I received a couple papers today from Bent Illum, Ph.D. of Sloyd Education in Denmark. Bent's research has to do with determining ways to measure the non-verbal narrative taking place in the teaching of Sloyd in schools.

We pay greater attention to those things that can be measured and compared in quantitative analysis. Those things we can't measure don't seem to matter, at least in an academic setting. They are too fuzzy and science tends to avoid fuzzy stuff. But the values of craftsmanship, and the understanding of the intrinsic rewards that arise through achieving beauty or quality in one's work are matters beyond external measure, and may lead a student on a life-long path of exploration and discovery.

Many of the things that matter most are beyond measure, and the best material offered in the classroom, may not reach the point of significance until years down the road. But, if Bent can get the academic world to look more seriously at non-verbal teaching and learning we will create a more habitable learning environment for all students.

Bent got my attention in Helsinki when he started talking about embodied learning. Those who read in this blog, will certainly understand from that alone why Bent was one of those at the conference with whom I felt a strong philosophical connection.

On another subject, I got a question from a reader that I'll share.

Doug - do you have a way of teaching children how to measure?

Say the board is 3 5/8 and I want to divide it equally into thirds how on earth do I do this and get a measurement that can be measured on a measuring tape? It has to equal something that is 1/8, 1/16, or even 1/32

OK - I should have learned this in 3rd grade, but when I do this it comes out to something unmeasurable.

Oh the wonders of math and wood.

Measuring is easy if you are working in halves or quarters, but thirds are a challenge because of the way that our measuring instruments are arranged.

If you want to divide by half, you double the denominator. So half of one fourth is 1/8th. A third of one fourth is 1/12th and the ruler is laid out in 1/16ths. So this is where things get fuzzy.

There are other ways to measure and divide that completely ignore measuring instruments. Take a piece of paper or string and fold it, it becomes half. Or fold it in thirds (a bit harder to do, I grant you). Or in 4ths. Or 5ths. These are done by just playing with things, and accurate enough for most things. Working with kids, we routinely use folded paper as a substitute for numeric math. In actual fact, it is math, even without numbers, and builds those spatial visualization skills that math educators believe are necessary for success in Algebra and Trigonometry. We also use folded paper as a means to develop symmetrical objects (like algebraic functions, one side is the equal of the other.)

Sometimes I'll do an approximation. For instance if I want to divide 3 5/8 into thirds, I know each third will included at least one inch. If I were dividing 3 3/4, it would be easy, so I know that each third will also have almost another 4th, but not quite, right? So I can guess that each third will have somewhere between 1 3/16" and 1 1/4".

So, you can see that lots of things are actually rather fuzzy. Both in math and in the study of education.