Teaching Through Problem Solving EDN 322

NCTM process standards Problem solving Reasoning and proof Communication Connections Representation The past two decades have witnessed a resurgence of interest in problem solving as an integral part of the mathematics curriculum. Problem solving is one of the five process standards identified by NCTM. NCTM tells us that PS should be the focus of the mathematics curriculum. Elementary students need to use problem solving approaches to investigate and understand mathematical content. In other words, problem solving should permeate the entire curriculum. This focus on problem solving may be interpreted as a shift from a concern with algorithms or fixed content to mathematical thinking and inquiry.

What is a problem? (Van De Walle, 2004) A problem is any task or exploration for which the solution has not been explained… that begins with the ideas that kids have, that is challenging mathematically, and for which justification and explanations of answers and methods are the responsibility of the students. What comes to mind when you think about problem solving? You may think of a challenging situation that you have encountered in real life, such as the time you got your car stuck in the sand at Wrightsville Beach and you had to place boards under the tires to get the car to move. It may be that you have to consider the most efficient route to UNCW from a number of locations. Perhaps you will go home this evening and examine the contents of your cupboard to determine what you will prepare for dinner. When you think about problem solving in the mathematics classroom, you may conjure up images of the word or story problems that you encountered in elementary school textbooks. After you learned to perform certain computations (say, multiplication of fractions), your text may have provided problems in context that used those very same skills. In many cases, these may not have been genuine “problems.” While such problems do encompass a portion of problem solving, they represent only a very small portion. Problem solving as envisioned by the NCTM standards, is much more than this. As it is commonly defined in contemporary education, problem solving describes the process an individual uses to respond to and overcome obstacles or barriers when a solution or method of solution is not immediately obvious. Given this context, problem solving is very much an interdisciplinary activity and should not be restricted to a single unit in mathematics. Not all problems are mathematical in nature, but the thought process behind solving problems is similar in all situations. A little later we will discuss a four-step model for solving problems.

Why Teach with Problems? (Van De Walle, 2004) Places the focus of attention on ideas and sense making rather than on following the directions of the teacher. Develops “mathematical power.” All five process standards are likely to be employed. Develops the belief in students they are capable of doing mathematics and that mathematics makes sense. Provides assessment data on an ongoing basis so that instructional decisions can be made. It’s a lot of fun!!!

Lesson Plan Components NC Objective(s) Materials Procedures Before During After Assessment (may be including in the “during” and “after” phase of the lesson.)

Teaching through Problem Solving Lesson Structure Getting Ready Get students mentally ready to work on the task. Be sure all expectations for products are clear. BEFORE Students Work Let go! Listen carefully. Provide hints. Observe and assess. DURING Class Discourse Accept student solutions without evaluation, Conduct discussion as students justify and evaluate results and methods. AFTER

In this puzzle you must help a farmer get a fox, a chicken, and a bag of corn safely across a river in a boat. The farmer may only take one thing at a time in the boat. She cannot leave the fox and the chicken together on either side of the river, or the fox will eat the chicken. Likewise, she cannot leave the chicken alone with the bag of corn or the chicken will eat the corn. How can the farmer get everything across the river without anything being eaten? AIMS - http://www.aimsedu.org/puzzle/farmer/farmer2.html

Problem Solving Strategies Guess and check Draw a picture, act it out, use models Look for a pattern Make a table, chart, or original list Account for all possibilities

Problem Solving Strategies Work backwards Try a simpler problem Write an equation or open sentence Logical reasoning