and probably should have checked on his site. Thanks for the heads up.

The last math PD I attended was painfully un-inspiring (boring), yet your brilliant stuff is right here, right now. We are a small one-school district, but I bring up your name and site whenever and wherever I speak math. What I appreciate most about your work, including the 5 design patterns, is its simplicity – it makes sense at the gut level.

@Amir I really believe behavior problems arise when the lessons are not engaging. Even I, an adult and a teacher, WANTED to misbehave when I’m bored at a 45-minute workshop.

I’ve been spreading the word regarding your work and this latest film has further inspired me.

We have a big problem in the UK at the moment regarding the available funding in schools for interactive media to support the use of Mathematics digitally, never mind the development of resources.

This, tied in with the big behaviour problem we have in schools in the UK adds to a double-whammy of stagnancy in the classroom.

I would be interested to know your thoughts on whether a more creative approach such as yours results in more engagement/better behaviour – or is there a need for the right attitude from students before one takes the great leap forward like you have?

This video is no exception; you have very clearly set out your thesis regarding the problems with print resources, and illustrated it brilliantly with examples of both print and digital materials.

My question at this point is, “Will this work with younger students?” I am thinking that if you are teaching place value, basic operations, manipulating fractions and so on, it may be harder to come up with the engaging sort of extended problems you are able to conjure up for algebra and geometry topics.

I am happy to be shown to be wrong; this is just the question I have reached so far.

First, the context:
a) I was their new math teacher.
b) I look younger than my age.
c) I told them that in life, it doesn’t matter where they start; it only matters where they end.
d) I challenged each of them to measure themselves on their level of progress from where they are now, and that math could help.
e) To jump-start the self-assessment process, I did pushups to failure in front of the class, put my “this week’s best effort” number on the board as my baseline for a future repeat assessment, and invited other students to do the same.
f) Five boys and one girl chose to do pushups in front of the class and post their numbers. I congratulated them for enduring good-natured laughs from their non-participating classmates and reminded the others that they could do this in the privacy of their homes.

Given the above context, a simple math problem surfaced in which the process by which it was solved turned out to be astoundingly more interesting than the actual answer.

I’ll share the problem, the process and the solution as well as I can in terms of your 5-point structure. Note: It seems to me that Step 3 (climb the entire ladder of abstraction) and Step 4 (crowdsource patterns) happened in reverse order, which I’ll show below. (Suggestions from readers for reframing my experience for future classroom use are welcome.)

1) Show, don’t tell.

They all watched me do my pushups on top of one of the tables (so they could see me). One of the students promptly asked: “How old are you?”

2) Introduce the task as early and concisely as possible.

I asked each of them to write down their best guess to the question: “How old is Mr. Foster?”

4) Crowdsource patterns.

I asked each student to share their guess with the class. We wrote all of their 22 guesses in a column on the board.
Pattern:
Lowest guess: 42
Highest guess: 72

3) Climb the entire ladder of abstraction.

I said to them: “Most of you know that the “range” for a group of numbers is the space between the lowest number and the highest number. I asked them: “What’s the range of your guesses about my age and how big is that range?” (They did the computations.)

I then said: “Aside from me giving you the answer to my age, how might you figure it out from the data we have on the board?” A pregnant pause…
Then I posed a philosophical question: “What if it’s true that all of you working together are more intelligent than any one of you?” Another pregnant pause…

5) Prove math works.

I asked them to compute the average of the class’s guesses.
They set about doing that and reported their answer: “61.1”
Another long pregnant pause…”OK MR. FOSTER, HOW OLD ARE YOU REALLY???”

The answer: “61”!

Only a couple students had guessed correctly, but the class as a whole nailed it! In fact, as I computed after the class, (we should have done this in-class), the average of their guesses when computed to the fractional year was exactly 6 weeks from my birthday! Not only that, but I had another class of 14 students guess my age, too, and their average was also 61.

I asked the class: “Given the intelligence that you just demonstrated when we combined your answers by mathematically averaging them, what does that say about the intelligence of a population of people in a democracy who cast votes for or against a proposed law or a candidate for office?” “Does the wisdom of the masses work, mathematically?” “Is there a time when it wouldn’t it work?”

I later read that if a crowd of a 100 people all guess the number of jelly beans in a large jar, the range of guesses will be wide, but the average will be very close to the actual number.

Finding the fact we depend on so literacy skills, quite telling.

Wonder if the assessment will ever change? Because that seems to be the biggest driver of change in the UK education system.