NUMERACY NINJAS
William Emeny
Head of Maths and Leading Practitioner
Wyvern College
+70%(AT LEAST)
Gains in mental numeracy strategies
and key skills important for
accessing GCSE Maths
WORKING MEMORYVS
LONG TERM MEMORY
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You can work around working memory capacity by having sophisticated schemas in long term memory
WHICH TOPICS SHOULD WE
CONCENTRATE OUR EFFORTS ON IN
MATHS, ENSURING STUDENTS HAVE THEM
STORED IN LONG-TERM MEMORY?
SHOULD WE PRIORITISE?
ARE SOME TOPICS MORE
IMPORTANT THAN OTHERS? I.E.
ARE THEY CONSISTENTLY WORKING
MEMORY BARRIERS TO LEARNING?
PRIOR LEARNING DEPENDENCIES
ANALYSIS
58% of topics on the
maths GCSE rely on the
timestables
45% rely on addition and
subtraction
Numeracy fluency is
critical
We redesigned our KS3
to focus on the top nodal
topics to ensure our
students were highly
fluent in these by the
time they started
studying GCSE maths
The big messages
HOW FLUENT WERE WYVERN COLLEGE STUDENTS IN THE
NODAL TOPICS AND MENTAL
CALCULATION STRATEGIES THAT UNDERPIN THEM?
QUICK KEY DIAGNOSTIC TEST
NUMERACY DIAGNOSTIC TESTING
Examples of what we found:
KS2 L4.7 63% (8 sec)
? + 32 = 100
KS2 L5.0 67% (15 sec)
77 + 50
KS2 L6.0 62% (15 sec)
3 + 3 + 3 + 3 + 3 has a value the
same as
53
5 + 3
3 X 3
35
5 X 3
KS2 L5.3 68% (20 sec)
12:42pm. How many mins to 1
oclock?
Examples of what we found:
KS2 L5.0 57% (8 sec)
6 X 8
KS2 L4.0 22% (8 sec)
6 X 8
KS2 L3.0 0% (8 sec)
2 X 7
Examples of what we found:
KS2 L6.0 19% (20 sec)
KS2 L5.7 25% (15 sec)
3 + 2 X 5
KS2 L5.0 57% (15 sec)
27 1000
KS2 L4.0 17% (15 sec)
Write 3/12 in its lowest terms
EVERY STUDENT IN THE YEAR GROUP
HAD AT LEAST ONE BASIC NUMERACY
GAP
HOW DO WE GO ABOUT TEACHING
THESE SKILLS AS EFFICIENTLY AS
POSSIBLE TO BUILD STUDENTS FLUENCY?
Growth in storage and retrieval strengths during a retrieval event
Retrieval
strength
Storage
strength
Growth in storage strength is
negatively correlated with current
retrieval strength.
The more something is automatic,
the more difficult it is to gain a
deeper level of understanding.
Make recall effortful. Limit growth in
retrieval strength whilst storage
strength is growing.
Growth in retrieval strength is
positively correlated with current
storage strength.
The deeper something is learned, the
faster it comes back after youve
forgotten it.
Rapid and sustained progress is
oxymoronic
Forgetting is a friend of learning
BJORK-IN ORDER TO REACH BOTH HIGH SS AND RS YOU MUST
LIMIT GAINS IN RS.
USE DESIRABLE DIFFICULTIES
S P A C I N G
INTERLEAVING
DOUG ROHRER- THE SHUFFLING OF MATHEMATICS PROBLEMS IMPROVES LEARNING
2 problems 2 problems Test1 wk 1 wk
Spacers
Over-learning is a waste of time if
you want learning rather than
performance
4 problems Test1 wk
Massers
2 problems Test1 wkLight
Massers
Filler task
Filler task
1 wk
1 wk
DOUG ROHRER- THE SHUFFLING OF MATHEMATICS PROBLEMS IMPROVES LEARNING
In-lesson visible progress (performance) is often a poor proxy for learning
BJORK-I CAN TEACH A COURSE THAT GETS THE HIGHEST STUDENT
RATINGS. I CAN TEACH A COURSE WHERE I DO
EVERYTHING I KNOW HOW TO MAXIMISE STUDENTS
RETENTION AND TRANSFER OF THEIR LEARNING.
THEY ARE DIFFERENT COURSES
2000+ SCHOOLS USING NINJAS
2000+ SCHOOLS USING NINJAS
1800+ schools using Ninjas worldwide
1800+ schools using Ninjas worldwide
1800+ schools using Ninjas worldwide
NUMERACY NINJASIMPACT STUDY
Year-long study with 470+
KS3 students
IMPACT STUDY DESIGN
3 cohorts
C1 NA. Control group (in Y7)- no Ninjas. 233 students
C1 NN. Used Ninjas (in Y8). 248 students
C2 NANN Used Ninjas (in Y7) 241 students
Diagnostic numeracy testing at start and end of
academic year
Sampled every students Ninja Score once per week
IMPACT STUDY RESULTS
IMPACT STUDY RESULTS- KS2 LEVEL 4 STUDENTS
IMPACT STUDY RESULTS- NINJA SCORES OVER TIME
Rise for approx. 10 weeks then plateau but later rise
Need to be very diagnostic to move scores on once plateau
CONCLUSIONS
Ninjas has been a transformative intervention to
improve students mental fluency of important
numeracy skills
Particularly effective on KS2 L4 and below students
After 10 weeks make sure teachers are using very
diagnostically
Spaced learning and interleaving research can be
applied successfully in secondary maths pedagogy
NUMERACY NINJAS-NEXT STEPS
Visiting Prof Bjork at
UCLA in California for a
week of collaborative
working this summer
looking at optimising
spacing and interleaving
techniques in secondary
maths pedagogy
Video tutorials for
students to
independently learn from
explaining each individual
Ninja skill
