7. Preview
• What causes difficulties in learning Math?
• What are the potential areas of difficulties
in learning Math?
• What information can we obtain from a
student’s work?
9. Mathematics is a symbolic language used to:
• express relationships – spatial, numeric,
geometric, algebraic, and trigonometric, in both
real and imaginary dimensions ;
• communicate concepts through symbols;
• reinforce and practise sequential and logical
thinking.
(Clayton, 2003)
10. A. Nature of Math (Chinn & Ashcroft, 1998)
• Interrelated
Parts are learned that later
on build into wholes.
What are needed to
learn:
• place values?
• adding dissimilar
fractions?
• long division?
11. A. Nature of Math (Chinn & Ashcroft, 1998)
• Interrelated
Parts are learned that later
on build into wholes.
What will happen
when a student does
not learn some of
these parts?
12. A. Nature of Math (Chinn & Ashcroft, 1998)
• Sequential
The learning of higher
skills depends on the
learning of basic skills.
13. A. Nature of Math (Chinn & Ashcroft, 1998)
• Sequential
14. A. Nature of Math (Chinn & Ashcroft, 1998)
• Sequential
The learning of higher
skills depends on the
learning of basic skills.
What will happen
when the basic
skills are not
learned?
15. A. Nature of Math (Chinn & Ashcroft, 1998)
• Reflective
The meaning of concepts
expand as lessons
progress.
17. B. Structure (Chinn & Ashcroft, 1998)
Math is learned
from concrete
to abstract
Levels of difficulty build
up as the lessons
progress.
18. B. Structure (Chinn & Ashcroft, 1998)
Implications:
1. If the basic levels are skipped or not well-taught, the
foundations of learning become shaky.
2. When foundations are shaky, learning becomes
segmented, thus the student has to resort to
memorization.
3. When lessons are simply memorized, more effort is
needed to learn higher-level lessons.
19. C. Skills and Processes
(DepEd Math Curriculum 2013)
• Knowing and understanding
• Estimating, computing, and solving
• Visualizing and modelling
• Representing and communicating
• Conjecturing, reasoning, proving, and
decision-making
• Applying and connecting
20. D. Characteristics of School Math
• There are rules but
they do not apply all
the time
• Answers are either
right or wrong
• Tasks require
concentration
21. E. Math Language
• Symbols + – x =
A = r2
• Vocabulary Algebra, perimeter, sine
even, pound, table
• Syntax and
Semantics
seven more than one,
quarter of a half,
a difference of two
22.
23. What are the potential areas
of difficulties in learning
Math? (Chinn & Ashcroft, 1998)
24. Preview
1. Direction and
sequence
2. Perception
3. Retrieval
4. Speed of working
5. Math language
6. Cognitive Style
7. Conceptual Ability
8. Anxiety, stress, self-
image
37. 9. Cognitive Style (Chinn & Ashcroft,1998)
Analyzing and Identifying the Problem
1. Tends to overview,
holistic, puts together.
2. Looks at the numbers and
facts to estimate an
answer or restrict range
of answers. Controlled
exploration.
1. Focuses on the parts and
details. Separates.
2. Looks at the numbers and
facts to select a relevant
formula or procedure.
Grasshopper
Inchworm
38. Solving the Problem
Grasshopper
Inchworm
3. Answer orientated.
4. Flexible focusing. Methods
change.
5. Often works back from a trial
answer. Multi-method.
6. Adjusts, breaks down/ builds
up numbers to make an easier
calculation.
3. Formula, procedure orientated.
4. Constrained focus, Uses a
single method.
5. Works in serially ordered
steps, usually forward.
6. Uses numbers exactly as
given.
Cognitive Style (Chinn & Ashcroft, 1998)
39. Solving the Problem
Grasshopper
Inchworm
7. Rarely documents method.
Performs calculation
mentally.
8. Likely to appraise and
evaluate answer against
original estimate. Checks by
alternate method.
9. Good understanding of the
numbers, methods and
relationships.
7. More comfortable with paper
and pen. Documents
method.
8. Unlikely to check or
evaluate answer. If check is
done, uses same procedure
or method.
9. Often does not understand
procedure or values of
numbers. Works
mechanically.
Cognitive Style (Chinn & Ashcroft, 1998)
41. 10. Conceptual Ability
• Impact of Brain-based Condition(s)
• Social or behavioral skills-related
• Autism
• Asperger’s Syndrome
• Attention-Deficit/Hyperactivity Syndrome
• Communication skills-related
• Language Acquisition
• Receptive / Expressive Language
Difficulties
42. 10. Conceptual Ability
• Impact of Brain-based Condition(s)
• Cognitive/learning skills-related
• MR/ Intellectual Disability
• Learning Disabilities
• Long and Short-term Memory Deficits
• Physical or sensory skills-based
• Visual Impairment
• Hearing Impairment
43. 10. Conceptual Ability
• Dyscalculia
• Dyscalculia is usually perceived of as a
specific learning difficulty for mathematics,
or, more appropriately, arithmetic.
(http://www.bdadyslexia.org.uk/)
• Dyscalculia is a brain-based condition that
makes it hard to make sense of numbers
and math concepts.
(https://www.understood.org/)
52. Preview
1. Introduction to Remediation
2. Some Remedial Teaching Strategies
3. Principles of Remediation
4. The Remedial Plan
53. The commonly accepted idea of
remediation as a careful effort to
reteach successfully what was not well
taught or not well learned during the
initial teaching. (Glennon & Wilson, 1972)
What is remediation?
54. Students who show lags in math
performance that are unlike his or her
potential or performance in other
academic areas
Who needs math remediation?
55. Do not allow children who may have special
needs to go from one grade to another
without a professional team assessing the
student for eligibility for services and
supports. "Waiting" is NOT an effective,
educational practice. Although the process of
referral can be cumbersome, it is well worth it
when it identifies needs that can be met
during the educational life of the child.
– Barbara T. Doyle, Johns Hopkins School of Education
56. The Remediation Process
1) Identify the concepts, skills, procedures to be
retaught.
2) Collect supporting information, such as
anecdotes, work portfolio, and assessment
reports.
3) Select appropriate re-teaching methods and
strategies.
4) Provide remediation.
5) Evaluate and determine next steps.
57. 1) Structure of Mathematics
2) The student’s strengths and
difficulties
• Error analysis
• Formal Testing
• Diagnostic Testing
3) Remedial instruction strategies
What a Remedial Math Teacher
Needs to Know
78. 1. Build on what the child knows
Show interconnectedness of lessons
Promote reasoning
Principles of Intervention
(Chinn & Ashcroft, 2007)
79. 2. Acknowledge the student’s learning
style
T’s best method might not work
Let student discover the strategies that
work for him
Principles of Intervention
(Chinn & Ashcroft, 2007)
80. 3. Make math developmental
Use the concrete-representational-
abstract progression
Employ gradual transfer
Principles of Intervention
(Chinn & Ashcroft, 2007)
81. 4. Use the language that communicates
the idea
Use the child’s language
Use visuals, real objects, experiences
Principles of Intervention
(Chinn & Ashcroft, 2007)
82.
83. 5. Use the same basic numbers to
build an understanding of each
process or concept
Make instruction success-oriented
Principles of Intervention
(Chinn & Ashcroft, 2007)
84. 5. Teach ‘why’ as well as ‘how’
Principles of Intervention
(Chinn & Ashcroft, 2007)
85. 7. Keep a
responsive
balance in all of
teaching
Principles of Intervention
(Chinn & Ashcroft, 2007)
If the child does not learn the way you
teach, then you must teach the way he learns.
- Harry Chasty
104. REFERENCES:
Bley, N.S. and Thornton, C.A. (2001). Teaching mathematics to students with
learning disabilities, 4th ed. USA: Pro-Ed.
Chinn, S. and Ashcroft, J. (1998). Mathematics for dyslexics: A teaching
handbook, 2nd ed. UK: Whurr.
Chinn, S. and Ashcroft, J. (2007). Mathematics for dyslexics: Including
Dyscalculia, 3rd ed. England: John Wiley and Sons.
Doabler, C.T., et.al. (2012). Evaluating Three Elementary Mathematics
Programs for Presence of Eight Research-Based Instructional Design Principles.
Learning Disability Quarterly, 35(4), 200-211.
Lalley, J.P. and Miller, R.H. (2002).Computational Skills, Working Memory, and
Conceptual Knowledge in Older Children with Mathematics Learning Disabilities.
Education, 126(4), 747-755.
Mabbott, D.J. and Bisanz, J. (2008). Computational Skills, Working Memory,
and Conceptual Knowledge in Older Children With Mathematics Learning
Disabilities. Journal of Learning Disabilities, 41(1), 15-28.
Miles, T.R. and Miles, E, Eds. (1992). Dyslexia and mathematics. USA:
Routledge.
