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Health & Fitness

Making Sense and Persevering with Problem Solving in Mathematics

The Massachusetts Curriculum Frameworks for Mathematics outlines practices that describe how students will learn mathematics.

 

The Massachusetts Curriculum Frameworks for Mathematics outlines content standards per grade. It also outlines 8 mathematical practices that describe how students will learn mathematics. The standards and the new mathematical practices represent a shift in the teaching of mathematics. These practices are habits of mind that all successful mathematical thinkers use to solve problems. 

The first mathematical practice emphasizes that students make sense and them persevere when presented with a wide range of problems.  The process of finding the answer to a problem will be just as important as getting to the final answer.

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When it comes to homework, many parents have had the dreaded question on many nights, “I don’t know”, “I don’t get it”, or “I need help.” Sometimes this is also accompanied with tears and an argument of asking them to try and work through the math problem they are struggling with.

To begin to solve a problem, students plan and think through the problem.   Students will have to understand what the problem is asking and what information is relevant.

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They persevere and perhaps even struggle as they try to solve the problem.  Students will show a positive attitude as they struggle with the problem. As they solve the problem, they may consider a simpler or similar problem to help them.  Concrete objects may be used to help visualize or act out the problem.  Their original plan may be refined and changed as they continue working through the problem. Students will try out several approaches and strategies to solve a problem.

Finally, they check their problem asking if it makes sense.  They’ll check their answers using a different method.

To help students develop this mathematical habit of mind, teachers will provide rich problems that will have multiple solutions. They will also ask questions to probe for students’ mathematical thinking instead of jumping into helping them solve the problem. They will give students time to process the problem and find solutions. Students will work individually, in pairs, and in small groups to solve problems. 

Much has been written about how to help children succeed.  Parents can help their children by praising the process students used to solve a problem. Praise also their effort and perseverance. Explain to children that repeated practice will help them develop their problem solving skills. While it may feel hard, it gets easier the more practice we have.  Show students how practice helps them in other skills they are learning, for example, how practice in sports or dance helps them improve in these areas.

Ask your child these questions as they work through problems to encourage making sense of problems and persevering:

  • What is your plan for solving the problem?
  • How would you describe the problem in your own words?
  • What is the question you are trying to answer?
  • What information do you have that can help you answer the question?
  • What other information do you need to answer the question?
  • Where might you get that information?
  • What other questions do you need to answer before you can answer this one?
  • How might you figure out the answers to those questions?
  • Does your answer or your strategy make sense? Try a different strategy to check your work.
  • How could you show the information in the problem a different way?

 

By Margaret Adams, Director of Curriculum, and Christina Cardella, Department Chair for Mathematics, Melrose Public Schools

Follow Melrose Curriculum on Twitter @MelroseCurricul

The purpose of the Melrose Public Schools Parent Connection is to help provide parents information on the school programs related to the curriculum and instruction. We also hope to share ideas and strategies for parents to use at home to strengthen home and school connections.

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