It’s so rewarding to see the things students do when given some parameters, a rubric, some help and their own creativity. The students seem to like the project, some of them get really into it. The featured image here is by Rowe S.

Many students want to rotate things and actually went beyond the curriculum to include trig functions we hadn’t learned yet using this video and info from this blog post by Suzanne von Oy:

As we head into finals season, students have asked to do another project! This blog post will be updated as we get underway, but so far, here is the updated rubric draft for Spring Semester! I thought I’d put it out there after the last post on this type of project has had so many views and downloads lately. 🙂

Sorry, I just can’t give the kids a real final. I’ve had a hard time giving quizzes and tests all year. I blame it on the Pandemania! Most of my students grades have been based on completing their notes, practice assignments, and few alternative assessments. Even when I would give a quiz I followed up with providing the solutions so they could resubmit, generating a lot of 100% scores.

I’ve gotten good feedback from the students who are earnestly doing their best. Themes tend to be they felt less pressure, felt like they could focus on learning and enjoyed coming to class. Students who said they didn’t like math in the past are enjoying this year. What a gratifying outcome given the majority of our year was virtual.

For the ‘final’ I am actually having them do a project (rubric available here). But, I was worried about their ability to hit the ground running in the fall if they are going into Pre-Calculus at our (or any) high school or college campus. I’m not sure how well they actually learned the material or retained it this year. So, I’m giving them a fake final.

It’s a regular final, but I call it fake because I will also provide the answers and links to Khan Academy in case they decide they should study the topics before they get into pre-calculus next year. I also won’t be grading it. They will. It’s also not required. They seem to like this idea, because they share my concerns for the most part. It’s not required because not every one is continuing on to high school level Pre-Calc – some are going to statistics, graduating, etc. But, they need to take placement tests if going to college, etc. This can help them prep for that if they need to.

Below are links to the pdf file and Khan Academy that can help them. If you want the Word version, just email me a laurie@quantgal.com

We did decide to skip some topics this year: Data Analysis and Trigonometry, so those topics are covered through Khan, but we didn’t cover them in class so you won’t see them on the exam. The arrangement of the video units on Khan Academy is different than our course arrangement, but hopefully, students know enough that they can navigate the topic list!

This is a project that I’ve used in one form or fashion with my AP Statistics classes. You can do it in pieces throughout the year or do it all after the exam. Students benefit by choosing a topic of interest, downloading data and creating histograms, generating descriptive statistics, regression equations and inference procedures to create a 21st century portfolio project that is uniquely theirs. All kinds of things can come up for them in this project – expect a range of outcomes.

Please post a comment or question for more info or for guidance on implementation options. Feel free to email me for a word version, if desired!

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.

According to recent data from the US Census, business applications are up almost 40% from last year, with most of that happening in the third quarter of 2020. The charts below show percent changes for week 41 (out of 52) for 2020 and 2019. For week 41, there are 38.9% more applications this year than in 2019. For comparison, the applications in 2019 were 12.7% higher than 2018, which was only 4.0% higher than 2017.

The chart below shows a skyrocketing increase in applications in the third quarter of 2020. We didn’t see these kinds of increases during the great recession (in red). So, why do we see this now? What is different this time around? I’m wondering if people are re-starting old businesses. Even so, I would have expected to see a dip in the second quarter, but there isn’t one.

Last time, there were financial factors creating the crash. This time, it’s much more intense, with entire sectors of the economy shutting down for months. World travel came to a near stand still. This is global and is greatly impacting supply chains for manufacturing and retails sectors. This is a horse of a different color. We are still having to wait and see what happens as we head into cold and flu season. Our physical health is at risk. Our financial and economic health is at risk. We are also heading into the retail sectors favorite time of year. But this year will be different – less travel, less shopping, less events and parties.

We still don’t know if we will see another wave of shut downs and hospital crises. We are still playing wait and see.

[ Note: You can learn how to create your own bar charts using FRED data with this pdf.]

A while back I was playing around with a data mapping tool from the Bureau of Labor Statistics. I thought it would be an interesting idea for something ‘real’ to do with my students. I wrote a post with some examples of maps of California and Mississippi with the intent of showing how much our national unemployment rate at the time (3.7% or something) doesn’t always mean things are rosy everywhere. Here the new map, post Covid-19 for California – the scale has moved from a low of 1.7% in the San Francisco Bay Area and a high of 20.7% in Imperial County to a new range of 6.7% to 22.9%, with many more counties in that top bracket.

This is a significant shift. These data are from August, five months after the economy shut down across the State. The San Francisco Bay Area maintains some of the lowest unemployment rates, but the number of counties with 10% or higher unemployment rates has moved from 1 to 20 out of 58 counties.

Here is a map of the net change from August 2019, one year prior. The darkest shades of blue represent the counties with the greatest percent increases in unemployment rates from August 2019 to August 2020. So, even those San Francisco Bay Area counties are seeing large percent changes in unemployment rates.

It will be interesting to see what the holiday season brings. Some expect to see less seasonal hiring this year. There’s a report about seasonal summer jobs from June 2020 for young adults from one of my favorite sources for great reporting on the economy, Marketplace. Here’s another great report on what we might see in our recovery period.

Overall rates are high in the US, particularly in California, Nevada, New York, and Hawaii.

Here’s map of the percent change from August 2019 to August 2020:

While some states are seeing change is the 1-2% range, others are in the 5-10% range. What makes these changes vary? The types of industries and employment in some areas are simply different. Some areas depend more on tourism, like Hawaii, where we see a 9.8% change in unemployment, one of the highest in the nation. ,Nevada Rhode Island, and Massachusetts are also among the highest with increases of 9.4%, 9.3% and 8.4% respectively.

California and New York are amongst the highest with increases of 7.4% and 8.5% landing them at unemployment rates of 11.6% and 12.6% respectively. That’s a big jump from last August when both of those highly populated states saw low unemployment rates of 4.2% (CA) and 4.1% (NY). That’s a lot of people out of work, and doesn’t account for the number of people who may have left the labor force or are currently underemployed.

Nationally, things are better for most states compared to July 2020. The darker, the better. Those blue states are showing a slight increase, with Kentucky going from 4.5% unemployment to 7.6%, the biggest jump nationally.

Let’s keep our fingers crossed that job growth continues to go up and there is reliable vaccine that comes out soon. Here is a link to Marketplace reports on the vaccine dynamics: https://www.marketplace.org/collection/fast-track-vaccines/

Today seemed to go really well. Students were submitting their Desmos Graphs in a shared Google Slide deck. After throwing piecewise functions, parent functions, and transformations at them in week 1 of online schooling, I thought it would be great to do something more interactive, more creative, and more collaborative with them than what I’d been doing so far.

I asked them to write the word WUX (a totally made-up word) using Desmos. We started out together and I helped them through W and U, with choosing a parent function, translating it to where we wanted it, applying a stretch factor to make it the shape we wanted, and limiting the domain and/or range to get the piece that we wanted. Glorious.

Once I got them started, I challenged them to go beyond the core piece of following my lead and to take some ownership of their project to change the location, the range, the colors, etc. I challenged them to help each other and ask for help. I want to get those conversations going. I challenged them to be creative and maybe do another word or their name.

I love these open types of activities. Kids will inevitably teach me something new or ask something that requires me to do some research. So, everyone is learning. It’s an opportunity to partner students and get to know them.

This was a super simple idea but was a great way to spend part of the period. I had students download their work and add it to a slide show. After 30-40 minutes and you have a slide deck with submissions for everyone. Here are a few of the graphs people made. We are just getting started with this and I’m hoping to see students enjoy the challenge of creating and customizing with Desmos.

Here’s a link to my Desmos graph and equations, if it gives you any ideas:

And here’s a link to a (terrible) video I made about piece-wise functions, but it shows you how to do them in Desmos and how to use some of the sharing options in Desmos.

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.

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 laurie@quantgal.com.