In one of my education classes, we are reading the book The Teaching Gap by James W. Stigler and James Hiebert. This book compares teaching styles and methods between math teachers in the United States, Germany and Japan, which is proving to be extremely interesting and eye-opening. We have also been learning about the Five Practices for Orchestrating Productive Mathematics Discussions and how to implement them in the classroom to help facilitate class-wide conversations. This blog post is going to reflect on what I’ve learned, what I’ve observed and what I want to implement in my classroom as a future teacher.
Chapter five of The Teaching Gap focuses on something that I had never thought about–how the use of a whiteboard (or other technological board) affects learning. Teachers in the US tend to use projectors, doc cams, smart boards, etc to project information, which focuses students’ attention on the “information of the moment.” Japanese teachers, on the other hand, start their work on the top, left side of the board and work their way to the right–never erasing the previous work. Their purpose for using visual aids is “to provide a record of the problems and solution methods and principles that are discussed during the lesson.” This makes so much more sense to me, because math is (supposed) to be all about making connections. So, having the ability to look back at what was done at the beginning of a lesson makes sense if we think about math as a system rather than separate, disjoint concepts. I knew there was a reason I disliked Smartboards so much! They’re machines that add “fluff” (which is often times irrelevant and simply added for visual effect) and allow for very little space to write. With a whiteboard I would have almost an entire wall length to work a math problem or proof, but with a Smartboard, I’d have to move from page to page–never allowing the students to view their work as one long process, but rather fragmented pieces. I know it comes down to personal preference, but I personally think the Japanese really have a handle on this concept here.
Another idea mentioned in chapter five is that of the student role in the classroom. How many of us have had a math class where the teacher shows us the procedure, we learn it and practice it and then perform it on the test…and then likely forget it after that? I’m assuming that most are nodding their heads along with that statement–but that’s not math! Math is all about problem solving, thinking critically, collaborating and making connections–none of which can occur if we’re simply programmed to execute specific procedures. German and Japanese teachers have their students work on problems which they’ve often never seen modeled before. And guess what? They can accomplish them just fine! We don’t have to spoon feed kids, because they’re actually incredibly smart–they might just need some motivation to realize that. Once they see that they’re going to have to exert some brain power to solve a problem, I almost guarantee you that most of them will rise to the occasion. This is something I’m hoping to do in my classroom. I don’t want mundane, boring worksheets that provide little challenge, but rather activities that are hands on or based on real-world situations. This will take a great deal of effort, no doubt, but I truly believe it will create more motivated students who have a desire to tackle a problem head on with confidence.
So how do I make sure the “big ideas” are still being transmitted to each and every student? I’m so glad you asked. 🙂 This is where the Five Practices comes in to play. They are: Anticipate, Monitor, Select, Order and Connect (click on the link for more detailed descriptions). While the students are working through these more complex problems, I (the teacher) would be circulating throughout the room looking for common misconceptions, picking out methods of solving that I think are well written out or would lead to beneficial class discussions and the order in which they are shared. This is the “monitoring, selecting and ordering” from the Five Practices. The most important practice (in my opinion) is connect. If students can’t make connections to previous mathematics, real-world situations, etc then the math will have no meaning. I would love to write the objectives for each day on the board and ask the students periodically how whichever point we’re at in the lesson connects back to the main objective. This gives substance to what the students are working on and empowers them to continue thinking critically and making those powerful connections.
In summary, I’m finding The Teaching Gap a must read for all math teachers–present and future! As for The Five Practices, learn them, internalize them and put them in practice. I firmly believe they will make a huge difference.