Count Down – Part One
Count Down
Summer is a great time to do some reading and reflect on things. This summer one of the books that I am really enjoying is called Count Down: Six Kids Vie for Glory at the World’s Toughest Math Completion by Steve Olson. The book is a quick read and very interesting from a number of perspectives including the stories of the competitors and food for thought for educators.
I wanted to use the next couple of blog posts to reflect on a couple of the aspects of the book that I think are relevant to teaching mathematics. I promise to keep the posts themselves short and sweet.
As this book deals with students who attend the International Mathematics Olympiad it could be argued that many of the statements are not applicable to the average mathematics student. I am not inclined to believe this but others may disagree. Regardless of your perspective the book is a great read.
Part One – Problem Solving
Problems solving is always a tough place to start as there are many definitions of what constitutes a good problem as well as the process of problem solving. This post does not argue for any particular definition or process but I would agree with the statement that
… high-level problem solving is the key to successful mathematics education – not just for the best students but for all of them. (p. 49)
I do however differentiate between problem solving and practice. I am not taking a stand on either side of the practice debate that seems to happen in mathematics; however, I do agree that high level problem solving is essential in a mathematically rich environment.
To accent this Olson highlights the results of the 1999 TIMMS Video Study noting the difference between American (Canada was not a part of this study) and Japanese classrooms. In particular he notes that
In Japanese classrooms, in contrast, teachers want their students to struggle with problems, because they believe that’s how students come to really understand mathematical concepts (p. 48).
However the study indicates that what happens in many American classrooms involves the teacher “leading their students in tiny steps.” (p. 48). Good problems in my mind do not have preordained steps. There can be multiple approaches and assumptions which affect the outcome and are open to interpretation.
I will leave it to each reader to check out the 1999 TIMMS Video Study or read the book to gather more information and draw their own conclusions. However, I am making the commitment to ask open-ended problems which involve collaboration and “high-level problem solving.” Hopefully I will get better at doing this every year.
Stay tuned for Part Two
Math in the Middle 
I look forward to reading about some of the challenges and successes you encounter including collaboration and high-level problem solving in your classes!
The question that comes to mind when I read about allowing space to struggle to solve problems is what happens when students give up or don’t care enough to work at it and just want the answer? I can think of more than a few things I did at school where I didn’t have much interest in the topic and just wanted to get through it…
I must admit this has been something that has crossed my mind as well. Perhaps one of the most important traits of a problem solver is the notion on perseverance. Anyone who knows me has heard me say that it is important to “teach” (or is promote) perseverance. I am not sure how it will go but I know that if things are interesting and intrinsically motivated there is more likely to be an increased level of perseverance. Stay tuned to the blog Nick and hopefully I will have some updates on how it will go.
On another note …. I think this notion of high level problem solving is not new but I do think it is one that is getting more emphasis as the ideas of 21st Century Learning (and learners) is discussed more. More on this as well I think.
Thanks for your thoughts.