What is dyscalculia Pete Jarrett Editorial team Equals

What is dyscalculia? Pete Jarrett – Editorial team, Equals Online

Equals Online The MA Journal of Mathematics and SEN. Equals Online is produced by teachers and curriculum/SEN specialists dedicated to opening up mathematics to low attainers.

Equals Online https: //www. m-a. org. uk/equals-online Editor: equals@m-a. org. uk

Let’s reflect – Dyscalculia? • Are maths difficulties under-recognised? • Is there a difference between Specific Learning Difficulties around mathematics and dyscalculia? • What is dyscalculia? • Are difficulties with maths a classroom problem or a SENCO problem?

Let’s reflect • Study of 2421 primary school pupils in NI (Morsanyi, et al. 2018) • 108 with official diagnosis of dyslexia 4. 46% • 6% of learners had persistent specific difficulties with maths • 1 official diagnosis of dyscalculia 0. 04%

Nuffield Foundation: Low attainment in mathematics (Hodgen, et al. 2020) • Prior attainment is the strongest predictor of future attainment. • No evidence of threshold concepts but some evidence that low attaining pupils have practically important weaknesses in number and calculation.

Cardinality and number sense, including difficulties decomposing numbers. Counting skills and multiplicative reasoning. Fractions and division Place value. COMMON STICKING POINTS 7

AREAS THAT MAY IMPACT ON MATHS LEARNING Mindset and resilience Confidence and anxiety Literacy Reasoning Memory and speed of processing Arithmetic –Numbersense - dyscalculia Another specific learning difficulty – dyslexia, dyspraxia, ADHD 8

CAN ANYONE LEARN MATHS? We can approach this from two directions: Can anyone do maths? Can anyone learn?

Number sense – Mathematical cognition and neuroscience As a neurobiological construct is not fully understood: • The relationship between cardinal magnitudes and continuous variables suggests that continuous variables may have the greater impact. • The connections between non-symbolic magnitude recognition and symbolic magnitude recognition are being researched

Number sense – Mathematics classroom A small, but readily identifiable, group have difficulties in: • Subitising • Non-symbolic and symbolic magnitude comparison • Ordering • Properties of numbers • Composition of numbers

Number sense – Mathematics classroom A small, but readily identifiable, group have difficulties in: • Subitising

Number sense – Mathematics classroom A small, but readily identifiable, group have difficulties in: • Subitising

Number sense – Mathematics classroom A small, but readily identifiable, group have difficulties in: • Subitising

Number sense – Mathematics classroom These difficulties are separate to problems with: • Fact retention and recall • Building memories of processes • Working on multi-step problems • Extracting the mathematics from numglish questions about watermelons

Actual proof that Kafirah did buy 24 watermelons, planning to give 1/3 to one friend and 25% to another friend! No clue why though!

The purpose of assessment What is that child failing to understand which others can? ” – Butterworth, 2019. “ “There comes a point where we need to stop pulling people out of the river. We need to go upstream and find out why they are falling in. ” Archbishop Desmond Tutu There is so much more to struggling with maths learning than just being bad at it! 23

AREAS THAT MAY IMPACT ON MATHS LEARNING Mindset and resilience Confidence and anxiety Literacy Reasoning Memory and speed of processing Arithmetic –Numbersense - dyscalculia Another specific learning difficulty – dyslexia, dyspraxia, ADHD 24

Copyright Tutorum Learning and Assessment Ltd 2020

Engagement – salience and attention EXECUTIVE FUNCTIONS Working memory and cognitive agility Emotional regulation, metacognition – thinking about what you are doing Education & Training Foundation 26

WORKING MEMORY, SPEED OF PROCESSING AND COGNITIVE LOAD We all have a limited capacity to process and manipulate information – like a mobile phone battery if lots of apps are open – this may be less efficient in many learners with SEND. Education & Training Foundation 27

The environment! Domain general indicators, Co-occurrence with other neurodevelopmental conditions and medical conditions Domain specific around sense of number dyscalculia Home, School, SES, etc!

Dyscalculia definition – SASC, BDA Dyscalculia is a specific and persistent difficulty in understanding numbers which can lead to a diverse range of difficulties with mathematics. It will be unexpected in relation to age, level of education and experience and occurs across all ages and abilities. Mathematics difficulties are best thought of as a continuum, not a distinct category, and they have many causal factors. Dyscalculia falls at one end of the spectrum and will be distinguishable from other maths issues due to the severity of difficulties with number sense, including subitising, symbolic and non-symbolic magnitude comparison, and ordering. It can occur singly but often co occurs with other specific learning difficulties, mathematics anxiety and medical conditions.

DYSCALCULIA AND OTHER NEURODEVELOPMENTAL CONDITIONS – WHAT TO LOOK FOR • Poor concept of place value • Poor estimation skills • Not recognising an answer as correct or incorrect • Long winded counting strategies – finger counting • Memory and speed of processing • Difficulty noticing patterns • Speed of work Education & Training Foundation 30

Other Indicators • An inability to count backwards reliably • Weakness in visual and spatial orientation • Difficulties in word problems and multi step calculations • Problems with all aspects of money • Marked delay in understanding the concept of time 31

When people ask me ‘When will I need this? ’ in Maths Class

What do we do as teachers? • Teacher hunch is really important. • Understand the assess, plan, do, review cycle. • Observe. • Teach well. Teaching does not have to be substantially different in the first instance. • Measure response to teaching. • Assessment for learning as an agile process and not as dogma

Language Procedure Concept 34 The three components of a mathematical idea

Six levels of mathematical knowledge Intuitive Concrete Pictorial Abstract Application Communication Education & Training Foundation 35

Learners can play their way through concepts around denominators A concrete representation of a known value helps with number sense The link between the concrete and the abstract ties in concept and process and provides a place to talk

What students find difficult: Having to answer in front of people Answering quickly Dividing numbers Maths tests Pythagoras Living up to the teachers expectations Jarrett, P. (2015) The Assessment of Self Efficacy. Equals Online. Pg. 8 -18. Vol. 20. 1

The learner voice: ‘What made maths at school a good or bad experience? ’: A good teacher, a non-disruptive classroom environment. Consistent teaching My teachers were fun and loved maths Great teachers, lots of opportunities to learn in different ways I had a patient teacher who was able to explain concepts in a number of ways and give me time and opportunity to practise My teacher made it a fun experience. And even thought I wasn’t good enough he pushed me to do more and higher.

Questions https: //www. m-a. org. uk/equals-online Editor: equals@m-a. org. uk pete@tutorum. co. uk