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

IF 0.3 Q4 EDUCATION, SCIENTIFIC DISCIPLINES Pythagoras Pub Date : 2022-11-17 DOI:10.4102/pythagoras.v43i1.647
Brian Chihodzi, W. Mwakapenda, B. Ngulube
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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.
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小学数学评估中的勾号和叉号:它们有什么用途?
在包括数学在内的许多学习领域,勾号和叉号是教师课堂实践中与评估相关的一个常见方面。将TC放在学习者的书面作品中是一种反馈策略。尽管这些TC经常用于不同类型的数学评估,但关于它们的实际含义、设计用途,尤其是它们最终在实践中的用途,研究有限。本文来自一项更广泛的研究,旨在探索4-6年级数学教师的课堂形成性评估实践、学习目标和文献分析。由于这项研究本质上是定性的,我们根据与我们的研究问题相关的预先选择的标准,使用定性、非概率抽样来招募受访者。研究参与者是来自茨瓦内南区的43名合格且经验丰富的中级数学教师和95名4-6年级的学习者,那里的低成绩现象非常令人担忧。我们对所有95名学生的数学练习册进行了文献分析。对43名教师进行了问卷调查。我们报告了对教师对4-6年级学生数学作业的评估实践的分析。我们叙述了南非豪登省Tshwane南区选定学校的教师使用TC的程度。我们的分析表明,虽然教师中普遍使用TC,但在评估数学时,在TC知识方面存在严重差距。我们提出了一个定性和定量的数据分析,以说明如何将这些数据用于评估与数字、几何和图形关系概念相关的学习者的数学工作。我们利用对小插曲的分析来探索和论证教师使用TC时,没有充分理解这些TC在广泛评估和旨在收集和明确数学学习目标的评估中的实际含义。尽管教师具有数学资格和丰富的教学经验,但大多数教师都在努力理解数学概念,以此作为他们如何标记学习者数学工作的证据。研究还发现,教师对数学评估的理解是多样的,并且在很大程度上与数学的正式定义不一致。贡献:这项研究表明,在评估数学时,TC的知识存在严重差距。明确的评分政策将指导教师使用TC进行有效的评分。
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来源期刊
Pythagoras
Pythagoras EDUCATION, SCIENTIFIC DISCIPLINES-
CiteScore
1.50
自引率
16.70%
发文量
12
审稿时长
20 weeks
期刊介绍: Pythagoras is a scholarly research journal that provides a forum for the presentation and critical discussion of current research and developments in mathematics education at both national and international level. Pythagoras publishes articles that significantly contribute to our understanding of mathematics teaching, learning and curriculum studies, including reports of research (experiments, case studies, surveys, philosophical and historical studies, etc.), critical analyses of school mathematics curricular and teacher development initiatives, literature reviews, theoretical analyses, exposition of mathematical thinking (mathematical practices) and commentaries on issues relating to the teaching and learning of mathematics at all levels of education.
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