Increase responsibility for thinking and participation

Discussion --> Argument

Explainer --> Listener

Expectations placed on explainers and listeners on themselves and others

Think about why the approach we are taking facilitates the learning of students

Green --> Typical classroom where teaching is transference

Move up through discussion contexts

What are students doing in explaining role, clarify, defend justify solutions

Students should be comparing and contrasting solutions, think about questions, ask them

Students should disagree and challenge

Rather than recall --> comparing and contrast - higher order thinking

Development of solution

Problem posing and solving

Students formulate their own questions

Investigation --> multiple pathways

CONJECTURE: Have you noted down observations and formulated an idea?

Note down observations

CHECKING: Does the conjecture hold for all known cases based on evidence?

Check the diagrams

TEST: Disprove the conjecture

Polygons are all convex --> midpoint figures for crossed and concave polygons

Make prediction on 6 7 8 side polygons

Modify conjecture to test of crossed or concave polygons

Every convex polygon has N sides

Each sides has one midpoint

Hence there are n midpoints

if N midpoints are joined in line segments, the convex polygon constructs a midpoint figure with n vertices

All segments joining must lie inside the convex polygon

No two of them can join at a straight angle