02 LD & DD Mathematics. Learning difficulties in mathematics on primary

learning difficulties in m mathematics

1. Learning Difficulties in
Mathematics
Ricardo Scott

2. SUPPLEMENTARY BIBLIOGRAPHY
In addition to this presentation and its links, and the
translated notes in UADRIVE, you can use the
following book (Ebookversion for less than 20 euros):
The Effective Teacher's Guide to Dyslexia and other
Learning Difficulties (Learning Disabilities)
Año 2011
Autor: Michael Farrell
Chapter 5: Mathematics disorder/dyscalculia

3. Learning Difficulties in Mathematics (LDM)
DSM IV
•Ability to calculate significantly
lower than expected.
•Not explainable by low IQ.
•Significant interference in
academics and life
•It cannot be explained by a
sensory deficit
DSM V
•Included as a subtype of SLD
(Specific Learning Disorder)
•Affected:
oThe sense of numbers
oMemorization of arithmetic
operations
oFluid calculation
oCorrect mathematical
reasoning

4. INSUMMARY,childrenwithLDM:
►Misunderstandnumbers,theirmagnitudeandtheirrelationships
►Countwithfingerstosumsingle-digitnumbersinsteadofremembering
themathoperationlikepeersdo
►Getlostinarithmeticandinterchangeofprocedures
Learning Difficulties in Mathematics (LDM)

5. PREVALENCE
2.2 -6.4%
Dyslexia
ADHD
+ Boys
Diagnosis: 6-10 years of age
Kuhn et al 2021 (Differences with gender)
https://doi.org/10.3389/feduc.2021.683672

6. Dehaene’s Triple Code Model

7. http://www.humanconnectomeproject.org/gallery/

9. Fronto-parietal section of the superior longitudinal fasciculus (SLF-FP)
Frontotemporal section of the superior longitudinal fasciculus (SLF-FT)
Parieto-temporal section of the superior longitudinal fasciculus (SLF-PT)
Diffusion tensor imaging (DTI) data and fractional anisotropy (FA)
https://link.springer.com/content/pdf/10.1007%2Fs00429-014-0975-6.pdf

10. a.Efficiency was measured as a
function of precision and speed
in answering arithmetic
problems.
b.Correlation between efficiency
and myelin development
c.Correlation between precision
and reaction time in solving
arithmetic problems and
change in myelin development
https://link.springer.com/content/pdf/10.1007%2Fs00429-014-0975-6.pdf

11. Lack of numerical skills is associated with the same impairments
as literacy problems
Does Numeracy Matter More?
Parsons & Bynner 2005;
https://www.researchgate.net/publication/245969683_Does_Numeracy_Matter_More

13. http://www.nrdc.org.uk/wp-content/uploads/2005/01/Does-numeracy-matter-more.pdf

14. What number is the next operation closest to?
7/8 + 12/13
a)1
b)2
c)19
d)21
Only 27% of students
between 13-14 years
old answered
correctly this
question
The nightmare of fractions...

15. China vs USA

16. BASIC COGNITIVE PROCESSES ALTERED IN LDM
Miranda, A., Fortes, C. y Gil, M. D. (2000). Dificultadesdel aprendizajede las
matemáticas. Un enfoqueevolutivo. Málaga: Aljibe.
•Selective attention:difficulties focusing on the
relevant parts of a problem and keeping track of
the sequence of operations.
•Perception:problems with figure–ground
differentiation, discrimination, spatial
orientation, recognizing the shape of numbers,
and distinguishing signs.
•Auditory processing:difficulties with mental
calculation or when problems are presented
orally in sequence.
•Memory:difficulties in number recall tasks,
suggesting problems with maintaining numbers
in short-term memory.

17. SOCIAL AND PERSONAL ASPECTS ALTERED IN LDM
Self-concept: due to the history of failures
(frustration)
Attributions: identification of reasons form
success or failure (“I am bad in maths,I am not
able”)
Behavior: anxiety and impulsivity
Metacognitive strategies: problems in identifying
their own ways of thinking erroneously
Identity theory: social role determines academic
perfomances

18. Initial learning
difficulties
(cognitive
challenges)
Ritual
participation
(mechanical,
right/wrong
focus)
Reinforcement
of failure by
teacher
responses
Formation of
math failure
identity
Reduced
engagement in
exploratory
learning
A case study (Dana)

19. EARLY CHILDHOOD (from 4 years of age)
Counting▪Inabilitytolabeleachitemofagroupwitha
number.
▪Inabilitytoapplyorunderstandthecardinal
valuerule.
▪Inabilitytoseparateuptofiveobjectswhen
asked.
Concept of
number
▪Inabilitytoassociatenumberswithagroupof
items.
▪Inabilitytogroupsetsbasedonagiven
criteria.
▪Falsebeliefthatthenumberofelements
variesdependingonthelocationofthese.
Sum ▪Deficitsintheabilitytodeterminethe
relationshipbetweenagivennumberandthe
onethatfollowsorprecedesit.
LDM RISK INDICATORS IN THE CHILDHOOD AND PRIMARY
EDUCATION

20. PRIMARY EDUCATION
Numerical sense▪Difficultiesunderstandingthepositionalvalueofnumbers.
▪Difficultiestoestablishcomparisonsbetweensetsofelements.
Reading ▪Errorsreadingandwritingnumbers.
Mathematical
language
▪Deficitsinunderstandingmathematicallanguageandsymbols.
Measure ▪Deficitsunderstandingtheconceptofmeasurement.
▪Deficitsunderstandingtheamountoftime,thevalueofmoney...
Calculus▪Difficultiesinsolvingsimpleproblemsmentally.
Arithmetic Sum ▪Difficultiestoautomatizethesum.
▪Needforphysicalsupporttosum(i.e.countingwithfingers).
▪Misplacementofquantities.
▪Notunderstandingtheconceptofcarryingover(theyplacethewhole
resultineachcolumn).
▪Beginningoperationsfromthetheleft.
Substration▪Misplacementoftheminuendandsubtrahend.
▪Difficultiesinplacing"carried"numbers.
▪Theystartfromtheleft.
▪Theyconfusethesignwiththesum.
Multiplication▪Difficultieswithmentalcalculation.
▪Difficultiesinmemorizingthetables.
Division▪Difficultiesinspatialdisposition.
▪Difficultiesinunderstandingwhyyouonlyworkwithdividendfigures.
▪Theystartworkingwiththedividendand/ordividerontheleftorright
interchangeably.
▪Conflictswhenworkingwithnumberslargerthanonenumberonthe
divider.

21. 2.EVALUATIONOFLDM
▪Contextual variables
▪Emotional and motivational aspects
▪Metacognitive processes
▪Difficulties in the area ofmathematics
•Declarative knowledge of mathematics
•Procedural knowledge
•Language mediation in mathematical activity
(comprehension)
•Absence of basic concepts
VARIABLES TO
CONSIDER

22. Contextual variables
Maths in the class
Do we teach
adequately?
•Are both computational skills and mathematical
thinking emphasized?
•Are a variety of techniques used to actively
engage students in learning?
•Are discovery-based or reflective learning
activities included?
•Are activities that create cognitive conflict used
to help students modify misconceptions?
•Is classroom discussion encouraged to elicit
students’ prior ideas and support them in
generating and discussing their own solution
strategies?
•Is the search for and application of original
solutions encouraged?
•Is sustained effort and persistence in problem
solving rewarded?
•Are students allowed to make mistakes and learn
by correcting them?

23. Evaluation of the emotional and motivational aspects
•Student's beliefs about
their own abilities
•Attitude towards
mathematics
•Identify possible cases of
anxiety or lack of
motivation.

24. Evaluation of metacognitive processes
Evaluate the student's ability to
reflect on the adequacy of:
•The strategies put into practice.
•The procedures used.
•The solution provided.

25. ❖Difficulties in the area ofmathematics
▪Declarative knowledge of
mathematics (problems to
understand and therefore explain
mathematical concept)
▪Procedural knowledge
▪Language mediation in
mathematical activity
(comprehension)
▪Absence of basic concepts
Specific assesmentof LDM

26. TEST EDAD DESCRIPCIÓN
Arithmetic subscale (WISC-R;
Whechsler, 1995)
Between 6 and 17 years
old
Arithmeticproblemspresentedorally
Subscale of Ability to Manage
Quantitative Relationships and
Concepts of the Primary-Revised
Cognitive Skills Test (Thorndike,
Hagen and Lorge, 2012)
Primary-RI: Between 6-7
years
Primary-RII: Between 7-8
years
Assesstheabilitytoestablishrelationshipsandmasteryofquantitative
conceptsthroughsimplepointcountingtests,additionsandsubtractions,
problems,andnumericalcomparisons
School Skills Test (TEA; Thurstone,
2004)
Level 1:
3rd-6th Primary
Evaluatesthedimensionsofverbal,reasoning,andcalculationskillsthat
aresubsequentlytransformedintoIQs.
Test for the diagnosis of basic math
skills (TEDI-MATH; Van
Nieuwenhoven, Noël y Grégoire,
2005)
From 2nd Child to 3rd
Primary
Itconsistsof25testsgroupedinto6areasofnumericalknowledge:
Count
Number
Understandingthenumericalsystem
Logicaloperations
Arithmeticoperations
Estimationofsize
Early Mathematical Assessment Test
(TEMT; Navarro et al., 2011)
Between 4 and 7 years oldIt consists of 8 subscales that evaluate two dimensions of early
mathematical competence (Piagetian and numerical or counting tasks):
Comparison
Classification
One-to-one correspondence
Seriation
Verbal counting
Structured counting
Resulting count or result of count
General knowledge of numbers
STANDARIZED TEST TO EVALUATE LDM
But not only
standardized tests
inform us about
learning difficulties.

27. RESOURCES AND
DIDACTIC MATERIALS
Handling
Physical
representation
Mathematical
concepts
Better Teaching,
active, playful,
creative
Positive
actitudes
3.INTERVENTION
The idea is not insisting in
doing many times the same
activities in which children
make mistakes, but to identify
the basic processes that are
failing and work with them
from different perspectives.

28. 1. Clarification of the structure and
requirements:
•Explain the objectives and requirements
of each activity.
•Promote student responsibility (related
to motivation)
•Provide a high degree of structuring.
How to teach math effectively

29. 2. Session planning:
•Briefly summarize the contents
addressed in previousclasses.
•Offer a broad overview of the new
topics.
•The tasks to be carried out
throughout this session will be
specified at the beginning of each
session.
•End each session with a synthesis of
what has been learned.
How to teach math effectively

30. 3. Active participation of the student:
•Actively involve the student in the
classroom.
•Team work
•Ask questions to students.
•Provide the necessary support so
that the student knows how to solve
their errors and difficulties.
How to teach math effectively

31. 4. Other strategies
•Use visual resources (diagrams, colors, etc.) that help maintain
attention in mathematical activities.
•Ensure the generalization of learning, proposing varied activities.
•Make use of the student's previous knowledge and experiences.
•Provide strategies to overcome difficulties.
•Adopt a flexible posture.
•Software (Geogebra, Mathblaster, etc)
•https://www.edarabia.com/top-math-apps-primary-school-
students/
How to teach math effectively

32. 5. Evaluation:
•Analyzethe errors in the result and in the
procedure.
•Provide clear instructions on how to do it
correctly
•Prepare the tests with the teacher's help
(training to make the exams: the objective
is that children passthe exams)
How to teach math effectively

33. DIDACTIC MATERIALS FOR LDM
LOGIC

34. DIDACTIC MATERIALS FOR LDM
CALCULUS

35. DIDACTIC MATERIALS FOR LDM
COUNTING

36. DIDACTIC MATERIALS FOR LDM
GEOMETRY

38. DIDACTIC MATERIALS FOR LDM
STATISTICS

39. DIDACTIC MATERIALS FOR LDM
MEASURING

40. PROGRAMS AND EXERCISES
Psychological
basis
•Psychomotor skills
•Body scheme
•Sensory aspects
•Perceptual aspects
•Motor aspects
•Basic notions
•Conservation
•Correspondence
•Reversibility
•Number
•Basic processes (attention and memory)
•Mathematical vocabulary (oral and written expression)

41. Specific to
mathematical
learning
•Numeration
•Association number / object
•Correct realization of numbers
•Understanding and use of mathematical signs
•Metric system
•Arithmetic
-Problems of understanding, spatial association
and automation
•Problem resolution
-Understanding of statements and procedures
•Geometry
-Spatial relationships and distance calculation
PROGRAMS AND
EXERCISES

42. Direct instruction
Reciprocal
teaching
Self-instructional
teaching
Recreational
mathematics
Guided discovery
learning
METODOLOGIES