Mathematics for Teaching Category: Teaching mathematics

Category: Teaching mathematics

What is reasoning? How can we teach it?

The world does not give us complete information that’s why call on our power of reasoning to complete this information the best we can and produce new knowledge.  Mathematics is one of its most famous product. What is reasoning? When do we learn it? Reasoning is defined as  the capacity human beings have to make sense…

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What is the role of visualization in mathematics?

Like abstraction and generalization which I described in my earlier posts here and here,visualization is central to the learning and understanding of mathematics. (Note that these processes are also natural human mental dispositions and so we can claim that doing mathematics is a natural human activity.) Visualization used to be considered only for illustrating otherwise…

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Making generalizations in mathematics

Making generalizations is fundamental to mathematics. Developing the skill of making generalizations and making it part of the students’ mental disposition or  habits of mind in learning and dealing with mathematics is one of the important goals of mathematics education.  Making generalizations is a skill, vital in the functioning of society. It is one of the reasons why…

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Mistakes and Misconceptions in Mathematics

Misconceptions are very different from the mistakes students make. Mistakes are not consciously made. Misconceptions are. Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps. Mistakes are made by a few, misconceptions are made by many and, repeatedly. Students can figure out their mistakes by themselves because mistakes are usually due to…

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To understand mathematics is to make connection

I’m sharing in this post some of the “theories” underpinning the lessons, learning tasks, and math teaching ideas that I blog here.  This is part of the literature review of my dissertation titled “A Framework of Growth Points in Students Developing Understanding of Function”. If you are a researcher and wants to see the references,…

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