problems of learning mathematics

8/9/2019 Problems of Learning Mathematics

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Problems of learning

mathematics

Prepared by :

Wan mohd hamdan bin ghazali

Azrol bin zahariMuhamad huzaifah bin semsuddin


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Introduction.

Mathematics disabilities are:

The child is having difficulties presistentdifficulty in learning mathematic

Tends to perform poorly on classroom mathassesment compared to the rest of the class

For example, the child may have trouble

remembering what the teacher had taughtMay have difficulty using effective strategiesto solve math problem


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Children with learning disabilities in basicmath may have little difficulty writing

numbers on paper, but they do notunderstand the relationship between numbersand quantities.

Time concepts, organization by number orquantity, and performing practical math taskssuch as measuring for recipes are difficult forpeople with learning disabilities in math.

They may understand how to solve problems,but the solutions are incorrect because ofcalculation errors caused by their learningdisabilities.


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Causes of failure to acquire

Mathematics Skills.Causes of failure Explanation Example intervention

Cognitive Level of cognitive

ability

(maybe it slow

and very weak)

Brain injury/disabilities

Slow-learner

Cerebral-palsy

Teacher has to

explain briefly,

clear and easy to

understand.

Emotional Students

readiness

/emotional andhealth

condition

Bad health

condition. So, no

mood to study.

Give

reinforcement

Physical Depends on their

Physicalabilities

Blind, deaf or

psychomotorproblems.

Blind-use Braille

Deaf-use signlanguage


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Problems in Learning Mathematics

among LD students.Problems Explanation Example Intervention

Visual/ auditory

perception

Perception =

pengamatan

To use eyesight

and hearing to

learn

Blinds- hard to

learn by visual

Deaf hard to

learn by audio

Student needs a

lot of practices

about size,

distance and

space.

Memory Ability to keep

and store

knowledge or

anything

Students with

difficulties to

remember

information and

concept

Ask student to

write a note

about the

important

topics.

Language Difficulties in

understanding

language and

maths concept.

Maths concept :

first, last, then,

more than, less

than.

Teacher uses

simple and

direct language

so that studenteasy to


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Problems Explanation Example Intervention

Abstract thinking

(penaakulan)

hard for LD

students to think

abstractly.

To imagine

something/

concept.

Use concrete

materials to

teach them

before ask them

to relate to

abstract concept

Metacognitive Readiness of their

cognitive to study

Some kids- 5years

old already can

count

Some kids- 7years

old still cannotcount


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Problems Explanation Example Intervention

Social Exposure from

family &

friends.

Through TV,

daily life

activites.

Family taught

them how to

count stairs,

money and let

them go to the

market.

Teach them

maths by social

skills.

Reading Abilities to read How to solveproblem if they

cannot read?

Teach them thrusymbols or

concrete

materials.


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VISUAL PROBLEM

Visual perception refers to the process of

interpreting and organizing visual information

(Kavale, 1982).

Visual perceptual skill is often subdivided into

areas such as visual discrimination and visual

memory.


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Visual discrimination involves the ability to

attend to and identify a figure's distinguishing

features and details, such as shape,orientation, color and size. Visual memory

refers to the ability to remember a visual

image. For example, good visual discrimination/

analysis skills could assist children in

discriminating between numbers,

differentiating between arithmetic signs, and

breaking down problems into manageable

components.


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In addition, good visual discrimination and

visual memory skills would be helpful when

spatially organizing calculations or solvinggeometry and word problems.

Furthermore, good visual memory skills could

also be instrumental when learningmultiplication tables, retaining what has been

read in a word problem, and copying

assignments from the board to the paper.


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In another light, while simultaneous visual

processing skills should be helpful when

solving geometry problems that must be

solved by looking at the problem as a whole,

sequential visual processing skills should be

instrumental when solving word problems andorganizing calculations that must be solved in

a sequential fashion.

In fact, a significant relationship betweenvisual perceptual skill and mathematics

abilities has been previously reported


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Computational Weakness

Many students, despite a good understanding

of mathematical concepts, are inconsistent atcomputing. They make errors because theymisread signs or carry numbers incorrectly, ormay not write numerals clearly enough or inthe correct column.

These students often struggle, especially inprimary school, where basic computation and

"right answers" are stressed. Often they endup in remedial classes, even though theymight have a high level of potential for higher-level mathematical thinking


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Difficulty Transferring KnowledgeOne fairly common difficulty experienced by

people with math problems is the inability toeasily connect the abstract or conceptualaspects of math with reality.

Understanding what symbols represent in the

physical world is important to how well andhow easily a child will remember a concept.

Holding and inspecting an equilateral triangle,for example, will be much more meaningful toa child than simply being told that the triangleis equilateral because it has three equal sides.

And yet children with this problem find

connections such as these painstaking at best.


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Making Connections

Some students have difficulty making

meaningful connections within and acrossmathematical experiences.

For instance, a student may not readily

comprehend the relation between numbersand the quantities they represent.

If this kind of connection is not made, math

skills may be not anchored in any meaningfulor relevant manner. This makes them harder

to recall and apply in new situations.


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Incomplete Understanding of the Language of

Math

For some students, a math disability is drivenby problems with language. These childrenmay also experience difficulty with reading,writing, and speaking.

In math, however, their language problem isconfounded by the inherently difficultterminology, some of which they hearnowhere outside of the math classroom.

These students have difficulty understandingwritten or verbal directions or explanations,and find word problems especially difficult to

translate.


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Difficulty Comprehending the Visual and

Spatial Aspects and Perceptual Difficulties.

A far less common problem -- and probably the

most severe -- is the inability to effectively

visualize math concepts. Students who have thisproblem may be unable to judge the relative size

among three dissimilar objects.


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This disorder has obvious disadvantages, as it

requires that a student rely almost entirely on

rote memorization of verbal or written

descriptions of math concepts that most

people take for granted. Some mathematical

problems also require students to combinehigher-order cognition with perceptual skills,

for instance, to determine what shape will

result when a complex 3-D figure is rotated.


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Memory problem

The memory demands for school-age children

are much greater than they are for adults.

As adults, we have already acquired much ofthe knowledge and skills we need to function

day to day.

Although the knowledge base for some fields

such as technology changes rapidly, the new

information is generally highly specific and

builds on existing knowledge.


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Many students have memory problems.

Students who have deficits in registering

information in short-term memory often have

difficulty remembering instructions or

directions they have just been given, what was

just said during conversations and classlectures and discussions, and what they just

read

Students who have difficulty with workingmemory often forget what they are doing

while doing it.


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For example, they may understand the three-

step direction they were just given, but forget

the second and third steps while carrying outthe first step.

If they are trying to solve a math problem that

has several steps, they might forget the stepswhile trying to solve the problem.

When they are reading a paragraph, they may

forget what was at the beginning of theparagraph by the time they get to the end of

the paragraph.


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These students will look like they have

difficulty with reading comprehension. In

facts, they do; but the comprehensionproblem is due to a failure of the memory

system rather than the language system.

Students who have deficits in the storage andretrieval of information from long-term

memory may study for tests, but not be able

to recall the information they studied when

taking the tests.


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They frequently have difficulty recalling

specific factual information such as dates or

rules of grammar.

They have a poor memory of material they

earlier in the school year or last year. They

may also be unable to answer specificquestions asked of them in class even when

their parents and/or teachers think they really

know the information.


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Styles of learning Mathematics

(stages of cognitive developmental;

Jean Piaget)Piaget identified four stages of cognitive

development:

The sensorimotor stage (Birth to 2 years)

The preoperational stage (Age 2 to 6)

The concrete operational stage (Age 7 to 11)

The formal operational stage (12 years and up)


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Sensorimotor stage (birth 2 years old)The

child, through physical interaction with his or

her environment, builds a set of conceptsabout reality and how it works. This is the

stage where a child does not know that

physical objects remain in existence evenwhen out of sight (object permanance).

Preoperational stage (ages 2-7)The child is

not yet able to conceptualize abstractly and

needs concrete physical situations


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Concrete operations (ages 7-11)As physicalexperience accumulates, the child starts to

conceptualize, creating logical structures thatexplain his or her physical experiences.Abstract problem solving is also possible atthis stage. For example, arithmetic equations

can be solved with numbers, not just withobjects.

Formal operations (beginning at ages 11-15)

By this point, the childs cognitive structuresare like those of an adult and includeconceptual reasoning


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Methods of understanding

Students with learning disabilities who

struggle with traditional instruction are likely

to respond to teaching using multisensory

methods.

These teaching tools involve using one or

more of the student's senses to teach

concepts and problem solving, improvememory, and strengthen application skills.


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often think of math as a nonverbal subject, we

actually use language based thinking to

understand its concepts and to perform the

tasks necessary to solve complex problems.

Use hands-on material.

Use familiar objects to set up and solve math

problems. Items such as money, cereal or

candy, or other small objects can be used to

demonstrate concepts such as adding,subtracting, greater than, less than, and equal

to


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Consider using flash cards or computerized

math toys and software with visual and

auditory prompts.


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Re-Write Word Problems to Enhance

Auditory Comprehension

Write the most important sentence first.

Reduce the words sentences, leaving only

those important to solving the problem.

Use simple sentence structure such as:

Subject/Verb/Object.

Use only words the student already knows and

can visualize.

Avoid pronouns, Use specific words.


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Use simple commands where "You" is implied,

such as "Add these numbers."

Use active sentences such as, "Joe drove the

car." Avoid passive sentences such as, "The car

was driven by Joe."

Avoid double negatives such as, "There are nocars that are not red."


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Provide Step-by-Step Models ofProblem

Solving

For specific learning disabilities (SLDs) in basic

math or applied math, provide step-by-step

models demonstrating how to solve math

problems. Math books often include problems requiring

the student to make leaps in logic to learn

new skills without showing the steps requiredto do those problems.


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This practice may frustrate students with

language processing deficits because they

have difficulty with the language-basedmental reasoning skills needed to make those

leaps. Instead, provide the child with models

to solve all types of problems included in theassignment so he can learn without verbal

processing weaknesses getting in the way.


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The following general strategies are

offered to help students develop a

more efficient and effective memory.


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Give Directions in Multiple Formats:

Students benefit from being given directions

in both visual and verbal formats.

In addition, their understanding and

memorizing of instructions could be checked

by encouraging them to repeat the directionsgiven and explain the meaning of these

directions.

Examples of what needs to be done are alsooften helpful for enhancing memory of

directions.


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Teach Students to Over-learn Material:

Students should be taught the necessity of

"over-learning" new information.

Often they practice only until they are able to

perform one error-free repetition of the

material. However, several error-free repetitions are

needed to solidify the information.


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Teach Students to Use Visual Images and

Other Memory Strategies: Another memory

strategy that makes use of a cue is one calledword substitution.

The substitute word system can be used for

information that is hard to visualize, forexample, for the word occipitalorparietal.

These words can be converted into words that

sound familiar that can be visualized.

The word occipital can be converted to exhibit

hall(because it sounds like exhibit hall).


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The student can then make a visual image of

walking into an art museum and seeing a big

painting of a brain with big bulging eyes

(occipital is the region of the brain that

controls vision).

With this system, the vocabulary word thestudent is trying to remember actually

becomes the cue for the visual image that

then cues the definition of the word.


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Help Students Develop Cues When StoringInformation:

According to the memory research,information is easier retrieved when it isstored using a cue and that cue should bepresent at the time the information is being

retrieved. For example, the acronym HOMES can be

used to represent the names of the GreatLakes Huron, Ontario, Michigan, Erie andSuperior. The acronym is a cue that is usedwhen the information is being learned, andrecalling the cue when taking a test will help

the student recall the information

problems of learning mathematics

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