Comments on: Conjectures are more Powerful than Facts in the Classroom

By: Dan Finkel

Dan Finkel — Mon, 16 Nov 2020 20:39:45 +0000

In reply to Telanna. That's really nice. I can imagine that going all kinds of places. I had a series of classes at a similar age where the conjecture/question was (this is in adult lanuage): for any n, there is an n-gon that tessellates the plane. Super fun to try to find families of polygons with various numbers of sides that could tessellate!

By: Dan Finkel

Dan Finkel — Mon, 16 Nov 2020 20:38:11 +0000

In reply to Neal Weisman. Frankly, I think it's hard. But I don't think it's impossible. It takes being realistic about how much time and energy it will take to reengage students, and then trying a bunch of different stuff to see what they'll respond to. But fundamentally, it's what we have to try to do!

By: Dan Finkel

Dan Finkel — Mon, 16 Nov 2020 20:36:54 +0000

In reply to Sue.

The digit sum one is really nice because it’s so natural to ask it for ANY digit. And then there are just a couple that it works for.

Approximating functions with polynomials is interesting… you almost need an intuition or definition of what approximating means in that context. (Though of course, that’s precisely where calculus goes with Taylor series).

I suppose an earlier version of that is, we can get as close as we want to any number with rational / irrational numbers.

By: Dan Finkel

Dan Finkel — Mon, 16 Nov 2020 20:35:00 +0000

In reply to John Golden. Those are both great!

By: Telanna

Telanna — Mon, 16 Nov 2020 16:22:02 +0000

A few years ago, my student in grade 3 made a conjecture that in regular polygons opposite sides are parallel. This was later refined to “in regular polygons with even number of sides”. This conversation lead to a search of more properties that are specific to different polygons and symmetry. Since the learning outcome was classifying polygons based on the number of sides, we’ve got a lot of practice with both skills and vocabulary as well. The prompt for the lesson was WODB.

By: Neal Weisman

Neal Weisman — Mon, 16 Nov 2020 12:33:01 +0000

I love this article but I have a question – how do you get the curiosity back after it has been beaten out of them by years of poor curriculum choices? The culture of my school has totally deemphasized the interest in learning over grades.

By: Sue

Sue — Fri, 13 Nov 2020 18:40:18 +0000

Area seems to be related to anti-derivative.
Multiples of 3 seem to have a digit sum of 3,6, or 9.
It seems we can approximate trig functions and exponential functions with polynomials.

By: John Golden

John Golden — Fri, 13 Nov 2020 18:02:49 +0000

Midpoint parallelogram on a quadrilateral?

Just heard this one… 1111…111 can only be prime if the number of digits is prime.