Tag Archives: angles

Reasoning abilities and conceptual knowledge needed for learning calculus

This post describes foundational reasoning abilities and mathematical knowledge students need to develop before beginning a course in calculus. Covariational reasoning – this involves recognition of two quantities that are changing together. A student who considers how two quantities in a dynamic situation change together is said to be engaging in covariational reasoning. This is… Read More »

What is variation theory of learning?

Variation theory of learning was developed by Ference Marton of the University of Gothenburg. One of its basic tenets is that learning is always directed at something – the object of learning (phenomenon, object, skills, or certain aspects of reality) and that learning must result in a qualitative change in the way of seeing this “something” (Ling & Marton, 2011).… Read More »

Embedding the idea of functions in geometry lessons

GeoGebra is a great tool to promote a way of thinking and reasoning about shapes. It provides an environment where students can observe and describe the relationships within and among geometric shapes, analyze what changes and what stays the same when shapes are transformed, and make generalizations. When shapes or objects are transformed or moved,… Read More »

Mistakes and Misconceptions in Mathematics

Misconceptions are very different from the mistakes students make. Mistakes are not consciously made. Misconceptions are. Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps. Mistakes are made by a few, misconceptions are made by many and, repeatedly. Students can figure out their mistakes by themselves because mistakes are usually due to… Read More »

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