*Your instructor brings you a board. Before you can use the board and play with it yourself, she tells you how to properly line it up on your table. Next, you practice this over and over again with everyone in your class practicing the same number of times regardless of when they master the skill. When you line it up in creative or fun ways, you get scolded, and sometimes even have your board taken away from you. You look around the room and notice that everyone’s boards all look the same.*

*Finally, after you are considered to have mastered the skill of lining a board up, your instructor takes your board away and gives you a nail. She shows you for 10 minutes all of the various ways you can line up a nail, but never shows you how this relates to the board, or any other possible tools. You want a chance to practice lining up the nail properly, but your instructor says that time is up, and assigns it for homework, and takes away the nail. "You’ll have to find your own nail to do this for homework," she says. You wonder if that is fair for the students who don’t have nails at home.*

*The next day, your instructor checks to see that all of you have practiced lining up the nail. She then gives you a chance to practice with the nail for a few minutes, before she again takes away the nail and gives you a hammer. You spend some time learning about the history of the hammer, and finally you learn some of the possible uses of the hammer. You ask if you can play with the hammer, but your teacher says, "That’s much too dangerous for you now, you’ll learn more about hammers when you are older, and then you can use them."*

*You never get a chance to see how the board, the nail, and the hammer relate to each other before the unit finishes. You don’t really understand how to use a board, and you’ve forgotten how a nail works by the time the test is given and so you fail the final assessment. You want a chance to practice some more with these skills your teacher says are "vitally important" but she moves onto another unit.*

*"Okay class, in our next unit we are going to learn about sanding wood. Everyone take out their boards and practice lining them up again…"*

*At no point in your learning of carpentry do you ever find out why people might want to use carpentry, how beautiful some works of carpentry look, or how to put it all together and make your own buildings.*

You might think that this would be a ridiculous way to teach, but this is **exactly how we teach mathematics today**. Each unit is separated from one another and the connections between the units, and often the lessons, are virtually never taught. Students almost never have the opportunity to **play with mathematics**, and never get a chance to use some mathematics once they have mastered it. If we even connect mathematics to the real world, we do it in arbitrary and often nonsensical ways. We teach mathematics as a bunch of discrete tools and not as a holistic study of patterns and our world. In fact, we don’t even really have a consensus as to **what mathematics actually is**!

It’s no wonder kids usually hate mathematics. They say, "Math makes no sense," and they are right.

## Rick Ackerly says:

Thank you for this analogy. I have been using soccer as an example, but I like your gross exaggeration of bad carpentry teaching as a good example of how mathematics is taught.

July 12, 2011 — 7:01 am

## Tim McClimont says:

Gday David,

I am a carpentry teacher from Melbourne Australia.

I just stumbled across this math carpentry comparison whilst looking for new and interesting ways to teach my students the maths module. I often run into comments like how does this relate etc, even after giving examples.

Anyway, your blog has given me some ideas.

Cheers,

Tim.

April 14, 2013 — 3:55 am

## David Wees says:

I’d love to see what you end up with. I think you’d want to relate the mathematics in the math module to actual carpentry projects. Sometimes I will give the problem first, and then see what students do, and then mentor them to finding a solution.

April 14, 2013 — 8:45 am

## Tim says:

Hello David – I stumbled onto your site while searching for on-line carpentry courses. As I read your thoughts on the way math is taught it brought me back to my school days. I then (and now) thought exactly as you so articulately state your case – there is no connectedness, incorporation, or use for much of the math taught beyond 4th grade (the “money counting year” of math in New York).

I did have a visionary teacher in high school who used carpentry to teach plane geometry. I to this day remember A2 + B2 = C2 (3squared + 4squared = 5squared) – the means to prove a right angle when framing a wall. We had 20 boys (military high school) building small right angles and testing for “square” with the formula.

The teacher didn’t teach the board, nail, hammer modules. Curiously all the boys knew how to use the three components to achieve an outcome. A good, square outcome, thanks to the math teacher.

May 8, 2013 — 10:02 am

## David Wees says:

One of the things I am hoping gets implemented at my school is some Maker space, where students can use tools to build things. I strongly suspect that even if their teachers don’t always make the connection, that they may see some of the connections for themselves.

I may try and write something outlining how one could "see" mathematical ideas in carpentry.

May 8, 2013 — 3:34 pm