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 Wow, what a great article by Jamison; far and away the best so far. He has such an easy way of describing the problems that math teachers need to consider, and how he himself deals with them.  

Overall the purpose of teaching mathematics is to teach reasoning and analytical thinking through intellectual discipline. To get there, students must go through two stages of mathematical development. Firstly the school-based “plug and chug” where students just plug in numbers to a formulas to get correct answers, and secondly, the quantum leap in thinking to a proof and argument level of thinking and expression. Unfortunately students typically do not develop to this higher level of expression.

 A great insight was the fact that students look for hidden assumptions in math problems, however there are none due to the exacting nature of mathematics. Students are so conditioned with everyday English with deciphering its ambiguities that this is transferred to their reading of math problems, and they create their own misconceptions just by looking for hidden meaning which does not exist. The clarity and precision of maths becomes a stumbling block to them.  “One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts”         – Albert Einstein   

Teaching and learning maths requires language to be used as a tool which requires just as much precision as the written expression. Students need to learn the “language of maths” with its rules of interpretation just as if it is another language and so many students fail to grasp this. Everyone loves Einstien but even Albert Einstein was a notorious underachiever as a child. At the age of 16 he failed the entrance examination which would have allowed him to study for a diploma as an electrical engineer. Quoted as saying “Do not worry about your difficulties in mathematics, I assure you that mine are greater.” So even the greats have struggled. It is encouraging that in 1900 Einstein eventually graduated as a teacher of mathematics and physics.

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