MATHEMATICS LEARNING DIFFICULTIES PART 3

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MATHEMATICS ANXIETY

School students with math anxiety are so worried about the prospect of doing mathematics that their fear and nervousness can lead to poor performance on math tests. Some students may have both math anxiety and dyscalculia.

  •  Both dyscalculia and math anxiety can impact students’ performance in mathematics.
  • They can show up in similar ways, and a child can struggle with both.
  • Understanding the difference can help you respond best to your child’s challenges.

DYSCALCULIA Vs MATH ANXIETY

Dyscalculia and math anxiety are different, but the signs and struggles can overlap. And it’s possible for students have both. This table help we better understand what seeing in our school students in our mathematics classroom.

Signs of Math AnxietySigns of Dyscalculia
Student’s worries he’ll do poorly on a math test, even though he/she understands the material and has studied.Students expect to do poorly on a math test because he/she doesn’t understand the material, even after studying.
Student worries he’ll do poorly on a math test, even though he understands the material and has studied.Student expects to do poorly on a math test because he doesn’t understand the material, even after studying.
Student does poorly on math tests, even after preparing for them, because anxiety gets in the way.Student does poorly on math tests, even after preparing for them, because he doesn’t understand the material.
Students can get through homework fairly easily and answers most problems correctly. But he may feel anxious about doing it. He may even make errors because anxiety makes it hard to focus on some details. It may also make him focus too much on other details.Student spends a long time doing homework and gets many of the answers wrong.
Student tries to avoid going to math class when there’s a quiz or test.Student tries to avoid going to math class, especially when there’s a quiz or test, because he’s sure he’ll fail.
Student gets good grades on math homework and classwork, but not on tests.Student gets poor grades on math homework, classwork and tests.

MATH LEARNING DISABILITIES

While student with disorders in mathematics are specifically included under the definition of Learning Disabilities, seldom do math learning difficulties cause student to be referred for evaluation. In many school systems, special education services are provided almost exclusively on the basis of students’ reading disabilities. Even after being identified as learning disabled (LD), few students are provided substantive assessment and remediation of their arithmetic difficulties.

DIFFERENT TYPES OF MATH LEARNING PROBLEMS

Students with reading disabilities, when math difficulties are present, they range from mild to severe. There is also evidence that children manifest different types of disabilities in mathematics. Unfortunately, research attempting to classify these has yet to be validated or widely accepted, so caution is required when considering descriptions of differing degrees of math disability. Still, it seems evident that students do experience not only differing intensities of math dilemmas, but also different types, which require diverse classroom emphases, adaptations and sometimes even divergent methods.

Mastering Basic Number Facts: Many learning disabled students have persistent trouble “memorizing” basic number facts in all four operations, despite adequate understanding and great effort expended trying to do so. Instead of readily knowing that 5+7=12, or that 4×6=24, these students continue laboriously over years to count fingers, pencil marks or scribbled circles and seem unable to develop efficient memory strategies on their own.

Arithmetic Weakness/Math Talent: Some learning disabled students have an excellent grasp of math concepts, but are inconsistent in calculating. They are reliably unreliable at paying attention to the operational sign, at borrowing or carrying appropriately, and at sequencing the steps in complex operations. These same students also may experience difficulty mastering basic number facts. Because there is much more to mathematics than right-answer reliable calculating, it is important to access the broad scope of math abilities and not judge intelligence or understanding by observing only weak lower level skills.

The Written Symbol System and Concrete Materials: Many younger students who have difficulty with elementary math actually bring to school a strong foundation of informal math understanding. They encounter trouble in connecting this knowledge base to the more formal procedures, language, and symbolic notation system of school math. Teachers often compound difficulties at this stage of learning by asking students to match pictured groups with number sentences before they have had sufficient experience relating varieties of physical representations with the various ways we string together math symbols, and the different ways we refer to these things in words. The fact that concrete materials can be moved, held, and physically grouped and separated makes them much more vivid teaching tools than pictorial representations. Because pictures are semiabstract symbols, if introduced too early, they easily confuse the delicate connections being formed between existing concepts, the new language of math, and the formal world of written number problems.

The Language of Math: Some mathematics LD students are particularly hampered by the language aspects of math, resulting in confusion about terminology, difficulty following verbal explanations, and/or weak verbal skills for monitoring the steps of complex calculations. Teachers can help by slowing down the pace of their delivery, maintaining normal timing of phrases, and giving information in discrete segments. Such slowed down “chunking” of verbal information is important when asking questions, giving directions, presenting concepts, and offering explanations.

Visual-Spatial Aspects of Math: A small number of mathematics LD students have disturbances in visual-spatial-motor organization, which may result in weak or lacking understanding of concepts, very poor “number sense,” specific difficulty with pictorial representations and/or poorly controlled handwriting and confused arrangements of numerals and signs on the page. Students with profoundly impaired conceptual understanding often have substantial perceptual-motor deficits and are presumed to have right hemisphere dysfunction.

Mathematics achievement problems are usually due to a combination of teaching and student factors including language, cognitive, metacognitive, motor, social and emotional factors, habits of learning, and previous experiences.

  1. Language problems: Most students with mild disabilities have primary or secondary language problems. A language disorder, according to the American Speech-Language-Hearing Association, is “impaired comprehension and/or use of a spoken, written, and/or other symbol system”. The disorder may involve form, content, or function of the language. Even if a student does not have an identified language disorder, he or she may exhibit language deficiencies related to his or her disability.
  2. Cognitive factors: Most students with mild to moderate disabilities have cognitive factors that impede learning. These may be perceptual, memory, attention, or reasoning factors. Perception involves taking in information from the environment and processing that information for storage or use. It’s not just seeing the symbols for numbers but seeing and copying them. It’s not just hearing the oral number sequence but hearing it and continuing the sequence. It’s not the seeing or hearing alone, it’s the discrimination and interpretation of visual and auditory input. Perceptual problems show up with difficulties keeping place on a worksheet or within a column of numbers, differentiating numbers or symbols that are close in form, copying shapes or symbols, following directions with algorithms or graphs, recognizing patterns or sequences, and understanding oral directions or drills.
  3. Metacognitive factors: Metacognition is an awareness of the skills, strategies, and resources that are needed to perform a task and the ability to use self-regulatory mechanisms, including adjustments, to complete the task. Sometimes called “thinking about one’s own thinking,” metacognition is the process involving being aware of and monitoring the use of executive and cognitive strategies. Students with metacognition problems have trouble selecting and using effective learning strategies. They don’t monitor their own use of strategies and have difficulty with generalization across time and setting.
  4. Motor factors: Motor problems with written work are most evident in younger students but even adolescents with no physical disabilities can struggle with number and symbol formation. Motor skills, like perceptual ones, involve more than one process. They may involve memory of the symbol along with its actual formation (visual and motor memories). They may involve visual perception and transfer (copying). Or they may involve integration of fine muscles with task demands. Indicators of motor problems are highly visible: poorly formed symbols, little control of spacing, excessive time for a task, and avoidance of written work.
  5. Social and emotional factors: Sometimes overlooked in the academic realm, social and emotional factors can cause as many learning problems as cognitive ones. The range of these factors is as diverse as the students served. Some students have trouble with peer or adult relationships, causing problems in cooperative learning settings or seeking assistance. Others have self-concept and self-esteem problems that lower motivation, task persistence, and effort.
  6. Habits of learning: A combination of environmental, cognitive, social, and emotional factors, habits of learning are formed from an early age but certainly can be modified throughout the lifespan. “Habits of learning” refers to how individuals view and participate in learning, their self-discipline and self-motivation, goal setting, engagement in learning activities, and acceptance of challenges. Habits that could interfere with math learning include avoidance, learned helplessness, impulsivity, little curiosity, poor assignment completion, disinterest, and working for the “right answer” rather than understanding. Even students with high mathematics abilities have habits, such as the drive for perfection that can interfere with strong concept development and flexible problem solving.
  7. Previous experiences: A student’s prior knowledge and previous experiences with mathematics are the best predictors of future success. Many of these experiences have been influenced by the factors described above. However, previous instructional experiences also can have a significant impact on achievement. If previous teachers did not explain concepts well, use effective teaching methods, or allow time for mastery and success, students’ mathematics learning will be affected. If the curriculum and materials used weren’t aligned with math standards, learning might be superficial or limited. And if the student wasn’t able to develop the deep concept understanding that comes from good teaching and sound curriculum, his or her math achievement will suffer.

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