Comments on: The Necessity Principle

By: dy/dan » Blog Archive » [Makeover] Boat Race

dy/dan » Blog Archive » [Makeover] Boat Race — Mon, 19 Aug 2013 17:43:53 +0000

[…] a need for the bearing format. We're going to take a cue from the research of Harel, et al. Rather than just introducing the bearing format as the next new thing we're doing in math class, […]

By: The 2013 Honolulu Sessions | The Red Dot

The 2013 Honolulu Sessions | The Red Dot — Sun, 19 May 2013 13:59:24 +0000

[…] LinkIntellectual Need […]

By: The 2013 21CLHK Sessions | The Red Dot

The 2013 21CLHK Sessions | The Red Dot — Wed, 23 Jan 2013 05:52:02 +0000

[…] LinkIntellectual Need […]

By: Sunday Strolls: 11/11/12 | Prime Factors

Sunday Strolls: 11/11/12 | Prime Factors — Sun, 11 Nov 2012 20:42:20 +0000

[…] math websites should add an introductory challenge that activates a student’s intuition and intellectual need. The video lecture should then be directed at satisfying that particular intellectual need. […]

By: dy/dan » Blog Archive » Better Online Math

dy/dan » Blog Archive » Better Online Math — Wed, 07 Nov 2012 18:29:11 +0000

[…] online math websites should add an introductory challenge that activates a student's intuition and intellectual need. The video lecture should then be directed at satisfying that particular intellectual […]

By: Additive recursion at dy/dan | New Math Done Right

Additive recursion at dy/dan | New Math Done Right — Mon, 29 Oct 2012 14:47:02 +0000

[…] /?p=14871 […]

By: Christine Lenghaus

Christine Lenghaus — Sat, 27 Oct 2012 04:37:04 +0000

Have you seen the Wii game of bowling where you practice starting with pins then after each bowl another row is added on? – then you can ask questions like “when will I be trying to knock down a total of 101 pins?” or “after 5 practice bowls, how many pins will be in the last (largest) row?” I knick-named it “Wii love maths”!

By: mr bombastic

mr bombastic — Fri, 26 Oct 2012 21:11:08 +0000

I think it would be more interesting, and actually have something to do with brick patterns, if you provide trapezoidal areas with given dimensions, a couple or three different sized brick options, and ask the students to try and create designs like that shown. If it isn’t possible, they need to provide the specifications for a new brick of reasonable size that would work. Obviously you want to move towards very large trapezoidal areas requiring custom bricks.

The recursive part in the original question is especially annoying in that it sends the message that math is used to take something that is totally obvious (two more brick in the next row) and somehow make it seem complicated.

I disagree that an explicit formula is needed for 1000 bricks. I add 2 bricks per row. So add 999 x 2 to the first row. Many kids think and do work this way because it is much simpler and more natural than writing out a formula and plugging 1000 into the formula. Again, asking for an explicit formula in this question is sending the message that math complicates something that is actually fairly simple.

By: Dan Meyer

Dan Meyer — Fri, 26 Oct 2012 19:33:50 +0000

@James, Word. Recursion in CS took me a lot of head-thumping.

By: James C.

James C. — Fri, 26 Oct 2012 19:32:23 +0000

I’m going to backtrack a bit here. When I was thinking of recursion, I was thinking of it in the computer science sense, where it’s usually referred to solving a problem top-down rather than bottom-up. Same “recursive formula” either way you solve it though. You’re both right that many sequences do not have explicit formulas and students would use a recursive formula to solve most sequences where an explicit formula is not obvious.