When I was asked to give a talk on some aspect of the history of mathematics a couple of years ago at Suffolk County Community College, I tried to bridge my research and teaching interests by presenting on the history of numerical algorithms. My Ph.D. was in numerical analysis and this was an opportunity to use my research background to present how using technology in math requires a great deal of conceptual understanding. You can view the presentation below. (It's really not as boring as the title suggests!)
Tuesday, November 24, 2009
Thursday, November 19, 2009
Teaching Reading in a Math class?
An often asked question from my students is "but this is a math class - and you want me to read and write?" When teaching my upper division Intro to Proofs class, I find a certain discomfort among students in extracting information from a math text. Most students are used to skimming over some examples and finding one that matches the homework problem. I don't really count that as "reading" - just a sort of search and replace operation. And so when we have to prove something - uh oh - the search and replace strategy no longer works.
I thought finding a readable text would be a solution. Well, a readable text is only good if it's read! So now I am finding myself teaching higher level reading skills and critical thinking skills. This is way tougher than teaching math. I've been looking at material from my college library on how to teach this type of reading. Here are some ideas from this literature I've adapted for college level math:
If critical thinking and critical reading skills in mathematics were taught in K-12 and in the computational courses in college, I may not have this problem at such a late stage in an undergraduate math student's career. Or, at least, it would not be so severe.
I thought finding a readable text would be a solution. Well, a readable text is only good if it's read! So now I am finding myself teaching higher level reading skills and critical thinking skills. This is way tougher than teaching math. I've been looking at material from my college library on how to teach this type of reading. Here are some ideas from this literature I've adapted for college level math:
- This is actually something I haven't seen in many intro to proofs books: Have students read and interpret lower level math material such as theorems from precalculus; if they don't understand how to read and interpret those, how can they understand a theorem in abstract algebra or real analysis?
- Start the intro to proofs course with topics in discrete math and nonstandard problem solving to jump start their thinking skills. These problems are not easily amenable to the "search and replace" approach to math.
- This is an old idea - an online reading quiz before class using Blackboard or some other LMS. You can also use Google forms very quickly for this.
- Too late for this semester - but for the start of next semester I'm going to have the students do a "mind map" to help sketch out their proofs. There are several available on the web and Maria Andersen has information about how she uses mindmaps in her blog
If critical thinking and critical reading skills in mathematics were taught in K-12 and in the computational courses in college, I may not have this problem at such a late stage in an undergraduate math student's career. Or, at least, it would not be so severe.
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