Monday, November 11, 2013

Sunday, November 10, 2013

Dyscalculia: Teaching Methods and Instructional Strategies

     As a continuation of my discussion about dyscalculia, let me present to you some teaching methods in helping pupils with dyscalculia. The beauty about these methods is that these can likewise be useful to students without dyscalculia. 
  
Concept Attainment Strategy

This allows the child to discover the essential attributes of a concept. This can enhance students’ skills in separating important from unimportant information; searching for patterns and making generalizations; and defining and explain concepts
 This can be applied through the following example:


Specific Objective: 
          Differentiate Proper from Improper Fractions (BEC PELC F.1)

The following are proper fractions:
3/7, 3/6, 5/89, 45/67, 23/47, 4/12, 2/30

The following are improper fractions:
12/7, 21/3, 4/3, 45/12, 31/21, 12/5, 5/2

Which of the following are Proper Fractions?
12/3, 34/6, 2/5, 7/5, 5/7, 12/5, 23/4, 5/23, 6/7

Expected Answers: 2/5, 5/7, 5/23, 4/8, 2/3

Therefore...

A proper fraction is ____________________.
(A proper fraction is a fraction whose denominator is 
greater than the numerator. An improper fraction 
is a fraction whose denominator is less 
 than the numerator.)


 


Model Approach

The Model Approach to solving word problems was developed locally years ago by Hector Chee, a very experienced Mathematics teacher, and has since been widely used in the teaching of kids math in primary schools in Singapore (Singapore was ranked 1st in the recent TIMMS last 2001).
         This method is especially useful when: the student responds better to visual stimuli (e.g. pictures, drawings, etc); tries the conventional methods but they do not really work well; and the student has not learnt algebra yet and solving the math problems with algebra is not an option.
        The example below is an illustration on how to use model approach in problem solving. (source: http://mathsexcel.files.wordpress.com/2011/06/part4a3.png?w=500&h=416


STAR

STAR is an example of an empirically validated (Maccini & Hughes, 2000; Maccini & Ruhl, 2000) first-letter mnemonic that can help students recall the sequential steps from familiar words used to help solve word problems involving integer numbers.
The steps for STAR include:
Search the word problem;
Translate the problem;
Answer the problem; and
Review the solution

Below is an example of a structured worksheet using STAR strategy in solving word problem:


Objective: Solve 2- to 3- step word problems involving whole numbers (BEC PELC II. A.1.2) 
Problem: Mr. Cruz had P4,500. He spent P2,500 for food; P750 for transportation; and P275 for other expenses and divided the rest among his 5 brothers. How much was the share of each?

Strategy Questions:

S-earch the word problem
a.    Read the problem carefully
b.    Ask yourself questions: "What do I know? What do I need to find?"
c.    Write down the facts:
·         Mr. Cruz had P4,500.
·         He spent P2,500 for food
·         P750 for transportation
·         P275 for other expenses
·         He divided the rest among his 5 brothers
I need to find share of each brother.


T-ranslate the words into an equation in picture form.

P2,500-food
P750-transportation
P275- other expenses
?=divided among 5 brothers

A-nswer the problem
If I add all Mr. Cruz’s expenses and subtract the sum from his original money, I can get the amount that was shared by his five brothers and divide this by 5.
Mr. Cruz’s expenses: P2,500 + P750 + P275 = P3,525
P4,500 - P3,525=P975
P975 ÷ 5 = P195
Each brother receives P195.

R-eview the Solution
a.    Reread the problem
b.    Ask yourself questions: "Does the answer make sense? Why?"
c.    Check the answer
I checked my answer.
When I multiplied P195 by 5 and added the product to the total of Mr. Cruz’s expenses, I got P4500 which is Mr. Cruz’s total amount.

Advance/Graphic Organizers

Using advance organizers is cognitive instructional strategy used to promote the learning and retention of new information (Ausubel, 1960). It is a method of bridging and linking old information with something new.
         An advance organizer is information that is presented prior to learning and that can be used by the learner to organize and interpret new incoming information (Mayer, 2003).

         I have posted and discussed examples of advanced organizers on the following links:




Games

Games can make math learning fun, enjoyable and interesting even for a child with dyscalculia. Aside from developing mathematical skills and ability, it is still important that the love and motivation to learn math will be present in a dyscalculic child.


The following math games are designed to develop numeracy skills (e.g. number sense and counting, calculation, place value,) that are basic but essential skills for developing mathematical ability. These games are recommended games lifted from the book The Dyscalculia Assessment (Emerson and Babtie,2010). The games can be used by children with mathematical disability (and even regular) from any grades (since the numbers can be modified depending on the grade level). 

a.    THE ESTIMATING GAME
      To introduce the idea of the structured number track.
      To develop the concept of the size of numbers.

b.    CATERPILLAR TRACKS
      To reinforce the importance of the base ten structure.
      To compare quantities.

c.    UNTANGLING -TEEN AND -TY
      Distinguish between the word-endings ‘-teen’ and ‘-ty’.

d.    THE STAIRCASE GAME
      To build a sequence using Cuisenaire rods.
      To develop the concept of comparison.
      To develop a strong visual image of comparative size.

e.    FOUR IN ORDER
(Putting number patterns in the correct sequence)
      To recognize number patterns.
      To sequence numbers.

f.     PATTERN PAIRS
(A matching and memory game)
      To learn to recognize numbers.
      To develop a strong visual image of the core patterns.
      To develop concentration.

g.    SHUT THE BOX
      To learn the dot patterns.
      To practice number bonds.

h.    BONDS OF TEN PAIRS
      To practise bonds of ten.
      To introduce the missing addend (the first step to learning subtraction).

i.      CLEAR THE DECK
(Based on the game ‘Clear the Deck’ in Butterworth and Yeo 2004.)
      To practise bonds of ten.

j.      THE TINS GAME
(The Tins Game was invented by Martin Hughes, 1986.)
      To understand the concept of addition.
      To learn to count on from a number.
      To understand the commutativity principle for addition.
      To practise estimating skills.

k.    TENS AND UNITS GAME
      To understand the place-value system

l.      FIRST  TO 30
(This game was devised by Brian Butterworth and Dorian Yeo, Dyscalculia Guidance.)
      To introduce concept of exchange and redistribution.

m.  BACK TRACK
      To practice subtraction and decomposition.

n.    THE MULTIPLICATION GAME
      To understand multiplication as repeated addition.
      To understand the array model of multiplication.
      To understand commutativity.
      To practice multiplication tables.

o.    FUN TIMES
(A matching and memory game.)
      To practice times tables.
      To improve memory.

p.    SPIN AND TRACK
      To practice exchanging ten ones for one ten.
      To explore the difference between addition and multiplication.
      To practice addition and multiplication.

q.    SPIN A STORY
      To highlight the difference between addition and multiplication.
      To put numbers into contexts.

Other effective strategies include:

a.    Cooperative Learning
b.    Projects
c.    Simulations and Role Plays
d.    Songs, Jingles and Raps
e.    Math Experiments and Hands-On Activities



REFERENCES:

Bilbao, P., et. Al(2009). Curriculum development. Manila: Lorimar Publishing
Butterworth, B. (2005). “Developmental dyscalculia," in Handbook of Mathematical Cognition, J. Campbell, Ed. New York: Psychology Press.
Corpuz, B. and Salandanan G.(2009). Principles of teaching 1. Manila: Lorimar Publishing
Corpuz, B., Rigor, D., and Salandanan G.(2009). Principles of teaching 2. Manila:Lorimar Publishing
Department of Education, Bureau of Elementary Education (2010). Lesson guide in elementary mathematics. Manila:  Book Media Press Inc.
Dimalanta, F. X. (2009). Understanding dyscalculia. Retrieved from http://www.mb.com.ph/articles/211578/understanding-dyscalculia
Emerson, J. and Babtie, P (2010). The dyscalculia assessment. United Kingdom: Continuum Internationall Publishing Inc.
Holdbrook, M.D. (2007). Standard based IEP examples. Alexandria: National Association of State Directors of Special Education
Internet Resources:

















Thursday, November 7, 2013

Principles of Teaching: Human Growth and Development



        The following are principles of human growth and development. These principles or facts help educators understand the nature and pattern of development. These principles are fundamental since each of these has significant implications to individual learners.As teachers, it is very important to know our learners' growth and development patterns in order for us to provide appropriate approach and methods of teaching and learning experiences to our learners.  


1. Early foundation are critical.  How the child developed in the first years of his/her life will bring great impact to the proceeding years of the child's life. This is so since early years of one's life serve as the foundation and can greatly determine if one will more likely to succeed in adjusting to life as they grow older.

2. Maturation and learning play important roles in development. Maturation is the unfolding of the individual's inherent traits while learning is development that comes from exercise and effort of an individual. These two factors are interrelated in various sense. First, individual differences emerged not only because of varied degrees of maturation by every individual but also because of the capability of human beings to learn. Patterns of behavior, interests and attitudes come not from maturation alone but from learning as well. Second, maturation  set limits beyond which development cannot progress, even with the most favorable learning methods and the strongest motivation on the part of the learner. Third, developmental readiness determines if an individual is ready to learn. There is a definite timetable for learning.

3. Development follows a definite and predictable pattern. There are orderly patterns of physical, motor, speech and intellectual development. For example, babies creep and crawl before they walk. Most of the time, attraction to opposite sex comes during puberty. Or failing health starts to happen as one reaches 60.

4. All individuals are different. Every person is biologically and genetically different from each other. No two people can be expected to react in the same manner to she same environmental stimuli. Bottomline: Never compare.

5. Each phase of development has characteristic behavior. Babies babble and crawl, school-aged children run, jump and play, adults find partners are just some of the examples.  

6. Each phase of development has hazards. It is essential therefore to be aware of and cope with these hazards, either be physical, psychological or environmental in origin, since these greatly affect on an individual's personal and social adjustment.

7. Development is aided by stimulation. Stimulation can be done so that development will reach its full potential.

8. Development is affected by cultural changes. Developmental pattern is most of the times based to conform to cultural standards and ideals. Girls and boys act differently in respect to the society's culture and expectations of what a male or female should act.

9. There is a social expectation for every stage of development. In every culture, there is a certain expectation for a member to master certain skills and acquire certain approved patterns of behavior at various ages during the life span.

10. There are traditional beliefs about people  of all ages. Stereotypes are widespread and greatly affect people's judgments of others and to oneself.


source: Hurlock, Elizabeth B. Developmental Psychology 5th Edition

image source: Google image search

Tuesday, November 5, 2013

Attitudes Toward Persons with Disabilities

Attitudes Toward Persons with Disabilities
People with disabilities generally have experienced discrimination and devaluation based solely on being different from the non-disabled public. They are often treated with the same discrimination and bias as other more traditional minorities (Bedini, 1992). They are treated as outsiders, and a certain social distance exists between them and the non-disabled majority.
The treatment and attitudes toward persons with disabilities has historically gone through a continuum: from rigid exclusionary attitudes to the currently emerging inclusionary attitudes. It has gone through several stages. These stages can be described as follows (Mishra, n.d.; Caldwell, 1973 in Porter, 2002):
Infanticide and Cruelty
Persons with disabilities were disregarded through the natural process as ‘‘survival of the fittest’’ was the principle for survival. There was no place for the weak and sick people for they were considered incapable to fight in wars or to hunt for food. Children born with handicap conditions were not protected and they were allowed to die at birth or in infancy. In some instances it was believed that physical deformities and mental disorders were the result of possession by demons and thus, afflicted persons were rejected, punished or killed.
Missionary Approach
With the advent of religious ideals like Christianity and Buddhism, the cruel practices were gradually diminished. Religious leaders later became concerned in the custody and care of the persons with disabilities. Yet during the Middle Ages, persons with disabilities particularly those with physical-motor disabilities were mocked at in the streets, treated harshly and driven to jugglery, begging or crime. They were often objects of amusement and were used for entertainment. Attempts were also made to cure the disabilities but the methods of treatment were rather primitive. Institutes were founded for the poor and destitute which also included those with disabilities.
Training and Education
A number of institutions were set up for the blinds, deaf and with severe disabilities. It was recognized that prevention and early care would relieve the society of the burden of supporting the persons with disabilities throughout their lives. This stage can be subdivided into two:
Forget and Hide
Until the middle of twentieth century, families, communities and the society as a whole still seemed to try to reject the existence of persons with disabilities. Families often were advised to immediately institutionalize a member with disability. Groups, such as the National Association for Retarded Children in America, were founded and pushed effort to identify children with mental retardation and other disabilities to bring them out of hiding.
Screen and Segregate. Special Education came into being in public school systems. However at this stage, special education was more of custodial care. Persons with disabilities were tested, labeled and segregated into a special facility and basically isolated again.
Identify and Help
Political and social movements paved the way for the recognition of the rights of persons with disabilities. These movements swayed the ideas on which much of the litigation and legislation involving persons with disabilities are based. Important court cases (e.g. Diana v. Board of Education; Larry P vs. Riles) present a progression of increasing rights for persons with disabilities. Together with this litigation, legislation (e.g. Americans with Disabilities Act, Individual with Disabilities Education Act) were started to be passed that provided further support for the rights of persons with disabilities.
Include and Support
This stage is signaled by the passage of legislations and litigation. As a result of breakthrough legislation promulgated in some of the progressive countries of the world, such as the IDEA, society has improved in understanding persons with disabilities. Thus the attitude of the society has been changing from hatred, to sympathy and tolerance to equal rights in school, in the workplace and in social settings.

Currently, the attitudes of the majority without disabilities toward the minority with disabilities are of especial importance because persons with disabilities are moving or being moved in the mainstream society. Yet, attitudes are the major barriers to people with disabilities’ full participation. According to Dalal (2006), attitudinal handicaps are pervasive and often far more devastating than the environmental handicaps. It is not the physical environment nor the actual limitations caused by their disabilities, but the discriminating attitudes imposed by the non-disabled people (Heward, 2003).

As Heward (2003) puts it, courts can decree or laws can mandate, but neither can alter the way attitudes in which individuals treat persons with disabilities. These stereotypical and negative attitudes hold people back:  from pity, awkwardness and fears to low expectations about what persons with disabilities can contribute (Massie, 2006). Whether the negative attitudes are of aversion, fear, guilt, anger, pity or sympathy, there is a need to change these attitudes to ensure better social integration of persons with disabilities.

Monday, November 4, 2013

Sensory Disability


Sensory disability is a disability resulting from the impairment of one of the senses, generally vision and hearing. These include visual and hearing impairments which refer to mild to severe loss of hearing or vision or both hearing and vision (UNESCO, 2009).
Visual impairment is a broad term used to describe the complete or partial loss of vision. It has both legal and educational definitions. The legal definition defines blindness as having a distance visual acuity of 20/200 or less with the best possible correction whereas partially sighted has visual acuity of 20/70. A visual acuity of 20/200 implies that a person who is legally blind can see at twenty feet, what a person with normal vision can see at a distance of two hundred feet; while a visual acuity of 20/70 means a persons who is partially sighted can see something at 20 feet what a normal vision can see at 70 feet (Mastropieri and Scruggs, 2000; Ashman and Elkins, 1998). On the other hand, educational definition involves processing of information specifically reading. For example, students with visual impairment may be assessed based on visual acuity but may each learn and function in different manner. According to Gargiulo (2012), students with low vision are capable to read using enlarged prints. Others are functionally blind that the primary mode of learning is through tactile or auditory mean like Braille.
The greatest challenges most persons with visual impairment face are difficulties in mobility; understanding and using non-verbal communication; and difficulties with written communication.
It is also important to note that individuals who are born blind (or with little residual vision), or who lost their vision at a very early age have relatively different needs, and face different barriers, than individuals who have lost their vision fully or partially later during their childhood.
Hearing impairment on the other hand is a general term to refer the total or partial loss of hearing. Hard of hearing is described as the partial loss of hearing while deafness is used to describe total or complete loss of hearing (UNESCO, 2009). According to Gargiulo (2012), persons who are hard of hearing are those whom the sense of hearing is defective but functional, either with or without hearing aid, for the purpose of processing linguistic information. Deafness on the other hand means the sense of hearing is non-functional for the ordinary purpose of life. It prohibits successful processing of linguistic information through hearing, with or without hearing aid. 
Hearing may be impaired in terms of the range of frequencies one can hear or the volume of sound, or the combination of both. As loss becomes greater, it has corresponding effect upon language and speech development as well as academic achievement in school.
Hearing impairment can differ in degree from mild to profound (Frederickson and Cline, 2009; Ashman and Elkins, 1998). A mild hearing impairment means having a BEA or Better Ear Average (the softest sound that can be heard) of 30-40 decibels (dB) of sound. A person affected may fail to realize being addressed by another person and may have some difficulty in conversation. Persons with moderate hearing impairment may have difficulty hearing at a distance and in noise. They can hear 40-65 dB of sound and may benefit from using hearing aid. Severe hearing impairment involves having a BEA of 65-96 decibels. In this case, normal conversation is almost impossible and may find the use of hearing aid quite useful. Lastly, individuals with profound hearing impairment can hear 95 and above decibels. Normal conversation is impossible for these individuals. They mainly depend on visual cues to communicate such as sign language.
The greatest challenge persons with hearing impairment face is difficulties with communication. This is so because the majority of the population uses oral communication. People with hearing impairment practice oral or manual means of communication, or a combination of both. Oral communication includes speech (vocal communication), lip-reading and the use of residual hearing, while manual communication includes sign language and fingerspelling. Total communication is a combination of oral and manual communication.

It has to be emphasized that both visual and hearing impairment do not affect a person's intellectual capacity or ability to learn. They are not a disadvantage if the educational, social and attitudinal structures of society enable them to learn and achieve their potential based on their unique needs and mode of learning. 
image source: http://www.kirklees.gov.uk/community/careSupport/healthWellbeing/images/sensoryServicesMenuIcon.gif