So, I attended a professional development session yesterday on early numeracy, and the presenter showed this video. I almost snorted Diet Coke out my nose! He said that when he has sessions for teachers (we were all instructional coaches), he asks them to rate on a scale of 1 to 5 how important they feel it is to let students struggle. Usually, the ratings are pretty high. He then asks them how that belief is reflected in their teaching practices. Ouch. That's usually a tougher question. It's so hard to let kids struggle and not jump in to help. The presenter reminded us of Vygotsky's Zone of Proximal Development and that the goal is to assign tasks just beyond what a student is comfortable with...not WAY beyond, but just beyond.
Here's an example to consider. Say that you've taught fractions and now you're moving on to fractions on a number line. Your first thought might be that you need to teach it. Hmmm, well let's see. Try this instead. Display the number line shown below, and ask students what they think A represents. Accept all responses. Don't forget to ask students why they responded as they did. I will assume that no students responded correctly with 3/4.
Next up, fractions greater than one on the number line. Now, this next part is assuming that the students have already explored fractions greater than one in their study of fractions and have practiced fractions less than one on the number line until they're comfortable with it. Instead of teaching a full-blown lesson on extending to fractions greater than one on the number line, put up the number line shown below. Huh...I wonder what A stands for here? Let the students struggle with the problem for a short while and see what happens.
Click here to grab a couple of sheets of number lines with fractions. Check out this blog post for instructions on how to use the snipping tool in Windows to insert the number lines into your own documents. :)