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

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?

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/

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.

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.

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

Can An Exam Enhance Student Learning?

Today was our AP® 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 AP® style questions that they would face on the AP® exam. And, it was about half the length of the exam. The AP® 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. 

 

 

 

Unit 1 Planning: Get them engaged on Day One!

(8/21) I will have my first day with my Algebra 2 students on Thursday (8/24). Here I sit, thinking about what to start with. Last year, we learned how to write numbers in different bases. Kids enjoyed it and asked to do more with it. But, we didn’t have a lot of time for it and it did not show up on the first test. It’s not part of the Algebra 2 curriculum. However, I remember learning about different bases somewhere in my high school math classes. It’s disappeared from the curriculum. Or, maybe it’s reappearing somewhere else.

Having kids learn to write the number 25 in base 5  (looks like 100), 7 in base 7 (looks like 10), 12 in base 4 (looks like 30), really is interesting for them. Their little neurons start firing. They say things like “Whoa!” and “That’s so cool!”

We also spent time issuing texts, getting kids signed up on Remind , and doing getting to know you activities. We went over some expectations, etc. But, I knew I had won them over. Then I started teaching.

This year, I want to do that again. And get them on Desmos quickly – download the app, etc. Play Marbleslides: Lines, etc.

(8/23) I make a plan often based on all of the great ideas and inspiration I get from Twitter math teachers (#mtbos #iteachmath), Jo Boaler, Dan Meyer and many others. I recently read a great article about not grading students in the first month (or some time frame like that) and I thought, “Wow, what a great way to build culture and address equity issues.”

So, I’m thinking about that right now.

I feel that the most important things I can do as a teacher is invite students to be curious, let them know they are an important part of the class, and teach them mathematical concepts. After meeting with my excellent colleagues, I’ve come up the following plan:

We are going to see if those iPads work. If they do (fingers crossed) I want to get students to do a card sort activity, and hopefully play some marbleslides and then get into some vocab around linear functions and translations. We will get signed up on Remind and learn about a few classroom expectations. Seriously kids, no phones and limit your bathroom breaks.  Be nice. That’s really it. However, when working with teens, there is always a need to discuss these things, come to an agreement and then move forward. They will test these agreements. We will need community building. I look forward to that.

I’m really excited to get going. I’ll be working some great activities and mathematical ideas into my lessons. We’ll explore some history, look at different bases, play games on Desmos, be creative, and have another great year!

Excellent Summer PD: Desmos Summer Institute

This summer I went to a two day Desmos training in sunny San Diego that was completely dedicated to improving student learning through activity builder.   Dan Meyer, their CEO, kicked off the training with his typical charismatic, humorous and collaborative way of learning about us and generating the goals and plans for the next two days. There were about 25 teachers and a group of Desmos staff and Desmos Teacher Fellows. So, we were surrounded with amazing support, creativity and collaboration.

The Desmos staff said we can share the materials from the workshop. I love that attitude of sharing. In that spirit, I’d like to share with you one of the great shares of Day 1, the Desmos scavenger hunt. The Hunt provides tasks and solutions so you can test your skills and learn new ones. We had great fun with that.

Using the activities or making your own requires you go to teacher.desmos.com. I recommend you get started by watching the one minute video and then create an account. You can login and start searching existing activities.

I recommend starting with searching the existing activities and activity bundles. There are individual activities or bundles of activities by topic (there is a list on the sidebar to the left of the screen). For instance, in Algebra 2, there is a bundle for exponential functions. There are currently seven activities. By doing a quick preview of each activity, you can decide which ones you want to use and when to use them during your unit. As you preview the activity, you’ll see a green pop-up that gives teacher tips. They are really helpful.

To make your own activities, I recommend using the materials provided by the Desmos team to help you build a great activity. To build your own, use this link to get started learn.desmos.com. Or, sign in to teacher.desmos.com, and click ‘Custom’ under ‘Your Activities’ on the left side bar. You can click ‘New Activity’ on the right and then click the ‘Get Started Here!’ link to take you to learn.desmos.com, to see helpful videos and examples. I also really recommend that you use the Teacher Guide when creating your activity. Each activity has a printable guide to help you build your activity and lesson plan. [FYI, the link to the Teacher Guide is an example, you will get one that corresponds to your activity]

I love the activities in Desmos and have had great success with them. Students work and I am freed up to circulate and help as needed. At a glance, I can see where every student is from the teacher dashboard. I can use the teacher tools to anonymize student names and project individual student work or entire class screen overlays so students can see multiple ways of solving problems. Students get instant feedback on their work. Pacing is individualized and many activities get more difficult as you progress, which challenges every student. Students naturally start to ask each other questions. I can partner students as needed. I can even pause an activity – which always leads to groans and the question, “Why did you stop it?!?” You can read about my marbleslides experience What’s great about marbleslides, if you want more details on a specific activity.

My takeaways:

  1. There are amazing educators out there. Find them and stick with them. Then, find more. Share your ideas. Share your lessons. Build better lessons together.
  2. There are great activities for Algebra 2 already built in Desmos. I’m not sure I want to build any myself. It’s not easy to do and more are being added all the time. There are teachers all over the country adding to the bank of activities.
  3. The activities are varied and can be used in many ways – introducing a topic, vocabulary builders, practice, and formative assessment. So far, the ones I’ve used have all provided differentiation for students.
  4. I will build some activities for my AP Economics classes, which I will be teaching for the first time and am very excited about. I’m picturing supply and demand shocks as a starting place. I built my story board using post-its, as recommended, and am ready to start building!

Having the time to really delve in and learn the tools and process for building activities was a gift. There is a second training August 10-11 in San Mateo, CA. Sign up by July 21

Helping Students Deal with Test Anxiety

Sixteen students and one parent just left my classroom after I hosted a math test anxiety workshop. The purpose was to provide some knowledge and insight about how to recognize the cause of their anxiety and to manage it before, during, and after a test.

We discussed what test anxiety is, the causes and symptoms, and then some techniques to manage those symptoms. I used three resources for the workshop (links at end of blog post). Most of the following is primarily from the Anxiety and Depression Association of America at this link. I used some prepared notes as we talked and had students write in causes and symptoms of anxiety, then reflect on what they were experiencing.

Here’s a play by play of the workshop:

Get ready:

First, set up the room with a seating arrangement where everyone can see each other. A circle is best, but tables pushed together to form a square works, too. Have some snacks out and ask student to pass them around and put away phones or homework.

20161209_115908.jpg

Provide a handout and let students have space to write down the  information and reflect on their own experiences. Here’s a test-anxiety-workshop-handout with the guided notes sheet I created and a printed article from teenshealth.org  available here. All of the links on the handout are listed at the bottom of this post (since you can’t click on the pdf links).

Encourage students to have a snack and pass the plate of mints (or other snack) around. This gets them to interact on a small (but fun) scale.

Intro: What is test anxiety?

Test anxiety is a type of performance anxiety. Much like a gymnast who has practiced her routine, she will feel nervous the day of the competition. Also, like the first day of school when we, as teachers, meet our class for the first time. We’ve prepared our greeting, have our course information organized and then suddenly get nervous as we actually start to speak. Students feel this during presentations, during competitions, and during tests. A little bit of anxiety can be a good thing. But, when it interferes with your performance, it needs to be recognized, examined and addressed.

Causes:

  1. Prepared or not prepared? If you’ve prepared and feel you know the math, you’ve been successful on practice problems and you’ve completed the assignments, you’ve paid attention during class and understood the material, then you are very likely prepared for the test. However, you may not have done all those things and you may be feeling like you should have studied more. As students walk in the room, they are talking about things you are suddenly feeling unsure of. You may now be feeling unprepared for the test. This may be the source of your anxiety.
  2. Fear of failure and/or the consequences of failing. It’s possible that you have really high expectations of yourself or someone else has really high expectations of you, putting a great deal of pressure on you to perform well on the test. Maybe you think you must get an A or you will not get into that prestigious college. You don’t want to do your best, you want to do THE best.
  3. Prior bad experiences in math or on tests resulting in a negative attitude towards your performance, or the test, or school. These past bad experiences can be causing anxiety.

After discussing these causes, students were given some time to reflect on what was causing their anxiety. It could be from one, two or all of the above. We took about 5 minutes to share out. This share out allowed students to talk and hear what was causing stress for others. They could share their personal specific situations. After the share time, the mood in the room was more relaxed. People were talking to each other about what was bothering them and what they were worried about.

Symptoms:

  1. Physical: headache, nausea, vomiting, diarrhea, sweating, shortness of breath, rapid heartbeat, light-headedness, and feeling faint. It can even lead to panic attacks which can make a person think they are having a heart attack or can’t breathe. All of these physical symptoms detract from a person’s ability to focus on other things.
  2. Emotional: People can feel feelings of anger, fear, disappointment or helplessness. All of these feeling interfere with one’s ability to concentrate. They can be a consuming. It is hard to simplify a rational expression on a test if you are dealing with these feelings.
  3. Behavioral or Cognitive: Having negative thoughts or comparing yourself to others can cause anxiety. Your concentration is lowered when you are telling yourself that you aren’t as good as others.Are you telling yourself you’re bad at math? Or that you are not a good test taker? Those are negative thoughts and they cause anxiety if you are about to take a test.

Again, give students time to write down their symptoms and share out.

Tips and techniques to manage anxiety

Before the test: (and maybe during for some)

  1. Minimize the susceptibility to anxiety by taking care of yourself. Get enough sleep. Not just the night before the test, but regularly. Eat a healthy breakfast – eggs, oatmeal, something nourishing. Drink water. Get exercise and take time to yourself on a regular basis.
  2. Make sure you’ve actually prepared. Ask your teacher for guidance. Check resources at TeensHealth.org for ideas about study skills. Studying takes place early and often. Cramming rarely results in sustained strong performance.
  3. Keep a positive attitude and remember that this test is not a measure of your worth as a person. Do your best and keep expectations reasonable. When you expect A’s and A’s only, well, that’s putting the highest expectation on yourself that you can. Would you do that to a friend? Probably not.
  4. What would you tell a friend? Tell yourself the same thing. Use positive self-talk. Remember that great 3-pointer you shot, or think about how great your boots look, or how you wrote a great poem, or paper. Think of your favorite song or book. Think of a favorite character from a favorite book and imagine what they would say or do.
  5. Have a reward planned for after the test. Give yourself something positive to look forward to. A movie after school, ice cream with friends, etc.

During the test:

  1. If you notice anxiety setting in, work to balance it. For physical symptoms, take three deep, slow breaths. Then, relax your jaw. Actually let your mouth open a bit, making sure your teeth are not touching. Wait 5 seconds. Then relax your shoulders. Pull your shoulder blades down your back and relax. Place both feet on the floor to relax your leg muscles. Jaw, shoulders, legs. Now relax your abdomen. Now your hands. Put the pencil down and rest your hands on the desk or your thighs. Take 3 deep, slow breaths.
  2. Then, tell yourself how great you are.
  3. Remember to read the directions and questions. Start with an easy problem. Scan the test before starting. Do the problems out of order. Where possible, check your answers. Always try something on every problem. Your idea is probably a great starting place.
  4. Focus on the test, not other students.
  5. Remember to look forward to your reward.

After the test, remember that you did your best. Enjoy your reward. For next time, if you need to study differently, ask your teacher for ideas. If you need more help with managing anxiety, ask the counselors for help, or check out the websites on the handout.

Give students time again to imagine which techniques they can see themselves using. Let them use some space to creat some positiev self-talk messages. Let them think of a possible reward for them selves. Ask them to share out.

Time’s up! Workshop over!

Resources: 

  1. ADAA: Test Anxiety
  2. TeensHealth.org : Test Anxiety Article
  3. Weber University: How to Overcome Math Anxiety

Teaching about Habits for Studying Math

This year, one of my focus areas is helping kids learn how to study math. It seems that Algebra 2 is a tough year for a lot of students. Students are combining so much of what they’ve learned – geometry, fractions, factoring, solving, graphing – and applying it to learning new and more complicated functions: polynomials of higher degree, rational functions, exponential functions, piece-wise functions, step functions, etc. The list is long!

I’m trying to teach habits that have worked for other students, using students who are successful as a model. However, a lot of the habits of successful students are those that are picked up from and reinforced by parents, teachers and friends. They are habits that they may even enjoy or at least find easy to do, and have likely been doing for years. They are the traditional obvious habits: go to class, take notes, practice in class, finish your homework, check your homework, make corrections, and find the answers to your questions. Finding the answers to your questions is important. You can check the book, online, ask a friend or the teacher during the next class.

What about some not so obvious habits? Maybe these traditional study habits are based on traditional learning styles that work well for traditional teaching environments. What about kids who’ve tried these, but need more? Well, this blog is meant to give some other ideas to try.

Here are some things to try:

  • Sometimes, just reading the question or concepts out loud helps. That’s a technique that’s not always taught. Sometimes, we just didn’t read the question and so we get the wrong answer and can’t figure out why.
  • Here’s a really helpful one that is often not used: look at the material before you come to class. The teacher will hopefully be following some sort of shared schedule and you can look at the topic ahead of time. That way, when you get to class, you have an idea about the topic and you are actually now hearing about it for the second time. This is a good idea as there are sometimes distractions during class and we don’t always have full focus every minute. This is a really helpful habit to use in college.
  • Make vocabulary flashcards.
  • Make a cheat sheet even if the teacher doesn’t let you use it.
  • Read the chapter review section and the practice test problems (back of the chapter) before the end of the unit. Look every week, not just at the end right before the test.
  • Get enough sleep.
  • Eat well.
  • Exercise.
  • Be realistic – it may not happen for you just by wishing. Do you need to put your phone in another room while you study? Are you really concentrating? Have you been avoiding thinking about math and avoiding spending time on it? Do you think you can study right before the test and do well?
  • Are you telling yourself positive things or negative things? Tell yourself you can learn, and you can succeed and do well. It takes work, and you can do it. If other people can do it, so can you!

I provide my Algebra II students with a list of habits – some traditional, some of the above – as well as a schedule. I keep getting better at presenting this. Every grading period (we have 3 per semester) I make a new one and each one is better than the first. The first time, I just put the space for them to write the topic, then I included the topics, then I included the topics and the dates. Prior to that, I had a separate calendar sheet, assignment tracker and habits checklist. Now, it’s combined. Attached is the most recent: r3-assignment-tracking-and-self-checks   The second page is the habits/topic schedule and checklist.

I really need to reinforce it, too. I want to spend more time reminding them to check the list.

What do you do that works well? Let me know!

My first #ObserveMe went poorly

Well, I was really looking forward to being observed using the #ObserveMe rubric from Robert Kaplinsky. I’ve really been consciously aware of elements from the rubric and want to make sure that in every class I am allowing time for students to work together, to ask questions, use diagrams and discuss strategies. I want them to do partner work, individual work, and participate in full class discussions.

Today, I had a colleague scheduled to visit me and do an observation for 30 minutes. I was trying to accomplish two things today:

  • Connect intercepts of a graph of polynomial functions to the factored form of the equation
  • Teach how to factor after creating a desire to use factored form

I’ve noticed that most of my students struggle with factoring. This year it seems to be that more students struggle with it than in the past. So, I don’t think they struggle, really, I think they just haven’t practiced it enough. Maybe it’s just not as emphasized as it used to be. No problem. But, for polynomial functions, factored form is pretty nice.

I’ve seen that most of my students can factor using GCF really well and they can factor quadratics really well when a is 1 and some do well when a is something other than one. They are good with the box method and the diamond method. Some are using the box method to factor higher order polynomials too (third degree, mostly). But, most struggle if they are used to the diamond method and a isn’t 1. Many also have a hard time recognizing a difference of two squares. So, lots to review and lots to learn.

Because we just finished a grading period last Friday, I spent much of the weekend grading and planning. I had some trouble finding what I was looking for for today’s actual focus. Polynomials: graphing, factored form, factoring. There’s actually a lot out there, but I can be picky and I didn’t want to create my own. I ended up purchasing a bundle on Teachers Pay Teachers. There was a good assortment of problems, note templates and it was well organized, covering all of the concepts and factoring that I was looking for.

Anyhow, for the observation, I had thought to focus our class discussion and activities on multiple representations of polynomials – equations, tables and graphs. Then, with the help of Desmos, students worked together to complete an assortment of questions. Some were lower level fill in the blank, others were more big picture, “How do you know when you are done factoring?” I’m still thinking about that. I can’t wait to see what they say.

Well, in the last 30 minutes of our 90 minute class, it was time to focus on factoring rules and patterns. Using what I thought was a pretty nice set of sample problems and a nice set of practice problems, I projected my note sheet so that we could all go through the problems together. But, suddenly it’s was 9:05. I had 5 factoring concepts to get through in 25 minutes. So, I pretty much grabbed the reigns, led/dominated the conversation and worked through the examples (too quickly), with students mostly following my lead.

First set: Factoring with GCF, difference of two squares, then together. Ideally, those were review, right? So, going quickly through those is okay, right? (No, Laurie, not right. The whole reason I was doing it was because there some people who needed to learn/relearn that.)

Next: Hurry, gotta get to the sum and difference of cubes!

We got there, and I really just told them the rule, did a couple of sample problems (which weren’t super easy) and gave them the assignment. I didn’t get to the fifth concept, so cut the assignment short. No problem, we can go over that next time. Class ends…

Observation wise, my colleague was there for the last 30 minutes – the transition, then the ‘I lead, you follow’ method of instruction. Not my finest. She gave me all zeros.

Well, as much as it hurt my pride, it was really good feedback. I’m glad that I know I don’t usually teach like that. And, my students are actually doing really well this year. Things are generally really good. That is not meant to be a deflection or me trying to give myself a pass. I took that feedback to heart and immediately tried to find better ways to teach it.

To be honest, on some of the nuts and bolts stuff, I default to direct instruction. I would have been complacent about that and never changed had it not been for that rubric. I never expected to be an all zeros teacher. I know part of the problem was getting stressed about the time. Usually, I don’t care about that. But, overall, I feel like I am behind schedule, so I was feeling pressured to get that factoring happening.

As I’ve had the day to think about it, the direct instruction was okay, the notes and practice problems were all fine. It was the way I organized the discussion that left no room for student input, problem solving, strategy analysis, practice or interactions with each other, much less with me.

I might have run my next class the same as the first had it not been for that feedback. Instead, I gave more time for the factoring, and had students suggest first steps. We tried various methods. I had students talk to each other and work on a problems together.

Time was a factor today, certainly. However, my conscious decision to organize the conversation around student input and interactions in my second class, allowed students to have more time to think and express their reasoning. More time to ask questions of each other and answer questions. Those processes lead to better retention and interest.

On the upside, I’m glad that I know where my students are with factoring and was taking steps to improve what they know and expand on it at the Algebra 2 level. I look forward to seeing my first class again in two days, to better address those concepts and get some meaningful conversations and practice happening. That’s one of the great things about teaching. You get to see them again and fix what you did wrong.

Thanks, Robert Kaplinsky for that rubric. Thanks, my dear Colleague, for your time and feedback.

The kids were a bit unruly today…

I take that unruliness as a challenge to work on a more engaging experience for them. Today I was teaching polynomial expression operations, which is, admittedly, one of the more nuts and bolts type of topics and not terribly exciting math. This blog post is about how to find ways to raise the engagement on some of the dryer topics that we cover.

And, what’s ‘dry’ to me means that I can’t readily think of great activities, applications, or problems that engage. 

To create a higher level of interest is to create a higher engagement level. This means less need for a disciplined atmosphere centered on direct instruction when the kids are just not in the mood. Which is often in my 5th period (after lunch) class.

The kids are energetic, they are social and they are comfortable enough that they interrupt, throw stuff and eat candy, throwing the wrappers on the floor, sometimes near the garbage can. God bless ’em. 🙂 I really do love these kids and I have fun with them. BUT, I do have a hard time getting through direct instruction for 20-30 minutes, so it drags out longer, which makes it even tougher for me and for them. Way too much!! Especially for the half of the class that is quietly waiting to get through a concept or problem.

Let me say, direct instruction has it’s place, but it’s not working well for me with this group. So, I need options. First stop: Desmos. What great activities already exist for us?

So many! Here’s a link to the classroom activities that come up when I search on Polynomial Functions: http://bit.ly/2drqtGd and a screen shot of the list. If you haven’t already, please set up a teacher account at Create Desmos Teacher Account and get inspired!

polynomial-function-activities-on-desmos

It think for polynomial function operations, though, I’m not really seeing anything that I could use. Bummer. Hmm… Let me think about a flipped approach.

What if I had thought sooner about this being a dryer topic and had planned in advance? I might have had student preview the material, using a YouTube video or checking out Flipped Math’s Algebra 2 topics. Ah, yes, there it is. Here’s a screen shot of the webpage with a video lesson and some links at the bottom, where kids can print the notes sheet or do an assignment. In the past I’ve printed the notes sheet ahead of time, made copies and distributed them during the previous class.

alg-2-flipped-math-7-3

At the site, you can click the Semester 2 tab, then click polynomial functions, there’s a lesson for operations. The site provides a student note page that students can print and fill out while they watch the video. This way, they have guided notes, they can go at their own pace, and they can ask questions when they get to class. In class, we can quickly summarize the key concepts and ask questions. They can do that in groups, or as a whole class.

Would this really help in terms of engagement? Well, hard to say, but at least I wouldn’t be trying to hold their attention so long when it’s just physically hard for them to stay tuned. They would get a very similar experience of direct instruction, just when they are not in a group with their friends after lunch on a warm day. So, I think it’s an improvement, but it’s not exactly innovative or exciting. 

Next, if I do the flipped math for instruction, what activity could I have this energetic group do during class? One option is some sort of matching activity. But, wouldn’t it be better to do a live matching activity where they are the variables? Like, everyone gets to be a cubed-x or a squared-x or a single-x or a constant term? Then, I could write problems on the board and they could group themselves as the equation and solution, and maybe make a video, and maybe put it on YouTube and maybe I could tweet it and blog about it. 🙂 Wow, I’m gonna do that next time.

Another option is to create some open questions. Ways to do this include using some closed questions, like most of the text book questions and simply withholding some of the information and/or instructions, then ask students what are we going to try to solve and what information do you need?

If only I had thought ahead. Well, for me, next time as I look ahead in my planning, I’m going to be a bit more proactive for the sake of this particular class.

Direct instruction + Dry topic = Headache by the end of the block. Never again. 🙂