Category: Metacognition

Group Exploration in Math

I am often asked how to get learners to spend more time “exploring” in their learning rather than just recalling or responding to specific prompts for information. Exploration of the learning space is particularly important because learners find the interesting nooks and crannies of the concepts that they would not otherwise discover. Let me share an example. Yesterday in class we needed to spend more time on exponential functions. I began class by displaying a graph of y=2^x and asking the class specific questions like “The graph of an exponential function has an asymptote, where is it?” Only to...

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Expectations About Studying and Syllabi

Recently we’ve seen more attention paid to self-regulated learning as it pertains to student success, especially for at-risk college students (especially first-year students). At least we are starting to recognize the serious contribution of the student in efforts at retention and learning. Anyways, I digress. Self-regulated learning (or SRL) involves students evaluating what they know, deciding what they need to learn, choosing strategies to bridge that gap, and then … actually using those strategies. Unfortunately, there seems to be a KAP (knowledge attitude practice) gap that is between students and their best intentions towards success. I found this dissertation, A Qualitative Inquiry...

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Learners Need to Focus on Errors

Let’s move on to the excellent article It’s Not How Much; It’s How: Characteristics of Practice Behavior and Retention of Performance Skills, by Duke et al. (2009), which is another dive into analyzing what leads to good retention of learning in music education.  Just to be different, I’ll start with the conclusion, and then circle around to the study construction. “The results showed that the strategies employed during practice were more determinative of performance quality at retention than was how much or how long the pianists practiced” 17 students (advanced piano performance students) were given a 3-measure passage from a difficult Concerto to...

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Can we Teach Students to Understand Math Tests?

A few weeks ago, I gave a test where the grades were less than stellar. Whenever this happens, I try to sit down and reflect on whether the poor test grades were a result of something I did differently in class, a poorly written test, or a result of poor studying habits. After careful reflection and analysis of my own, I was pretty sure that this was the result of lack of studying (a theory which was verified … later in this blog post). I was dreading the task of passing back these tests and prepared myself for an onslaught of questions aimed at trying to discredit the test (or the teaching).  Then I got one of those great last-minute ideas that come to you right before you walk in to face the students.  Maybe I should let them “pick apart” the test BEFORE they see their own tests.  The class in question is Math for Elementary Teachers (MathET) and I figured that a detailed test analysis would not be an inappropriate topic for us to spend class time on. First, I made some blank copies of the test (enough for each group to have one).  I also created a handout with every single learning objective and assignment that I had given the students for each of the sections on the test (these are all available in their Blackboard...

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