STUDENT EFFICIENCY FORMULA

I created a fictional student and marks based on assignments and test we had completed already.
ex.

Algebra test: 15/20
Algebra Assignment: Level 3 (based on a rubric)
Homework Checks: 9/10
Angles Test: 30/32
Angles Poster (take home): 4/5

After presenting these numbers I said, “Any Questions?”

many students: “What’s her average?”
one or two: “What’s her mark going to be?”

Taking a closer look each of my classes came up with the idea of WEIGHT (or worth). Homework checks (90%) is a classroom management technique and not necessarily a significant assessment. The take home poster (80%) was a weekend assignment used to practice terms not checking for knowledge. Algebra Test was huge.

The students came up with their own FORMULA…their own WEIGHTING…and then used their formula applied to their marks and calculated. Excel came into play.

Instead of a Player Efficiency formula, this was essentially a Student Efficiency formula.

(sorry i’m late…i’m catching up on my starred google reader items!)

You’re narrowing the field of possibilities. Curriculum development means putting together ideas that will help teachers do the best possible job of teaching a particular math idea even a mundane one like the associate law. It’s not about finding a specific real world or mathematical hook. Its about finding an appropriate, engaging hook (multimedia etc.) so that the math becomes a reasonable thing to do. When I was teaching advanced classes in a private school in NYC almost any context (within reason, of course) worked. These were kids that loved to e.g. discover the formulation of the quadratic formula and they would yell at me if they thought I was jerking them around; which BTW was a strategy I actually used to see if they were getting the point of the lesson.

If anyone’s interested, the working applet and source code are available here:

http://cautery.blogspot.com/2010/11/crazy-geometry-of-basketball-courts.html

Julia: I agree that pseudo-contextual questions are just ugly and horrid and should be avoided. But if we are choosing between mathematical and “real-world” context, why isn’t mathematical context enough?

Great question. I suppose students enjoy seeing math applied to the world around them. I don’t begrudge them that. Math has made my own real-world context a much happier, clearer, more interesting, and more profitable place. The mathematical context has to be enough, though. If we go into curriculum development on the notion that “we can’t teach [x] unless we find a real-world hook for [x],” we’re about to do a lot of damage.

josh g.: Also, at a bit of a loss here; did my submission to the previous post get missed or do you see it as something other than pseudocontext?

Yours was the definition of pseudocontext. It was too long to excerpt, though.

Aaron: The standard height of a basketball hoop is 10 ft. It is quite easy to get a estimate for how far it is from the free-throw line to the point on the floor directly beneath the center of the hoop (“pacing it,” for example). One can then use the pythagorean theorem to determine the distance from the three point line to the center of the hoop (in the air).

You could also construct a rectangle using the two dimensions given and ask for the area. But in both cases, we’re using dimensions from basketball to ask a question that has nothing to do with basketball.

Karim: If a skill can’t fit into A, B or C, what do we do about Category D: I have to teach [topic x], and the only way to do it is to teach [topic x] ?

Right. This is a whole ‘nother discussion and, since classroom teachers don’t usually have the luxury (like you and I do) of waiting for [A], it’s worth having. But maybe not here. Short answer (for me) I guess is that I try to locate the pressure point between [skill x] and [skill x – 1]. Then the students develop [skill x] to alleviate that pressure. Makes total sense, right?

Also, I think if this is going to make any sense via second-hand examples, there needs to be a name for the irrelevancy factor as well, and it needs to be highlighted along the way as such. If there are two axes along which something can be messed-up, but we only ever talk about the Pseudocontext axis when we give examples, it’s going to be really easy for people (ie. myself) to misinterpret and confuse the two.

I guess I just suggested “irrelevancy factor” as a potential name by accident, but I’d gladly hear a better suggestion.

A. Here’s a real-world scenario. What math can I get out of it?. This is
B. I have to teach [topic x]. Where does it occur in the real world?
C. I have to teach [topic x]. How can I fit it into a basketball context?

According to my understanding of Dan’s definition, problems of pseudocontext become more likely as you move from A to C. This makes sense, since the funnel becomes more narrow; A is wide-open; C is fairly closed. (@Aaron: regarding calculating the hypotenuse, if students asked why they were doing it, how would you respond?).

On the flip-side, what happens with topics that simply don’t occur naturally: either in the real-world, or as methods of solving not real-world but potentially interesting anyway questions? (Simplifying polynomials, for instance). If a skill can’t fit into A, B or C, what do we do about Category D: I have to teach [topic x], and the only way to do it is to teach [topic x] ?

I agree with you. I gave a full response to your comment on my blog.

“Determine the hypotenuse using the distance from the free throw line to the center of the hoop and the height of the hoop.”

The standard height of a basketball hoop is 10 ft. It is quite easy to get a estimate for how far it is from the free-throw line to the point on the floor directly beneath the center of the hoop (“pacing it,” for example). One can then use the pythagorean theorem to determine the distance from the three point line to the center of the hoop (in the air).

This can be made into a good case that the problem in question is not pseudocontext. It is true that the question “What is the distance between the free-throw line and the center of the hoop (in the air)?” is not important to basketball players, but that (if I understand correctly) is not the issue of pseudocontext. The issue is whether the physical situation has anything to do with the mathematics of the question. Here the physical situation is relevant, for it is common knowledge that the height of a basketball is 10 ft and it is easier to measure distance along the floor than distance through space. In this situation the pythagorean theorem allows us to make the easier measurement and then compute the distance that would be more difficult to measure.