What is mathematical problem solving?
One of the main reasons for studying mathematics is to develop the ability to solve problems. Problem solving is the process of applying what we already know to new and unfamiliar situations. This ability is not only critical to our children’s future needs, but also to a productive society and even human progress itself. In the early years, children develop attitudes and beliefs as to their ability to learn mathematics. By learning mathematics through problem solving, children can make sense of why they need to know their basic facts.
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The best way for your children to become good problem solvers is for them to solve problems, lots of problems (practice, practice, practice)! Also, it benefits children to think about how they solved the problem afterwards. In this way they may use their particular strategy to solve similar problems in the future. There are no best ways of solving a problem. We are interested in what makes sense to each individual. Problem solving is a skill that students develop over long periods of time - in other words - it doesn't happen overnight!
There are many problem solving approaches out there. Most of these approaches hit at the core ideas of problem solving that include:
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Problem Solving Skills and Strategies
In general, problems are not supposed to be easy. So do what good mathematicians do. Keep on trying and think about strategies to help solve the problem. If what you try first doesn't work, don't worry, just look at what you've done and make another try. This happens all the time to the best problem solvers.
The table to the right shows some of the most popular problem solving strategies and skills. How many of these have you tried? Parents, ask your child to show you how to solve some of their homework problems by using one or more of the strategies in these lists. |
Holly Young is a former teacher from Washoe County School District here in Reno. She developed the ACE Constructed Response materials you'll see below. I've included her thoughts about how she taught her students to tackle these more challenging types of problems in the mathematics classroom.
From Holly Young's Website: Reading, Writing & Reflecting Mathematics from Holly Young, NumberFix Coordinator Teaching students the fine art of problem-solving can be incredibly difficult! This issue has really come to the forefront lately with the onset of constructed response problems in math and science. I have found that text-books and "programs" teach problem-solving in a linear fashion, such as, first do this, then do this, etc, until you magically arrive at the answer. Unfortunately, step one - highlight important information - usually is the step none of the students can get past. Instead of following a linear/sequential problem-solving formula, I designed a cyclical process of reading, writing, discussing, and reflecting on problems. As most brain research reports, humans solve problems in many different ways and enter problems at many different points. |
If a teacher uses the reading, writing, and reflecting posters as questions that help students enter problems and provide direction for solving problems, then students have an easier time discussing and writing about their solutions and methods for solving. Any question provided on the three posters can be an "exit ticket" to check for student understanding or can be used as a discussion point in a group or as a class. (Not every question given on the posters can be answered for every problem) The format for these posters, "ACE," mirrors/extends my instruction used in teaching students how to answer constructed response questions (see the constructed response link).
I also designed a graphic organizer that can be handed out to the students when a new problem is tackled. As a class, it can be decided which questions need to be answered or discussed on the graphic organizer. As with all good writing, students need direction. This strategy can get students to plan their problem writing, write with a purpose, and reflect upon their thinking. You can find out much more about my ACE Constructed Response materials at my personal website: Making Mathematicians. |
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