The Barriers to Learning Maths
www.stevechinn.co.uk
Overview
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This is a complex problem.
There will not be one solution.
The approach should always be multi-dimensional.
The many factors involved will interact and will interact differently between individuals
and, at different times, within the individual.
The spectrum of difficulties
Numeracy
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Michael Girling (HMI) suggested a definition of numeracy as:
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Basic numeracy is the ability to use a four function electronic calculator sensibly
Recent Evaluation
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He didn’t really highlight a good method, so I am left thinking that there is no ‘ideal’
method and that being aware of the deficits in a method is what is required.
Learning takes place in a relationship (Giocelli)
‘It’s more complicated than that’
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John Hattie. ‘Visible Learning’ 2009
Feedback: ‘it is the feedback to the teacher about what students can and cannot do
that is more powerful than feedback to the student, …’
(80% of feedback is from other students and 80% of that is incorrect.)
‘errors’ are welcomed and used as key levers for enhancing learning
Some of the factors
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#1
Visual and aural aspects
Directional issues
Sequencing demands
Short term memory/working memory
Long term mathematical memory
The vocabulary of mathematics
The language of mathematics
Organisation in space
Some of the factors
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Ben Goldacre
Speed of working
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#2
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Thinking style
The structure of the curriculum
The style of the curriculum
Anxiety, expectations, self esteem, risk taking
Motivation, attributional style
Categorising
Visual/Vision
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Can they see?
Does print/paper contrast/colour make a difference? (scotopic sensitivity)
Is the work cluttered?
Does the page look intimidating?
Is the font clear?
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
Are they visual learners?
Do they confuse symbols?
Subitizing and arithmetic skills
Fischer and Hartnegg 2008
Recognising or counting from visual memory a number of dots presented for 1/10
second
Lower capacity or children with problems in acquiring basic arithmetic skills
Subitizing and arithmetic skills
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Fischer and Hartnegg 2008
The basic visual capacity of subitizing and number counting can be improved by daily
practice. (Success rate 85%)
The training transferred to arithmetic skills (7 – 13 years)
Colour
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Screening:
Overlays:
Crossbow Education
Spoken vs Written
I asked a student, ‘What is half of 50?’
She replied ’25’
Later I showed her ½ x 50 written on paper.
She didn’t know the answer. I asked, ‘Is the answer bigger or smaller?’
She said ‘Yes’
Direction
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Counting backwards
Transposals….Hears ‘Fifteen’ writes 51
Two digit numbers 13
(1 2 3 4 5 6 7 8 9)
Decimal numbers… interaction with language
5348.435
Add, subtract, multiply….. then division
Direction and time
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Six twenty
6:20
Twenty past six
Twenty to eight...what do you need to know?
Quarter to eight…. Seven and three quarters
Ten to nine
8:50
Too much choice
#1
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We can now write the division operation in three ways…………….
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Read from left to right, ’12 divided by 3’
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12  3
Too much choice
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Read from top to bottom
’12 divided by 3’
12
3
Too much choice
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#2
#3
Read from right to left ’12 divided by 3’
3 )12
Sequencing Skills
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Recall/retrieval of sequential information
Numerical sequences
10, 20, 30…….
14, 24, 34……
Reversing the sequence
Interaction with stm
abcdeabcdeabcdea….. abc dea bcd eab
Fraction sequence.
‘Long’ division
Language sequence
Sequencing and place value
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Five hundred and six thousand and eighty
500,6000,80
6580
Short term/working memory
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Chunks of information
(instructions, copying, methods)
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Repeating information
Mental arithmetic
Written work
Overload
Link to thinking style
Sequential short term memory
(28 dyslexic, 27 non-dyslexic, Year 11, matched for predicted GCSE grades)
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‘Breakdown’ at 3, 4 and 5 items
75% dyslexics
48% controls
No. failures at first items
28 (16 students)
9 (7 students)
No. failures at last item
63 (23 pupils)
43 (21 students)
Correlation
Mathematical memory
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Quick retrieval of basic facts
Recall of procedures
Language, for example instruction words
Multi-sensory input
Secure knowledge
School Reports #1
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I am constantly having to prompt her to look at Mrs Smith and listen to her. She seems to
spend a lot of time rubbing out and sharpening her pencil!
Mrs Smith paces the lessons very well and Ellie should be able to follow what she is teaching.
I also feel that Ellie has become rather lazy from the point of view of always saying she
doesn’t remember how to do any maths processes. She will seem to have grasped a concept
yet the following lesson she will have forgotten it.
I am beginning to insist that she tries to remember how to do the work.
Organisation in space
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2x
x2
x2
1 1
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368
257+
625
Write today’s date in the middle of the page
Teacher-identified math weaknesses. Bryant, Bryant and Hammill, JLD, 2000
12th …. (out of 33)
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Orders and spaces numbers inaccurately in multiplication and division
13th ….
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Misaligns vertical numbers in columns
Vocabulary and language
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The power of first learning experiences.
The language of mathematics is not English as we know it.
Communication……. For all?
The flexible use of vocabulary
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Young girl from Belgium
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‘It’s cold today. It’s take away five degrees.’
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Speed of working
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Mental arithmetic
Slow to start work
Slow written work
Less experience
Impulsivity
Is this a necessary expectation?
Classroom study. Chinn. ‘95
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16 + 37 308 + 897
12.3 + 5 19.09 + 10.91 63 + 2.1
67 – 32 72 – 48 813 – 668 601 – 346
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37.6 – 4 21.003 – 2.114
5 x 6 5 x 60 33 x 20 44 x 21 25 x 202
2)39 6040  10 3)906 5)668 15)345
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(122 dyslexic pupils, 11-13, 8 schools)
(122 from upper sets of 9 mainstream schools)
Speed
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Dyslexic pupils
13.00 mins, SD 5.41
Mainstream pupils 8.50 mins, SD 3.41
Anxiety survey: Ranked 4th – 7th
Accuracy
Dyslexic pupils
10.1, SD 5.6
Mainstream
15.6, SD 4.1
Teacher-identified math weaknesses. Bryant, Bryant and Hammill, JLD, 2000
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Ranked 6th ….
Takes a long time to complete calculations
Thinking Style…. Later!!
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The Structure and Style of the Curriculum
It could be overly prescriptive…. Do it this way….. We spend five lessons on division and
then move on…. This term we are doing fractions.
Returns to topics could be too far apart.
There may not be sufficient time for review.
There may not be enough practice/reinforcement of ‘old’ ideas built into new topics.
It may be at the abstract/symbolic stage too soon.
TES April 3rd 2009
Emotions and Maths
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Research by Cambridge Assessment found that the better pupils were at expressing
their emotions, influencing other peoples’ feelings, networking, using social skills and
general social awareness, the worse their maths results were at GCSE
Anxiety and Expectations
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Anxiety impacts on short term memory
Avoiding risk.. ‘Never mind, you did your best.’
Where do expectations come from?
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Are ‘targets’ expectations? And is it possible to set the perfect target?
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Anxiety survey: 2nd – 4th Long division
Data and Scarfpin (1983)
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Mental block anxiety can be triggered by a symbol or a concept that creates a barrier
for the person learning maths.
Socio-cultural maths anxiety is a consequence of common beliefs about maths, such
as, if you cannot learn facts you will never be any good at maths
High Anxiety Items
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Taking an end of term maths exam
Doing long division questions without a calculator
Having to take a written maths test
Having to work out answers to maths questions quickly
Waiting to hear your score on a maths test
Dyslexic students
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Averaging all Year groups:
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Long multiplication without a calculator (#7)
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Learning the hard times table facts (#14)
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Hearing your score on a maths test (#15)
Attributional Style
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Permanent. ‘I’ll never be able to do fractions.’
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Pervasive. ‘I can’t do this division stuff. I can’t do any maths.’
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Personal. ‘I’m too stupid to do maths.’
Barriers to learning and attributional style
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Maths is judgmental. Right or wrong for a computation is down to the maths not to the
teacher’s judgment…. But the marks awarded are within the teacher’s control.
How many barriers will a learner experience before he says, ‘I just don’t get maths and I guess
I never will.’
Success
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Failure
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Specific
Universal
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Temporary
Permanent
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External
Internal
What do learners need to be good at maths? (Krutetskii)
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The ability for logical thought and the ability to think in mathematical symbols.
The ability for rapid and broad generalisations of mathematical objects, relations an
operations.
Flexibility of mental processes in maths
Striving for clarity, simplicity, economy and rationality of solutions
Being able to switch from a direct to a reverse train of thought
Mathematical memory
These components are closely interrelated, influencing one another and forming in
their aggregate a single integral syndrome of mathematical giftedness.
A Few Golden Rules
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Don’t create anxiety
Experiencing success reduces anxiety
Experiencing failure increases anxiety
Understand your students as individuals
Teach more than one way to do things
Remember where each topic leads mathematically
A few more….
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Understanding is a more robust outcome than recall
Try to understand ‘errors’… don’t just settle for ‘wrong’
Prevention is better than cure
Praise the work, not the learner
All the above rules have exceptions!
10 year old Australian boy
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“I am good at x + and – divide is sometimes hard. I would love to be a bit better at 
and x. If you want me to be better at maths you should show me a pattern in it like a
rhyme.
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I like maths when I get it right. I don’t like getting maths wrong. You should show me
how to get my errors right by giving me a strategy.”
At what age are you noticing poor motivation and anxiety in pupils doing maths lessons?
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79 responses
Age 5
8
Age 6
32
Age 7
30
Age 8
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Reasons:
(120 responses)
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Rate as: 1 minor
2 significant
3 major
Mental arith:
(116)
2.34
Memorising facts: (117)
2.56
Answering quickly: (118)
2.75
Writing up sums:
2.00
(113)
Other reasons
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Being asked to move on too quickly and not consolidating understanding of basics
Parental pressure and expectations
The change to ‘sit down’ maths
Peer pressure to be ‘normal’
Absence
Vocabulary and language
Other reasons….
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(Cumbria) ‘Having a child with S.N.s and being forced to change schools several
times, I’ve found the lack of awareness of teachers very concerning. Too quick to
judge children as naughty, lazy, etc’
Visible Learning
Hattie, 2009
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‘The highest effects accrued when teachers provided feedback data or
recommendations to students.’
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The programmes with greatest effect were strategy based methods’
Least effective were using technology for independent practice,
And the strategy of working within a peer group
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