Thinking out Loud…

A super brief post here – hoping to find some great advice from the world outside.

Two years ago our school launched a Discrete Math course. We realized that we had a number of students who were not being served well by our curriculum – a relatively standard one, really – that served to deliver most of our students to the doorstep of Calculus. I loved Calculus as a student and I have been happy to teach some form of it for most of my teaching career. However, we realize as a department that not all of our students need to see Calculus as the pinnacle of their high school math career. We also offer AP Statistics but we still saw a groups of students who were not being served properly. We have a vision of this Discrete Math elective being a lively, provocative course that exposes these students to more (and different) mathematical ways of thinking. We adopted the text For All Practical Purposes (9th Ed) and in the first year we had the course, the publisher released a new edition. I am teaching the course this year and I really like the students in the course and I feel that we are making some real progress in showing a different side of mathematical thinking, something other than algebraic reasoning and equation-based mathematics. However, I am not thrilled with the text. I am not sure that the level of the writing is suited well to my kiddos and I spent most of the fall term writing my own problem sets. Since the text is not available anymore I am faced with a choice of moving on the the 10th edition, finding a new text to serve as the center of the course, or going text-free and writing/borrowing unit notes and problem sets to support the students.

I know that there are people who visit my space here who have experience with math electives outside of the algebra to Calculus stream. I would love to hear some advice from them either in the comments here or through my twitter feed (I am @mrdardy over in the twitterverse) The ability / interest level of the students varies in this group. Some are taking the math course out of good conscience/concern about the college process. They know it is a ‘good idea’ to have a fourth math course. Some are taking it to fill out their schedule. Some end up in it after dropping back a bit from another math course that was more of a challenge than we/they expected it to be. This year we spend some time on elementary statistics/probability already. We spend a little time in the fall getting ready for a last swing at standardized tests. We are currently immersed in a unit on elections and voting strategies. We will visit some finance ideas and we will dip our toes into graph theory / network theory ideas. I am not married to any of these particular ideas, but many of them pop up in most discrete math text options out there. I kind of love Jacobs’ text Mathematics: A Human Endeavor but it seems not to be currently in print and I do not want to go down the path of a text I cannot reliably get my hands on.

So, dear readers, I would appreciate any wisdom you can share from experiences at your schools.

Lovely Explanations

I have not been writing here as much as I want to because, for the second year in a row, I am creating daily HW problem sets on the fly for a new class. This summer, with about two weeks left before school began, I found out that a colleague had taken another job. She had a fantastic opportunity that she felt she could not pass up. One of the side effects of her decision was that I inherited an extra section each day and I inherited a new course – Discrete Math – meeting twice a day. I am still feeling my way through it but I have a wonderful group of students. One section has seven students and the other has eight. We have been sitting around a pod of desks together sharing ideas. I think that this has been a bit of a culture shock for some of the students but I am thrilled with their flexibility.┬áThis elective was introduced last year and we are feeling our way through it. The students in here are not necessarily great math fans and I wonder whether many of them are used to feeling that their mathematical opinions are particularly pertinent. I have been working hard to develop an atmosphere of trust where the students are willing to share their opinions, their answers to questions, and, most importantly, their questions for each other and for me. I have been thrilled by the level of engagement and today, in each class, students offered explanations to a probability idea that just knocked me out. We are just introducing the ideas of compound probabilities and talking about how to interpret AND versus OR situations. For example, I offered an example telling the students that approximately 10% of American adults are left-handed. I asked what was the likelihood of two randomly selected adults both being left-handed. Students quickly offered the idea that 10% of 10% was the way to go. A different problem outlined percentages of blood types and mentioned that type B people can accept donations from type O or from type B. Here, the students quickly offered addition as the way to work through the problem. I congratulated them for seeing this quickly, but challenged them as to why they had this gut feeling. One student in my early class said that he thought of the two left handed people as one event where one thing happened then another, while he thought of the blood type question as two ways an event could happen. I was so pleased to here this developing intuition. In my later class the same scene unfolded and here a student simply offered the idea that two blood types gave you more opportunities so we want to combine them in a way that increases the result while the left handed question seemed to necessarily narrow the likelihood of being satisfied with the result.

I find both of these explanations to be much more appealing than tree diagrams or a simple rule that AND = multiply while OR = add.

So pleased with how the class is unfolding. I just wish that the problem sets would write themselves…