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Investigations

 

ABOUT INVESTIGATIONS

               An investigation is a complete mathematics program for grades K-5. Students using Investigations in Number, Data, and Space are expected to learn arithmetic, basic facts and much more. The focus of instruction is on mathematical thinking and reasoning. Students using the complete Investigations develop an understanding of:

 

  • number, operations, and early algebraic ideas

  • geometry and measurement

  • data analysis and probability

  • patterns, functions, and the math of change, which provide foundations for algebra

 

               An investigation is based on our goals and guiding principles, years of being students, and research about what we now know about how children learn mathematics. It is carefully designed to invite all students into mathematics and to help them develop a deep understanding of fundamental mathematical ideas.

           "Understanding refers to a student's grasp of fundamental mathematical ideas. Students with understanding know more than isolated facts and procedures. They know why a mathematical idea is important and the contexts in which it is useful. Furthermore, they are aware of many connections between mathematical ideas. In fact, the degree of students' understanding is related to the richness and extent of the connections they have made.

 

As a natural part of their everyday mathematics work, Investigations students:

 

  • Explore problems in depth.

  • Find more than one way to solve many of the problems they encounter.

  • Reason mathematically and develop problem-solving strategies.

  • Examine and explain mathematical thinking and reasoning.

  • Communicate their ideas orally and on paper, using "clear and concise" notation.

  • Represent their thinking using models, diagrams, and graphs.

  • Make connections between mathematical ideas.

  • Prove their ideas to others.

  • Develop computational fluency - efficiency, accuracy, and flexibility.

  • Choose from a variety of tools and appropriate technology.

  • Work in a variety of groupings - whole class, individually, in pairs, and in small groups.

 

 

DOING MATH TOGETHER

                    Expect Your Child to Work Hard and be Able to Learn Math Many adults leave school thinking that mathematics doesn't make sense. The way they learned math did not always enable them to efficiently solve problems in ways that made sense to them. When working with your child, keep in mind that children can make sense of mathematics if given the opportunity and support. Encourage your child to stick with a task even if it seems challenging. Be sure to talk through what the problem is asking and discuss some of the strategies that might be used to solve the problem. Help your child learn that there are many ways to solve problems.

           "When parents and teachers alike believe that hard work pays off, and when mathematics is taught and learned by using all the strands of proficiency, mathematics performance improves for all students.

 

Ask Questions

          There are many different types of questions that you can ask your child. Try to use productive questions that promote mathematical activity and reasoning such as "What do you think…?" or "Why do you think…?" These questions encourage children to develop ideas and test and defend their thinking. Other helpful questions include:

  • Why did you solve the problem in this way?

  • Will your strategy always work?

  • What else did you try?

 

          After you ask a question, be patient. Don't automatically give your child the answer. Instead, give your child time to think about the question and how s/he might answer it. If your child gives the wrong answer, ask how s/he got it. Probe to gain a better understanding of their thinking. Suggest alternate strategies that might help your child find the correct answer. Help him/her think about where their thinking went wrong. For example:

          "How did you add the 7 and the 8? Sometimes, I start with 7 + 7 because I know that equals 14. Then I know that 7 + 8 = 15. What strategy are you using? Let's try it again."

Even if your child answers correctly, it is important to ask how s/he came up with the solution and to probe to learn more about their thinking.

 

          "A good [productive] question is a stimulating question, which is an invitation to a closer look, a new experiment, or a fresh exercise."

 

 

Solve Problems and Explain Thinking

          Encourage your child to ask questions and explain his/her thinking and do the same yourself. When you see a method that you do not understand, take the time to analyze and figure it out. Prove to yourself that the answer makes sense. In school, children will use pictures, symbols, diagrams, words and numbers to explain and prove their thinking. The ability to use different representations and mathematical tools are an important part of a child's growing understanding and ability to explain and defend their thinking. As children describe and compare their representations, their understanding of mathematics deepens.

 

          You can model successful approaches to solving problems by verbalizing your math thinking and sharing your methods. For example, when shopping, talk out loud about how you are figuring out how much money your items will cost or how much change you will get back. When building an object, sewing, or organizing your closet, think together about problems that arise and potential solutions.

 

          When you ask questions, make mistakes, and talk about what you think, children see the importance of working through a problem and make connections with mathematics in everyday situations. Don't worry about using the same strategy that your child uses. People have many different, effective ways to solve everyday problems. What is important is that each person uses a strategy that makes sense to him/her.

 

 

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