Friday, December 11, 2015

Math problems of the week: from the "reform math" curriculum at Phillips Exeter Academy

Commenting on Dan Meyer's blog post about Barry and my recent article on online Atlantic, David Griswold posts a link to the Reform Math curriculum used at Exeter. Griswold writes:

I’m sure many would be shocked to hear that Exeter, with all the New England Prep School implications, uses a reform curriculum, but there it is.
The first few problems of Exeter's Math I (9th grade) curriculum:

(I've chosen the first eight problems because, accordingly to the curriculum, teachers typically assign eight problems per night. Also of note: calculators are allowed.)

1. Light travels at about 186 thousand miles per second, and the Sun is about 93 million
miles from the Earth. How much time does light take to reach the Earth from the Sun?

2. How long would it take you to count to one billion, reciting the numbers one after another? First write a guess into your notebook, then come up with a thoughtful answer. One approach is to actually do it and have someone time you, but there are more manageable alternatives. What assumptions did you make in your calculations?

3. It takes 1.25 seconds for light to travel from the Moon to the Earth. How many miles away is the Moon?

4. Many major-league baseball pitchers can throw the ball at 90 miles per hour. At that speed, how long does it take a pitch to travel from the pitcher’s mound to home plate, a distance of 60 feet 6 inches? Give your answer to the nearest hundredth of a second. There are 5280 feet in a mile.

5. You have perhaps heard the saying, “A journey of 1000 miles begins with a single step.” How many steps would you take to finish a journey of 1000 miles? What information do you need in order to answer this question? Find a reasonable answer. What would your answer be if the journey were 1000 kilometers? 

6. In an offshore pipeline, a cylindrical mechanism called a “pig” is run through the pipes periodically to clean them. These pigs travel at 2 feet per second. What is this speed, expressed in miles per hour?

7. Your class sponsors a benefit concert and prices the tickets at $8 each. Dale sells 12 tickets, Andy 16, Morgan 17, and Pat 13. Compute the total revenue brought in by these four persons. Notice that there are two ways to do the calculation.

8. Kelly telephoned Brook about a homework problem. Kelly said, “Four plus three times two is 14, isn’t it?” Brook replied, “No, it’s 10.” Did someone make a mistake? Can you explain where these two answers came from? 

Extra Credit

Discuss the reform math aspects of these problems.

Discuss how incoming Exeter 9th graders might do with this curriculum, given Exeter's 19% admissions rate and "smartness rating" (which includes things like average SSAT scores, average SAT scores, student teacher ratio, percentage of faculty with advanced degrees, and number of AP and advanced classes.)

(In my next post, I'll take a closer look at the reform vs. traditional aspects of Exeter's curriculum, and how well it appears to work in practice.)


Anonymous said...

I looked at the Exeter problems a few years ago and I like them. I would hesitate to call them "reform," though. If I remember correctly, quite a few of the problems require substantial knowledge of Algebra to solve them.

I think that this approach is basically a "sink or swim" situation. As a teacher in the public sphere, I think about what I would have to teach so that students would be capable of solving, or even engaging in a solution of these problems. The Exeter situation seems to assume that their students come to them WITH the skills, which are then honed through solving these problems. Either that or those who can't solve them fail out - at Exeter that the way it goes. But at public schools, we don't have that luxury, we need to teach these skills rather than only identify the students who either already know them, or acquire them independently. Now, this is not to say that the teachers at Exeter aren't teaching, but I believe that it is a very different environment than what we face in the public sphere.

It reminds me of the Juku system in Japan where the skills and practice are handled by the private cram schools while the public schools simply assume that everybody (who is anybody) will be paying for the Juku and thus the public schools focus almost exclusively on conceptual problem solving.

The Japanese style problems are here:

Again, I would hesitate to call these reform problems because they require so much real mathematical knowledge.

An interesting comment of the juku phenomenon is here:

Auntie Ann said...

Those are all essentially unit conversion and simple rate problems. I would think a competent 5th grader should be able to do them.

SteveH said...

Andover (more traditional) and Exeter (Harkness Table) are two opposing pedagogies that seem to work well in their own ways, but Exeter's use of oval table discussions bears little resemblance to anything the usual "reform" K-12 math pedagogues push. Exeter's students also have enormous homework requirements and have to come prepared to take a position and defend it. It's not a hands-on, engagement-driven, "trust the spiral" approach. However, I'm still not a fan of the Harkness Table because it's too easy to get wrong and waste time. Then again, a poorly prepared teacher can waste a lot of time. However, Andover and Exeter are populated with driven (internally or externally), high achieving students. Both schools go out of their ways to bring in top math students. I was considering each for my son and Andover would be the choice, but I decided to save a LOT of money and stick with our AP-pushing public high school. This is JUST high school material and both schools don't have some magic "understanding" formula outside of pushing and hard work, and they don't try to go further than AP Calculus. They just push the AMC math contests. Actually, I'm rather annoyed that AMC is now the "beyond" score of choice for colleges.

Anonymous said...

If the case of the son of a family connection is typical, Exeter expects incoming freshman - at least those not coming from known prep schools or very high-performing publics- to have completed their freshman year at their previous schools. This was also true at an another big-name New England school, when another family connection entered. Both kids had been good students - I don't know details - at academically solid public high schools. As the old non-PC, saying goes; if you want better schools, get better students.

Anonymous said...

This is exactly what you would expect for students who had taken Algebra 1 in 8th grade.

lgm said...

Some of these are given in Earth Science here, a class normally taken by students concurrently enrolled in Regent's Alg. 1. They arent considered 'reform'.

Anonymous said...

I could do these, but I'd have to privilege the symbol. Is that allowed?

Anonymous said...

@Anon 4:47pm


Anonymous said...

These problems seem too easy for 9th grade EXCEPT for the fact that several of them require estimation using an understanding of the real world. The math isn't hard, it is figuring out what is reasonable that is the sticking point.