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UNIVERSITY OF CADIZ, SPAIN
DEPARTMENT OF PSYCHOLOGY
J.I. NAVARRO, E. ARAGON & M. AGUILAR
(Study supported by Spanish Grant # EDU2011-22747 )
TEACHING EARLY MATHEMATICS IN SCHOOL
USING ICT AN EVIDENCE-BASED INTERVENTION
TEACHING EARLY MATHEMATICS IN SCHOOL
USING ICT AN EVIDENCE-BASED INTERVENTION
UNIVERSITY OF NEW MEXICO, USA
COLLEGE OF EDUCATION
R. HOWELL
http://www.uca.es/grup-invest/psicologia
IMPORTANCE
MATH is a GATEWAY to:
•Employment Options
•Income
•Work Productivity
MATH has more impact than reading and general intelligence on a person’s future
PREVALENCE
Significant percentage of students have difficulty in math: Global Learning Disabilities = 5%-9% Math underperformers in NM = 50% (Anglos) 80% (Hispanic, Indian)
INTRODUCTION STATEMENTS INTRODUCTION STATEMENTS
1.Some 5-year-old children have a
well-developed basic number sense
for their age:
• For example, they know that when
we add 1 or substract 1, the result
is always the previous or the
following number
1.Some 5-year-old children have a
well-developed basic number sense
for their age:
• For example, they know that when
we add 1 or substract 1, the result
is always the previous or the
following number
INTRODUCTION INTRODUCTION
• They have an informal awareness
of doubling the first digits up to
10 (2+2, 3+3, 4+4, 5+5)
• They can read and write the
first 10 digits forwards.
• They can count numbers up to
20 both forwards and
backwards.
• They have an informal awareness
of doubling the first digits up to
10 (2+2, 3+3, 4+4, 5+5)
• They can read and write the
first 10 digits forwards.
• They can count numbers up to
20 both forwards and
backwards.
INTRODUCTION INTRODUCTION
2. However other children:
•Only know the first 10 digits •When they count forwards, they always start from 1
•They cannot count backwards from 10 to 1
2. However other children:
•Only know the first 10 digits •When they count forwards, they always start from 1
•They cannot count backwards from 10 to 1
Some studies show that individual differences increase during early school years
INTRODUCTION INTRODUCTION
3. Some early arithmetic
learning difficulties continue
during childhood, adolescence
and adult life.
3. Some early arithmetic
learning difficulties continue
during childhood, adolescence
and adult life.
INTRODUCTION INTRODUCTION
4. When they persist in
children, it sometimes means
a negative attitude to
anything related to “number
literacy”
4. When they persist in
children, it sometimes means
a negative attitude to
anything related to “number
literacy”
Goals Goals
1. What can we do to reduce the impact of early math learning disabilities or under-achievement?
1. What can we do to reduce the impact of early math learning disabilities or under-achievement?
2. Use a new piece of software for learning early math intervention with pre-school students in order to reduce low math performance.
2. Use a new piece of software for learning early math intervention with pre-school students in order to reduce low math performance.
• 128 third preschool year.
•Girls: 58 (45.3 %)
•Boys: 70 (54.7 %)
• Age range: 59 to 72 months
• Mean age: 65.8 (3.3 sd) months
• Social level: middle and
low-middle class
• 128 third preschool year.
•Girls: 58 (45.3 %)
•Boys: 70 (54.7 %)
• Age range: 59 to 72 months
• Mean age: 65.8 (3.3 sd) months
• Social level: middle and
low-middle class
Participants: Participants:
Experimental groupExperimental group Experimental groupExperimental group 30 30
Control group Control group Control group Control group 98 98
Participants Participants
ENT-r-A SCORE < 19
OUT OF 45OUT OF 45
Assessment Assessment
SPANISH EXPERIMENTAL ON LINEON LINE
VERSION
ORIGINAL VERSION:
Utrechtse Getalbegrip Toets-R
Johannes E. H. van Luit, &
Bernadette A. M. van de Rijt.
www.graviant.nl
“THE UTRECHT EARLY
NUMERACY TEST-R” (ENT-R)
“THE UTRECHT EARLY
NUMERACY TEST-R” (ENT-R)
• Number of sessions = 30
• Time per session = 30 - 45 m.
• Small group (6 students)
• One laptop per student
Procedure Procedure
ENTENT--AA INTERVENTION PROGRAMINTERVENTION PROGRAM ENTENT--BB
NOV. 2011 JUNE 2012NOV. 2011 JUNE 2012 NOV. 2011 JUNE 2012NOV. 2011 JUNE 2012
Phase A Phase B Phase CPhase A Phase B Phase C Phase A Phase B Phase CPhase A Phase B Phase C
ENTENT--AA INTERVENTION PROGRAMINTERVENTION PROGRAM ENTENT--BB
Phase A Phase B Phase CPhase A Phase B Phase C Phase A Phase B Phase CPhase A Phase B Phase C
Early Mathematical
Learning Software
Early Mathematical
Learning Software
2.02.0
• Previous experience developing educational software
• Cognitive and Behavioural Theories of Learning
• Counting theory by Gelman & Gallistel
• Preschool and 1st grade Spanish Curriculum
• Previous experience developing educational software
• Cognitive and Behavioural Theories of Learning
• Counting theory by Gelman & Gallistel
• Preschool and 1st grade Spanish Curriculum
Bas
ed o
n …
Bas
ed o
n …
Des
igning
Char
acte
rist
ics
Des
igning
Char
acte
rist
ics
• Motivating for students &
easy FRIENDLY use
• Reinforcing & interactive
• Different complexity levels
• Adapted to the target population
• To develop appropriate skills to access early math knowledge
• Motivating for students &
easy FRIENDLY use
• Reinforcing & interactive
• Different complexity levels
• Adapted to the target population
• To develop appropriate skills to access early math knowledge
• Last 2 years in kindergarten (4-6)
• First year primary school education (6-7)
• Pupils with low math
performance
• Last 2 years in kindergarten (4-6)
• First year primary school education (6-7)
• Pupils with low math
performance Tar
get
popu
lation
Tar
get
popu
lation
BASIC SOFTWARE STRUCTURE BASIC SOFTWARE STRUCTURE
77 ACTIVITIESACTIVITIES
- SKILLS TO DISCOVER DIFFERENCES AND
SIMILARITIES BETWEEN 2 OR MORE
STIMULI.
- TASKSTASKS FOR
DISCRIMINATION
BETWEEN
STIMULI, AND BY
“MATCH TO
SAMPLE”
DIFFERENTIATION
COMPARISONCOMPARISON
CLASSIFICATIONCLASSIFICATION
TASKSTASKS FOR
GROUPING STIMULI
BY ONE
CHARACTERISTIC
SERIATIONSERIATION TASKS TRAINING
SKILLS ORGANIZING
STIMULI BY ONE
CHARACTERISTIC.
SOME STIMULI ARE
ORDERED, SOME ARE
NOT.
TASKS FOR ORDERING
NUMBERS LOWER
THAN 20
PART/WHOLE COMBINATIONSPART/WHOLE COMBINATIONS
MATHMATH--BASED PROBLEM SOLVING TASKSBASED PROBLEM SOLVING TASKS
1. STUDENT HAS DATA ABOUT PARTSPARTS AND IS
ASKED ABOUT WHOLEWHOLE
2. STUDENT HAS ONE ONE PART AND WHOLEWHOLE, AND IS
ASKED ABOUT THE OTHEROTHER PART
SKILLS FOR
INHIBITION AND
NUMBER SENSE
NUMBER DISCRIMINATIONNUMBER DISCRIMINATION
PARTITIONPARTITION
SKILLS FOR
DIVIDING
NUMBERS
BETWEEN
DIFFERENT
PARTS
NUMBER LINENUMBER LINE
TASKS TO TASKS TO
ESTIMATE ESTIMATE
POSITION POSITION
FROM 0 FROM 0
TO 100TO 100
RESULTS RESULTS
PREPRE-- POSTPOST--
EXPERIMENTAL EXPERIMENTAL
GROUP GROUP
n = 30n = 30
14.33 14.33 (2.6)(2.6) 26.0 26.0 (5.4)(5.4)
CONTROL CONTROL
GROUP GROUP
n = 90n = 90
24.35 24.35 (5.5)(5.5) 25.4 25.4 (5.1)(5.1)
STATISTICAL ANALYSISSTATISTICAL ANALYSIS
BETWEEN GROUP COMPARISION
INT
RA
GR
OU
P C
OM
PA
RIS
ION
9,2
12,6 12,5
5,10
11,6012,90
**13,9 **
12 14,33
25,4
24,3**26
0
5
10
15
20
25
30
PRETEST POSTEST PRETEST POSTEST
EXPERIMENTAL GROUP CONTROL GROUP
ME
AN
SC
OR
E
0
5
10
15
20
25
30
PIAGETIAN SUBTESTS
NUMERICAL SUBTESTS
TOTAL TEST
PRE AND POST TEST EXP. & CONTROL GROUPSPRE AND POST TEST EXP. & CONTROL GROUPS PRE AND POST TEST EXP. & CONTROL GROUPSPRE AND POST TEST EXP. & CONTROL GROUPS
p < 0,001
MEAN INCREASE IN MEAN INCREASE IN ENTENT SCORES AFTER TRAININGSCORES AFTER TRAINING MEAN INCREASE IN MEAN INCREASE IN ENTENT SCORES AFTER TRAININGSCORES AFTER TRAINING
Experimental Group Control Group
Piagetian 4.73 0.3
Numerical 0.73 0.3
Total Test ENT-R 11.67 1.13
4.73
0,3 0.73
0,3
11.67
1.13
0 1 2 3 4 5 6 7 8 9
10 11 12 13
ME
AN
IN
CR
EA
SE
EN
T S
CO
RE
S
t gl Sig
-13.037 29 .001
-9.290 29 .001
-9.039 29 .001
t” COMPARISON PRE & POST TESTS FOR EXP.
GROUP
CONCLUSIONS CONCLUSIONS
1. TRAINING WAS USEFUL. EXPERIMENTAL GROUP INCREASED ENT-B SCORES
2. INTERVENTION DRAMATICALLY REDUCES DIFFERENCES BETWEEN GOOD AND BAD MATH PERFORMERS
3. TRAINING WAS BETTER FOR
PIAGETIAN THAN NUMERICAL
TASKS
4. NO GENDER DIFFERENCES WERE
FOUND
5. ESTIMATION TASK WAS THE MOST
DIFFICULT TASK
CONCLUSIONS-2 CONCLUSIONS-2
GENERAL CONCLUSION GENERAL CONCLUSION
• PLAYING WITH NUMBERS-2.0
SOFTWARE WAS EFFICIENT
AND REDUCED DIFFERENCES IN
NUMBER SENSE FOR EARLY
STUDENTS.
• PLAYING WITH NUMBERS-2.0
SOFTWARE WAS EFFICIENT
AND REDUCED DIFFERENCES IN
NUMBER SENSE FOR EARLY
STUDENTS.
