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

1. 音乐是愉悦人的心灵体验从没有意识到它计数计数。

2. tyqvpksbzxyqlmkrqqmdzblwp

3. tuafingpokintoobuptialocatys

4. treerunverbmatbounddormantowlspiressinceritydutch

5. Musicisthepleasurethebraingetsfromcountingwhenitdoesntknowitiscounting

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

o’clock?

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 you’ve

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 student’s 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