I recently wrote a reflection on a prompt given by our middle school director on how I know students are learning. He’s followed up and given us a couple articles to read. I reflected on what I felt I was already doing, what I’ve done before but stopped, and what I should start doing.
The first article was an excerpt from Checking For Understanding by Fisher & Frey. The second article was the New York Times article Why Flunking Exams Is Actually A Good Thing by Benedict Carey.
This entry is on the first article.
Checking For Understanding by Fisher & Frey
The article speaks to how we see if our students have learned through the following means:
- oral language
- questioning
- writing
- projects & performances
- tests
Oral Langauge
I am using think-pair-share continuously throughout the day; I pose problems, have students answer it independently, share with their partner, and then hear several different ideas as a class. It gives everyone a voice at some point and helps them practice articulating their mathematical thinking. During ‘share,’ I need to allow students who may not have the right answer up to explain their thinking to the class, especially I’m I’m seeing a lot of other folks also got it incorrect through my observations. I guess I think ‘It’ll take a while to break down why that’s wrong in a group discussion- better get the person who will do it right & let others ask questions.” I guess that’s OK sometimes; when is it worth the time to really slowly tread through the misconceptions and when should they be corrected quickly?
Questioning
In addition to the questions students answer in their ‘Math In My Own Words’ reflection journals, when I call students up, I ask them
‘what was your thought process on this one’
instead of
‘show us how to solve this problem.’
The latter communicates ‘tell me the right way to do this’ where the former has them articulate their mathematical thinking. When they don’t know, I just ask them something on how to get us started or to estimate a reasonable solution. I’m trying to come up with more meaningful reflection journal questions (ex: ‘Explain why a/b and (a+b)/b can never form a proportion’ vs ‘walk through how to solve a proportion’)
Writing
Students struggle to write about math, especially when they are trying to articulate things that are intuitive to them. I want them to think through why things work and their reflections really show me who understands the depths of the concepts and who just divided “b/c that’s what you’re supposed to do”
Projects
What stuck out to me was to check for understanding DURING the project, not just when it’s done. I did that with the equations project as I knew they’d be a bit hung up on some of the forms, even after the initial teaching of the concept.
Tests
I want to do more pre-tests but I’ll usually go over the most commonly missed problems on quizzes and tests. I never do multiple-choice; I figure that most problems we encounter won’t be multiple choice. Wonder if I should include at least a few on each test. There’s value in knowing how test-takers may try to trick you.
I write about the take-aways I had from the second article in my entry: So Failing Exams Can Be A Good Thing?
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I think the methods you mention should give a good understanding on how your students have progressed.
.. Thanks for the tips.
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