Category Archives: algebra 2

Math Proficiency Scores in California are not improving, despite all of our changes. What are we to do about it?

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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 11th 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 11th 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:

Source: Hailer-O’Keefe, Algebra 2, Gatekeeper Course, Master’s thesis

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 8th grade – the popular thought at the time was that younger students were doing better, so have all students take algebra in 8th 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.

You can read more about my experience with math and data analysis here: https://quantgal.com/2019/12/17/algebra-2-college-prep-career-prep-or-both/

You can learn more about my professional background via my linked In page here: https://www.linkedin.com/in/lauriehailer/

R-Bloggers site (free resource for learning R): https://www.r-bloggers.com/learning-r-for-free-free-online-resources/

Algebra 2: College prep? Career prep? Or both?

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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.

Source: Student Project by Audrey F.

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.

Source: Student Project by Audrey F.

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 laurie@quantgal.com.

Additional related posts:

Looking at the global economy using United Nations Development Programme data: https://wordpress.com/block-editor/post/quantgal.com/3033

Unemployment using Census data: https://wordpress.com/block-editor/post/quantgal.com/3082

For more on data science in the classroom from Jo Boaler, check out: https://www.youcubed.org/resource/data-literacy/