When I began to use Desmos and Geogebra in maths lessons, the tasks were lacking in structure. “Click on this link and have a play” I would say optimistically, hoping the students would be self-motivated enough to wonder and ask questions themselves. Varied success. Here are two first attempts at providing specific purposes for technology in the Maths classroom.
Simpy put: “Click on this link, have a play, and then do this subsequent exercise”. Allows teacher assessment, students given some (but not total) direction. Examples:
- Desmos has many excellent pre-existing exercises. For example, this one introducing coordinates.
- Using this app in geogebra, explore patterns in the angles of a triangle.
Here are three levels of marking:
- Teacher holds the answers, and marks herself. Teacher has good knowledge of student’s understanding, but the delay between question and feedback can be long, and this is time-consuming for teacher.
- Student is given the answers somehow (back of textbook, on a separate slide…) and passively checks their work against it. Immediate feedback, but often lack of cognitive depth in feedback
- Student works out the answer in a different way. This level encourages building of links between separate areas of maths, and allows the student to continually assess their progress. Let’s call it Proactive Self-Checking.
Here are some examples of proactive self-checking (do you think it is important enough to need capitalisation?):
When practising plotting points from an equation, students can compare their hand-drawn graph to a desmos graph.
This is a bit obvious, no real links made. How about encouraging the use of area models to check expanding brackets?
How about starting to understand simultaneous equations,to check that I solved any equation? If I am using bar modelling or the balance method to solve my equation, then being able to link the answer to a picture is deep stuff!
How about using pictures to make sure you can simplify expressions?
Your next steps:
Think about providing structured exploration for angle rules?
- Vertically opposite
- Angles on straight line
- Angles at a point
- Triangle, with no numbers
- Triangle, with numbers
- Triangle, a proof
- Quadrilatelal, no sum
- Quadrilateral, with numbers
- Quadrilateral with proof
Design proactive self-checking for your next lesson?
Use this collection of exercises as an intro to Geogebra with your class?
Try this challenge?