Feb 252010

I think the following entry from WikiPilipinas needs revising. “Learning of facts”? Check also the last statement. “Teaching for understanding” is the main tenet of UbD. In this framework, course design, teacher and student attitudes, and the classroom learning environment are factors not just in the learning of facts but also in the attainment of an “understanding” of those facts, such as the application of these facts in the context of the real world or the development of an individual’s […]

Feb 162010
Teaching combining algebraic expressions with conceptual understanding

In Math investigation about polygons and algebraic expressions I presented possible problems that students can explore. In this post, I will share some ideas on how the simple investigation of drawing polygons with the same area can be used as an introductory lesson to teach operations with algebraic expressions with meaning and understanding. Like the rest of the lessons in this blog, this lesson is not so just about learning the math but also making sense of the math and engaging students […]

Feb 122010
Math investigation lesson on polygons and algebraic expressions

Understanding is about making connection. The extent to which a concept is understood is a function of the strength of its connection with other concepts. An isolated piece of knowledge is not powerful. To understand mathematics is to make connections among concepts, procedures, contexts. A lesson that has a very good potential for learning a well-connected mathematical knowledge is one which is organized around a mathematical investigation. This is because of the divergence nature of this task which revolves around a single tool […]

Feb 122010
swimming, math, and life

Just like one learns to swim by swimming, one learns math best by doing math.       But unlike swimming where the swimming style one learns is NOT a function of the type of water one swims on, the style of mathematical thinking and communicating one learns is a function of the mathematical tasks one engages in. Like learning mathematics, one learns about life by engaging with it. The quality of one’s life is a function of the relationships […]

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