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. What is the equation of the line tangent to f(x)=x2 at the point (2,4)? Solution using the idea of discriminant The function f(x) and the line y=mx+k [...]

If you’re a math teacher and are looking for fun ways to motivate your class or lighten the atmosphere, here are some great kids’ math games to help you along. Needless to say, the kids are definitely going to love them! Fun Kids’ Math Games – Fun Classroom Ideas for Teachers 1. Simple Mental Math Game Skills – Number sense, computational fluency Grade –1-5 Instructions: Ask the students to put away their notebooks and pens and pay close attention to [...]

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 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. The following excerpts is from Paper 6 – Algebraic Reasoning of Nuffield Foundation Math Education Report. The review of math education studies in the project was written by [...]

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 [...]