Structured Exploration, Proactive Self-checking

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.

Structured Exploration

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.  Proactive Self-checking

Here are three levels of marking:

1. 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.
2. 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
3. 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. Desmos doesn’t have that weird kink in the line – what have I done wrong? The line on Desmos is going up but mine is horizontal – something is wrong!

This is a bit obvious, no real links made. How about encouraging the use of area models to check expanding brackets? I might use a more efficient method to calculate, but by using this method to check I am constantly reminded of the link

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! 2x + 5 = 3 has a solution at x = -1

How about using pictures to make sure you can simplify expressions? I don’t know what I have done wrong, but at least now I know I need to ask a peer for help!

Think about providing structured exploration for angle rules?

Design proactive self-checking for your next lesson?

Use this collection of exercises as an intro to Geogebra with your class?

Search the excellent Geogebra database or Teacher Desmos Site for ideas?

Try this challenge? 