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Anna Stokke's avatar

Great article Barry! I find this quite disturbing "One of those legs is way more important than the others. I argue that the stool should sit upon a strong base of understanding. Most of those procedures and skills are no longer needed (and actually hinder understanding). I definitely do NOT place procedures or skills at the same level as conceptual understanding or applications. And, you can have strong conceptual understanding that will get you to a point where you can engage with interesting mathematics even if the skills are lacking."

Particularly disturbing given the fact that conceptual understanding seems to have no clear definition. I fear that such an attitude likely produces students who neither understand nor have skill. Perhaps it's an excuse to skimp on the practice that it takes to produce students who are fluent with procedures and skills - a way to get off the hook so to speak. After all, skill takes lots of practice and it's hard work.

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Michael Steele's avatar

This is a perfectly articulated treatment of your arguments as you’ve laid them out over the last few months. The statement “procedures and understanding occur in tandem” feels like a math education motto deserving of a t-shirt.

Our year is winding down over the next few weeks, but I would love to introduce a discussion about this topic in summer PD or before the fall session begins. Could I use this post as a starting point for discussion? I feel like you hit all your best points really effectively and in one piece here.

Regardless of that answer, thank you for continuing your advocacy and your posting here.

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