As we move toward the new Common Core State Standards, the issue of how to incorporate the all-important Standards of Practice tends to elicit lots of discussion and differing opinions, especially when it comes to assessment.
I found this interesting new post by Dan Meyer about the role of computers in mathematics assessment: What Silicon Valley Gets Wrong about Math Education Again and Again. Here’s a quote:
‘Explain whether 4/3 or 3/4 is closer to 1, and how you know.’
It's
simple enough to write down an explanation. It's also simple to speak
that explanation out loud so that somebody can assess its meaning. In
2012, it is impossible for a computer to assess that argument at
anywhere near the same level of meaning. Those meaningful problems are
then defined out of ‘mathematics.’
This is a good read to follow Conrad Wolfram’s talk I mentioned earlier in this blog.
I
like the Roman mosaic question Dan includes in his post. This would be fun to give to
students. I, personally, would need plenty of time to come up with a
coherent answer.
Less helpful. That is Dan Meyer’s tag line on his blog.
He is a high school math teacher who says we must give
students more time and less help in solving real math problems.
Here is an excerpt from Dan’s talk entitled Math Class Needs a Makeover:
David
Milch, creator of "Deadwood" and other amazing TV shows...swore off creating contemporary drama,
shows set in the present day, because he saw that when people fill their
mind with four hours a day of, for example, "Two and a Half Men," no
disrespect, it shapes the neural pathways, he said, in such a way that
they expect simple problems. He called it, "an impatience with
irresolution." You're impatient with things that don't resolve quickly.
You expect sitcom-sized problems that wrap up in 22 minutes, three
commercial breaks and a laugh track. And I'll put it to all of you, what
you already know, that no problem worth solving is that simple. I am
very concerned about this because I'm going to retire in a world that my
students will run. I'm doing bad things to my own future and well-being
when I teach this way. I'm here to tell you that the way our textbooks
-- particularly mass-adopted textbooks -- teach math reasoning and
patient problem solving, it's functionally equivalent to turning on "Two
and a Half Men" and calling it a day.
Right
now I am taking a fantastic class with Sandi Stanhope about math
problem-solving in elementary school. She frequently mentions the need
to “sit on our hands”. We’re so used to teaching, guiding, instructing,
that we deprive students of the opportunity to develop into competent
problem-solvers and mathematicians. Our homework for Sandi’s class is to
pose appropriately challenging problems to our students and then to
encourage them to solve them in whatever way makes sense to them. We
work on our ability to ask good questions and to facilitate high-quality
dialogue among students rather than to front-load students with
algorithms and strategies we hope to see.
So
far, it has been incredible to work with students this way and to hear
others in the class describe their experiences doing the same. Our
students tend to pleasantly surprise us with when we let them. They also
demonstrate the ability to work long and hard on a single problem when
we allow and encourage that.
Be Less Helpful
can be applied to homework as well. If you find yourself very involved
in a young person’s homework, it might be time to take a step back and
rethink things. I have applied this principle to my involvement in my
own children’s homework. I find I am still helpful and supportive, but
just in different (better) ways.
In Sandi’s class, we’re using a book by Larry Buschman called Share & Compare. I highly recommend it. Buschman has also written many great articles in NCTM’s Teaching Children Mathematics magazine.
I'll close with Buschman's two most important discoveries as a teacher:
Teachers give themselves teachable moments by carefully listening to children.
Teachers give children magic moments by letting go.
