A study was released about 5 days ago. The title: The Advantage of Abstract Examples in Learning Math. A number of articles about it share the title" Concrete examples don't help students learn math, study finds. (Supporting material can be downloaded as a pdf here.)

From the article:

Teachers often use real-world examples in math class, the researchers said. In some classrooms, for example, teachers may explain probability by pulling a marble out of a bag of red and blue marbles and determining how likely it will be one color or the other.

But students may learn better if teachers explain the concept as the probability of choosing one of n things from a larger set of m things, Kaminski said.

If Ms. Kaminski (one of the authours of the study) tried this in any high school classroom she'd bang up hard against a confused wall of silence from all except the most gifted students.

About 2500 years ago Aristotle wrote about how presenting an argument from the general to the specific (deduction) is only one of two forms of presenting information (teaching). Arguing from the specific to the general (induction) is the other. Both have their place.

Anyone who has taught mathematics in a high school classroom knows kids really need to learn and understand both. Often, they just can't grasp general concepts until they have seen several concrete examples. This is what Aristotle calls induction. It is a weaker form of argument than deduction (arguing from general principles to specifics) but is a necessary step in the learning process. Generally speaking, kids find inductive arguments far more compelling than deductive ones, even though the reasoning behind deductive arguments is far more sound.

One of the authours of the study also said:

Story problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching.

Sometimes a study is just plain wrong. This one is just plain wrong. "Story problems" are excellent tools for both teaching and learning, particularly when students are taught to recognize the underlying patterns of the general mathematical ideas they contain. I find teaching mathematics is something of a dance; constantly flipping back and forth between induction and deduction and guiding students through the process of teasing out the underlying patterns that tie several problems together; problems that on the face of it seem to be quite different are in fact the same ideas in different clothing.

In general, mathematics is the science of patterns. It is the job of the classroom teacher to help students recognize and identify those patterns so they can use them to solve many different problems as they come to recognize the connections between seemingly disparate situations.

I wonder too about the methodology of the study. The article says: "students were taught artificial mathematics". It seems possible (likely?) that the results were skewed as a result of the interference effect.

Dean Shareski tweeted that these results might take root. It made me think of the controversy surrounding The Learning Pyramid. I hope Dean's concerns don't materialize. From teaching hundreds (thousands?) of students over many years I know this study is just plain wrong.

In this episode Timothy, a grade 12 AP Calculus student, comes back to high school on a Friday afternoon to talk about his week attending the miniUniversity program at the University of Winnipeg. He talks about the differences he finds between teaching and learning at high school and university and describes learning in the university classroom using a thought provoking metaphor, listen for it. Also, we have a cameo appearance by two very special people at the very end.

Please feel free to leave Tim_MATH_y your comments here or on this post on her class blog. You can find the archive of his most recent online work in his class blog.

(Download File 7.2Mb, 15 min. 3 sec.)

I was talking to one of my students earlier this week while helping her review over the lunch hour. I found her comments so compelling I asked her (and later her parents) if I could record and publish her comments so other students could hear what she had to say. I've long thought students need to hear from other students how they best learn to help them all learn.

This is the first in what I hope will be a series of podcasts called Student Voices. I'm hoping to have one of these short conversations with a student published each week.

I was inspired by the powerful presentations done by my students on Monday at the Pan-Canadian Interactive Literacy Forum. Hearing how students talk powerful learning experiences in their own words fascinates me; I find it very compelling when I begin to doubt if "all this web 2.0 stuff" is worth mine and my students efforts. Listening to Jessie talk gave me a shot in the arm at a time when I really needed it.

In this episode Jessie, a grade 12 Applied Math student, shares how she uses her class blog to learn and describes her personal "tipping point" from being confused to understanding the class material very well. She also discusses the value of learning conversations and how sometimes being a "teacher" and sometimes a student helps her learn.

Please feel free to leave Jessie your comments here or on this post on her class blog. You can also find the archive of her most recent online work in her class blog.

(Download File 5.6Mb, 11 min. 40 sec.)

UPDATE

I cross posted this to all my class blogs. I'm thinking this might be a way to help build community between them and encourage cross commenting by students.

Chris and I were invited by Cheryl Prokopanko, along with six of our students, to participate in a panel presentation at Canada's first Pan-Canadian Interactive Literacy Forum.

Preparing for today led to a collaboration that involved introducing my students to Box.net, where we shared our evolving presentation slide decks in a space where we shared access, and several skype calls with Chris.

Cheryl opened the presentation with an overview of Manitoba's new Literacy in ICT curriculum continuum which has evolved over the last several years (next year is the first year implementation is required by all schools in the province). It began with this video ...

Then Cheryl introduced Chris and I and our students. Chris and I bookended the kids presentations. Chris made some opening remarks, I made some closing remarks (actually, it was an invitation). But the highlight of the entire event was the kids. They so rock! Watch and see ...

| View | Upload your own

... and it continues with my students, then me, here ...

| View | Upload your own

We ended off with a question and answer session (Podcast: 16.8 Mb, 27 min. 55 sec. Now available as a slideshow with photos from the presentation) which you may find interesting. Some of it is hard to hear but there are some really great moments; like when one of the grade 8 students explains texting to a 63 year old member of the audience.

When it was all over the kids were swarmed by people who wanted to chat with them and hear their thoughts. Chris and I hung back and just left them to soak up all the well deserved accolades they collected. Each kid spoke for about 5 minutes and each kid must have spent over 5 hours preparing for it; and it showed. Chris and I are so proud of them.