Yeah, who has these questions?

I teach physics in addition to math and I saw a great presentation by a Reed College professor called, “The Physics of Rainbows.” It was filled with interesting questions and great “content” about light, reflection, refraction, etc. And I often wonder if I could teach an entire year’s worth of physics “content” just by asking a series of “How does X work?”

Are there particular standards you are stumped by? You’re more likely to get mileage out of “give me something related specifically to this” than “give me everything you have”.

In the last two days my students played Let’s Make a Deal (Is it better to switch? I don’t have large doors in the classroom so we did it with envelopes) and put bets on the Birthday Paradox (What are the odds two of us here have the same birthday?).

But probability is easy. Throw down something hard.

I’ll attempt a counterexample: factoring polynomials. Does there exist a simple interesting motivational problem related to factoring polynomials?

Geometry and probability seem to lend themselves to real-world situations, but I expect there’s some algebraic concepts that are a bit harder to motivate with simple setups.

If Core Plus ISN’T what you have in mind, I’d be curious to know why.

I’ve been thinking about exactly these wonders / questions myself as our new education reform here in Quebec is built on learning and evaluation through real-life contextual problems. I would really love to teach my whole course through problems like these, but as others have mentioned here, get stuck on examples for algebraic topics such as factoring, etc.
Wouldn’t it be wonderful if there was a place for everyone to post their simple, but challenging contextual problems and have them organized by concept?

sweet jesus i’d pay at least $100 for that book. an extra hundred if it had a scenario where a kid needed to graph a parabola. like REALLY NEEDED to, not some b.s. throwing a baseball to first base contrivance.

and i’m totally stealing your ping pong ball for proportions tomorrow.

Congrats on that award, if you’ve heard about it.

I never ‘got’ calculus in calculus classes. It wasn’t until I started to use it in engineering classes that the bulbs began to glow.

Having said that, I’m not sure that the question of theory vs. application or proof vs. problem solving is easily solved. It’s a bit of a chicken or egg first puzzle isn’t it? You really can’t afford to go after one without the other. Maybe it depends upon what side of the brain you favor or something. I always needed the anchor/example of constrained domains found in engineering and found the 5-n dimensions of theoretical math daunting.

Dan:

Here’s a challenging and fascinating real world problem. Try corealis effect. It’s got N/S hemisphere challenges, latitude challenges (function of cos of latitude), scale challenges (doesn’t work small scale), it’s a four dimensional challenge, and it touches us all as an engine of storm circulations. Have kids do it for different planets.

Here’s the question to kick off the month… Why do high pressure systems circulate clockwise (N Hemisphere)?

One of the challenges of public school teaching is five periods per day with 180 days of compressed time– it’s a challenge for learners and teachers. I’m not sure how many of these type of questions exist, but certainly if there are best ways (questions) for key learning concepts, value is added by sharing those best practices. That seems to be a big part of what I’m seeing here–an effort to share how to support students in realizing important learning outcomes.

I’d wonder if having this type of learning as a part of many units, among other learning strategies wouldn’t make the most sense–an occasional activity, rather than daily fare. It’s a naturally interesting and engaging question which I’d think everyone could have an opinion, an involvement — by a long shot, not all the real world questions are.

Same topic (Law of Sines / Cosines).

How fast do you have to be driving to outrun a speed camera?

Start with perpendicular for ease of calculations, and then work your way to pointing towards the road at an angle.

Also fun: you can declare the angle of your digital camera to be identical to that of whatever speed camera we’re talking about, and the students will have to figure out how to set up an experiment to calculate that.

Also, I really do like your ‘secondary openers’. (Your letter one on this slide.) I’m thinking of trying them next year. How much mileage do you get out of them? Have they been worth the time?

OK, I see what you mean, quick openers, not an extended word problem a day.

What we really need, imho, is a strong free content curriculum that can be the skeleton for framing and distributing lesson-scale innovation. Or perhaps we need a national curriculum to provide that framework. Unfortunately, since pitchfork-wielding partisans would demand a hand in shaping it, I’m not very hopeful that such a thing could be written in the US in 2008.

Also, this kind of innovation is what Japanese Lesson Study practices are designed to foster, and why they drink our milkshake, educationally.

Dan,

I keep throwing it out because it seems like such an exact fit for your point of view. But yes, it takes time, and time takes money. This is why I get so frustrated with arguments that funding is not a central problem for school reform. Even if you aren’t just throwing money at a problem, just about everything meaningful costs some money, and in any other kind of enterprise, that’s understood.

Oh, fudge. Meant from this article. Go down to common angles of view.

http://en.wikipedia.org/wiki/Angle_of_view

This is kind of funny, These comments have run the gamut of my insights and frustrations from the last 3 years of teaching math.

– basing lessons on an interesting, engaging problem is where it’s at
– where do I find these types of problems
– they have them in Japan, as a result of their lesson-study PD format
– I don’t read Japanese
– nothing published in English is what I’m looking for
– I don’t have the power to completely restructure PD for my district. Conversations with administrators have resulted in uncomfortable silence.
– Japanese style lesson study would take convincing me and several of my friends to voluteer many unpaid hours to PD. This is where this train of thought runs off the rails.

I ordered and read the Singapore math books, the problem being their concept development doesn’t line up with my curriculum, like not even close. Just today I ordered an examination copy of Core Plus, so we’ll see. My guess is I will probably find a few good problems I can incorporate into lessons where I haven’t found a good problem yet, but it’s not going to be the holy grail.

I have found that with wikis and listserves, lots of people want to sponge off them, and hardly anyone will contribute. Observe this fizzled effort: http://nysalgebrareview.pbwiki.com/ in which dozens of people said they wanted to participate, and only 4 teachers ended up contributing.

It all leaves me wishing our educational “leadership” would get its head out of its ass.

@Jason: I need to motivate finding axis of symmetry, plotting 5-9 points, and drawing a smooth curve on 1/4″ graph paper. Rockets aren’t going to work for me. The best I do is a rectangle perimeter vs. area thing, but it’s the most boring day of the entire year.

@Kate,
A cool picture for axis of symmetry would be a trick mirror type thing like:
http://www.exploratorium.edu/imagery/stills/Floating_symmetry.jpg

This topic is morphing into ‘why isn’t this stuff possible in our curriculum’ and at the risk of a shameless plug, let me say, I’m up for that.

I’m ready to open my Kimono now at When Galaxies Collide which is about just that question.

What is it that prevents so many smart, dedicated, energetic people from effecting change in our profession and what might we do about it?

Just a comment or two.

Steven, as far as a motivation for factoring polynomials, there may not be one good opener question that would spark interest. But what about motivation for doing bicep curls? I coach basketball , so I have some cred when it comes to bringing athletics into the classroom. My analogy is you will never be asked to flex your bicep, or do a bicep curl during a (insert athletic event here). However, the training aspect (that may on it’s own appear tedious and unrelated) allows one to perform better at other more elaborate athletic tasks. Learn how to do the exercise well, practice it, and know when it is necessary, and it then becomes useful, part of the bigger picture, even if on its surface it may appear irrelevant.

That usually is a response to the generic “when are we ever going to use this” comment, and of course it is lost on some students…

With regards to the general tone of what “style” of questioning/problem solving/curriculum choices is best, I am sure that if there was a one-size-fits-all program that worked for everyone, some Prentice Hall/Wiley/Key Curriculum/Disney/GE/Microsoft conglomerate would be marketing it to all. One of the most frustrating, yet I find interesting things about teaching is the mixing together all of these differing techniques, philosophies, activities, styles and curriculum design all come together to form a classroom environment. The ability to adapt is I feel one of the strongest traits teachers have. If I ever find that holy grail of teaching that works for all students, in all disciplines, on all of the standardized tests, hitting all of the various learning styles, accomodating all student needs, I think I would get bored.