Category: Active Learning in Math

AMATYC Keynote Notes: Challenge and Curiosity

In the 2016 AMATYC keynote, I covered three main themes: Interaction & Impasse (last post) Challenge & Curiosity (this post) Durable Learning Here are references and resources for Challenge & Curiosity: First, I have to point you to one of my favorite books on the subject, A Theory of Fun for Game Design, by Raph Koster. Quote from Game Design: “How do I get somebody to learn something that is long and difficult and takes a lot of commitment, but get them to learn it well?” – James Gee How do players learn a game?  They give it a try They...

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Cognitive Psychology and Math Education

In the last three weeks I’ve read or skimmed about 2,000 pages of scholarly articles about math reform efforts, technology for teaching, innovations, change movements, faculty development, community college statistics, learning theories, and distance ed statistics. If you had any idea how many topics I want to blog about every day, but don’t have time for right now …well, just forgive me for lame posts for a little while, okay? In the meantime, you can read this paper called “Applications and Misapplications of Cognitive Psychology to Mathematics Education” by Anderson, Reder, and Simon.  The full text is available at the link.  Interestingly, this was never published, although a similar article (not specific to math) was published.  I’ll warn you that I’ve read a few books on cognitive psychology, and it was still a difficult read because of all the terminology.  However, I assure you, it’s interesting reading.  If you find the first few paragraphs daunting, try skimming to where you read an applied example, then back up to read the section before it.  It’s easier to get the vocabulary when you have a concrete example in your head to pair with it. As a math teacher, I use a lot of student-centered learning strategies.  I incorporate technology into my classes and emphasize the rule-of-four.  However, I still insist on students learning some procedural skills (like derivatives and integrals) because...

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Teaching Math with Clickers

Today’s guest blogger is Derek Bruff, Assistant Director for the Center for Teaching at Vanderbilt University. Derek writes a blog you may have stumbled across called Teaching with Classroom Response Systems. Here’s a question I ask the students in my probability and statistics course: Your sister-in-law calls to say that she’s having twins. Which of the following is more likely? (Assume that she’s not having identical twins.) A. Twin boysB. Twin girlsC. One boy and one girlD. All are equally likely Since I ask this question using a classroom response system, each of my students is able to submit his or her response to the question using a handheld device called a clicker. The clickers beam the students’ responses via radio frequencies to a receiver attached to my classroom computer. Software on the computer generates a histogram that shows the distribution of student responses. I first ask my students to respond to the question individually, without discussing it. Usually, the histogram shows me that most of the students answered incorrectly, which tells me that the question is one worth asking. I then ask my students to discuss the question in pairs or small groups, then submit their (possibly different) answers again using their clickers. This generates a buzz in the classroom as students discuss and debate the answer choices with their peers. After the second “vote,” the histogram usually...

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Speed Rounds: Test Review Game

Here’s a game we play on Test Review days that engages all the students at once and gives every team a chance at points in every round (unlike Jeopardy). I count the students off into groups of 3-4 students. Each group gets an answer sheet for the game (a piece of colored paper with a letter, A, B, C, D, …) at the top. I make a “scoreboard” on the board to tally the results of the rounds (12 in this case). Here’s what that looks like: Then we begin the game. Here’s a sample game – the one we played today in class. Uploaded on authorSTREAM by wyandersen For each round, the students work with their group to come up with an answer they can all agree on. Group A writes this on their answer sheet, Group B on their answer sheet, etc. If a group does not want to submit an answer they can write “HOLD” or just hold on to their sheet for the round. When all answers are in, I put up the answer and, if necessary, work through the problem. By the end of the game, the scoreboard might look something like this: The students seem to like the game whether you play it for points or just for fun. I always choose the more difficult problems for the game because it has the...

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Activities for Algebra

I have always tried to teach algebra in a way that is understandable, interesting, and active. Although you can find activities for teaching algebra to younger students (6th and 7th graders), I have never found a good classroom resource to use with adult students. Even in the resources for younger students, the activities always seem more like busywork, when they could provide an opportunity for students to truly understand difficult concepts or explore the similarities and contrasts that abound in mathematical procedures and ideas. I have enjoyed taking the time to sit down and write what I hope are interesting and useful resources for teaching algebra to adult students. It has grown from a small idea into a behemoth with a life of its own during the writing process, as the pedagogies described in the Teaching Guides continued to force more activities to be written. I am still writing, but there are currently over 500 pages of activities, assessments, and teaching guides. For their assistance on the Elementary Algebra IRB, I owe a great big thank you to my faithful mathematics assistant, Megan Arthur, who tirelessly filled in a lot of the necessary (but boring) detailed mathematical work and graphics on these activities all summer – without her time and energy, this work would not be a reality today. Also, I extend a grateful thank you to Maryanne Kirkpatrick,...

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