Sunday, February 07, 2010

Language and Retention of Math Concepts

I've been thinking lately that one of the reasons my students have such difficulty with long-term retention of mathematical concepts is due to the small number of times I ask them to thoroughly summarize what they have learned.  They do lots of problems, but the language of the problems often does not enter into their brains.  As we learned in Orwell's 1984, without language, there is no thought.  So I am going to start providing more explicit opportunities for the students to summarize and discuss what we are doing in class.

Comic Strips  (Unit 5, Lesson 9:  doc / keynote / powerpoint)
Quite a few students are still struggling with graphing lines.  They know the general process, but don't pay attention to the details - is the slope positive or negative; if a term is missing, is it the slope or the y-intercept, and how does that change the graph?  So, I had all students draw comic strips to summarize the process in these different cases.  I like how this went, but I definitely did not provide them with enough time to do all I asked.  Here are a few good examples.  The first didn't scan that well, but he did an awesome job.

Think-Pair-Share  (Unit 5, Lesson 11: doc / keynote / powerpoint)
This is a tool that our humanities classes tend to use a lot.  I got some advice from them, and will be trying these periodically during the next couple of units.  We did one so far, and it went reasonably well for a first try.  Students need a lot of practice both writing down their ideas and sharing them out.  Here is the handout I gave (it was used immediately after doing a Do Now problem of the type described).

Mrs. H said...

Dan, I love this idea, and I am definitely going to use it next year. I have a couple of questions though. I noticed that all the kids used 5 frames. Did you give them the comic strip template? Also, did you show them any examples, or did you just let them use their imagination?

I love this post. We had some professional development in quick-writes which involves the same thing you are talking about. A way to summarize your learning. Extremely effective. Every time I've used a quick-write technique I am so surprised at the number of students who can "do" the problem but have no clue how to summarize what they are doing in words. I think it is the key to sending informaation to long term memory.

Mr. K said...

I like this idea too. I've been attempting one sort of summative assessment for several years now, but there's a lot of stalling and discomfort in the process. I think the frame by frame nature of the comic strip makes it a lot easier for them to break stuff down, as well as setting some expectation for how much they're supposed to do.

Ima steal it and see how it works.

Sue VanHattum said...

Great idea! Thanks for sharing it. I'll definitely use it in the fall, when I get back to teaching.

Dan Greene said...

Mrs. H, I did give them both a template and an example, because it was the first time we did this activity. There were quite a few kids who got stuck on my example, and did one almost exactly the same. I knew that would happen, so I only made an example for the first situation, and none of the others. I just wish I had left more time for this in the lesson, so I could see how they would do with the other situations. Most students only finished 2 out of the 4. I will try this again later, and leave more time.

That being said, I did my best to tell them that the example was just an example, and not a very good one at that. Some kids did get creative, but some were still struggling with just getting the basic steps down.

I hope lots of people try something like this and post the results. These compiled could make a good study reference for students.

teachingninja said...

Great idea for recapping! and MUCH easier to grade than paragraphs. Yesss.

Kari said...

Great way to get students to summarize what they have learned. I have seen teachers use journals at the end of class for the students to summarize in and have had great success - but I like this for a change of pace. How do the students like this activity?

Tarah said...

Dan,
I think this is a great activity for students to show how the graph of a line can change with different slopes (positive and negative) and different y-intercepts. I especially like how you turned it into the activity of making a comic strip. This engages the students creative thinking skills along with showing what they have learned about graphing lines. I think students struggle the most with the equation when either the slope or y-intercept is missing. I am currently subbing long-term at my hometown high school for Algebra 2 and Algebra 3. Most of the students got really confused when there was no slope or y-intercept. They didn't know how to graph the line and gave up. Very few students asked questions about these situations. The next day I went over how to graph the line in both cases. This helped the students to better understand what to do in either case. I might have to try the comic strip activity the next time when I am in a full-time teaching position. I hope to find one for the 2010-2011 school year. I already filled out three applications and hoping to get an interview. Thanks for sharing all of your unique techniques in different activities relating to Mathematics. This is one area of teaching I am working on - integrating more activities. I will have to try some of these out! Take care and hope you are having a good weekend.

Anonymous said...

How can I engage the students who refuse to draw a comic strip?

Dan Greene said...

In terms of engagement, I'm not sure how it's that much different than any other activity. What reasons do they give for not wanting to do it?

Anonymous said...

they say that they don't know how to draw and that they are not interested in drawing.
By the way thank you for your prompt response. I really admire teachers like you.

Dan Greene said...

Oh, I see. I don't tell the students that they have to draw pictures - that's only for those who enjoy it or find it helpful. It might be better to present it as a storyboard instead, where students clearly show each step in the process in the different panels. I tell students that this is a good way to clarify the process in their own minds. It's also a good way to summarize, which helps with longer term retention. Additionally, I sometimes let students use this comic strip as an aid during a test, but no other notes. That can help build motivation as well as thoroughness. Finally, some students are motivated by the ability to be recognized and/or helping others, so I tell students that I want to use the best ones to help teach others. Something in there hopefully will help!

Eric Buffington said...

Great way to integrate Writing and Math. I read an article called 'If you teach - You teach reading' and it emphasized the importance of teaching reading in all subject areas. This is a good way to bridge the gap from Math to English.

Anonymous said...

I like the idea of letting student use their comic strips on the quizzes.

the believe it or not bride said...

I am an aspiring Math teacher going into my junior year. The comic strips are such a good idea. I have never seen anything like that. This is such a good idea.

cheesemonkeysf said...

This is a beautiful lesson concept in every possible way.