Language Pitfalls and Pathways to Mathematics
The point was usefully made in the reading that teachers can assist students in thinking through problems by modelling the Mathematical processes involved themselves. In this way teachers are able to scaffold problem solving skills by asking the questions needed to solve the problem rather than simply giving the students the answers they want. Eventually students will ideally go through the process themselves, with teacher questions (”what do we know?”, “what are we trying to find?”) used as prompts.
The use of correct and precise Mathematical language is also a good suggestion made, so that students are used to terminology and are not confused with commonplace language more familiar to non-mathematical settings. I think it is just as easy for students to understand what an integer is rather than ‘positive and negative numbers’.
Again the authors point out some common student misconceptions that have been a feature of the required readings so far in the course. These possible student errors are things we as teachers will benefit from being aware of.