This summer, I am writing a textbook for the class. Today I wrote my first problem set, which I am sharing with you all. I would LOVE any feedback. Last year, I gave seven or eight problems on a problem set. I gave one problem set just about each week. Students would get them at the beginning of the week and they would be due at the beginning of the next. One thing they said I should do is keep it to six problems. They thought anything more was too much, especially when one or two problems are often really tough.
Last year, they wrote solutions in composition books, but this time, I would like it to be on the paper I give them so that it is more structured. If they need more paper, they can staple it to the page. The back of the page is for things they learn from other students when we go over the problems (so this should not be double-sided when copied). I should explain that we go over the solutions Exeter style, which is to say, each student picks a problem at the beginning of the class and writes the solution on the board. Then that student presents it, and anyone can chime in to explain a different solution or approach. It's awesome, and I learn more from them, perhaps, than they learn from me. There are so many times that they have found a more elegant solution than me!
Some of the problems are famous ones, but many are calendar problems from Mathematics Teacher. In each set, I try to include one geometry problem, one probability problem, one number theory problem, and then the rest are just interesting problems.
I added a reflection page at the end that I will likely change after each problem set. I think I will hand the Problem Sets out each week, separately from the text, so students can't go ahead (I have some students who would do that, I think), especially as some of it will coincide with the curriculum I will be teaching them. So, without further ado, here is the link via dropbox: Problem Set 1 and below is a picture of the first problem.
13 comments:
I love this! I was wondering about the textbook you are talking about writing to go with your course. How are you arranging it? By problem solving strategy or some other method? What level are the students in your class?
Right now I think it will be based on units: problem solving techniques, figurate numbers, solving the Rubik's Cube, probability and counting methods--it's only a semester course but it will also include a problem set for the week and warm-up problems that are famous problems that may or may not tie into the curriculum.
I wouldn't like to answer the Reflections questions, especially the "Describe how you felt ..." makes me uncomfortable.
I like the idea of sharing problem sets. I took a quick glance at this one and have a few pieces of feedback.
1. I wouldn't leave space for work and have the students submit their own pages. That's partly to reduce photocopying and partly because I'd expect some of the problems not to fit anyway.
2. For problems #2 and #3 I'd add a diagram.
3. #3 is a bit ambiguous as phrased.
I've been going back and forth between a themed set of problems vs. a medley. One of these days I'm going to experiment and see which approach is more effective.
Ben
Katrien: Interesting, as I just wrote a reflection page for my second set, and that was the one question I took out. I'd like to see how they answer it once, the first time they complete a problem set. I guess I'm including the reflections because I found that they often just wanted to complete it just to get it done, and I'd like them to think a little more about some of their favorite problems, and what they tend to like. Thanks for your input!!
Ben: I had all of the problems for each problem set on one page last year, and it was a mess for me to grade. I am really doing this to help me be better organized. I will look back at 3--I do remember it being challenging last year. THANKS! I'd love to see your problem sets.
Lisa
My first thought is to question the direction to write in pencil. I have long urged my students to write in pen and to not erase. This way I, and they, can look back at their idea trail. I find that pencils encourage erasing and erasing often results in the same mistake being made again. My second thought is a question - when students select problems to present, are they crossing or do you in some random way choose who presents what? My third thought, and I will have some more later, is that this is a really rich set of problems. If you are looking for about thirty of these sets over the course of the year I think you have taken on an admirable , and large, task. Thanks again for sharing, I'll share some stuff back to help balance the karma.
Hey Jim! Such a good point about the pencil! I'm actually one of the few who never cares when students do hw in pen or pencil...BUT there is a reason to my madness. I found that this past year, when students made corrections during class, I couldn't tell if they were adding to their work or if they were actually making a correction. So I could say use a differently colored writing utensil, but it's "easier" for me to say use pencil...I may change that depending on what I see that first week...such good ideas I'm getting from people!
The students put problems up in the order they come into class...they pick...so that students can feel like their can present "their" problem. I found that this works for me...however, if they get to class late, then they are usually assigned the one no one wants, and they hate that!
Luckily, this year it's a one semester course, repeated. So I guess I only need about 14 problem sets...maybe more second semester because it's longer. As I'm writing the book, I really feel like it will be edited a lot--I'm getting such good feedback and I'm accustomed to only get that feedback from students. Last year was a "trial and error" year, this first semester will be a "ok, here's what I think will work," and second semester, it will hopefully be a pretty polished course!
Also, Jennifer, I forgot to mention...my students are in high school, and they need to either be in an honors math class or in Pre-Calculus AB in order to enroll in the course. It's a nice mix of accelerated Pre-Calculus students and honors students that could be enrolled in algebra 2 all the way to Differential Equations. There is a lot of differentiated learning as necessary.
Lisa
Another question. Do you hope/plan to have any themes emerge over the course of the problem sets? I am thinking of a presentation I saw years ago at Exeter with someone who had a series of problems that he referred to as 'Goat on a Rope' problems that increased in complexity and called upon previous themes.
Great feedback
Jim--I love the idea of themes...it's hard to do. I was thinking of doing it with the typical "hat" logic problems...and I think there will be a couple, but not like Exeter...whoever was on that team to make those problem sets were brilliant! Thanks for your resources!!!
Love this work. Thanks for sharing! I have found that my students need some explicit help with developing problem solving strategies - the natural default is to stop, raise their hand, and wait for the teacher. I especially like that your instructions specify that they are not allowed to ask the teacher for help!
I developed a suggested protocol and rubric for Grade 10s to use based on Polya's four step cycle. Here it is in case it might be useful for you. https://www.dropbox.com/sh/wafg8cgthgkaa9r/AABxMZvZyYxcWSa3n8hpS-bLa?dl=0
Thanks again for sharing! I'm looking forward to the next set.
Thank you Nat! This is great!! I really appreciate your comments and your link!
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