Comments on: Two Warmup Questions, Worlds Apart

By: Touzel

Touzel — Sat, 14 Mar 2009 18:42:17 +0000

Hell yeah, Dan. I knew you’d like it.

I look forward to reading your take on it–I’m sure you’ll have plenty of ideas I never even considered.

By: Dan Meyer

Dan Meyer — Fri, 13 Mar 2009 17:19:08 +0000

Jackie, Touzel, I checked out IMP years one through four from my school’s bookroom (which kept some copies around even after the community here ran the curriculum out at the end of a pitchfork) and I’ve gotta say I was really, really impressed. Really impressed. I need to blog a review with page scans and everything, and I need to take another pass at CPM, but for now this is as close as it gets.

By: Jackie Ballarini

Jackie Ballarini — Thu, 12 Mar 2009 22:12:52 +0000

@Touzel I teach IMP. I’m currently teaching one of the units that doesn’t have a central problem – “The World of Functions”. I think this may be my favorite unit of all of them. The depth of understanding my students are displaying (mostly seniors) in this Year 4 unit is blowing me away.

By: International Educational Directory > The Missing Challenge

International Educational Directory > The Missing Challenge — Sun, 08 Mar 2009 12:56:45 +0000

[…] a brief but excellent post, Dan explains why, when it comes to doctrine math, we requirement to provide our kids less, not […]

By: Touzel

Touzel — Mon, 02 Mar 2009 07:58:40 +0000

Yeah, I think you would totally love the beginning of most IMP units. There are five units in each year and most start with some hook (like the Pit & the Pendulum, or Fireworks, or Cookies) and the first assignment of the unit involves the students trying to figure out what it is they need to know in order to even be able to continue.

There are two units in Year 1, however, that don’t have a central problem, but there are many other good ones.

Here are some of the units (with the unit question paraphrased):
Year 3: Small World (how long until there are so many people in the world that they are all pressed up against each other?)
Year 2: Do Bees Build It Best? (is a honeycomb the best arrangement for maximizing volume while minimizing surface area?)
Year 1: The Game of Pig (what’s the optimal strategy for the dice game “Pig”?)
Year 2: Cookies (how much of each type of cookie should a bakery make to maximize profits?)
Year 2/3: Fireworks (where will the fireworks land?)
Year 1: Pit & the Pendulum (will the prisoner escape or will he die?)
Year 3: Pennant Fever (what are the odds–with a week left in the season–that a given team wins the pennant?)

By: Dan Meyer

Dan Meyer — Mon, 02 Mar 2009 05:33:47 +0000

@Touzel, next on my to-do list is to track down editions of IMP and CPM. I have a great deal of respect for the president of CPM but what little I recall of both texts is an overarching, chapter-long scenario framed by a visceral question ("will the pendulum etc. ...?"), all of which sounds like it ought to thrill me. But the rest of my recollection has students proceeding through a section fairly schematically from question a) through question f), each building on the last. This used to impress me but now I wonder if that doesn't offer students too clear of a road map when, really, the students ought to be deciding on the road map for themselves. @Clint H, this is only a contradiction if you imagine a class exclusively driven by procedure or exclusively driven by concept. I want my kids to aim for the conceptual high-hanging fruit but I won't fail them if they can't reach it. However, if they can't handle the basic procedures that comprise Algebra II (for example) I won't pass them on to Math Analysis. That is the division of labor between concept & procedure, assessment & digression, and like I mentioned in a previous post, the two factions have teamed up in some cool ways.

By: Clint H

Clint H — Sun, 01 Mar 2009 08:58:45 +0000

Dan, do you see an inherent contradiction in your assessment methods and your quest for a highly conceptual framework? A strong grasp of the individual skills does not imply a fundamental grasp of the concepts involved. Do you include conceptual questions on your skills assessments?

By: Touzel

Touzel — Sat, 28 Feb 2009 23:26:01 +0000

Dan, I agree with your disdain for most textbooks and especially agree that we are over-focusing on procedures. Most of the big publishers (Holt, Glencoe, McDougal-Littel, Prentice Hall, etc) just pump out these massive, 1000+ page textbooks bloated with fancy bells and whistles that really aren’t so fancy (websites with lame animations, online computarized procedural tutors, test generators that generate tests filled with procedural questions and–even worse–word problems that are very poorly written, like bcarrera said).

What do you think of IMP (http://mathimp.org/)? EduGroups that love procedures (like http://www.mathematicallycorrect.com/) reeeeeally hate IMP, which in my mind is one of the best compliments that can be given.

By: Dan Meyer

Dan Meyer — Sat, 28 Feb 2009 00:03:13 +0000

Ben, in terms of acceptable outcomes, I am looking for a single, succinct answer followed by, you know, a-page-and-a-half of rigorous justification. I didn't preface this problem with any verbal instructions. I acted a little taken aback when they first claimed the problem was unsolvable. I then doled out information to students only as they asked for it. Nick, good eye. This sort of questioning is, I think, a trait of good teaching – whether founded on digital media or not. Frank, thanks for the links. Kenny, no, it isn't. And I'm not saying my textbook is useless or that I never use it. It's just a lousy tool for developing conceptual understanding.

By: Tim

Tim — Fri, 27 Feb 2009 13:08:02 +0000

I taught Algebra through Pre Calculus for many years and always told my students to show their work on any assignment. I did that not so much to check their process against what the book said was the correct one (and only!) but to be amazed at the unique and wonderful ways some kids would arrive at an answer. (AN answer, not necessarily a right one. :-)

In math, and many other areas of school, we need to help and encourage kids to create their own path rather than insist that they use the one in the book.