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Development of a Computerized Assessment Tool for Mathematics Difficulties for Primary School Students.

Authors:
Marios A. Pappas at National Centre of Scientific Research "Demokritos"
Marios A. Pappas
Fotini Polychroni at National and Kapodistrian University of Athens
Fotini Polychroni
Alexandra Economou at National and Kapodistrian University of Athens
Alexandra Economou
Athanasios Drigas at National Centre of Scientific Research "Demokritos"
Athanasios Drigas
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Abstract

Early math skills are considered a strong predictor of students' later mathematical performance [1] as well as of general subsequent academic performance [2]. Μathematics difficulties are associated with specific cognitive processes, such as working memory, attention regulation and information retrieval deficits [3]. This study investigates the cognitive, psychological, and metacognitive variables that are linked to mathematical achievement in primary-school students of second and third grade. In particular, the present study aims to examine the correlation of working memory, math anxiety, and sustained attention with mathematical achievement. Another aim of the study is to investigate the role of executive function, such as inductive reasoning and problem solving in mathematical achievement. In addition, this study investigates differences between second and third graders, as well as gender-based differences in cognitive and psychological measures. Final aim is to design a computerized assessment test for the detection of mathematics difficulties during second and third grade of primary school.
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Development of a Computerized Assessment Tool for
Mathematics Difficulties for Primary School Students.
Marios A. Pappas1, Fotini Polychroni1, Alexandra Economou1& Athanasios Drigas2
1 Department of Psychology, National and Kapodistrian University of Athens
2 Net Media Lab-Mind & Brain R&D, I.I.T., N.C.S.R. ‘Demokritos’
Correspondence: mpappas@ppp.uoa.gr
inspiring change
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the Beta Version
of BrainMath.
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This research is co-financed by Greece and the European
Union (European Social Fund-ESF) through the
Operational Programme «Human Resources
Development, Education and Lifelong Learning» in the
context of the project “Strengthening Human Resources
Research Potential via Doctorate Research” (MIS-
5000432), implemented by the State Scholarships
Foundation (ΙΚΥ)
Early math skills are considered astrong predictor of
students’ later mathematical performance [1] as well as of
general subsequent academic performance [2]. Μathematics
difficulties are associated with specific cognitive processes,
such as working memory, attention regulation and
information retrieval deficits [3]. This study investigates the
cognitive, psychological, and metacognitive variables that
are linked to mathematical achievement in primary-school
students of second and third grade.In particular, the
present study aims to examine the correlation of working
memory, math anxiety, and sustained attention with
mathematical achievement.Another aim of the study is to
investigate the role of executive function, such as inductive
reasoning and problem solving in mathematical
achievement.In addition, this study investigates differences
between second and third graders, as well as gender-based
differences in cognitive and psychological measures.Final
aim is to design a computerized assessment test for the
detection of mathematics difficulties during second and
third grade of primary school.
1. Introduction
The design of the assessment tool should be based on the
cognitive profile of students with mathematics difficulties.
For this reason we designed the Mathematical Achievement
Test, a curriculum-based assessment test which will be the
basis for the computerized assessment tool for mathematics
difficulties.This assessment test along with other
psychometric tools were used at the pilot study.
Sample
Materials
Mathematical Achievement Test
Test of Attention for Elementary School Students [4]
Working Memory Rating Scale [5]
Executive Function Test for Elementary School Students [6]
Mental Arithmetic Test (WISC-III) [7]
Abbreviated Math Anxiety Scale [8]
2. Method
3. Results
F Change
Model 1 .292 .284 .292
Mental Arithmetic
Model 2 .378 .364 .086
Mental Arithmetic
Sustained Attention
Model 3 .424 .404 .046
Mental Arithmetic
Sustained Attention
Working Memory
4. Discussion
The results of our study indicated that mathematical achievement of second and
third graders is positively correlated with students’ mental arithmetic ability,
sustained attention, and working memory.These results are consistent with the
findings of extant literature in the field of mathematical cognition.Furthermore,
as revealed by the multiple regression analysis, mental arithmetic ability,
sustained attention, and working memory could be used as predictors for an
important portion of the overall variance of mathematical achievement.
As expected, third graders had ahigher performance on the mathematical
achievement standardized test as compared to second graders and especially in
subtraction, multiplication, and division.These results are consistent with our
previous findings, as these mathematical skills are affected most by working
memory, which expands during childhood.
Students with mathematics difficulties
present low performance at number
awareness, recall of numerical facts,
execution of numerical calculations, as
well as mathematical reasoning.The
need for the development of areliable
and user-friendly tool, which aims at the
early detection of mathematics
difficulties, raises urgent.Moreover,
there is an increasing interest on using
digital educational tools for assessing
and supporting students with learning
disabilities.For this reason, we develop
an online tool which will incorporate
Information and Communication
Technologies for the assessment of
primary school students with
mathematics difficulties.
Year 2 (N=53) Year 3 (N=38)
Measures M SD MSD
Mathematical Skills 22.38 (32) 5.80 27.68 4.11
Counting 3.77 (4) .64 3.63 .67
Addition 2.91 (4) 0.96 3.66 .48
Subtraction 1.61 (4) 1.24 3.05 1.11
Multiplication 2.02 (4) 1.39 3.34 1.14
Division 2.30 (4) 1.55 3.24 1.28
Patterns 3.57 (4) .84 3.87 .41
Number Line 3.38 (4) .90 3.61 .87
Problem Solving 2.83 (4) 1.40 3.29 1.09
Sustained Attention 0.24 0.03 0.26 .04
Inductive Reasoning (Stories) 4.02 (5) 1.07 4.05 .93
Inductive Reasoning (Geometry) 8.08 (12) 2.81 9.63 2.07
Mental Arithmetic 11.06 (30) 2.90 11.79 2.89
Math Anxiety 20.89 5.54 18.24 6.02
Working Memory 8.96 12.90 5.61 9.19
Table 1: Multiple Regression Analysis predicting Mathematical Achievement
Table 2: Descriptive statistics for math measures and cognitive skills in terms of the school grade*
* 0.05 significance level, ** 0.01 significance level, *** 0.001 significance level
* Maximum score for each measure is shown in parenthesis. The optimal score for Math Anxiety & Working Memory is 0.
5. Conclusion
The next stage of this study is the finalization and standardization of the
computerized assessment test for mathematics difficulties (BrainMath)which
will incorporate curriculum based tasks, as well as tasks related to working
memory, sustained attention and inductive reasoning.It is anticipated that
BrainMath will enable accurate and early detection of mathematics difficulties.
BrainMath
Workin g
Memory
Sustained
Attention
Mental
Arithmetic
Ability
Arithmetic
Operations
Pattern
Recognition
Number
Line Sense
Problem
Solving
1. Rodic, M., Cui, J., Malykh, S., Zhou, X., Gynku, E. I., Bogdanova, E. L., ... &Kovas, Y. (2018). Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.British Journal of
Developmental Psychology,36(2), 255-276.
2. Price, G. R., Mazzocco, M. M., & Ansari, D. (2013). Why mental arithmetic counts:brain activation during single digit arithmetic predicts high school math scores.Journal of Neuroscience,33(1), 156-163.
3. Morgan, P. L., Farkas, G., Hillemeier, M. M., & Maczuga, S. (2016). Who is at risk for persistent mathematics difficulties in the United States?.Journal of learning disabilities,49(3), 305-319.
4. Simos, P., Mouzaki, A., & Sideridis, G. (2007). Test of attention for elementary school students.Athens:Greek Ministry of Education (in Greek)
5. Alloway, T. P., Gathercole, S. E., & Kirkwood, H. J. (2008). Working Memory Rating Scale. London: Pearson Assessment.
6. Simos, P., Mouzaki, A., & Sideridis, G. (2007). Test of Executive Function for Elementary School Students.Athens:Greek Ministry of Education.
7. Georgas, J., Paraskevopoulos, I., Besevegis, E., & Giannitsas, N. (1998). Greek Wechsler Intelligence Scale for Children, WISC-III:Manual.Athens:Ellinika Grammata.(in Greek)
8. Carey, E., Hill, F., Devine, A., & Szűcs, D. (2017). The modified abbreviated math anxiety scale: A valid and reliable instrument for use with children.Frontiers in psychology,8,11.
References
ResearchGate has not been able to resolve any citations for this publication.
Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation
Article
Full-text available
  • Jun 2018
The study investigated cross‐cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non‐symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6‐ to 9‐year‐old children from the United Kingdom, Russia, and China. Cross‐cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross‐cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non‐symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? • Cross‐cultural differences in mathematical ability are present in preschool children. • Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. • Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? • Cross‐cultural differences in mathematical ability become greater with age/years of formal education. • Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. • Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations.
View
The Modified Abbreviated Math Anxiety Scale: A Valid and Reliable Instrument for Use with Children
Article
Full-text available
  • Jan 2017
Mathematics anxiety (MA) can be observed in children from primary school age into the teenage years and adulthood, but many MA rating scales are only suitable for use with adults or older adolescents. We have adapted one such rating scale, the Abbreviated Math Anxiety Scale (AMAS), to be used with British children aged 8-13. In this study, we assess the scale's reliability, factor structure, and divergent validity. The modified AMAS (mAMAS) was administered to a very large (n = 1746) cohort of British children and adolescents. This large sample size meant that as well as conducting confirmatory factor analysis on the scale itself, we were also able to split the sample to conduct exploratory and confirmatory factor analysis of items from the mAMAS alongside items from child test anxiety and general anxiety rating scales. Factor analysis of the mAMAS confirmed that it has the same underlying factor structure as the original AMAS, with subscales measuring anxiety about Learning and Evaluation in math. Furthermore, both exploratory and confirmatory factor analysis of the mAMAS alongside scales measuring test anxiety and general anxiety showed that mAMAS items cluster onto one factor (perceived to represent MA). The mAMAS provides a valid and reliable scale for measuring MA in children and adolescents, from a younger age than is possible with the original AMAS. Results from this study also suggest that MA is truly a unique construct, separate from both test anxiety and general anxiety, even in childhood.
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Who Is At Risk for Persistent Mathematics Difficulties in the United States?
Article
Full-text available
  • Oct 2014
We analyzed two nationally representative, longitudinal data sets of U.S. children to identify risk factors for persistent mathematics difficulties (PMD). Results indicated that children from low socioeconomic households are at elevated risk of PMD at 48 and 60 months of age, as are children with cognitive delays, identified developmental delays or disabilities, and vocabulary difficulties. In contrast, children attending preschool either in Head Start or non-Head Start classrooms are at initially lower risk of PMD. Kindergarten-aged children experiencing either low socioeconomic status or mathematics difficulties are at greatest risk for PMD across third, fifth, and eighth grades. Also at risk for PMD between third and eighth grades are children displaying reading difficulties or inattention and other learning-related behaviors problems, children with identified disabilities, and those who are retained. Educationally relevant and potentially malleable factors for decreasing young children's risk for PMD may include increasing children's access to preschool, decreasing their risk of experiencing vocabulary or reading difficulties, and avoiding use of grade retention.
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Why Mental Arithmetic Counts: Brain Activation during Single Digit Arithmetic Predicts High School Math Scores
Article
Full-text available
  • Jan 2013
  • J NEUROSCI
Do individual differences in the brain mechanisms for arithmetic underlie variability in high school mathematical competence? Using functional magnetic resonance imaging, we correlated brain responses to single digit calculation with standard scores on the Preliminary Scholastic Aptitude Test (PSAT) math subtest in high school seniors. PSAT math scores, while controlling for PSAT Critical Reading scores, correlated positively with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex, brain regions known to be engaged during arithmetic fact retrieval. At the same time, greater activation in the right intraparietal sulcus during calculation, a region established to be involved in numerical quantity processing, was related to lower PSAT math scores. These data reveal that the relative engagement of brain mechanisms associated with procedural versus memory-based calculation of single-digit arithmetic problems is related to high school level mathematical competence, highlighting the fundamental role that mental arithmetic fluency plays in the acquisition of higher-level mathematical competence.
View
Test of attention for elementary school students. Athens: Greek Ministry of Education
  • Jan 2007
  • P Simos
  • A Mouzaki
  • G Sideridis
Simos, P., Mouzaki, A., & Sideridis, G. (2007). Test of attention for elementary school students. Athens: Greek Ministry of Education (in Greek)
Working Memory Rating Scale
  • Jan 2008
  • T P Alloway
  • S E Gathercole
  • H J Kirkwood
Alloway, T. P., Gathercole, S. E., & Kirkwood, H. J. (2008). Working Memory Rating Scale. London: Pearson Assessment.
Test of Executive Function for Elementary School Students. Athens: Greek Ministry of Education
  • Jan 2007
  • P Simos
  • A Mouzaki
  • G Sideridis
Simos, P., Mouzaki, A., & Sideridis, G. (2007). Test of Executive Function for Elementary School Students. Athens: Greek Ministry of Education.
Greek Wechsler Intelligence Scale for Children, WISC-III: Manual. Athens: Ellinika Grammata
  • Jan 1998
  • J Georgas
  • I Paraskevopoulos
  • E Besevegis
  • N Giannitsas
Georgas, J., Paraskevopoulos, I., Besevegis, E., & Giannitsas, N. (1998). Greek Wechsler Intelligence Scale for Children, WISC-III: Manual. Athens: Ellinika Grammata. (in Greek)