main graphic that shows the break down of proficiency level by grade for Algebra 2 is below:

This chart shows proficiency levels by grade for Algebra 2. You can see that the younger students are doing better than the older students. The reasons for this are explored in the thesis. This post is meant to focus on whether or not things have improved since then. The thesis examines breakdowns of proficiency levels by grade (above) and by gender and race and ethnicity levels. For comparison purposes, let’s look at the California dashboard for math proficiency scores for 2017-2018. I would think, with seven years of transition time, an easing of the standards, more emphasis placed on understanding relationships and an interactive test, we will see a strengthening in our proficiency levels. Below are the overall results for proficiency levels for the state for 2018-2019.

Source: California Department of Education Website, 01/20/20.

I don’t know about you, but the 32.24% met or exceeded Standard for Math does not seem very good to me. Back in 2012, many students were taking Algebra 1 in 8^{th} grade – the popular thought at the time was that younger students were doing better, so have all students take algebra in 8^{th} grade. That has since gone by the wayside as many students were not successful in that model. For tenth graders, though, proficiency levels for the state were at 42% (link to report and view pages 22-23 for detailed state and county information).

Unfortunately, with all the implemented changes, there doesn’t seem to be an improvement in outcomes. The reasons are plentiful, but it’s got me questioning our system. We are teaching an antiquated model: Algebra 1, Geometry, Algebra 2 in an attempt to move students to Calculus and be successful. However, I question this goal. In practice, many people working in analytic fields requiring mathematics backgrounds are using computers to solve problems and make calculations. Those computer skills – programming, analysis, and data use, are not making it into the classroom until much later in a student’s education career.

There is a move to make more changes to our system that incorporate some data science which includes analyzing data, learning to write some code, and understanding how to create data displays. I have no idea if this approach would raise proficiency scores, but I don’t really care. I think the testing system is dramatically flawed and we keep trying to get the teaching and testing right around these antiquated approaches to the curriculum pathway.

I believe the core three years of mathematics education should shift from proof and abstract problems to applied problems that prepare students for careers other than mathematicians. Our system builds from generations of candlelight and paper and pencil-based tools. That simply is no longer our reality and we need to make some jumps in our methods and expected outcomes.

We should keep teaching about functions and lines and logarithms and conic sections. It’s just that we should include applications. Applications are abundant. We need people who work in fields that use these functions, programs and relationships to help design effective and interesting problems for students. I know that I can do this in economics, and there are others who can do this with physics, medicine, engineering, etc.

We can teach students some coding using R, but teachers need to learn it, too. There are free resources to help with that! Just google “free resources for learning R.” Wait, I just did and have included a link at the bottom of this post.

The opinions stated above are mine alone – oh wait! They are not mine alone. Please check out Jo Boaler’s YouCubed website if you don’t believe me: https://www.youcubed.org/resource/data-literacy/ Then, Scroll to the bottom and see all of the articles and resources that back up this idea.

My other big concern is how today’s math teachers, who may not have had experience with data analysis, are going to be able to implement changes. I am hoping to help with this.

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!