I mean isn't this the thief we are referring to?
Or perhaps THIS is the thief that we should really be addressing. I must raise my hand and be the first one to admit that I was the preacher for this riddle/rhyme when teaching my students long division. I cared not about students' frustration with learning acronyms, giving them steps that had no real mathematical meaning and thus robbing them of whole number- number sense and more importantly robbing them of the true meaning of division! For me, the vocabulary for this unit was:
- Outside number
- Inside Number
- Number on top
- Divide
- Multiply
- Subtract
- Bring Down
- Check
- Answer
Did you count the true academic vocabulary in that list? I did not hold my students accountable for academic vocabulary, mathematical thinking nor articulation of repeated subtraction with efficient methods.
Research says that division isn't only similar to subtraction in that it involves the separating mechanics, but that it is (just like subtraction) a difficult concept to grasp for students. And difficult concepts should NOT be approached, tackled nor attempted with abstract methods. If not all concepts, those which are most complex should be gradually approached with concrete manipulatives and connection to pictorial representations. Consistency in practice should take place at these levels before we make the connection to a more abstract algorithmic method.
So I share this video (based on approaches that I've read are more developmentally appropriate for students) and I wish I would have used when I was a classroom teacher. Now, I get chances to work with students in small groups and I claw at every chance I get to expose them to these strategies and raise the level (bar) of mental math for them. After all, students can learn at high levels if we simply embrace those methods and take the risk of exposing them to those strategies! Will you try it?
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