Programmes

University of Johannesburg: Development of standardised Mathematics tests in four languages

This project was designed to build knowledge, tools and practices for the teaching and learning of Foundation Phase Mathematics in four languages. More specifically, the initiative produced a standardised test to assess Grade 1 pre-numeracy readiness.

Research into Relationship between Language Competence and Mathematics Performance: Summary of Key Findings

Name of Service Provider: University of Johannesburg Centre for Early Childhood Development

Duration of Project: Jan 2013 - Dec 2015

Introduction

The research project by the University of Johannesburg Centre for Early Childhood Development was aimed at developing a better understanding of the relationship between Language competence and learning Mathematics in the early grades.

This is particularly pertinent in South Africa in the light of the Language in Education Policy (1997) which supports the use of learners’ Home Language as the medium of instruction in the early grades. This is also pertinent in the context of the reality that many learners are not learning in their Home Language.

Whilst there is widespread agreement that Language is critical in the development of concepts in Mathematics, there is little empirical research on understanding the relationship between Language acquisition and the development of early concepts in this key subject in South Africa.

To add to the body of knowledge in this field the UJ study opted to explore this area through cognitive science.

Methodology

The study comprised the following elements:

  • Development of standardised tests in four Languages to establish learners’ competence and changes in competence in Mathematics.
  • Testing of 1000 learners from a range of schools in Soweto over a period of three years.
  • Design and implementation of a teacher support programme to help teachers diagnose learner problems and remediate with a strong understanding of the relationship between Mathematics and Language.

Findings

Overall the study developed a sound and reliable instrument, a teacher training programme and some insights on Language that could contribute to both knowledge and practice in the field.

Development and translation of test instruments

In the initial phase, the researchers focused heavily on the development of assessment instruments. The study began with the search for a reliable diagnostic instrument to test the Mathematics competence of learners as they entered Grade 1. However, there were no South African standardised tools with which to capture conceptual development of Mathematics at this age. The University decided to adapt the German MARKO-D test into four Languages: English, Afrikaans, IsiZulu and Sesotho.

The test is able to indicate the knowledge that learners have, their knowledge gaps as well as their cognitive levels based on the five level cognitive capability framework. This allows the teacher or remedial specialist to have a more fine-grained sense of the learners’ gaps and possible remediation thereof.

The project resulted in an educational assessment tool that can be applied 1) to assess children who show signs of Mathematics learning difficulties and 2) to make judgments about the readiness of children at the beginning of Grade 1.

In addition, the researchers developed a less complex version that can be administered by teachers to diagnose learners’ competence as they enter the system. The tests and manual will be freely available for NGOs, government and donors to use in their projects.

The researchers also recommend that the diagnostic instruments be translated into more South African Languages.

Learner performance in the tests

The test results show that most learners are performing on average at Level Two for the age group 4-8 years. This means that the majority of the children could 1) count and 2) had knowledge of number order. As such learners can count and arrange numbers but they cannot understand the relationship between the rote counting and the meaning of that number and cannot process this visually or linguistically.

This is problematic because entry level Grade 1 learners need to be at level three to successfully engage with the CAPS Grade 1 curriculum. As such children need to have a solid concept of the cardinality of small numbers in order to successfully undertake learning in Grade 1.

The test results also show that very little learning gains are made in Grade 1. As such, pre and post tests are similar, with learners at the end of Grade 1 still largely located at level 2.

Development of a teacher support programme

In addition to the assessment tool, the team developed a remedial programme (learner support programme) that teachers can utilise to support learners. This programme was informed by an analysis of the test results. The programme, Calculia SA, will be made available in open access format and offered to the DBE and provincial education departments should it prove successful.

The remedial programme comprises three modules. The first module focuses on how learners’ minds develop. It deals with the relationship between Language and Mathematical learning through theories of cognitive science. The second module focuses on helping teachers to build mastery in their learners using small numbers. The assumption is that if learners develop mastery of the Mathematical principles with small numbers they can generalise these to larger numbers. This module also focuses on supporting teachers to understand what the prerequisites are for starting new concepts. The third module focuses on being explicit about teaching teachers to combine general vocabulary, Mathematics vocabulary and Mathematics learning.

Insights into Language and Mathematical competence

Overall the study calls for an approach that combines both the use of English and Home Language in the Mathematics classroom. The study highlighted the following key findings with respect to Language and Mathematics:

First, it is important to note that only 22.5 % of children that learn in English are from homes where English is used as the main Language and that most children in Gauteng do not learn in their Home Language.

Second, overall learners did better when they learnt Mathematics and wrote their assessments in their Home Language.

Third, there were differences in the ways that learners tackled and understood Mathematical questions in the different Languages. Words and sentences in different Languages denoted subtle differences of meaning and these differences in semantics impacted on their understanding of Mathematical concepts.

Fourth, learners showed patterns of poor performance in similar questions within a Language group. For example learners in IsiZulu got similar question incorrect and similar questions correct.

Fifth, there was no consistent pattern of performance on the different topics in the different Languages. For example IsiZulu learners did poorly at number classification, but stronger at cardinality, which was different from Sesotho learners who did better at cardinality than number classification.

Sixth, the study suggests that learners can maximise Mathematical learning through combining English and Home Language (if not English) in the Mathematics classroom. They found that a dual-Language approach allows learners to access Mathematical concepts more successfully.

Some Recommendations

The study makes the following recommendations:

Curriculum: The study proposes that the early grade curriculum be redesigned to focus on fewer concepts in greater detail instead of too many topics covered superficially.

The study suggests that the Foundation Phase Mathematics curriculum assumes too much about the conceptual development of school beginners and argues that most children are not ready to work with the number concepts that are taught in rapid succession in the Grade 1 curriculum.

There is strong argument in the study that the early curriculum should be reduced and the initial number concepts done more thoroughly and slowly. The study argues that the current curriculum covers too many topics superficially instead of fewer topics in greater depth. This they say is in line with cognitive science theory which suggests that it takes a child of 5 - 6 up to 6 months to master a concept.

Teacher pre-service development: The study recommends that cognitive psychology and neuroscience form part of the teacher education curriculum which explains how children learn Mathematics and how Mathematics is influenced by linguistic principles and practices.

Language: The study recommends that teachers combine both English and African Home Languages to teach and explain Mathematics. In addition they recommend that teachers use both Languages to strength learners’ repertoire of Mathematical terminology and support learners to engage with and formulate Mathematical concepts including word problems.

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