Monday, July 27, 2015

What does "understanding" really mean? (or "the question not asked..")

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This is from the June 2015 Algebra I (Common Core) Regents Exam in New York:
This jogger, based on evidence given, took two full minutes to achieve a pace of 3 mph.
The same jogger, 16 minutes later, maintained a 8 mph pace (7.5 min/mile) for a full minute.
This jogger maintained perfectly constant speeds interrupted only by intervals of constant acceleration and deceleration.
 Is this real?
I know that one of the big deals in math education is to make it "relevant" and "real".

The students confronted with this graph had to answer the following question:

Which statement best describes what the jogger was doing during the 9–12 minute interval of her jog?
(1) She was standing still.
(2) She was increasing her speed.
(3) She was decreasing her speed.
(4) She was jogging at a constant rate.

A truly mathematical question would have been to have given the graph (uncaptioned) to the students and then asked them the following question:

Which statement best describes the graph on the interval 9(1) f(x)=0
(2) f(x)) is increasing
(3) f(x) is decreasing
(4) f(x) is constant

Mathematically the questions are identical, but the second does not exhibit that debilitating push towards "relevance".

For those who prefer the question as stated in the exam, I would ask them to answer this question as a test to whether or not the truly understand the situation they have created:

At what time had the jogger traveled exactly half the total distance jogged?

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