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  • 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.

    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

    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

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