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# Tag Archives: mathematics

## On mathematics

Mathematics is regarded as a demonstrative science. Yet this is only one of its aspects. Finished mathematics presented in a finished form appears as purely demonstrative, consisting of proofs only. Yet mathematics in the making resembles any other human knowledge … Continue reading

Posted in education, logic, mathematics, mathematics education, quotes
Tagged education, induction, mathematics, plausible, polya, reasoning
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## Unreal and Useless Problems

We had previously talked about problem with contexts given in mathematics problems. This is not new, Thorndike in 1926 made similar observations. Unreal and Useless Problems In a previous chapter it was shown that about half of the verbal problems … Continue reading

Posted in children, education, mathematics, mathematics education
Tagged didactics, education, mathematics, psychology, word problems
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## Dialectic vs Algorithmic Mathematics

Dialectic mathematics is a rigorously logical science, where statements are either true or false, and where objects with specified properties either do or do not exist. Algorithmic mathematics is a tool for solving problems. Here we are concerned not only … Continue reading

## On not learning or con in the context

We will, we will, fail you by testing what you do not know… We live in a rather strange world. Or is it that we assume the world to be non-strange in a normative way, but the descriptive world has … Continue reading

Posted in education, mathematics, mathematics education
Tagged critique, education, mathematics, philosophy, research
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## What is a mathematical proof?

A dialogue in The Mathematical Experience by Davis and Hersh on what is mathematical proof and who decides what a proof is? Let’s see how our ideal mathematician (IM) made out with a student who came to him with a strange … Continue reading

Posted in education, mathematics, mathematics education
Tagged mathematical ideas, mathematics, norms, proof, teaching
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## Implicit cognition in the visual mode

Images become iconified, with the image representing an object or phenomena, but this happens by enculturation rather by training. An example to elaborate this notion is the painting Treachery of Images by Belgian surrealist artist René Magritte. The painting is also … Continue reading

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Tagged cognition, education, graphicacy, learning, mathematics, science, visual
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## Mathematical Literacy Goals for Students

National Council of Teachers for Mathematics NCTM proposed these five goals to cover the idea of mathematical literacy for students: Learning to value mathematics: Understanding its evolution and its role in society and the sciences. Becoming confident of one’s own … Continue reading