Jul 282010
 
Teaching the properties of equality through problem solving

I like to teach mathematical concepts via problem solving. It right away engages students mind. It creates a need for learning a more systematic way of doing things and hence a reason for learning the concept. It provides a context for making connections. Most important of all, it gives students opportunity to learn before they are taught. One of the ways of creating a problem solving task for this kind of lesson is to start by giving the solution/answer.  For [...]

Jul 272010
 
Properties of equality - do you need them to solve equations?

Should students learn the properties of equality before we ask them to solve equations in one variable? Would it be too hard for them to solve the equation 2(x + 7) = 4x without knowing the properties of equality? In the grades, pupils learn to find equivalent ways of expressing a number. For example 8 can be written as 4 + 4, 3 + 5, 4 x 2, 10 – 2. Now, what has the pupils previous experience of expressing [...]

Jul 262010
 

Whit Ford left this comment on my post Curriculum Change and Understanding by Design: What are they solving? He makes a lot of sense. I just have to share it. I believe the method of planning lessons is less important than WHAT you are asking the students to think about. Most Algebra I and II texts I have come across suffer severely from “elementitis” (see “Making Learning Whole” by David Perkins), which makes it very challenging for teacher to convey [...]

Jul 182010
 
Patterns in the tables of integers

Mathematics is said to be the science of patterns. Activities that involve pattern searching is a great way to engage students in mathematical thinking. Here are some of my favorites for teaching positive and negative integers. If you are wondering why most of my posts are about integers it’s because I’m doing a Lesson Study with a group of Mathematics I (Year 7) teachers about this topic. Last week we concluded the first cycle of our research lessons on teaching [...]

Jul 162010
 
Technically, Fractions are Not Numbers

It is misleading to put fractions alongside the sets of numbers – counting, whole, integers, rational, irrational and real. The diagram below which are in many Mathematics I (Year 7) textbooks is inviting misconceptions. Fraction is a form for writing numbers just like the decimals, percents, and other notations that use exponents and radicals, etc. The fraction form of numbers is used to describe quantities that is 1) part of a whole, 2) part of a set, 3) ratio, and [...]

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