Comments on: [One-Minute Makeover] Algebra 1 • Topic 1 Assessment

By: Peter

Peter — Wed, 29 Jan 2014 14:00:18 +0000

Michael,

Very interesting post. One thing I tried this year with the properties was similar to what mrdardy suggested. We would ask is something like the following. Is the equation below always true? Explain how you know. If not, provide a counter example.
a/b = b/a

we were trying to get through the idea that the properties allow us to verify a statements without having to check for all values of the given variables. Then, if a property does not apply it only takes one counter example to indicate that something is not always true.

Thanks again for the thought provoking post.

-Peter

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By: Michael Fenton

Michael Fenton — Sun, 19 Jan 2014 07:04:35 +0000

@mrdardy I like your line of thinking there, both in general (trying to salvage a poor question, rather than abandon it completely) and in this particular case. If I go with the “correct the statements which are false” approach, I would still want to “upgrade” the statements in question. You might need to glance at some of the other forms (I’d be happy to share, if you want) to see just how bad some of this first round of T/F questions were. Rather than simply getting a read on student understanding, I think I introduced some extra layers of confusion by asking things in a strange way. For example, a*(b+c)=a*b+a*c because of the commutative property of addition. Ugh. For shame.

@mathnerdjet Nice! I’d love to see a few more questions along those lines for arithmetic and geometric sequence/series questions. If you write them sometime, will you share?

By: mathnerdjet

mathnerdjet — Sat, 18 Jan 2014 18:49:24 +0000

I’m having similar thoughts about arithmetic and geometric sequences questions which have always been mostly plug and chug formula problems. One question I thought of is explain why a1 + (n-1)d gives you the nth term of an arithmetic sequence.

By: mrdardy

mrdardy — Sat, 18 Jan 2014 12:05:07 +0000

Michael

You are certainly correct that the second batch of questions is more thoughtful, However, I think that the True/False can also be salvaged (somewhat) by asking something along these lines – If you think that the statement is false, correct it so that it is a true statement. Or, use something closer to what you did in your modification – If you think that the statement is true, show this with a specific example.
This would work whenever your original T/F question is framed with unknowns in the question.