Reasoning In Mathematics

Hi there. In this math & education post, I would like to talk about the importance of reasoning in mathematics. I do think that a lot of (early) math education focuses too much on numbers, computations, number drills and the like. There should be more emphasis in explaining answers on top of answering questions.

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Being Able To Explain Answers

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Explaining answers is not just limited to mathematics. In a lot of subjects, it is important to explain answers, ideas and viewpoints verbally and in writing. In mathematics education, I think that there is a large emphasis in problem solving, algebra and number computations. There may be a few good teachers out there that try to have students explain math concepts verbally through presentations or in writing through assignments and short answer questions.

As an extension those who are good in explaining technical concepts verbally and in writing to less technical audiences could thrive in fields such as teaching, consulting, coaching and even in the legal field.

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Examples Of Math Reasoning

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Why Is A Rectangle Not A Square?

This question is a common question for young math students when it comes to learning basic geometry. Both shapes has four right angles and opposite parallel sides. The rectangle cannot be a square as all four sides of the rectangle are not the same. All the sides of the square are of the same length.

 

Order Of Operations Case

Bob has an order of operations (BEDMAS) algebra expression to simplify

Bob obtains an answer of 16. Is Bob correct? Explain your answer.

 

Bob's answer is incorrect. The answer here is not 16. From order of operations the first step is multiplication before subtraction and addition. This first step would be 3 x 7 = 21 which would yield

 

The next steps now is six minus 21 plus 2 which would be negative 15 plus 2. The actual answer is negative 13.

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Extension - Math Proofs

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At the higher levels of mathematics (university), mathematics is more theoretical. It is more about ideas, structures, systems, applications along with philosophy. Every math major at university/college will have some sort of exposure to math proofs through an introductory course of real analysis. After that course, students can choose if they want more theoretical math in the form of pure mathematics or choose mathematics branches that have more real world applications.

Reasoning in math proofs is much more detailed and precise. Definitions are much more technical and it is difficult for many to clearly communicate their written work. Sometimes a single sentence in a proof may require multiple rereads and thinking to fully understand it.

 

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Thank you for reading.