15. Mathematics ability is regarded more as a specialized function rather than as a general indicator of intelligence.
16. More than 90 percent of parents expect their children to go to college and almost 90 percent of kids want to go to college, fully half of those kids want to drop mathematics as soon as they can.
17. Fear of Mathematics Some children develop a fear (or phobia) of mathematics because of negative experiences in their past or a simple lack of self-confidence with numbers.
18. Quality of Teaching Student achievement in mathematics is strongly linked to the teacher’s expertise in mathematics.
25. General Symptoms Inconsistent results with addition, subtraction, multiplication, and division Inability to remember mathematical formulas, rules or concepts Difficulty with abstract concepts of time and direction Consistent errors when recalling numbers including transpositions, omissions, and reversals Difficulty remembering how to keep score during games
28. Number Concept Difficulties Most children with mathematical disorders nevertheless have their basic number competencies intact.
29. Children with mathematical disorders have deficits in counting knowledge and counting accuracy. Counting Skill Deficits
30. Difficulties with Arithmetic Skills Children with mathematical disorders have difficulties in solving simple and complex arithmetic problems.
31. Procedural Disorders ~ use arithmetic procedures (algorithms) that are developmentally immature ~ have problems sequencing the steps of multi-step procedures ~ have difficulty understanding the concepts associated with procedures ~ make frequent mistakes when using procedures
32. Memory Disorders Have difficulty retrieving arithmetic facts Have a high error rate when they do retrieve arithmetic facts Retrieve incorrect facts that are associated with the correct facts
33. Visual-Spatial Deficits Have difficulties in the spatial arrangement of their work, such as aligning the columns in multicolumn addition Often misread numerical signs, rotate and transpose numbers, or both Misinterpret spatial placement of numerals, resulting in place value errors Have difficulty with problems involving space in areas, as required in algebra and geometry
34. What is the Future of Research in Mathematics Disorder?
35. By learning more about exactly how infants’ brains process arithmetic calculations, we can build on this foundation when exposing children to more complex mathematics.
36. Researchers need to determine which types of mathematical disorders are simply delays in development and which may represent more fundamental problems.
37. What genetic factors affect the neural networks and cognitive skills that support mathematical operations?
38. What types of mathematical disorders are related to reading disorders, and why?
39. The ultimate goal of research is to develop remedies to help individuals deal with their problems.
41. Determining the Source of the Problem The first task facing educators who deal with children with mathematics disorder is to determine the nature of the problem.
42. Prerequisite Skills 1. Follow sequential directions. 2. Recognize patterns. 3. Estimate by forming a reasonable guess about quantity, size, magnitude, and amount. 4. Visualize pictures in one’s mind and manipulate them.
43. 5, Have a good sense of spatial orientation and space organization. 6. Do deductive reasoning, that is, reason from a general principle to a particular instance, or from a stated premise to a logical conclusion.
44. 7. Do inductive reasoning, that is, come to a natural understanding that is not the result of conscious attention or reasoning, easily detecting the patterns in different situations and the interrelationships between procedures and concepts.
45. Less is More Students with special needs are likely to be more successful if taught fewer concepts in more time. Students with special needs should focus on mastering a few important ideas and learn to apply them accurately.
46. Use of Manipulatives Students with special needs who use manipulatives in their mathematics classes outperform similar students who do not.
47. Search for Patterns Many children with learning disabilities – including those with mathematical disorders – can learn basic arithmetic concepts.
48. Build on Students’ Strengths Teachers can often turn a student’s failure into success if they build on what the student already knows how to do. Most people learn mathematics best in the context of real-world problems.
56. Help students develop conceptual understanding and skills. Consider giving more oral and fewer written tests. Develop meaningful (relevant) practice exercises. Maintain reasonable expectations. Build on children’s strengths.
57. Use manipulative appropriately. Help students make connections. Determine and build on a student’s informal learning strategies. Accommodate individual learning styles as much as practicable. Use technology appropriately.
59. 1. Level of Cognitive Awareness. 2. Mathematics Learning Profile. Quantitative and Qualitative Learners 3. Language of Mathematics 4. Prerequisite Skills
60. 5. Levels of Learning Mastery Level One. Connect new knowledge to existing knowledge and experiences. Level Two. Searches for concrete material to construct a model or show a manifestation of the concept. Level Three. Illustrate the concept by drawing a diagram to connect the concrete example to a symbolic picture or representation.
61. Level Four. Translates the concept into mathematical notation using number symbols, operational signs, formulas, and equations. Level Five. Applies the concept correctly to real world situations, projects, and story problems. Level Six. Can teach the concept successfully to others, or can communicate it on a test.
63. Appraising abilities in Mathematics. Selecting the language of instruction. Moving from concrete experiences to abstract concepts. Using strategies for concept development. Using Mathematics to develop language. Using student’s strengths.
