Questioning techniques
to challenge all learners
at A level
Mohammed Basharat
Nick Thorpe
1730-1830 Thursday 25th June 2015
While we are waiting….
Change one coefficient of the quadratic
𝑦 = 𝑥 2 + 6𝑥 + 8
so that the graph touches the 𝑥-axis
Watson and Mason ( 1998)
1. Change one
aspect of ….
so that …
Change one aspect of……so that…..
Change one coefficient of the quadratic
𝑦 = 𝑥 2 + 6𝑥 + 8
so that the graph touches the 𝑥-axis
Change one aspect of
1
(2𝑥
0
Change one aspect of
2
−1
𝒓 = 3 + 𝑡 1 so the line
1
2
intersects one of the axes.
+ 3)𝑑𝑥 = 0 so it is true.
Time for you to…
Think about these
questions and/or try and
design your own question
using this question stem.
GeoGebra input:
(x - a)² + (y - b)² = r²
Change
1
(2𝑥
0
GeoGebra input:
+ 3)𝑑𝑥 = 0 so it is true.
Integral[a x + b, c, d]
Change one aspect of
2
−1
𝒓 = 3 + 𝑡 1 so the line
1
2
intersects one of the axes.
GeoGebra input (3D view):
Line[(a, b, c), (p, q, r)]
Time for you to…
Think about these
questions and/or try and
design your own question
using this question stem.
2. Give me
an example
of……
GeoGebra input:
ax+by+c=0
Give me an example of…
…a question involving simultaneous equations
with solution 𝑥 = 2, 𝑦 = −3
…a cubic curve with no stationary points
…a transformation so the image of
𝑦 = 𝑥 − 1 2 passes through (2,4)
…a function with (natural domain) 𝑥 > 0 and
range 𝑦 ≥ 0
3. What is the
same and what
is different
about ….
The actions of comparing and contrasting force us to think
about the properties of mathematical objects and students may
make connections they might not normally consider. They are
prompted into mathematical thinking processes such as
generalising, conjecturing about what stays the same and what
can change (called ‘variance’ and ‘invariance’), and then
verifying these conjectures.
What is the same, and what is different about…
…𝑦 = f 𝑥 , 𝑦 = f( 𝑥 ) and 𝑦 = f(𝑥)
…𝑥𝑛+1 =
𝑥𝑛 +1
, 𝑥1
2
= 5 and 𝑦𝑛+1 =
𝑥𝑛 +2
, 𝑦1
3
=5
…the roots of f 𝑥 = 0 and f 𝑥 + 2 = 0
…summing an arithmetic series and the area of
a triangle.
Preparing the learning
Environment
“Everyone gets stuck. It
cannot be avoided, and it
should not be hidden. It is an
honourable and positive
state, from which much can
be learned.”