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:

















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