Thanks for the examples also. I’m having a really hard time on which problems to choose to start getting their feet wet on these.

and I LOVE the fact that you explicitly went over the difference between solving problems and problem solving. Brilliant! =) Thanks!

From a meta-cognitive (I love that word!) point of view, I find one of the most important things to ask the students to articulate is why they chose the techniques that they did; what was it about the problem that made them decide to approach it in that way? It can generate some fabulous conversation when two students saw two different (but equally valid) ways of solving the same problem. It can also help highlight misconceptions.

I think if you have exemplars (which you now do thanks to this batch of work) and a solid rubric for each criterion that you are interested in assessing (mathematical skills, problem solving technique, communication, evaluation of results) then there is no need for the re-writing bit. Guide the students in how the assessment criteria will be applied, allow them the chance to assess one or two examples and then let them at it!

Finally, I think with enough practice your students will have the confidence and, more importantly, the mindset to approach any problem. But this does take considerable practice and buy-in from students, parents, colleagues and administrators since it may mean a reduction in the amount of content that you can cover (and an increase in the actual understanding of mathematical concepts).

Sam

As for the grading question, I handed out a rubric with some critereon. I would copy them here but it’s on my other computer. If you want, just email me at samjshah atsymbol gmail dot com and I’ll get it to you.

But I’m grading more holistically. What I did was I had kids in each group of two each choose 2 problems to do formal writeups so the group had a total of 4 writeups. I told them what they needed and what made a good/bad writeup (but I didn’t have time to write up examples this year) and told them to try their best writing them at home. They did their writeups at home, came in the next day, and I had them exchange them with their partners, and they had to read and critique. (Again, I’d liked to have an example to have critiqued together in class, but no time.) I emphasized that the reader show know what’s going on at each step, and since the reader was a little less capable than they were, that they needed to explain WHY various steps were being taken.

Finally, they each had to rewrite one of their own (with their partner’s feedback in mind) and one of their partners and turn those in.

I don’t know about the exchange and rewrite thing. My kids were miffed about having to do a formal writeup and then having to do it a second time with revisions. I might find a way to change that. The writing part was the part that seemed to be the biggest turn off.

As for grading, since this is the first one, I am grading them holistically. I’m marking places which are great / confusing and making a few additional comments.

The biggest thing I learned is: I can’t think about problem solving as picking tricky or elegant problems that I find fascinating. I mean, I can, but those problems are not usually within the grasp of my kids. I want them to feel like they accomplished something (which they did). I learned that by just watching them struggle with the basic problems I gave them, these were the right level of problems; problems in a slightly different form, problems that required just one additional thing that we hadn’t talked about in our class but they had learned previously (e.g. systems of equations or parallel / perpendicular lines).

I’m curious to know how you graded these? Did you have a series of criteria for each aspect of the student’s work? Knowledge, Choice (and justification) of Technique, Communication, Reflection?

Also, I’m giving an MYP Mathematics workshop in March and I was wondering if I could use your post in my workshop when we discuss criterion-related assessment. Thanks for your consideration.

I kept on them to make sure they were explaining why they’re doing what they’re doing in the problems, and that they are writing for someone a little less capable than themselves. You’re writing this to help THEM. After I reminded them how much they struggled to understand and be able to solve the problems, I told them they needed to be extra explicit about the parts they struggled on, because their slightly-less-capable reader will definitely struggle there too.