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From the Bulletin Learning Difficulties Australia www.ldaustralia.org Dyscalculia and Difficulties with

Tanya Forbes • recognising patterns in Attention • understanding the structure of deficits: A numbers such as place value and high level of grouping sustained • telling the time concentration is • and interpreting graphs and required to learn charts. maths concepts. • grasping abstract concepts like Students need multi-step algorithms, fractions and to maintain

Dyscalculia and Difficulties with Mathematics with | Dyscalculia and Difficulties LDA Bulletin algebra attention to yscalculia is an inherited • applying mathematical concepts effectively neurological condition to everyday life, such as budgeting process new information, to recall maths that affects the acquisition and time management skills facts and to self-monitor for careless of skills in mathematics. (Understood, 2017) mistakes. Attention deficits can have DDifficulties in are thought to As well as basic difficulties with a significant impact on mathematical be as widespread as difficulties; sense, students may experience learning. Mental calculations follow an however, there has been much less other limitations that impact on their ‘order of operations’ and problem solving research on dyscalculia than success in the mathematics classroom: is often a multistep process. Students (Butterworth, 2004). The incidence processing problems: need to sequence each step in the right of dyscalculia is currently estimated Accurate word reading and good order to calculate the correct answer to be between 6-7% of the general comprehension are essential to Anxiety: Poor performance in population (Callaway, 2013), although understand word problems and maths can have a significant emotional the figure varies because researchers recognise relevant information impact. Constant failure leads to a loss use different criteria to define severe in a question. Many words have of confidence, low self esteem and mathematical difficulties. several meanings so students need anxiety. When a student has a negative Generally, students with dyscalculia a comprehensive vocabulary to experience, they feel discouraged and will lack number sense: they will be understand the precise meaning of this can lead to avoidance. High anxiety unable to grasp number concepts, will mathematical terms (Garnett, 1998). can have a direct impact on working have problems learning number facts, Visuo-spatial problems: Some memory leading to a further drop in will have trouble performing simple students may have difficulty making performance. Some students soon calculations, and will be unable to apply sense of visually presented information believe that maths is difficult, so they their mathematical knowledge to solve and visualising concepts. Visual-spatial give up and disengage from learning problems. These students tend to be difficulties can result in a poor sense (Ashcraft, 2002). resistant to good instruction and may of direction, mixing up left and right, be unable to retain and apply what they confusion between ‘less’ and ‘more’, Ways to support students with have learned. and trouble with measurement (Szucs, numeracy difficulties Every student’s profile will be Devine, Soltesz, Nobels & Gabriel, 2013). Avoid rote learning, rapid fact different, but students will typically have Memory difficulties: All aspects of recall and repetitive drills – these are difficulties with: memory are involved in mathematics. empty of meaning and difficult to • learning to count. Students may Short term memory allows recall of remember. Instead, we should teach use immature strategies to calculate sequences and procedures. Working the relationships between maths facts such as counting by ones, often with memory provides temporary storage to develop students’ understanding of their fingers. of facts and figures while performing a basic number and operation concepts. • recognising number symbols calculation. Long term memory allows By teaching for meaning, students are • understanding mathematical immediate recall of facts and information. able find a solution using logic and operations and performing If one area of memory is weak, then that reasoning when their memory fails them. calculations will have a significant impact on maths Pre-teach and review relevant • learning and recalling basic performance. Often a slow processing skills and introduce new vocabulary mathematical facts, particularly the speed will accompany problems with to ensure that students have a correct times tables memory (Lee Swanson, et al. 2001). understanding of the essential sub-skills

6 | Volume 49, No 2, Winter 2017 From the Bulletin Learning Difficulties Australia www.ldaustralia.org LDA Bulletin and Difficulties | Dyscalculia with Mathematics required to complete the task. Build Provide scaffolding to promote memory and inhibition impairment. on prior knowledge by connecting new success and build confidence. When Cortex, 49 (10), 2674-2688. information to background knowledge students demonstrate mastery, you Understood (2017). Understanding to provide the student with a solid can gradually increase task difficulty dyscalculia [webpage]. https://www. foundation to build knowledge and skills. as you decrease the level of guidance. understood.org/en/ learning-attention- Develop a conceptual framework to store Most importantly, teach for success so issues/child-learning-disabilities/ new learning and provide strategies so students see themselves as competent dyscalculia/ understanding-dyscalculia information is easily retrieved and applied. problem solvers. Then they will be more Westwood, P. (2000). Numeracy Use simple, clear and concise willing to attempt tasks and persevere and learning difficulties: approaches language during explanations – always with difficult problems. to teaching and assessment. focus on critical content and break Canberra: ACER. complex skills into small manageable References and Further steps. Provide a step-by-step Reading: Witzel, B. S., Mercer, C. D. and Miller, demonstration of problem solving - Ashcraft, M. (2002). Math anxiety: M. D. (2003). Teaching algebra to model the skill by thinking aloud as Personal, educational, and cognitive students with learning difficulties: An you solve the problem. Students will consequences. Current Directions investigation of an explicit instruction learn to ‘self talk’ through the process. in Psychological Science, 11(5), model. Learning Disabilities Research & Then lead students through a range of p181-185. Practice, 18: 121–131. worked examples, using prompting and Bird, R. (2009). Overcoming difficulties questioning to actively engage students Tanya Forbes is an LDA Council with number: Supporting dyscalculia in the problem solving process. member, dyslexia advocate and and students who struggle with maths. Use manipulatives (concrete campaigner. She is the London: Sage. materials such as blocks) and visual creator of the documentary film Outside representations (drawings or figures) Butler, F. M., Miller, S. P., Crehan, the Square and is the founder of the to help students to learn basic maths K., Babbitt, B. & Pierce, T. (2003). Gold Coast Dyslexia Support Group. She operations, solve story problems Fraction instruction for students with is committed to closing the research to and master abstract concepts like mathematics disabilities: Comparing practice gap in our education system fractions and algebra, as well as to two teaching sequences. Learning and has been working closely with explain, simplify and clarify problems. Disabilities Research and Practice, 18, local schools in her area to promote Manipulatives and diagrams function as 99–111. evidence-based practice. cognitive tools to connect students to Butterworth, B. (2004). Developmental concepts: they may make difficult ideas dyscalculia. In J. Campbell (Ed.) understandable, complex problems Handbook of mathematical cognition. solvable and abstract concepts tangible New York: Psychology Press. (Butler, Miller, Crehan, Babbit & Pierce, Callaway, E. (2013). Dyscalculia: 2003; Cass, Cates, Smith & Jackson, Number Games, Nature, 493, 150–153. 2003; Sowell, 1989; Witzel, Mercer & Cass, M., Cates, D., Smith, M., Miller, 2003). & Jackson, C. (2003). Effects of Encourage students to verbalise manipulative instruction on solving area their problem solving process – provide and perimeter problems by students opportunities for students to explain with learning disabilities. Learning concepts, describe procedures and Disabilities Research & Practice, 18, discuss the ideas they are developing. 112–120. Questioning helps students make sense of information and provides Chinn, S (2014). The trouble with maths: teachers with insight into learning. A practical guide to helping learners with Frame questions to help students’ numeracy difficulties. Routledge. gain new understanding, consolidate Garnett, K. (1998). Math learning their learning and monitor their disabilities. Division for Learning progress. Use feedback to check for Disabilities Journal of CEC understanding, and to provide positive Sowell, E. (1989). Effects of manipulative reinforcement and corrective feedback. materials in mathematics instruction. Reinforce that mistakes are an important Journal for Research in Mathematics part of the learning process – we learn Instruction, 20(5), 498 – 505. from our mistakes. Give students plenty of time. Students Swanson, H. & Sachse-Lee, C. (2001). will need extra time to learn skills, process Mathematical problem solving and information and perform calculations. in children with Allow plenty of opportunities to practise learning disabilities: Both executive to consolidate learning and achieve and phonological processes are mastery. Practice will increase fluency important. Journal of Experimental Child in processing, improve retention of Psychology, 9(3), 294-321 information, facilitate recall and develop Szucs D., Devine, A., Soltesz, F., Nobels, understanding. Students with learning A., & Gabriel, F. (2013). Developmental difficulties will need more practice. dyscalculia is related to visuo-spatial

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