There is a debate amongst teachers using Cognitively Guided Instruction in Math (CGI Math) as to whether or not to keep posing the same problem type for a week or two, changing the problem type almost daily, or flipping the problem type (we’ll talk more about that in a minute), let’s examine the pros and cons.
My CGI math work is primarily done in Title I schools with large, diverse urban populations and many English language learners. Full disclosure, I lean towards keeping the same problem type for a week or so for a variety of reasons. Read the following arguments and let me know what you think.
Repeating the same problem type allows students to become familiar with the structure and the language of the problem. For example, The blue string is 12 inches long. That is 6 times as long as the red string. How long is the red string? The language in this problem type (multiplicative comparison) is abstract as is the concept of measurement. Students from a variety of backgrounds often need time to make since of this language and make meaning from it. One or two times may not be enough for English language learners and beginner’s to grapple productively with the problem.
Sometimes when posing a particular problem type, students may be able to come up with an accurate answer fairly quickly, if not immediately. This makes me wonder if 1) is the problem type challenging enough, and 2) are we concerned with getting the correct answer or are we concerned with flexibility and the sophistication of the answer? For example, if a student can quickly solve a multiplication problem by drawing picture, do we want them to stop there? If a student can quickly solve a multiplication problem with the standard algorithm do we want them to stop there? I say, “No.” I want to see strategies develop from pictures to skip counting, to decomposing, to the distributive property and on. How can these strategies become more complex and diverse if kids only get one shot at them? How will teachers learn to extend students’ thinking and increase precision, fluency, and accuracy if they only get one chance at them?