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Making Sense of the Problem by Using a Solving Structure  

Metacognition and deep conceptual understanding are both needed in order to consistently answer word problems correctly. Math practice #1 - Make sense of problems and persevere in solving them - is a mindset used to help students on their path toward solving word problems correctly.

There are many different types of structures used to help students unpack the context surrounding a word problem - tape diagrams, numbers bonds, and organized sketching - to name and few and all students deserve the time and space in the classroom in order to find and use the type of structure that makes the most sense to them.

 

Using a variety of models in your teaching fosters algebraic thinking in many ways

  • Making sense of more complex problems

  • Thinking about the information that is present 

  • Thinking about the information that is missing

  • Looking for similarities and differences 

  • Making Connections

  • Focusing on change

  • Explore the different concepts of a variable

Examples of Structures used to make sense of word problems 

Tape Diagram

Number Bond

Part-Part-Total

Researchers Swee Fong Ng and Kerry Lee, in their study on The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems (2009) explore this idea of using a specific structure when attempting to solve word problems and argue that no matter the specific name for a diagram that is used, children go through and between three phases of word problem solving.

 

Below, I have developed a figure which synthesizes the thinking presented in this study.

 

 

 

 

 

 

 

While not explicitly stated, Phase one seems to draw from the 3-reads Protocol developed by the San Fransisco Unified School District and helps a student engage with a word problem for an extending period of time.

Metacognition within Phase One could be further extended by having students act out each chunk of information and then put all the pieces together to create a story.

 

Taking the time to develop deconstruct and reconstruct will also increase student access to the problem at hand as the class will have the time and space to talk about and create a shared concept image of the mathematics involved. 

Phases of Word Problem Solving

Ng, S. and Lee, K. (2009). The Model Method:Singapore Children’s Tool for Representing and Solving Algebraic Word Problems.

    Journal for Research in Mathematics Education, 40 (3),282-313.