# Algebra 2 Final Projects 2021!!

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:

Here are some screen shots and links to other projects. Next year, I plan to have students work on their project throughout the year.

Izzy S.

https://www.desmos.com/calculator/q7mal7aeh5

Avery G:

https://www.desmos.com/calculator/qi8lc5etvz

# AP Statistics Project – Year long or after exam

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.

# Surprises abound for this Algebra 2 final project

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?

Here’s the rubric from Fall semester 2020: (click here for Spring updated final project rubric!)

Here’s some feedback:

“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.

Here are some examples:

https://www.desmos.com/calculator/9kezqiy4zr

https://www.desmos.com/calculator/peecc5jfri

https://www.desmos.com/calculator/obud0a6jkp

# Can’t get a job? Create your own. That seems to be plan for many in 2020.

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.]

# WUX up?!? Teaching Piecewise Functions remotely using Desmos

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 Iâ€™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. Itâ€™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.

Hereâ€™s a link to my Desmos graph and equations, if it gives you any ideas:

My graph and equations in Desmos: https://www.desmos.com/calculator/rvmna70gg5

And hereâ€™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.

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

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.

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/

# A closer look at unemployment rates in California and Mississippi

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.

You can get more details and play around with the BLS mapping tool here: https://data.bls.gov/lausmap/showMap.jsp

For the past two years, I’ve been branching out career-wise and reflecting on my experiences as a teacher. I felt I needed a break from the classroom. I thought I might be burning out, or maybe I just needed a change. I switched up the courses I was teaching, went part-time, volunteered with some organizations, interviewed for other jobs and even took a position outside of education altogether. However, it’s now November, and I will be returning to teaching, full-time math, in January. I could not be more excited!

I’m writing this post to explain why I’m asking you to share your teaching story. I have a survey I’m doing because I really want to know what other teachers are going through. I read a lot about the profession and am involved in professional development activities. I’m engaged in my profession. Yet, I still had this wonder – is this the right job for me? Why am I so tired all the time? How can I respond to all the needs of my students and the demands of my schedule? Is something wrong with me?

I learned that there’s nothing wrong with me. There are so many articles and studies about burn-out, the increased demands on schools, and increased scrutiny of teachers. So, I know that’s all real. However, to me, the individual experiences are not always explored in these articles. I’m particularly interested in California math teachers’ experiences but would be happy to hear from anyone who is willing to share.

So, let me share my story (briefly) so you can understand where I’m coming from:

I got into teaching as a second career. Prior to teaching, I earned my master’s degree in economics and worked in the credit industry and then as a statistician for UC San Francisco, studying the health care labor force. I have a background in research and labor studies – no wonder I’m interested in issues surrounding the teacher labor force.

I went into teaching after having kids, thinking I would reduce my commute and have more time with my children and family. That was true – sort of. I had the summer and holiday breaks, but the workweek was incredibly time-consuming. I had no time for socializing or hobbies or other fun stuff. But, it was okay – I really loved what I was doing.

I started teaching at a public middle school as a full-time paid intern and worked on my credential at night. So, I was able to forgo a few courses, since I was already working full-time in the classroom. After earning my credential, I kept going to earn my master’s in education. I felt I would eventually go into education research. (That still hasn’t happened, but this project is my starting point).

I went from middle school to high school, eventually landing at the school where I graduated and where my oldest daughter was attending. She wasn’t totally sold on me teaching at her school, but I reminded her she would have access to money and car keys and I promised to leave her alone, and she was more accepting of the idea.

I loved it at first. For a few years, I felt like everything was really great. By my sixth year there, though, I was coming home in a bad mood, exhausted, wanting to pursue other things. I thought, did I only go into teaching because of my kids, and now that they’ve graduated, do I not like it anymore? No, I was really just getting burnt out. I was neglecting my own needs and teaching in a high performing community where expectations frequently went a bit beyond what was reasonable.

For 2017-2018, I was able to move from teaching math full-time to teaching 2 sections of AP Economics. I loved teaching economics but was still feeling pretty worn out each day, trying to manage some unruly behavior in one of my classes and manage expectations around grades. For 2018-2019, I took a partial leave of absence, so I could have a bit of a break and pursue some other career avenues. I volunteered with NCTM and took on a fellowship with the Federal Reserve Bank of San Francisco.

These experiences were just what I needed. I was ready to go back to full-time teaching, and applied for a position at a different campus, thinking a change of scenery would be good. I had been working and living in the same community and thought maybe everything was a bit too close for comfort. However, on July 1st, I received an offer for a position with a large corporation, working as an associate economist. [Background: the summer before this, I had applied to positions outside of education and interviewed with this company and received an offer, but turned it down because it was a junior position and long commute and a pay cut and it was already September – I couldn’t really quit at that point.] But, in the summer of 2019, it was re-posted and re-offered to me, and despite the drawbacks, I took it thinking it would be worth checking out and would lead to bigger and better things.

It didn’t work out. I won’t go into detail, but suffice it to say, I didn’t feel challenged, I wasn’t doing anything that used my analytic skills, and I really did miss the interaction of the classroom and helping people. What I really learned from this experience is that I have a wealth of education experience and have a lot to offer to the field. I was able to go corporate and see if the grass was any greener, but it wasn’t. I learned that I need to manage the expectations that I put on myself to be perfect and instead, do my best to be a great teacher, within reason. Letting myself burn out is not okay.

Fortunately, with teaching, there are big chunks of time off where we get to pursue other interests, such as blogging about teacher labor market issues. Mostly, I’m focusing right now on the teacher experience. So, if you can take a bit of time and share your experience, I would really appreciate it. You may be in year one or year 30 of teaching. I’m not sure where this will lead, but I hope it leads somewhere.

I want to know where you teach, how long you’ve taught, how has your career evolved, have you ever thought of leaving? If so, why didn’t you or why did you and did you return? How do you feel about your decision?

Because I am just starting this project, I would love feedback on the survey questions and organization – I’m really just kind of throwing it out there as a Beta Version right now.

How will your responses be used?

Great question! I will try to aggregate the submissions in terms of state, region, courses, level (elementary, middle, high, college) to see if there are any trends. I may put up a chart of some responses, but I would remove all identifiers, and make sure there are at least 5 respondents included in any particular breakdown so that no one could be identified – this is standard practice in most government research projects.

There is a question at the end that asks your preferences about possibly being quoted, with no quote as an option. You can leave your email so that I can email you before printing anything. You can also email me if you want to discuss anything: laurie@quantgal.com

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# Measuring an Economy

Today I’m giving a presentation at the College of Marin to the hiring committee for the Social Studies department. I’m applying to teach Economics. I’ve taught at COM in the past, in the Business Department. Since then, I earned my teaching credential in mathematics and economics and an MS in Education to add to my other MA in Economics. So, I should feel well prepared, but I’m nervous, of course.

They asked me to give a 20-minute lesson where I “utilize current economic models to introduce students to contemporary issues of development, underdevelopment, and globalization.”

Hmmm… Twenty minutes worth. How will I narrow this down?

Well, what are contemporary issues in globalization? I’ve recently read Hillbilly Elegy. In that book, the author K.D. Vance, tells a story that spans several generations of his family who moved from Appalachian Kentucky to a steel town in Ohio, only to see the industry become automated and globalized away. Those are contemporary issues, for sure and they fit in with economic models of unemployment and GDP.

I created a PowerPoint presentation that I’m sharing here. It looks at the Phillips Curve, GDP and other ways to measure the wellbeing of a nation. I use a lot of indicators and resources to get the audience to think about other measures that define the health of a nation and we compare them across the globe. I end the presentation with some summary information about what would make a nation developed or underdeveloped and we do an activity that highlights those ideas.

In the end, globalization can be helpful and harmful. As we globalize, we have a long way to go in terms of equality.

COM Presentation 04302019

# Can An Exam Enhance Student Learning?

Today was our APÂ® Microeconomics exam on industrial organization, market failure, and government interventions. It was covering eight chapters in the text. After creating it, I had a few concerns:

• it was too long
• there were a couple things on there that I didn’t feel we thoroughly covered
• I didn’t want to shorten it or postpone it

So, it was time to be creative. I know my students want to do well and that they care about learning. They want to get good grades, go to college, and have nice lives. I want all that for them, too. This test had the potential to cause a bunch of stress, complaints, and grade damage. I needed a solution.

You may be thinking, well, just shorten it! Yeah, I thought the same thing. However, I wanted them to have the full range of possible APÂ® style questions that they would face on the APÂ® exam. And, it was about half the length of the exam. The APÂ® exam is only two hours and ten minutes long and we had 90 minutes for our test period. So, I felt it was actually a fair length, just longer than our usual in-class exams. I also liked all of the questions and knew we had covered everything except for a couple of terms that I felt they could figure out, like “average tax rate.”

To take a pulse of how the kids were doing, I went around the room and checked in with everyone. “How’s it going?” “Any questions?” Most of them said no. They said it was okay.

But, I still wanted to provide an opportunity for them to do better. With about 15 minutes left in the period, I told the students to review the exam, read any questions they hadn’t gotten to and scan the vocabulary and diagrams. I told them they could have ten more minutes to work on the test. At the end of the test, I told them they could go home, study again and have their tests back during the first 15 minutes of the next class (in two days – we have block periods).

During our tutorial period today, a group of students came in to work together and to try to ask me more questions. I didn’t want to answer but paid close attention to their discussions. It was thrilling to see them argue about ideas, look things up, work together and come to a consensus with how monopolists make profits and engage in price discrimination, how deadweight loss occurs, how a tax can fall unequally on consumers and producers and other microeconomic concepts.

The best moment was when one of the students said, “This is great, I’m learning so much from this!” He’s a strong student anyway, who typically gets high grades and I was pleased to know that he was getting a lot out of the process.

I know this breaks the tradition of testing, but I also knew these students appreciate a break and have an opportunity to know exactly what to study. It’s almost a way to build in a retake or have them do test corrections. Whatever the case, it accomplished what I hoped it would. A targeted re-studying session and a highly engaged discussion amongst the students where they strengthened their knowledge and improved their ability to demonstrate content mastery.