Assessing mathematical thinking for
KS1, KS2 and KS3 teachers
Education Show 2016
An ATM presentation
Heather Davis
Why do we assess?
To find out what learners know
for
teaching them so they know more
and
giving ‘others’ information so …
Assessing whilst learning
A rich task:
• avoids dead time on tests
• allows learners to show process skills
• encourages independent use of content
• gives opportunities to enhance progress
• differentiates
• develops mathematical thinking
• allows teachers to assess thinking
What do
you notice?
Write down, in order, some consecutive
numbers.
Choose either addition or subtraction
to put between each number and the
next to make a calculation.
Work out the result.
Repeat for a different arrangement of
subtraction and addition, and for
different sets of consecutive numbers.
Why does
that
happen?
Investigate
further
Consecutive Integers
For your Key Stage/Year:
• What outcomes would you anticipate?
• What content is likely to be involved?
• What process skills are likely to be used?
• How can you move children on?
Consecutive Integers KS1
Y1 Read, write and interpret
mathematical statements
involving addition (+), subtraction
(–) and equals (=) signs.
Y1 Add and subtract one-digit and
two-digit numbers to 20.
Why does
that
happen?
What happens
if you add two
consecutive
numbers?
What happens if
you put a
subtraction sign
between the
numbers?
Consecutive Integers KS1
Y2 Recall and use addition
and subtraction facts to
20 fluently.
WM Recognise patterns in
numbers e.g. odds, evens.
Why does
that
happen?
What if you try
different sets of
three
consecutive
numbers?
What do
you
notice?
Consecutive Integers KS2
WM Reason mathematically
by following a line of
enquiry, conjecturing
relationships and
generalisations.
Notices that the answers
are always even and that
the - - + answer is always
zero, and attempts to
explain why.
Y4 Count backwards
through zero to include
negative numbers.
Calculates the remaining
three answers by counting
back through zero.
What do you notice about your
sets of answers for each set of
numbers? Why is that?
Consecutive Integers KS2
Y6 Use
simple
formulae.
Writes the
numbers
as N, N+1,
N+2, N+3.
WM Make, test and
justify conjectures in
respect of patterns and
relationships.
Y6 Enumerate
possibilities of
combinations of two
variables.
Call the first number
of the four
consecutive numbers
N, and write
formulae for the
others using N.
Develops an argument that may
involve some manipulation of
the algebraic expressions.
Lists all 16 of the arrangements
of + and – signs.
Consecutive Integers KS3
WM Begin to
reason deductively
in algebra.
Use and interpret
algebraic notation.
Why do some of the
arrangements give
the same answer
each time?
Identifies that the expression for the
arrangements with two – operations do
not involve n so always give the same
answer.
WM Look for
proofs or counterexamples.
What
else do
you
notice?
Notices that the expressions
for the other calculations are
identical to the nth terms.
In the classroom
Be realistic about what learners can reach
without support but prompt rather than hint.
Learners may not think of calling the first
number N but they can work out an expression
for the next number (N+1)
In the classroom
Hints remove the opportunity for learners to do
it for themselves.
Work done in response to hints does not suggest
confidence and competence (mastery) with the
material.
Without any intervention (prompts) learners
may make no progress.
In the classroom
How can you best use what the learners have
done in this task for assessment?
Prompts follow immediate assessment of the
need for them.
What could you record?
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