Category Archives: differentiation

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.

 

Last minute quiz inspiration

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:

  1. Make more copies of the questions – it slowed them down to have to share.Yes. Done. Easy.
  2. 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.
  3. 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.
  4. 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.

 

Teaching Past Grief and Cancer

Well, I had my surgery and I’m back to school. I’m fine. I have a few stitches and a small band-aid on my nose. This picture is with my husband, Doug, right after the surgery. We went sunscreen shopping.

I let kids knwp-1462574706701.jpgow the truth if they asked about it. It was almost always greeted with, “My mom had that!” or someone else they know. Then they told a little story about it. I smiled and said, “Yeah.” Then we got back to the math.

After blogging about things going on with me outside the classroom and how they subtly impacted the classroom in Teaching Through Grief and Cancer, so many people said wonderful things and shared their experiences. Most comments reminded me of the resilience and acceptance of my students. They were right on.

What prompted me to write about it, well, in fact, what stared me in the face making me very aware that I had not managed to make my absences seamless for my students, was when I gave a test and almost no one finished. That really surprised me. I gave the test last Thursday. Only a couple kids finished. At the end of the period, not sure what to do, I told the kids to go study, come in for extra help if they needed it, and continue with their test on Monday. Many of them still didn’t finish on Monday. So, I let them finish today. Turned out, I was giving a three day test over a week long period. That had never happened before. 

One of the unplanned benefits was that they were very motivated to study and knew what to study. Plus, the test wasn’t easy. It was on circles, secants, tangents… with lots of formulas and relationships and complicated diagrams. I’ll probably still end up curving the grades.

I also learned that I didn’t need to hold back on testing because of my absences. I had delayed their test because I had been absent so much. For my Geometry class, I had created a flipped unit, which began the day my dad passed away. I wrote about it here Flipped Circles Unit in Geometry and thought I had done a great thing by flipping the unit, making my absence a non-issue. Never mind that it ended right before a week break. When the kids came back from break, they’d probably forgotten much of what they’d done. Plus, some said the videos weren’t helpful. But, I was also hearing that from just a few kids.

So, we reviewed for a couple of weeks – three more absences for me, then we finally took the test. As described above, it didn’t go great at first. A week later, everyone has finally taken it. And, I missed two more days. That’s okay, though, I gave a final exam review packet. Actually, I gave lots of misc review materials when I was out this semester.

I wonder if the sporadic review packets also had the students going in too many directions. But, isn’t that also spiraling? Hmm… where’s the sweet spot on that? I certainly didn’t get there. That’s a great topic to research: disjointed and sporadic versus ‘spiraling.’ 

Anyway, I’m not blaming myself. Many of the absences were beyond my control. And, I think giving the test over several days ended up being a great differentiation strategy that I would possibly use again. They didn’t memorize the problems and all share the answers, as one might fear. They went away and studied. They came back and asked great questions. So, I think it all is turning out really well.

The last month of school looks good. There will be continuity and plenty of time to review. Everything seems like it’s getting back to normal. I’m so grateful for the ability to blog and reflect and interact with others about this. My spirits have totally lifted from the experience.

Thanks to Dan and Erin and Julie for your kind words on your comments. Thanks to all the friends and colleagues who stopped by today or asked how I’m doing. And thanks to all those friends and family who sent kind words on Facebook or through messages. Putting personal stuff out there is generally outside my comfort zone. I really meant to talk about how it was impacting my students. I didn’t think I would get such a personal response from others. The benefits were really beyond what I expected and I didn’t imagine that I would hear from so many people with similar experiences. I heard from old dear friends and felt the support of strangers. That is really wonderful.

Feeling grateful….

Teaching Through Grief and Cancer

Teaching math is always a tough job. Kids often need more from you than you can give. The bell rings and kids are still not understanding the material.

Throw in some personal problems for the teacher. My dad died about six weeks ago. I got a cancer diagnosis about five months ago, that I basically ignored, because my dad was really sick, on chemo, and shrinking. So, I didn’t want to be laid up or worrying anybody with my own cancer.

Granted, my cancer wasn’t that big of a deal on the surface. That’s kind of funny because it was skin cancer. Get it … surface? Ha ha. It was just basal cell carcinoma. On my face, my nose. So, I’ll be going to school with an obvious wound. However, it was my third cancer. The others were a bit more serious. So, I’m a bit upset about it. I’m only forty-eight. Okay, truthfully, I’ll be forty-nine this month.

So, today was my surgery. It went really well. Mohs surgery. I only needed one round. That’s rare. Most people need two or more. So, I’m feeling pretty good.

But, my students have suffered. My daughter is having to deal with a pretty solid amount of turmoil, grief and upset feelings during her last semester of high school. She and I are at the same school. So, she may need to field questions about my stitches and bandages on my face. I’m worried about all of this and I’m still grieving.

So, how are my students doing? Well, I’m not sure. I haven’t been there much. I’ve been out of the classroom a lot this semester because I also served on a hiring committee (two days) proctored the SBAC (one day) and serve on a countywide committee for Algebra 2 alignment (two days).  My daughter went to State championship for wrestling (two days) my surgery was today and I’m taking tomorrow (2 days) plus out for bereavement (three days).

So, my plans for my classes are all blown to shit.

And, even when I have been there, I’ve been less than I’d like to be. Even though I do forget about my troubles when I’m at school. I love teaching. I have good relationships with my students. But, they need more than that from me.

So, this blog outlines my problems and hopefully sets the stage for my next blog, which is going to be about how my students are doing in light of it all. And, about how I’m planning to compensate for it in the last month of school.

Many of us have dealt with or will deal with these kinds of serious issues while teaching. If you have, post a response below. How did you handle it? What do you wish you had done differently? What would you keep the same? What advice would you give a teacher going through these types of things?

 

How 2 questions took 1 hour to solve

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:2016-04-22-13.44.41.jpg.jpg

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!

More about problem three in another post. Maybe.

The origin of a project…

It wasn’t until they actually took a bite of the hot dog that they had an authentic experience. That bite transformed what was kind of a silly project meant to be fun into a life skill for cooking food when they are hungry and have no other resources. Like camping. Or, maybe lunch.

Two of my enthusiastic students were so happy with their results, they asked to have a couple more hot dogs, skewers and buns so they could cook more during lunch.

Yes, we made solar hot dog cookers.   20160406_123653.jpg

I had thought about this for the past year or two. Prior to this year, I had asked students to answer some questions about designing a solar hot dog cooker after working on a unit on conic sections.

This year, I said, let’s make them. I didn’t really have a rubric and didn’t want to give them instructions. After all, this stuff is all over the internet (just Google it). I also didn’t want to make this so complicated that I would feel overwhelmed. And, I didn’t want to take away from the much more involved project one of my collegagues does with his Engineering student (we have a couple students overlapping our classes).

So, to me this is a great evolution of a project. Think about it, try it, formalize some things for next year. The kids said I should always do this, so I have to take that feedback at point value.

This year, I made it optional. Next year, everyone must do it. This year, I planned it for this week, which is right before spring break. I thought this was a fun thing to do during this week where lots of students are absent due to trips or have big tests or papers due in other classes. Next year, I’ll do the same. This was a good week for this, luckily.

This year, vague rubric written on board:

For a C, it must be parabolic and made from inexpensive materials, with the hot dog at about the right place.

For a B, document your process: how did you decide your shape, take some pictures while building, record problems and your solutions to the problems. Present in a power point, a paper, a movie or a poster board (or whatever other great idea you have).

For an A, all of the above and a calculation showing how you determined where your hot dog should go. And, maybe present it to the class. Actually, I have one student who wants to present, so he is.

Next year, I’ll type that up. I actually think it’s pretty good and the kids didn’t balk, complain or ask for clarification. Well, maybe some clarification. But, next year, I’ll have photos and example to show!! Yay!