Understanding-1st, Procedures-2nd ... How Keen Are You?
Note: This page is also used in a different, related PD.
How keen are you to embrace an Understanding-first, Procedures-second approach?
Are you keen to adopt it across all/most lessons? Or do you think it's a once-per-month thing?
Are you feeling inspired?
What reservations, if any, do you have?
Some past comments ...
Over the years, i have seen students point out teachers in their past that they thought were really good teachers. When asked why they remember them, they usually respond with something like this.... "They always helped me understand the maths I was doing!" It would be interesting to try and discover what the teachers were doing for students to create these types of memories. I would think that even fairly feeble attempts of teachers trying to help in the understanding of concepts prior to teaching procedures or algorithms, has a big impact.
That is a great question you pose Rod. I would say that the example I provide is a clue. Asking probing questions that help kids connect the dots, drawing diagrams, making analogies, investigating, etc. A good start would be setting an activity that requires the student to think their way through, activities to which a formula cannot be applied.
I was very successful at high school maths, and actually remember saying to my maths teacher that I thought I was just good at remembering procedures and when to use them - pretty insightful I would suggest. So many concepts clicked into place when I started teaching.
I really believe procedures have to come second, after students have had time to grapple with the concept and to make connections with prior understanding. I have been guilty, however, when a student just does not understand, to say, ok do this. I always feel like a failure at this point, but reason that if this allows them to engage initially, I can then work on the conceptual understanding afterwards .... which often does not happen. :(
That's a very honest and insightful post Sam. We are all guilty Sam, but only through ignorance. And sometimes, to say 'ok do this' is appropriate under the circumstances'.