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.

Creating a culture of observation and sharing

I’m really interested in trying to perpetuate a culture of classroom observations with my colleagues at school. I think most of us value the opportunity to observe and be observed, but we are all soooooo busy!

Fortunately, we have had some funds become available for instructional coaching in our district. One of the ways this can manifest is through release time to observe other teachers. I’d be happy to do it during some of my prep time, but not everyone feels the same way or is able to do it during that time.

After some discussion with the coaches, and knowing we have two new teachers this year who would probably enthusiastically sign up for this, I’ve just sent the email, hoping to get back some positive responses. Oh wait… my email just dinged… YES my first yes, “I am interested.” Now, just a few more and we can get this going, right?

What could go wrong? Well, a lot if people aren’t on the same page about observing and reflecting and respecting the vulnerable position of the observed. For help with learning how to be observed and how to be a good observer, check out this Education World article.

I’m really excited about getting this going. I think it can really transform our teaching and our sense of collegiality and support. The main thing is that it’s really best for students when it’s done well.

I can’t wait to write about how it goes…

PS. Check out Robert Kaplinsky’s #Observe Me post

Partner Quiz + Evaluation = Fingers Crossed!

Last week I gave a partner quiz to my Algebra II classes.They liked the quiz and seemed to be highly engaged. The rules were simple. Work with a partner – open note, open book, scientific calculator – all allowed. I was also being observed and evaluated by one of our Assistant Principals. So, I had my fingers crossed that everything would go well.

My job was in the partnering and in giving feedback during the quiz. My goal was to give each partnership feedback as they worked. The feedback came in the form of green dot (correct) or pink dot (not quite correct). Or no dot, if a problem was in progress or not started.

As I moved through the tables with my two highlighters, kids were very excited and filled with anticipation as I examined their quizzes and marked either green or pink. Some errors were small – losing track of a negative or not writing the plus/minus symbols in front of the answer to a square root problem. Those things they could find themselves usually. Other errors were bigger, more along the lines of not fully understanding the question or how to start a solution.

When students were not understanding how to start on a solution or not understanding the language of the problem, I was able to discover this gap and then help out. All students were getting feedback and I was learning who needed more help. The nice part, was that I was able to check in with every student multiple times during class and help them where they were. It felt like a pretty good differentiation strategy on hindsight. I didn’t realize that going in to this activity.

The first round of me going through the room was just to give green or pink dots. I didn’t give much help or feedback beyond that for most pairs. I would approach each pair of students and look only at one person’s quiz. The next round I would look at the other person’s quiz and give deeper feedback as needed.

By the end, I had several pairs of students who had completed every problem correctly. I asked them to help out certain students who were having questions or just wanted to know if they were getting green dots on the rest of the problems I hadn’t checked or on any pink dots that needed to be looked at again. By the end of class, everyone had reached 100% green. Well, almost everyone. Two students returned during our study hour to get some more help and finish up. Then everyone had green dots.

I did ask for feedback about the quiz process. The students seemed to like it and wanted to do it again. I got a couple of suggestions for improving the system of checking at the end. Next time, I’ll give the students who finish early a green and pink highlighter just like mine so they can officially check quizzes of students who are finished and waiting.

So, while I didn’t want to give a quiz during an observation lesson, this type to be good for an evaluation. Overall, I think it was an engaged class period where students and teacher learned in a formative way about mastery of concepts. It was low risk and ended in better understandings for all students. A couple of students reported that they learned from the quiz. Excellent.

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Student feedback

As far as the evaluation part, my Assistant Principal gave me some ideas for managing the quiz differently next time. One suggestion that I liked was about having each student in the partnership have a different version of the questions and the other one have the solutions. That way they could coach each other. I think that would work well for a maximum of 5-10 problems and would be a good idea to use as an assessment activity after a few lessons. I could circulate and listen to conversations and help out with guiding how students could coach each other. I think it would have been too long of an activity during midterm level review (which this was), covering  good deal of content. But, I will use that idea sometime in the next month. It sounds like a great way to have students use and learn the vocabulary, too.

It was a great day for learning in my classroom.

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. 🙂

My Classroom Culture Is Shifting

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.

 

Demonstrating the Structure of Quadratic Functions with Desmos

I am a big fan of empowering students to look for and make use of structure in Algebra 2. This is most true for me as we work with functions, parabolas, and quadratics.  I’m writing this post about what I’m finding to be an indispensable tool for helping students quickly learn about the structure of the equations of quadratic functions. This tool is easy to use. Simply project the Desmos calculator (use the links below) and activate the sliders.

One of the many great things about Desmos is some of their built in functions on the calculator. Like this one, using vertex form of a parabola:

Link 1: Vertex Form of a Quadratic Function

In this window, you can activate the sliders* individually to demonstrate to students (and share with your math team)  how a, h, and k affect the parabola. You may want to stop the slider and manually slide a to values you want to emphasize with the class (a = 2, 1, 1/2, 1/3, 0, -1/3, -1/2, -1, -2 for instance).

*To activate the sliders, click on the arrow buttons in rows 2, 3 and 4. To stop them, click again, or manually move the slider to any spot.

Next, move to standard form, which is really interesting.

Link 2: Standard Form of a Quadratic Function

I suggest you first let c slide and have students watch as the parabola moves up and down. Ask them whether the shape is changing. Some will think it is, but it’s just an optical illusion. Tell them to look again.

Then, stop c and let a slide. Kids can see how the parabola stretches, shrinks and reflects just as it did with vertex form.

Last, the fun one. Ask them to predict and then tell their partner/group what they think will happen when b slides. Will the shape change? Will it move up, down, left, right? Then, activate the slider.

This is where the math just gets cool. Ask them, as they watch the motion, “What is the path of the vertex?” (it travels along a parabolic path); “What is happening to shape of the graph?” (nothing, it stays the same); and, “What is happening to the y-intercept?’ (the parabola travels through the point (0, c) and the intercept doesn’t change).

I found this to be so helpful to me as a teacher and to students to see quickly what the structure of these equations do. To get to them and many others, just click on the bars at the top left corner of the window for the desmos calculator. There are all kinds of great functions to work with. Here’s a picture I made in paint – screen shot, save in paint, edit with brush – to help you find the drop down menu.

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P.S. I need to create a note sheet for this where they summarize these structures and the impact of the key components. Next week. Yep, next week. 🙂