problems of learning mathematics
TRANSCRIPT
-
8/9/2019 Problems of Learning Mathematics
1/38
Problems of learning
mathematics
Prepared by :
Wan mohd hamdan bin ghazali
Azrol bin zahariMuhamad huzaifah bin semsuddin
-
8/9/2019 Problems of Learning Mathematics
2/38
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
-
8/9/2019 Problems of Learning Mathematics
3/38
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.
-
8/9/2019 Problems of Learning Mathematics
4/38
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
-
8/9/2019 Problems of Learning Mathematics
5/38
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
-
8/9/2019 Problems of Learning Mathematics
6/38
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
-
8/9/2019 Problems of Learning Mathematics
7/38
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.
-
8/9/2019 Problems of Learning Mathematics
8/38
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.
-
8/9/2019 Problems of Learning Mathematics
9/38
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.
-
8/9/2019 Problems of Learning Mathematics
10/38
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.
-
8/9/2019 Problems of Learning Mathematics
11/38
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
-
8/9/2019 Problems of Learning Mathematics
12/38
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
-
8/9/2019 Problems of Learning Mathematics
13/38
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.
-
8/9/2019 Problems of Learning Mathematics
14/38
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.
-
8/9/2019 Problems of Learning Mathematics
15/38
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.
-
8/9/2019 Problems of Learning Mathematics
16/38
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.
-
8/9/2019 Problems of Learning Mathematics
17/38
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.
-
8/9/2019 Problems of Learning Mathematics
18/38
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.
-
8/9/2019 Problems of Learning Mathematics
19/38
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.
-
8/9/2019 Problems of Learning Mathematics
20/38
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.
-
8/9/2019 Problems of Learning Mathematics
21/38
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.
-
8/9/2019 Problems of Learning Mathematics
22/38
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.
-
8/9/2019 Problems of Learning Mathematics
23/38
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)
-
8/9/2019 Problems of Learning Mathematics
24/38
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
-
8/9/2019 Problems of Learning Mathematics
25/38
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
-
8/9/2019 Problems of Learning Mathematics
26/38
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.
-
8/9/2019 Problems of Learning Mathematics
27/38
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
-
8/9/2019 Problems of Learning Mathematics
28/38
Consider using flash cards or computerized
math toys and software with visual and
auditory prompts.
-
8/9/2019 Problems of Learning Mathematics
29/38
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.
-
8/9/2019 Problems of Learning Mathematics
30/38
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."
-
8/9/2019 Problems of Learning Mathematics
31/38
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.
-
8/9/2019 Problems of Learning Mathematics
32/38
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.
-
8/9/2019 Problems of Learning Mathematics
33/38
The following general strategies are
offered to help students develop a
more efficient and effective memory.
-
8/9/2019 Problems of Learning Mathematics
34/38
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.
-
8/9/2019 Problems of Learning Mathematics
35/38
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.
-
8/9/2019 Problems of Learning Mathematics
36/38
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).
-
8/9/2019 Problems of Learning Mathematics
37/38
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.
-
8/9/2019 Problems of Learning Mathematics
38/38
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