A popular approach for teaching numbers is to use it to describe a property of an object or a set of object. For example, numbers are used to describe the amount or quantity of fruits in a basket. In introducing integers, teachers and textbooks presents integers as a set of numbers that can be used to describe both the quantity and quality of an object or idea. Contexts involving opposites are very popular situations to show the uses and importance [...]

To teach for conceptual understanding requires assessing for conceptual understanding. The principles that guide teaching for understanding must be the same principles that should guide assessment. What are some of these? Open-ended, problem solving tasks To teach for conceptual understanding, it is not enough that students engage in problem solving task. The tasks should be (1) open-ended which means that it can be solved in many ways using a range of concepts; (2) accessible, that is , not too easy [...]

A lot of online resources on integers are about operations on integers especially addition and subtraction.  Most of these resources  show visual representations of integer operations. These representations are almost always in the form of jumping bunnies, kitties, frogs, …  practically anything that can or cannot jump are made to jump on the number line. Sometimes I wonder where and when in their math life will the students ever encounter or use jumping on the number line again.  If you [...]

I have so far written three posts about understanding by design. The first is about my issues about DepEd’s adoption of understanding by design (UbD), the second is about the information posted about UbD Philippines in WikiPilipinas and the third is about curriculum change and UbD. These posts are very popular especially for readers from the Philippines. This is understandable as our Department of Education wants teachers to implement UbD this June 2010, barely two months from now. I don’t [...]

This is my third post on constructing test items based on TIMSS Assessment Framework. My first set of examples is about assessing understanding of zeros of polynomial function and the second post is about graphs of rational functions. Of course there are other frameworks that may be used for constructing test item like the Bloom’s Taxonomy. However, in my experience, Bloom’s is not very useful in mathematics, even its revised version.  The best framework so far for mathematics is that [...]