By Charles Bird, John Hutchison, Mamadou Kante
Read Online or Download Beginning Bambara An Ka Bamanankan Kalan: With Bambara-English Glossary (English and Bambara Edition) PDF
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Extra info for Beginning Bambara An Ka Bamanankan Kalan: With Bambara-English Glossary (English and Bambara Edition)
Limitations of approach There is a tendency to think additively, followed by tendency to assume linearity as students get older. There is a need to understand either the algebra or the situation well in order to connect the two and evaluate predictions. Students tend to make ad hoc decisions that do not extend mathematical knowledge. There is no need to manipulate or simplify expressions or transform equations as the modelling software will do that. Students tend to join up data points without considering whether the same relation applies across the whole domain, and without considering what happens at zero on the horizontal axis.
Algebra is needed to describe and predict, so students appreciate its power. Real phenomena can be used. Algebra has a purpose and students can relate empirical experience to formal mathematics, maybe controlling a spreadsheet to store and predict events. Covariation can be expressed algebraically and graphically. The formal relations that underlie existing models, for example physical ‘laws’; traffic light systems; savings accounts, can be understood. Dimensionality can be addressed and there is the potential to discuss rates of change, turning points, maxima and minima.
Older children might be encouraged to predict numbers by looking at the structures of the handshake patterns. This produces a formula (maybe in the form of spreadsheet instructions) which will work for any number of people – a new mathematical object. This formula can then become a focus for enquiry: How quickly do the numbers grow? Do we get zero for one person? Can we find the number of people who will take the number of handshakes over 100? and so on. Development through this kind of activity depends on repeated experiences, so that algebraic reasoning becomes one of several tools that teachers and students use in any mathematical context.