Why should I blog?

When I started blogging I did it with the assumption that I’d be doing it mainly for reflection. Then I started reading other peoples’ blogs and noticed that many of them were sharing resources that I could implement into my classroom. This meant two things for me. First, I should only “reflect” on activities/tasks that other people might find useful and second, sharing my thoughts and using the blog as a way to process my ideas was out the window. Who cares about my struggles with getting the pod 7 to engage in a normal curve activity? In short, without realizing it, my blog became about other people. How could I format my site so that it had only my best activities so that people who visited would find it useful and pass it on?

Now part of this is fine. If a math teacher visits my blog they’ll likely find something at least mildly interesting to read and maybe something they can use in their class. This pushes me to create tasks that are pretty solid. The drawback is that, because I’m fairly self critical, only about one or two activities a month make the cut and get posted. I have several draft posts that are unpublished because I didn’t think others would find them useful.

I went from a goal of writing for me, to writing for anybody else that might wander over to my site. This summer and next year my goal is to write more often and more for my reflection. I firmly believe that the process of writing and reflecting helps me organize my ideas, identify shortcomings in my teaching, and grow as an educator.

Engage in the Challenging

This year I’ve noticed a trend that made itself even more clear today. I tweeted it earlier, but I think it’s worth exploring a bit more in writing.

I gave a short lecture today on right triangle trig to my algebra II class. (I had been doing more activity based, student centered lessons, so to be fair to the students it was probably a bit more boring than the last couple days.) I noticed many students, throughout the hour, whether it was during the lecture or group work, were on their phone much more than last week. I think this is because right triangle trig is a bit of an uptick in difficulty for many of them. Or maybe difficulty isn’t the right word. It’s just not as familiar to them. This causes them to go to something they find comfortable (their phone) very quickly.

I notice myself doing this at times. If I’m grading tests that aren’t that good or it’s taking me a long time, I find myself getting on Twitter or reading blogs. These are activities that are not very cognitively demanding and are much easier than the task at hand. Maybe that isn’t a great example because I’m not trying to learn something, but you get the idea. So I guess my question is, how do we help students persevere in these situations? I don’t think that taking away the phones is the best move. Once they get to college or their career, an employer isn’t going to say “you aren’t focusing enough, you can have your phone back at the end of the day.”

This is an open question that I can’t really answer. What are your thoughts or ideas? How do you help students see value in maintaining focus when class (life?) gets difficult? I’d love to hear your feedback, either here or on Twitter.

Concept Mapping My Trigonometry Exam

This trimester in precalculus I’m taking a bit of a risk and trying an alternative final exam for the trigonometry unit. Students are building concept maps including each topic that we covered in the trig unit and the connections between them. (Full disclosure, I’m borrowing the format and rubric for this activity from @cheesemonkeySF and you can read the post here.)

I put a great deal of thought into why I think this exam is more effective then a traditional multiple choice test (like I did last year). Steve and I put a lot of time into trying to get students to see connections between concepts and to get them to truly understand the mathematics behind each individual concept. My goal is to help students become mathematical thinkers, not just people who can memorize certain steps in time for the final exam only to forget (or never actually learn) the concepts. Because of this I have issues with giving a multiple-choice final exam which tests them over the exact thing that isn’t my main objective. I understand they are easier to grade, but for the last year I’ve been looking for some alternative to the traditional multiple-choice final exam.

Enter the concept map idea. At its core the concept map forces students to find connections between topics and think deeply about how those topics fit together in mathematics. In addition to just finding the important concepts maybe the most important part of it is justifying the link between the concepts. This should provide me a window into the reasoning skills and their grasp of the big ideas in the from the course.

Day 1

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Students got started on working on outlines for how their concept maps were going to look. Some students started sketching concept maps on the mega whiteboards, others made outlines, and some stared for a while not knowing where to start. It was awesome to see all the different methods and reasoning for how each concept map was going to be designed. There was already thinking about the “big picture” connections between topics. This was a great start and every student was engaged all hour.

Day 2

Many students came ready to begin putting their concept maps together. Once again

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engagement was at a very high level. One student said, “I think this is the hardest we’ve worked as a class all year.” Just this fact alone makes me think this style of exam is worth hanging on to. To have full engagement with every concept in trigonometry and constant conversations about the meaning of concepts for two days straight is great. I’m starting to see how students made connections throughout the trimester and I’m excited for their final products.

Day 3

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Students came in and went to work without me saying anything and worked hard the entire hour. It was fun to watch all of their ideas come together. By the end of the hour there was no doubt that I would be doing something similar for my final exam next year.

Thoughts and Reflections

I couldn’t have been happier with the outcome of this project. There are a number of reasons I deem this project a success and worth doing again next year. First, students were forced to think about the context of all the concepts. It happens so often in math class where students just chug through the course without seeing the bigger picture. I think there is a tremendous amount of value in creating activities where students can step back and look at the context of the concepts they’re learning. If my goal is for students to see mathematics as more than just pushing around numbers and symbols then I have to incorporate this type of activity.

In addition to seeing the bigger picture, this also gives students a chance to collaborate on a project that has more meaning then a final exam. They have to collaborate and analyze the course together, and think critically about the connections between concepts. This is a skill that students will most certainly use in college and in the work force.

Also, this style exam creates a learning experience for students. Over the course of three months concepts become fuzzy or connections are lost and this forces students to go back and really decipher the meaning of the concepts and connections between them. Often as students move through content they miss the connections (even though I try to create activities to help with this). Reflection allows students see the connections (maybe for the first time) and they’re more likely to have really learned them because the learning moments are happening in the context of the concept map project. I don’t see how this could happen with a traditional exam.

Finally, my favorite quote of the last day convinced me that this activity was worth keeping: “Mr. Cresswell, I’m actually really proud of this. This so much more meaningful than regular assignments.”

As I alluded to above, my goal is to create individuals who are  mathematically minded and critical thinkers. I think this activity does a far better job of pushing students in that direction then a traditional exam.

Here are a few pictures of the process and the final products. Here are the links to the instructions and the rubric.

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Multiple Methods for a Simple Problem

For each video I have students watch I ask them, among other things, to submit one question they have after watching the video. After a student watched the “Solving Logarithmic and Exponential Equations” video, he submitted the following question.

How would you solve 8^x = 16^x ?

The following day I used this question in our WSQ chat over the video. What appeared to be a simple problem revealed some interesting solutions. I’ve provided the main types of solutions that I found.

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I anticipated the second method from most students but only two of the five groups approached it that way. All methods are valid and what I really liked is that not only were they different methods but also different thought processes that led to the method/solution.

I would love to hear your feedback or observations that you have seen in your class!

A Better Friday then Expected

Today was a much better than expected. Quite often Friday, especially Friday afternoon, is a tough day from a teaching standpoint as students tend to be less motivated. However, today was not like that at all. My students in calculus, with several options for how they could manage their time, all worked hard for the entire hour. In both my precalculus classes students were engaged in different tasks. (Some watched and took notes on videos, some work on demonstrating mastery on certain concepts they had missed on tests, and others worked on book assignments.) Even students who almost never work hard for the entire hour gave a full effort. Last hour was maybe the least motivated (The weekend is so close!) but even many of them finished the assignment before the end of the hour.

This is part of a larger trend, especially in precalc, of students being much more independent. In this class students have many options for how they manage their time. At a given moment in class yesterday I had some students working on C.A.R.E projects, some working on book assignments, some completing WSQ forms, and some taking notes on video lessons, and almost every student was fully engaged. This is what a flipped classroom should look like, in my opinion. The goal of flipclass is greater differentiation and students taking ownership of their learning. The last couple days have been the best demonstration of that so far this year.