Maths disability. Sean Loughran D07117735 DT202Inclusive Learning through Technology assignment1. What we will cover. Introduction Maths difficulties Characteristics of Maths Disabilities Learning theories Using technology . Introduction .
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Maths disability Sean Loughran D07117735 DT202\Inclusive Learning through Technology assignment1
What we will cover • Introduction • Maths difficulties • Characteristics of Maths Disabilities • Learning theories • Using technology
Introduction • Mathematics comes into nearly every aspect of our lives, managing a budget, keeping track of the score during a game or within our working lives. • It is a symbolic language that enables us to think about, record, and communicate ideas about elements and relationships of quantity • It has meaning for all cultures
History • The most ancient mathematical texts available date back to nearly 2000BC, containing such items as Pythagorean theorem • 17th century • Kepler formulated mathematical laws of planetary motion • Isaac Newton discovered the laws of physics • 18th century • Leonhard Euler named the square root of minus 1 with the symbol i, and he popularized the use of the Greek letter π to stand for the ratio of a circle's circumference to its diameter • 19th century • mathematics became increasingly abstract • Carl Friedrich Gauss did work on functions of complex variables, in geometry, and on the convergence of series • 20th century • mathematics become a major profession • the scientific age led to specialization with hundreds of specialized areas in mathematics
Some fact and figures of Maths difficulties • Figures from the States show • approximatly 6-7% of students show evidence of serious mathematical difficultythat • about 26% of students with learning disabilities and related mild disabilities have difficulty in learning mathematical skills • Nearly half of those identified in 4th grade (Irish equivalent; 3rd class) with serious maths difficulties are still classified as having serious difficulties 3 years later • Dyscalculia is a medical term that describes a severe disability in mathematics related to a neurological impairment
Negative outcomes • Maths disability is not only a problem in school years but it impact goes on to effect the individual in their daily lives as an adult • There is much less attention devotes to maths difficulties as compared to reading difficulaties and hence its identification and treatment
Positive outcomes • Not all students with learning disabilities have problems with number thinking as some individuals with severe reading disabilities have a strong aptitude for maths
Although all maths disabilities are unique for an individual characteristics are likely related to difficulties in information processing difficulties, language and reading and or maths anxiety Characteristics of Maths disabilities
There are various elements of human information processing that may cause difficulties Motor problems such as not being able to write number and symbols legible, or writing inaccuracy Attention problems such as the attention required for performing a sequence of mathematical steps or during class teaching Memory and retrieval problems like forgetting mathematical formulas or how to solve problems Visual – spatial problems for example problems aligning numbers Auditory processing – such as difficulty with auditory instructions Characteristics of Maths disabilities (Information Processing)
Having a problem with language and reading will magnify any maths difficulties. It may lead to the confusion of terms such as “carry”, “borrow”, “take away” etc. Understanding a worded maths problem is essential before it can be solved Characteristics of Maths disabilities (language and reading abilities)
Being confronted by a maths problem for some individuals may cause anxiety making it difficult for them to solve or learn It may stem from a fear of school failure or from low self esteem. Guidelines to reduce maths anxiety include Have students compete with themselves rather than others Provide ample practise with similar test Make sure students understand what they are do in tests Give students time to complete tests Characteristics of Maths disabilities (Maths Anxiety)
Think-Pair-Share Consider a student who is having difficulty with basic algebra such as the problem 4x + 2 = -5x -16 What earlier algebra concepts must the be learnt before moving onto this more advanced level?
Addition, subtraction, multiplication and division of integers 7 + 2 3 + -4 3 x -5 -6 ÷ -2
Simplify addition, subtraction and division equations (3x + 2) + (4x + 3) = x + 2
Solve expression with variables 5x = 20 3x = -9 -7x = -21
Solve 2 step equations 4x – 5 = 3
Solve multi step equations 4x + 2 = -5x -16
Learning Theories for Mathematics Instruction Active involvement As part of maths learning active involvement will allow students to explore ideas for themselves. Using manipulative material will allow a student to see, touch and move objects. Consider the problem where a child wants to find out how many toys they have over their friend. The child is likely to match each others toys together and see how many are left over. The child constructs meaning of the problem and does not need to ask “should I add or subtract”
5+7 = _ Concrete to abstract learning Learning Mathematics is a gradual process. We need to master the basics before we more on to more abstract tasks To learn at the concrete level a child can manipulate materials such as blocks or marbles in order to work out solutions. Once this is mastered they can progress to pencil and paper by using marks on the paper to represent objects. Finally when the student is then ready a more abstract level can be introduced such as using numbers only
Learning Theories for Mathematics Instruction Problem solving This involves the thinking required to work out worded problems. Students must interpret information in different settings and then apply a maths concept to the problem For students with maths difficulties much practice is required in order to combine their thinking, language and knowledge of mathematical concepts together.
Learning Theories for Mathematics Instruction Direct Instruction of mathematics This is where material is carefully structured and planned for the students. Material can be planned so that it is initially broken out into small basic tasks and then increase in complexity. Diagrams can be used to enhance understanding. Teachers assess students to see whether they are learning, supply immediate feedback and allow students lots of independent practice. It has shown to be very effective for students with learning disabilities.
Learning Theories for Mathematics Instruction Learning strategies Instruction With this learning strategy the teacher teaches the students how to learn rather than teach the content of the curriculum. They are taught how to learn a new procedure and then use it to solve problems. With a skill in learning strategies the impact of a learning disability can be lessened
Using technology • Technology such as calculators and computers can be helpful for students with maths difficulties. • When using a calculator students can get quicker to the point of understanding a maths concept. A student may find it hard to memorise basic computational facts and may get bogged down without getting the chance to apply and learn the maths concept. Calculators with built in speech synthesisers may be useful in order to get auditory feedback of the calculation. • There are many mathematical teaching programs available and online resources. The advantage of using computers is that they can be motivating, they enable a student to work independently at their own pace, they can provide immediate feedback, provide repetition or be customised for the individual. • Some computer applications can quickly visualize data using various charts or graphs.
Consider having a serious maths disability, what do you think the impact would be on college and adult life?
Summary and finish up • Maths is very much part of our every day lives • Some individuals with learning disabilities also have serious maths difficulties • Maths disability is usually related to problems in information processing difficulties, language and reading or maths anxiety • Using learning theories can help lessen the impact of maths difficulties • Technology such as calculators and computers can be helpful for students
Maths Resources Maths is Fun is an online resource that teaches basic Maths skills such as adding, subtracting, algebra, geometry, time and money concepts and much more. Students can practice sums and play educational games online. http://www.mathsisfun.com The BBC caters for a wide maths skill level. Early maths skills is presented using games. http://www.bbc.co.uk/schools/ks1bitesize/numeracy/ http://www.bbc.co.uk/schools/ks2bitesize/maths/ http://www.bbc.co.uk/schools/ks3bitesize/maths/ http://www.bbc.co.uk/scotland/learning/bitesize/higher/maths/algebra/ This site aims to bring collect together and order a range of free resources discovered on the Internet, which can be used for teaching Maths in Primary Schools http://www.mathszone.co.uk/ For more advanced maths students the following offers lots of worked examples covering a wide range of Maths topics http://www.mathcentre.ac.uk/ Maths for the first year college student to postgraduate level http://mathworld.wolfram.com/
Bibliography • Albert M. Cook, Susan M. Hussey 2002 Assistive technologies: principles and practice • Learner J, Beverly J, 2008, Learning Disabilities and Related Mild Disabilities