Thursday, January 21, 2016

Math problem of the week: Common Core-inspired 9th grade test question

A sample 9th grade test question from the California Assessment of Student Performance and Progress (CASPP), California's Common Core-inspired test:

Extra Credit:

For which 21st century careers and college courses are 9th graders preparing for in learning to reason verbally about reflections and translations?


lgm said...

EC A: science. Many need to develop their visualization skills, and their ability to understand someone else's reasoning on the spot.

David Walker said...

What college courses does this prepare students for? Many students from Algebra II all the way to college-level math believe that all operations are commutative. This question helps to clear up that misconception -- to visualize why not everything commutes.

In this question, steps 2 & 3 don't commute, but 1 & 2 do commute, as do 1 & 3. Therefore a correct counterexample is any permutation that places step 3 before step 2. I do agree with the author that a full-blown explanation is unnecessary -- just listing the three steps in any order that doesn't map A to A' should suffice (such as 1, 3, 2).

Why would students learn about reflections and translations? In pre-Core texts SSS, SAS, and ASA are postulates, but one postulate ("reflections preserve angle measure, betweenness, collinearity, and distance") implies SSS, SAS, and ASA as proved theorems. And mathematicians consider it to be more elegant when there are as few postulates as possible, which is why there is one Reflection Postulate instead of three Congruence Postulates.

I do agree with the author that many PARCC and SBAC questions are poorly worded. Such questions hide the elegant relationship between transformations and congruence.