Turning stumbling blocks into building blocks.
These resources give ideas for addressing common misconceptions. They are free to download and adapt.
Each section address a key concept in mathematics that is an important building block for many other topics.
The minus sign
The minus sign is a potential minefield of misconceptions because it has so many different meanings. The meaning can even change part way through a problem!
Further reading and examples
Base Blocks
Base blocks are a powerful tool to explore the structure of the base system from base 2 to base x. This deepens students understanding of base 10 and can be used to address misconceptions with the four operations. It is also an excellent introduction to manipulating algebraic expressions using algebra tiles.
The ideas in this section are inspired by Exploding Dots adapted from https://www.explodingdots.org/ by James Tanton.
This version stacks counters rather than exploding dots. This exposes the exponential growth of different bases.
The same concept can be applied using multi link cubes exposing the geometrical structure of the base system.
Mathsbot has an easy to use set of interactive Dienes blocks in different bases.
More coming soon …