The Panel first examined whether constructed-response formats measure different aspects of mathematics competency in comparison with the multiplechoice format. Many educators believe that constructed-response items (e.g., short answers) are superior to multiple-choice items in measuring mathematical competencies and that they represent a more authentic measure of mathematical skill. The Panel examined the literature on the psychometric properties of constructed-response items as compared to multiple-choice items. The evidence in the scientific literature does not support the assumption that a constructed response format, particularly the short-answer type, measures different aspects of mathematics competency in comparison with the multiple-choice format.
National Mathematics Advisory Panel FINAL REPORT
p 60
This comes at a timely moment as I'd been planning to put up a post asking for opinions on the "explain your answer" items on last year's NY state 8th grade test.
e.g.:
Zach earns $160 per week at a local market. He makes a payment of $12 per week for a new bike. He spends $75 each week on food and entertainment. Zach deposits the rest of his money in a savings account. Zach estimates that he deposits about 25% of the $160 into his savings account each week.
Is Zach's answer correct?
On the lines below, explain how you determined your answer.
How much of his weekly earnings would Zach need to deposit in order to save 40%?
source:
NYSED 2007 tests
Mathematics Test Book 3
Grade 8
March 12-16, 2007
To me, this looks like an opportunity for kids who don't know how to solve the problem to gain a point or two because they "understand" the concept. (This item is worth 3 points, the highest possible on any items on the test.)
By the same token, it is also an opportunity for kids who do know how to solve the problem to lose a point or two because their verbal explanation was incoherent.
The extended response item as equalizer.
Amen! "Explain your answer" is indeed a great leveler. It seems to me that the easier the problem and the brighter the child, the harder it is for her to explain how she solved it. It's one thing to say "show your work" for a challenging multi-step problem; quite another to request explanations for that which a bright child does automatically and non-verbally in his head.
ReplyDeleteI've been reading your blog on and off for about a year now; this entry really resonates with recent developments in my life, about which I've just blogged (oilf.blogspot.com). When I later saw your entry, I added a link back to it.
Oh great - thanks! Can't wait to read.
ReplyDeleteMy own child did this problem correctly & quickly - then wrote a fairly incoherent explanation which I'm pretty sure would lose him a point.
The irony for him is that math isn't his strength, and the fact that he can now do problems like these is a major triumph.
And yet he would probably lose a point for bad writing!
My son often merges steps together and just answers things.
ReplyDeleteIf the point is to assess kid's math ability, then I think they often fail with the mathematically bright ones who have moved on in their thinking.
SusanS
oh my gosh!
ReplyDeleteI had no idea you were out there!
Thanks so much for the link.
I'm just glancing at the front page - I think there's an eide neurolearning post that would be up your alley. (Will find it in a bit.)
Lefty--love your Out in Left Field blog.
ReplyDelete