Original Research

Ticks and crosses in primary mathematics assessments: What purpose do they serve?

Brian Chihodzi, Willy Mwakapenda, Beatrice Ngulube
Pythagoras | Vol 44, No 1 | a647 | DOI: https://doi.org/10.4102/pythagoras.v44i1.647 | © 2023 Brian Chihodzi, Willy Mwakapenda, Beatrice Ngulube | This work is licensed under CC Attribution 4.0
Submitted: 25 August 2021 | Published: 11 October 2023

About the author(s)

Brian Chihodzi, Department of Maths, Science and Business Education, Faculty of Humanities, Tshwane University of Technology, Pretoria, South Africa
Willy Mwakapenda, Department of Maths, Science and Business Education, Faculty of Humanities, Tshwane University of Technology, Pretoria, South Africa
Beatrice Ngulube, Department of Maths, Science and Business Education, Faculty of Humanities, Tshwane University of Technology, Pretoria, South Africa

Abstract

Ticks and crosses (TCs) are a common aspect of teachers’ classroom practice in relation to assessment in many learning areas including mathematics. Putting TCs in learners’ written work is a strategy of feedback. Even though these TCs are frequently used in different types of mathematics assessments, there is limited research in relation to what they actually stand for and what functions they are designed for and especially what purpose they eventually serve in practice. This article emerged from a broader study that aimed at exploring classroom formative assessment practices of Grades 4–6 mathematics teachers, a learning goals and documentary analysis. Since this study was qualitative in nature, we used qualitative, non-probability sampling to recruit respondents according to pre-selected criteria relevant to our research questions. The study participants were 43 qualified and experienced Intermediate Phase mathematics teachers and 95 Grades 4–6 learners from the Tshwane South district, where a phenomenon of low achievement was of great concern. We engaged in document analysis of all the 95 learners’ mathematics workbooks. Questionnaires were administered to the 43 teachers. We report on an analysis of teachers’ assessment practices of Grades 4–6 learners’ mathematics work. We narrate the extent of the use of TCs among teachers from selected schools in Tshwane South district in Gauteng, South Africa. Our analysis shows that while there is prevalent use of TCs among teachers, there are critical gaps in relation to knowledge of TCs in assessing mathematics. We present a qualitative and quantitative data analysis to illustrate how these were used in connection with assessment of learners’ mathematics work linked to the concepts of numerical, geometric, and graphical relationships. We use our analysis of the vignettes to explore and argue that teachers use TCs without adequate understanding of what these actually mean in relation to assessment broadly and assessment intended at collecting and clarifying goals for mathematical learning specifically. Despite teachers having mathematical qualifications and a repertoire of experience for teaching, the majority of teachers grappled with understanding mathematical concepts as evidence in how they marked learners’ mathematics work. The study also found that teachers’ understandings of assessment of mathematics were diverse and largely inconsistent with the formal definitions of mathematics.

Contribution: This study indicated that there are critical gaps in relation to knowledge of TCs in assessing mathematics. A clear-cut marking policy will guide teachers to provide effective marking using TCs.


Keywords

ticks; crosses; assessment; primary mathematics; classroom practices; feedback; primary school learners; low achievement.

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