The discriminant of a quadratic equation, ax2 + bx + c = 0 is D = b2 – 4ac. If D>0, the quadratic equation has two distinct roots; if D<0, then the equation has no real roots; and, if D=0, the we have two equal roots. Let’s apply it in the following problem. Continue reading “Application of the Discriminant”
Types of Problem Solving Tasks
The phrase ‘problem solving’ has different meanings in mathematics education. Even its role in mathematics teaching and learning is not clear cut. Some view problem solving as an end in itself. Others see it as starting point for learning. Nevertheless, here are some of the types of problem solving tasks we would see in textbooks and teaching. They are arranged according to cognitive demand. Remember that learners will only consider something a problem if they experience some sort of barrier in a situation they are curious about. There’s a difference between an exercise and a problem. Continue reading “Types of Problem Solving Tasks”
When is it algebra and when is it arithmetic?
In the post Algebra vs Arithmetic, I distinguished between arithmetic and algebra by arguing that it has nothing to do with the use of letters. That algebra is about letters and arithmetic is about numbers is an oversimplified view of algebra and can create misconceptions. Here are more ways of characterizing algebra. Continue reading “When is it algebra and when is it arithmetic?”
Free Fractions Pamphlet
I just want to promote in this post James Tanton’s latest pamphlet on fractions. It’s FREE for download. Just click Pamphlet on Fractions. Tanton writes:
If fractions are pieces of pie, then what does the multiplication of fractions mean? (You can’t multiply pie!)
If fractions are proportions, then what are their units? Amount of pie per student (and not just pie)?
If fractions are points on the number line, then what does half a pie mean?Fractions are slippery and tricky and, in the end, abstract. It is actually unfair to expect students to have a good grasp of fractions during their middle-school and high-school years. This pamphlet explains why, and offers the means to have an honest conversation with students as to why this is the case. Their confusion and haziness about them is well founded!
What do you say about the statement I highlighted above? What a relief to know that? 🙂
I highly recommend that you also checkout his collection of past MATH ESSAYS.
You may also want to read a couple of my posts on fractions: