I teach college students and wanted to make my classes more engaging. I found this recent article interesting/useful http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html? My question is besides Lampert's book are there other books that discuss math teaching techniques that promote class participation?
I have made my classes more participatory over the years. I made great strides after I began reading math teacher blogs. Participating in math circles, and leading them, has also helped. Even in discussion, if we keep asking students if they agree with another student's proposed step, and keep asking why something works or is useful, we can get a lot more mathematical thinking than with a conventional lecture.
One recommendation that I have also given in response to similar questions, check out Jo Boaler's edX course: How to Learn Math for Parents and Teachers. It's currently in progress, but I'm sure it will run again. (I don't know if you can join while it's going on).
Also, the book Powerful Learning: What We Know About Teaching for Understanding has a chapter by Alan Schoenfeld on an approach to mathematics learning that involves inquiry. This book is also good for references to the research that supports the teaching of mathematics with a focus on understanding.
Some thoughts on making engagement and participation relevant to mathematics learning:
I try to think carefully about both engagement and participation as they apply to mathematics education. Sometimes people consider students engaged if they look interested. I consider engagement in a math classroom not to be interest, but to be "students are engaged in explaining, demonstrating, or arguing about mathematics." I might also add "listening, because they are about to do one of those other things" but that is not observable.
You'll see workshops about how to get students engaged by using candy, or how a particular technology increases student engagement and participation because suddenly students appear interested or they are doing more than sitting in their chairs.
Yes: activity and apparent interest are good things. But when we're talking about student engagement and participation, I recommend you ask an additional question: what mathematics is a student engaged in? And how are they participating in some mathematical practice? When a person tells you an engaging app is teaching kids math, ask them: what kind of mathematical thinking is going on? The 2048 game involves numbers. And it's certainly engaging. But apart from matching symbols (you can replace all the numbers with pictures and still play the game without ever thinking of doubling or powers of 2), it's not a mathematical game.
To circle back around to your question, if the classroom expectations are that students must argue and explain using mathematics, and they understand how (or how to make) their contributions are both valuable and mathematical (even when they are struggling), the classroom will be engaging. The students may need to become accustomed to this new way of being a student in a math classroom, but that's mathematical engagement In My Humble Opinion.
Since there have been a number of questions along these lines, the following observation may be useful:
As a mathematician, I've often read summary background material in a very high powered groundbreaking paper that makes me wonder why, if the only persons who will read the paper are specialists, it is important to include such material.
It may be related to the fact that thinking about mathematics effectively (at least in the "algebraic" subjects) requires that the practitioner hold a reasonably well-developed and compressed picture of the whole of a project in mind at one time. The brisk and highly compressed "review" serves to activate the memory of the expert so that the requisite facts are more easily in reach while thinking about the new details.
This said, writing a very "jokey" or "entertaining" mathematical text while keeping the level of compression high may become very difficult. The reason is that certain difficult-to-process sentences might compress a precise intuition of the author. The ability to remember the sentence becomes the ability to recall the details associated to a construction. A good joke or entertaining real-world application may help with this, but more often than not such information blocks the ability to remember what is truly essential for processing an argument or calculation! It feels (to me) like trying to memorize something in a room full of loud noises like people yelling and blaring music. (the yelling and blaring music being analogous to the joke or application.)
Anyhow, I think that at the root this may be why many of the very entertaining and witty mathematicians I know don't opt to be entertaining while writing mathematics texts.
Another way to think about this: Imagine this were a golf forum and someone posted the analogous question "Why don't we teach golf in a more engaging way?" The fact is, golf (and math) is hard and the only way to get better at it is to practice and concentrate very hard on what you are doing. Hoopla while teaching math (although we all involve some...just ask my students) is sort of like talking during someone's swing. Golf (and Math) is its own reward, when you have very occasionally succeeded in doing something difficult with a beautiful result. There's a good chance this would never be seen if we changed the teaching of the game to make it easier or more engaging to learn...which is what most entertaining approaches inadvertently do.
This "comment" addresses a narrow aspect of your post, the article in the New York Times (July 23, 2014). This article was very disappointing. It confuses arithmetic (and implicitly basic algebra) and mathematics which is a much bigger subject than arithmetic (and algebra). Arithmetic and "realistic" applications of arithmetic are very important but how about discussing with elementary school students the mathematics behind how some spell checkers work (Hamming distance and/or edit distance)?. If we teach "content" that is not optimal for the K-12 audience (and there is no wide agreement about what content goals here should be despite CCSS-M "hype") then no matter how well we teach it there is a high price to pay. Oversimplifying very greatly (smile, there is a CCSS-M that deals with modeling) we have designed a curriculum with too much attention to the needs of future STEM majors.
You might find this article of mine of interest here:
or it can be downloaded from this site, which also contains other background articles about some of these issues: