Nov 172015
How to orchestrate mathematically productive class discussion

Show and tell activity (aka lecture method) may work for some but never in a mathematics class. Getting students to explain and ask questions are nice but only when the explanation and the questions are mathematical. Reasoning and justifying are good habits of mind but they are only productive if they are based on mathematical principles.  Explaining, asking questions, and substantiating one’s conjecture or generalization make a productive class discussion but they are only productive for learning mathematics if the […]

Oct 182015
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 a foundational way of thinking that is needed to construct meaningful formulas and graphs to model relationship in applied contexts. There are four mental actions […]

Jul 272014
What math can students learn from the way we teach algorithms?

It is a bunch of procedures. That’s how people perceive algorithms are. And they are right. Algorithm has been defined as 1) “step-by-step procedures that are carried out routinely”; 2) “a precisely-defined sequence of rules telling how to produce specified output information from given input information in a finite number of steps”. It is no wonder then that teaching algorithms is perceived by many as teaching for rote learning and produces not conceptual knowledge but procedural knowledge. Teaching algorithms promotes […]

Jun 012014
Teaching the Derivative Function to Grade 10

Most Grade 10 syllabus do not yet include the concept and calculation of derivative. At this level, the study of function which started in Year 7 and Year 8 on linear function is simply extended to investigating other function classes such as polynomial function to which linear and quadratics belong, the exponential function and its inverse, rational function etc. There is no mention of derivative. This should not prevent teachers from deriving functions based on the properties of the function students […]

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