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!

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. 🙂

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.

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.

(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!

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:

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.

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.

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.

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

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!

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.

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. 🙂

Well, it looks like the past six weeks of having students sit in groups and emphasizing that they work together is possibly paying off. Today, instead of hearing, “I have a question…” I heard “We have a question…”

That was beautiful to me. I had just rearranged the seating chart. At our school, we have moved into our second of three grading periods for the semester. These kids knew to work together with their new partners, and they were doing it. They knew I was pretty much only answering questions no one in the group could answer. They are learning to check in with the other students in the group before asking me for individual help.

I highly recommend this type of group seating and emphasis on student-to-student communication. It’s been so helpful to have students talking to each other about math. This should happen during warm-ups, work times, activities, and class discussions. To get them to start talking to each other, I sometimes ask why something works a certain way and ask them to discuss it with each other. Then, I might walk from group to group to check in with the group. Then I might summarize for the class what I learned from the groups.

Full disclosure: I used to be afraid to have them “Discuss at your tables…” because I was afraid they would talk about other things. And, that was often true because I was letting them sit with their friends. Better to mix them up. I first made a seating chart that was alphabetical. That was helpful to get to know their names and faces and to check off homework and take attendance quickly. Now that I know them better, I mix up the seating thinking about male/female, test scores, personalities, etc. I plan to change the seating every grading period. We have six throughout the year.

Groups are working better than two partners. I think it’s because students have more people to talk to who might know the answer. It’s important for me as the teacher to circulate to each group several times during the class period. I ask if the table has any questions. If there are questions, I ask if anyone at the table can answer. Then, if so, I’ll listen to that discussion and help if needed. Or, I’ll walk to the next group and repeat. I try to only answer what students can’t answer.

Students learn that I’m available and want to help, but can’t take the time to answer every single question from every single student. It’s like an economic situation where the teacher’s time is the scarce resource. Students are learning to make their questions be worthwhile to their group.

Yesterday, I suddenly decided on a new quiz format. I had been writing a quiz for my Honors Algebra 2 class and I just didn’t like it. It wasn’t interesting or challenging. I really didn’t want to make a second version (my kids sit at tables), and was hoping for several days that some inspiration would hit. Our text has a set of alternate assessment questions, but they are a bit involved.

So, in the 5 minutes before class started, inspiration hit like a tons of bricks.

I let them use the alternate questions, and work in pairs. There are 6 students at a table group and we were covering two chapters. I gave them packets of the questions. There were about 7 questions for Chapter 1 and 6 questions for chapter 2. The guidelines were that they had to answer one question from each packet and couldn’t answer the same questions as the people at the table group. So, that’s a total of 6 questions for the table, three from each chapter, two for each pair of students.

To make it an actual quiz, they couldn’t use notes. They also couldn’t ask me questions. Actually, they could, but they would lose a point. Each question was worth 10 points, for 20 points total. Asking one question would still yield an A. But, no one asked any questions. The kids were engaged and worked steadily for about 35-40 minutes. Most finished, no problem.

I called time at 45 minutes. Some students hadn’t finished. I gave 5 more minutes. However, a couple of groups didn’t get to the second question or had just started it. Uh-oh.

So, as this is a group of motivated, grade-stressed students, I allowed them to come back at lunch or after school or during our tutorial time to finish. They appreciated it, so we were good.

The best part, was in the ask for feedback about the quiz format.

I gave them three prompts:

Partner quiz again? yes/no

This would have been better if…

This was good for…

They unanimously liked the partner quiz because they had another brain to work with. Asking for feedback is gold! Making myself vulnerable was scary. Here I had changed up the quiz in the last few minutes, kids didn’t finish, they were afraid to ask a question even when it would have gotten them to the finish.

Would I do it again? Yes! Overall, it was a positive practice for them and for me. In fact, I’m doing it again today with my other section of that class. I’m happily incorporating their feedback with what I observed to make the following changes for the next class and next partner quiz. Here’s my list:

They asked me to:

Make more copies of the questions – it slowed them down to have to share.Yes. Done. Easy.

Allow questions. Well, I’m thinking no on that, because I think they will ask me a million questions. So, modified practice: they can ask the question. If it’s a fair question, I will guide with no point deduction. If it’s a question about not understanding the content, then I will take a point if I answer. They can ask the question, then I will answer or respond with, “Yes, I’ll answer, but it will cost a point.” Then they can decide if they want the answer.

Give more time. No, but I will advise students to read the entire question before choosing (most have multiple parts) and remind them that they can change the question if they get really stuck. Also, I will be more active in making sure everyone is employing strategies to finish on time.

No one mentioned this in the feedback, but I didn’t give them a time frame before they started. I wasn’t sure how long it would take. When half the class was finished, I announced 10 more minutes. I should have circulated a bit to check on their progress at around 20 minutes to let students know they should start on their second question within 5 minutes, so they have time to finish.

Now, I just have to grade them. That’s nice too, because I only half the number of quizzes to grade. Another teacher benefit from the partner quiz.

Please comment below with questions or ideas or practices you have tried. If you want to know more about the course or text, send me an email.

I was responding to a post by Dan Meyer about his awesome recent talk at NCTM. Here’s what I wrote in my comment:

I am working hard to keep engagement high. This week, we actually started with two blank triangles, one right and one obtuse. I asked kids to solve the triangle, and ask me questions. There were no measurements on the triangles. The triangles were to scale. They could ask me for one value.

From there, they had to measure another part of the triangle and let the solving begin. They could only measure one other part, no more. So, depending on what they chose, they would use different tools to solve the rest of the triangles. They used rulers or protractors, ratios, triangle sum rule, right triangle trigonometry and Laws of Sines/Cosines. They worked in groups to try to figure out what information they needed, they worked together to try different strategies. In the end, the only way they knew the answers were correct was by rationalizing whether or not they made sense.

We spent 1 hour on two problems. Engagement was high, completion rates were nearly 100%, participation was 100%. It was a really great day for me and I was able to coach them. They did the lifting. It was great. Great conversations.

So much of Dan’s work inspires mine. I love his 3-act-math ideas, though I don’t use them much. More so, I respond to the idea of opening up questions. I love the idea of putting out a skeleton and asking kids what they need. They actually answer, they actually engage in the problem and start to think and ask questions. Once they are invested like that, they don’t like to give up. Giving up has been like an epidemic in mid level high school math classes like geometry and Algebra 2.

Today’s geometry warm up looked like this:

We didn’t even get to the third problem. Yes, it was hand drawn. Like, free hand. That actually made the problem kind of interesting because I don’t really have a right triangle, do I? Just almost one. So, depending on what side or angle students measured (by the way I told them the base side of the triangles in both problems one and two was 15 units) the answers they got might be a bit different.

It was also a great talking point about how real life problems are rarely perfect and we rarely get to check the back of the book to see if we did it right. We have to trust our methods and our team.

Great conversations. Such a great day. It was hard for some of them to keep going to finish the second problem. They were a bit tapped out. We have block schedules, which means 90 minute periods. This took way longer than I expected. But, totally worth it. We’ll do the third problem next week. They actually asked for a book assignment when we were done. I guess their brains were tired. But, they did it! And, they did really well! Go team!