Very often when I work with a group of teachers, I hear the question, “How much time do you spend doing Problem Solving?” I have two different answers for this question. I will share both answers below.
For the first response, I remind teachers that problem solving is one of the process standards clearly discussed in the Principles and Standards of School Mathematics (PSSM), NCTM 2000. As is stated in the National Council of Teachers of Mathematics’ Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM, 2006),
“Organizing a curriculum around these described focal points, with a clear emphasis on the processes that Principles and Standards addresses in the Process Standards—communication, reasoning, representation, connections, and, particularly, problem solving—can provide students with a connected, coherent, ever expanding body of mathematical knowledge and ways of thinking. Such a comprehensive mathematics experience can prepare students for whatever career or professional path they may choose as well as equip them to solve many problems that they will face in the future.”
Therefore, the answer to the question would be, “I would ‘do’ problem solving as often as I possibly can.” For example, whenever I introduce a new concept, I create a problem solving task as part of the introductory Warm Up. Asking students to reflect on their understandings, communicate their thinking, utilize a variety of strategies and so on are the foundations of a problem-based curriculum and are all part of my instructional standard operating procedures.
However, I believe what the questioner really intended to ask was, ” How do you structure your daily and weekly math times? Then, the answer would be the following. My main block of math time runs about 50 minutes. As mentioned above, if the lesson focus is on developing a new concept, the structure will definitely be problem-based. If we are at a point where I want students to practice and reinforce skills, that block will likely consist of small group station activities. Often these games and activities have a problem solving strategy component built into them, as well. At other times of the day, I have a calendar time for about 20 minutes I use to develop math vocabulary and reinforce and practice skills previously taught and a math journaling time that usually runs for another 15 minutes or so, where students reflect and self-evaluate around the concepts they have been learning. Therefore, 90 minutes a day are usually devoted to math in my usual daily routine.
My answer would be a little different if on the other hand, the question being asked is really, “How often do you use the Making Sense of Problem Solving (MSPS) materials?” In that case, the answer would be that approximately once a week I use the MSPS materials. Because there are 15 units, one week I focus on introductory Warm Up activities followed the next week with Problem Solving and Enrichment tasks assigned to the appropriate level students. I may carry over to a second day, student presentations of their solutions. How about you, my readers? How much time do you spend doing math and how is it structured?
Tags: Mathematics Problem Solving, NCTM Curriculum Focal Points, NCTM Process Standards, Principles and Standards of School Mathematics (PSSM)