Reasoning and sense making. Reasoning and Proof Process Standards

W. Gary Martin & Lisa Kasmer
Reasoning and sense making

What is reasoning and sense making? Essentially, it is learning. Learning is an active process; data is imputed into the mental machine, processed and filed away with all the other data, according to its type. Students learn how to make sense of new data, new material by an active reasoning process. It is the process of breaking large pieces of information down into manageable pieces, reassembling the information, assessing the intended computation and working through the problem to reach an answer. Students need to challenge the question, they need to challenge the answer, and they need to challenge each other. It is essential that students learn how to talk about math. It is essential that students learn how to defend their ideas. Students are naturally curious and endless worksheets do not foster that curiosity. Students who are taught in this way are given the foundation for advanced problem solving and creativity, skills that are important not only in high school and college but in the world, as they enter the job force. A teacher can create this type of atmosphere by making students feel comfortable. Students have to feel that they can make mistakes. The teachers must learn the right questions to ask.

Consider a specific example: the teacher asked the student to work through a word problem on subtraction. The students were permitted to use any subtraction process they liked. One of the students decomposed the numbers in the problem before subtracting. The teacher and students asked questions about how and why the student worked through the problem and she, the student, was very comfortable and eloquent in defending her choice. This is wonderful example of a classroom where mathematical reasoning is used and questions are encouraged.

Martin, W. G. and Kasmer, L. (2010). Reasoning and sense making. Teaching children
mathematics 16(5), 284-291.