Mathematics as Problem Solving, Communication, and Reasoning

Helping your child learn to solve problems, to communicate mathematically, and to demonstrate reasoning abilities are fundamental to learning mathematics. These attributes will improve your child's understanding of and interest in math concepts and thinking. Before beginning the activities in this book, let's first look at what it means to:

Be a Problem Solver,
Communicate Mathematically, and
Demonstrate Reasoning Ability.

A problem solver is someone who questions, investigates, and explores solutions to problems; demonstrates the ability to stick with a problem to find a solution; understands that there may be different ways to arrive at an answer; considers many different answers to a problem; and applies math to everyday situations and uses it successfully. You can encourage your child to be a good problem solver by involving him or her in family decisionmaking using math.

To communicate mathematically means to use words, numbers, or mathematical symbols to explain situations; to talk about how you arrived at an answer; to listen to others' ways of thinking and perhaps alter their thinking; to use pictures to explain something; and to write about math, not just give an answer. You can help your child learn to communicate mathematically by asking your child to explain a math problem or answer. Ask your child to write about the process she or he used, or to draw a picture of how he or she arrived at an answer to a problem.

Reasoning ability means thinking logically, being able to see similarities and differences about things, making choices based on those differences, and thinking about relationships among things. You can encourage your child to explain his or her answers to easy math problems and to the more complicated ones. As you listen, you will hear your child sharing his or her reasoning.

Important Things To Know

1. Problems Can Be Solved in Different Ways While some problems in math may have only one solution, there may be many ways to get the right answer. Learning math is not only finding the correct answer, it's also a process of solving problems and applying what you have learned to new problems.

2. Wrong Answers Can Help! While accuracy is always important, a wrong answer could help youand your child discover what your child may not understand. The wrong answer tells you to look further, to ask questions, and to see what the wrong answer is saying about the child's understanding. It is highly likely that when you studied math, you were expected to complete lots of problems using one, memorized method and to do them quickly. Today, the focus is less on the quantity of memorized problems and memorized methods and more on understanding the concepts and applying thinking skills to arrive at an answer.

• Sometimes, a child may arrive at the wrong answer to a problem, because the child misunderstands the question being asked. For example, when children see the problem 4+____ = 9, they often respond with an answer of 13. That is because they think the problem is asking, "What is 4+9?" instead of "4 plus what missing number equals 9?"
  
• Ask your child to explain how a math problem was solved. The explanation might help you discover if your child needs help with the procedures; the number skills, such as addition, subtraction, multiplication, and division; or the concepts involved. In working with your child, you may learn something the teacher might find helpful. A short note or call will alert the teacher to possible ways of helping your child learn math more easily.
  
• Help your children be risk takers. Help them see the value of trying to do a problem even if it is difficult for them. Give your child time to explore the different approaches to solving a problem. Your child's way might differ from yours, but if the answer is correct and the strategy or way of solving it has worked, it may be a great alternative. By encouraging children to talk about what they are thinking, we help them to have stronger math skills and become independent thinkers.

3. Doing Math in Your Head Is Important

• Have you ever noticed that today very few people take their pencil and paper out to solve problems in the grocery store, restaurant, department store, or in the office? Instead, most people estimate in their heads, or use calculators or computers.
  
• Using calculators and computers demands that people put in the correct information and that they know if the answers are reasonable. Usually people look at the answer to determine if it makes sense, applying the math in their heads (mental math) to the problem. This, then, is the reason mental math is so important to our children as they enter the 21st century. Using mental math can make children become stronger in everyday math skills.

4. It's Okay to Use a Calculator

• It's okay to use calculators and computers to solve math problems. In fact, students are taught to use calculators at young ages and are often required to use them to do homework and take tests. The Scholastic Assessment Test (SAT), for example, permits the use of calculators for its timed tests. Many schools teach computer courses that include how to do spread sheets, statistical display, and computer-assisted designs for mechanical drawing and graphics. Schools often sell calculators to families at a low cost or supply them for all students to use. Knowing how to use a calculator and computer is a benefit for all students.

How Do I Use This Book?

This book is divided into introductory material that explains the basic principles behind the current approaches to math, sections on activities you can do with your children, and lists of resources.

The activities are arranged by levels of difficulty. Look for the suggested grade levels on each page that indicates the level of difficulty. The activities you choose and the level of difficulty depend on your child's ability. If your child seems ready, you might want to skip the easier exercises and go straight to the more challenging ones. Each activity includes a tip box with a simple explanation of the mathematical concept behind the activity, so that when your child asks, "Why are we doing this?" you can explain.

Let's Go and Explore Math!

Mathematics is everywhere, and every day is filled with opportunities to help children experience it. So flip through the pages, find an activity, and get ready to help your child explore math and have fun at the same time.

Taken from : http://www.ed.gov/pubs/parents/Math/intro.html