Proof in mathematics challenges students to extend their prior learning through precise mathematical reasoning. This is often achieved through the use of algebraic notation to generalise nonspecific cases.
An example of differentiating with proof could be:
One of the things that I like most about mathematics is its continuous nature. Linking various aspects together often serves to consolidate the student’s understanding of each topic while adding depth to the learning objective
An example of differentiation by working the problem in reverse could be:
Applying a simple concept to a series of more challenging questions can increase the pace and challenge of a lesson. Students can use the success criteria of a lesson to create a series of questions for their peers to attempt. The person who created the questions would later mark and feedback to their partner who attempted to solve them.
Whether its angle geometry, ratio or algebra mathematics is full of patterns. Learning to look for them and understanding their origins is key to a deeper level of understanding. They illustrate how all of mathematics is connected and can be generalised.
Some examples could be:
How do you differentiate in a maths lesson?
Comments and ideas are very welcome.
When calculating instantaneous rates of change students need to visualise the properties of the gradient for a straight line graph. I use the starter activity to see if they can match four graphs with their corresponding equations. The only clue is the direction and steepness of the red lines in relation to the blue line […]
Fractions, decimals and percentages are ways of showing a proportion of something. Any fraction can be written as a decimal, and any decimal can be written as a percentage. In this blog I discuss how to use the place value table and equivalent fractions to illustrate how fractions, decimals and percentages are connected. You can […]
In my experience, students, in general, find the concept of a mean straightforward to calculate and understand. However, the mean alone does not provide a complete picture of a set of data. To achieve this, a measure of spread is also required. The range is the simplest measure that can be used for this. Not […]