You might have heard of TIMSS, the study that lays bare where the US ranks in terms of science and math education – and hypothesizes some possible reasons for our low placement. One part of this study was a video study of math and science lessons in the US and other countries around the world. The video study showed that in countries where students perform well in math, the way math is taught is fundamentally different. Lessons involve more open-ended questions, more teaching of problem-solving, less teaching of procedures and memorization. Students get through fewer problems and work through them more deeply.
Over the summer, I read a book published by the NCTM: Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development by Stein, Smith, Henningsen, and Silver. The dry title doesn’t do justice to what is a fantastic book. It’s a handbook for teaching in the way the TIMSS study recommends, and it’s a very accessible book, written in the form of case studies from many different lessons presented by different teachers.
I devoured the book and determined that I would do my very best to step up my teaching style – to present lessons in a way that would have a higher cognitive demand, more challenge, more depth.
The book suggests categorizing student tasks by cognitive demand. I’m going to steal just a little and write the example given in the front of the book that they use to demonstrate the four levels.
Memorization (example: give the decimal and percent equivalents for 1/2 and 1/4.)
Procedures without Connections (example: Convert the fractions 3/8 and 4/11 to decimals and percents.)
Procedures with Connections (example: Use a 10×10 grid to show the decimal and percent equivalents of 3/5.)
“Doing Mathematics” (example: Shade in 6 squares of a 4×10 rectangle. Using the rectangle, explain how to determine the percent of the area that is shaded, the decimal part that is shaded, and the fraction of the area that is shaded.)
The book then goes through a series of lessons with reflections written by teachers, and discusses the cognitive demand of the lesson and factors that contributed to the cognitive demand. At times, a lesson can start as a high-cognitive-demand task, but as the lesson progresses and conditions deteriorate, students find themselves doing tasks with less and less cognitive demand – due to one or more factors. A task may be inappropriate for a student’s background knowledge. The teacher may not manage his or her classroom effectively. The teacher may answer questions so completely that he or she ends up teaching a procedure and not problem solving. Questions may not be appropriate for the level of cognitive demand. It seems to be very tough to start, see through, and finish a task that has a high level of cognitive demand.
I would like to learn to do it well.
I’ll reflect on the lessons I try here, and use this blog as a tool for improving the way I create a problem-solving environment in my classroom.
I will also post the awesome things that seventh-graders say in response to my best efforts to teach them. 🙂