There were a few interesting points given in the readings. The semiotic systems, dense sentences and ‘mathematish’ used in the mathematics classroom have areas of concern for me.
The semiotic systems used in mathematics such as graphing, equations and diagrams are not very well connected in the classroom. Students often do not understand the significance of graphing say y = x +2. I feel that the lack of connectedness makes it difficult for students to see the connection between these two semiotic systems. A graph illustrating the exponential dissipation of heat for example could help students make this connection. A graph illustrating the dissipation of heat of coffee in a mug could be converted into an equation. Students then can see how long it takes for their coffee to be half its original temperature or have a discussion about how the function never touches the time axes or could work out it’s temperature after ‘x’ seconds.
Dense sentences make written proofs confusing for students. In teaching students I am hesitant to put a written proof up because it seems that it only makes everything more confusing. I feel that it is better to discuss an important concept and then put the written proof up. After this discussion students have a chance to understand the meaning of the written proof.
The ‘mathematish’ used by teachers in the classroom can cause problems. For example the equation ax + by + c = 0 is always written in this form but not in the form xa + yb + c = 0. I feel that students need to understand why teachers write this equation in this order. These reasons are often only to present information in a visually pleasing way. When students explore other ways of writing out such equations they will understand why mathematical writing has such a set style.
Semiotic systems, dense sentences and ‘mathematish’ can cause problems for students only because it is so difficult for teachers to pass on their tacit knowledge to students.
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