Hot take: We need to stop racing to the final answer in math class. If we only teach the procedure to get the answer, we would get so many false positives. Yeah, they got the right answer, but do they actually understand the math?

Wish I could retake math with a teacher like this. Procedures without purpose fail so many (in math & life). Geometry & graphing made sense: visual, reasoning tangible. But number manipulation without the ‘why’ never clicked. Understanding had no anchor. Rote memorization.

Was taught Maths (am British😊) the old way & though got decent grades I didn’t understand ‘why’ I got through with a good memory & being quick Once I began to teach the Maths associated with Economics I taught it your way - so those less ‘mathematically minded’ understood it

Part of my struggle is understanding why “two divided by 1/3” means “if two is 1/3, what is the total?”

Howie is absolutely correct on the importance of understanding why a procedure works. It develops a heuristic/intuition that years later can be easily transfered to other areas outside mathematics, like writing computer software.

I like Howie’s content in general, but he’s kinda wrong on this. Us adults often confuse the very deep understanding we generate AFTER we have wrestled with many facets of division (in this case) with how we expect new learners to FIRST gain knowledge. I’d argue it’s far superior to get the symbolic and procedural mastery and worry about the deeper understanding LONG after.

Nothing but neo-marxist constructivism driven by ideological dogma... 🤣

A lot of this depends on the grade level. Dividing fractions is honestly more of a topic for high school math. Dividing a whole number by a fraction isn't that difficult, but it becomes harder as you're dividing a fraction by a fraction.

This is amazing! Thanks!

Does this help at all with understanding 2 divided by 5/4?

A/B = 1/ (B/A). Obviously 1/3 / 2 = 1/6 Thus 2/ (1/3) = 1/ (1/6) = 6

I agree sir