Hello All,
Here is a blog that I thought might be an interesting read about. "Why Is Teaching Problem Solving Important to Student Learning?" This is a great illustration of reaching the deeper level of understanding with out learners that we all strive for in our math classrooms.
What resonated with you in this article?
Brooke
Comments
... was this supposed to link to something about teaching problem solving? I get to something called "complex instruction" and ways to make sure group work is done with *everybody* having to know things (so if somebody in a group calls the teacher over, the teacher can ask *anybody* in the group what the question is, and if that person doesn't know, s/he says "well, your group needs to talk it over"...)
It's interesting, but is it the article/blog you were trying to link to?
I've noticed that links to NCTM tend to go anywhere and everywhere. A Twitter link that looked like it would get to a specific article (like your link) got to a very general page... but I was attracted to a link labeled "understanding exponential relations," until I clicked through and actually, the article was about proportions.
Susan,
This issue has been fixed. I embedded the wrong link to this blog. Try it now.
Thanks!
Brooke
Anotehr thing I would be *really* interested in seeing get explored would be how to encourage that "problem solving" attitude with simpler problems. I begrudgingly respect the way ALEKS software has many problems that are *just* complicated enough so students can't just plug and chug... but they'd better have somebody handy to explain, because ALEKSs "explain" is 100% procedural, w/ no "why."
Susan,
I have noticed that most software programs (ALEKS, MyMathLab, Khan, etc.) seem to focus more on the procedural and are not good at connecting to the "why". I would be interested to know if anyone has found a good math software that doesn't just show procedures but allows learners to develop conceptually, too.
Does anyone use such a thing...does it even exist?
Brooke
http://www.conceptuamath.com/ and http://www.dreambox.com/ are much more visual and conceptual. We tested out dreambox and I'd have liked to purchase it, but they are not set up to deal with colleges; no way to sell it as if it were a text, so students could use financial aid (and they weren't interested in figuring that out -- they are making Big Bucks Big Time in K-12).
Both of those programs have a lot more visual; my guys would need more practice to connect the visuals to the math language but that's a lot easier to add than figuring out all those visuals.
I'm going to be collaborating with our distance ed folks and seeing what we can come up with, too...
Susan,
I really liked both of these websites. I wish there was something for free that was available so that more adult educators could use these awesome tools. Let us know what comes from your collaboration.
Brooke
Afraid that waht resonated for me (especially 'cause it's been happening here a lot this week) is that my students would think this kind of problem was horrible and unfair, thank you. They've been taught their procedures and rituals... and this doesn't fit.
The other thing that stuck out was how many of my students wouldn't be able to hold onto ideas like "well, the 38 is his age some time in the future... and his niece is 7 years old now... " While the second example is, I suppose, supposed to be better ... nobody ever explained how they actually got to the solution. Most of the folks I work with would need something visual -- and/or would need lots of practice with simpler problems in one place and time.
I've been spending this week doing negative integer operations in my rolling swivel chair... dealing with students who are utterly confused because the problem says "write [decimal form number] as a fraction in simplest terms" .. but some of them can't be reduced. If you say to do it, you're supposed to have to do it...
We want to know who or what company produced/published the impossible math problems you refer to, and even more, we want to know what those problems were.
Ladnor,
I am not sure to whom your comment is for so I thought I would seek clarification. Is this comment towards the blogger or to Susan?
Brooke
If it's directed at me, it's not the problems that were impossible. The students, because of their previous experience and (lack of) background, would find them impossible. They could be from any publisher; if they do not use the language and procedures students are familiar with, so they can follow the procedures they've learned, they do not know waht to do.
It's that problem that is, exactly, why they *should* be taught a 'problem-solving' approach. However, if they haven't learned that, and then are presented with problems that expect them to apply the knowledge they don't have... it's usually not a good experience.
Our Math Literacy course does a pretty good job of acclimatizing students to a "problem solving" approach by working with problems that don't involve multiple variables and going forward and backwards in time. THe age problem would be one the authors would probably consider to be a "real world" problem because ... age is real... but the students would correctly say, "Who would ever need to know this?" Our Math Literacy course has them looking at contour maps and figuring out interest on car purchases.... which is much more "real world."