<p>In case anyone reading enjoys thinking inductively, not deductively, in other words building a case from the ground up, I offer this recollection from a First Grade faculty meeting over how we would teach “Measurement” to First and Second Grades. This was in a poor American elementary school. I will guess that as a result of the following riDICulous meeting, my students from then would not attempt that problem, or solve it wrongly, today as teenagers. I take full responsibility, too, for not simply committing hari-kari in the middle of that meeting to stop it. I wish I had Monty Python to act it out…</p>
<p>New Math Administrator: Teachers, we’re going to introduce a new curriculum in the coming year.</p>
<p>Teachers (groan): That’s the fourth one in five years.</p>
<p>NMA: Yes, but it’s better than those. And besides, I’m your new boss and your annual evaluations depend on my approval.</p>
<p>Teachers (groveling): Well, then. We’re all ears.</p>
<p>NMA: As you see, this curriculum requires a special week-long unit on measurement as arbitrary. In other words, we need to inculcate in young children the concept that units of measurement can be of any length, and regardless, we CAN MEASURE things. Whether it’s by one’s knuckle, a meter or a yardstick, things are measureable.</p>
<p>Teachers: Go on…</p>
<p>NMA: On the first day of the unit, you take your Cuisinaire Rods and have the children lay them against objects of varying lengths: a comb, a paperclip, a large book. Have them say, “The comb is two orange rods long; the paperclip just one orange rod; the large book needs three…”</p>
<p>Teachers: We’re with you…</p>
<p>NMA: Once that’s internalized they are ready, in First Grade, to be given these newly purchased rulers with checkerboards. The checker-markings happen to each be an inch long, but don’t call them “inches” yet. Just teach them to measure many things around the room, and record how many “blocks” long they are.</p>
<p>Teachers: (getting uncomfortable) Sounds like a lot of moving around…</p>
<p>NMA: I know you can handle that. You are all ACES when it comes to classroom management.</p>
<p>Teachers: Yes, we ARE!</p>
<p>NMA: Do this for a week, and then the following week you may introduce them to the concept that “inches” is a unit of measurement we use in our country. They’ll measure for a week using “inches”, and you can teach some about how 12 inches equals a foot, how the King’s foot was used to measure, and all kinds of interesting lessons about measurement you may have in your older files. We want you to integrate this concept of arbitrary measurement units into whatever you’ve already taught before becausem although I’m the New Math Administrator, I don’t want you to hate me and have me thrown out of here after 1 year, like the last 3 Administrators who made you change curricula upon their arrival.</p>
<p>Teachers: You’re so very right.</p>
<p>NMA: Any questions?</p>
<p>Young Teacher: But the state tests ask questions with inches AND meters on them at the end of First Grade!</p>
<p>Old Teacher: Here, you can have my mimeograph sheet from l958 with cute dolls to measure in inches… I’m retiring and have to get rid of a lot of stuff (want to buy it?)</p>
<p>NMA: Didn’t I tell you all to destroy any previous lesson taught before my arrival? How are we going to get this new curriculum to fly if you all keep confusing the children with old lessons that work?</p>
<p>Teacher: We’re so stupid in this country not to teach metric right from the outset.</p>
<p>Teacher: I hate those Canadians. I get a speeding ticket every time I drive in Ontario. Dang those kilometrrrres.</p>
<p>Teacher: Oh, knock it off. It’s easy. An “M & M” candy is one gram. Here, have one. </p>
<p>Teacher: But, NMA, if we teach metric and inches all in the first year, so the kids will do well on that ONE question on their state tests, then we lose the clarity of teaching them first: arbitrary measurement units; next: inches; last: metrics.</p>
<p>Teacher: I want my kids to do well on the test.</p>
<p>NMA: Don’t we all. So you can decide how to teach measurement within your own classrooms, since you are all old enough to be my mother, but understand that I WILL be coming around once each year to check that you’ve thrown away all the old curricula from my 3 predecessors and aren’t using any old units you may have xeroxed from them, which is a copyright violation. And remember, as I said, be creative and teach it the way that works for you, as long as the kids know all of this by the end of First Grade: Arbitrary Measurement as a concept; how to calculate in inches, and how to calculate in metrics. </p>
<p>See you next time. Our next Professional Development day, we’ll all workshop to align the new curriculum to state standards.</p>
<p>Teachers: We did that last year, and the year before…</p>
<p>NMA: Yes, but now we have a new currriculum so we have to redo all of that. Bye.</p>