Teachers’ explanations of learners’ errors in standardised mathematics assessments

Abstract

With the increased use of standardised mathematics assessments at the classroom level, teachers are encouraged, and sometimes required, to use data from these assessments to inform their practice. As a consequence, teacher educators and researchers are starting to focus on the development of analytical tools that will help them determine how teachers interpret learners’ work, in particular learners’ errors in the context of standardised and other assessments. To detect variation and associations between and within the different aspects of teacher knowledge related to mathematical error analysis, we developed an instrument with six criteria based on aspects of teachers’ knowledge related to explaining and diagnosing learners’ errors. In this study we provide evidence of the usability of the criteria by coding 572 explanations given by groups of mathematics educators (teachers and district officials) in a professional development context. The findings consist of observable trends and associations between the different criteria that describe the nature of teachers’ explanations of learners’ errors.

When the Fractional Cookie Begins to Crumble: Conceptual Understanding of Fractions in the Fifth Grade

“…The screener may be perceived as a naming and blaming tool to be used against them and their teaching. The teachers' reactions in Kolkata are similar to teachers' reactions in a study of South African teachers (Shalem, Sapire, & Sorto, 2014). The screener should not be used as a teacher evaluation tool.…”

A Critical Analysis of Errors Made by Rural and Urban Students in ‘O’ Level Mathematics Paper 1 (4008/1) in Shurugwi and Gweru Districts, Zimbabwe

“…It was difficult to answer Research Question 4 since this study could not establish the reasons why the students made the errors nor why a larger number at the rural school made the errors. However, if the teachers and students were interviewed immediately after the students' scripts had been marked, perhaps the 'reasons behind these errors' as echoed by Lourens, Molefe andBrodie (2011) andShalem, Sapire andSorto (2014) could have been discovered. After reviewing related literature, it was speculated that if teachers were knowledgeable enough in error pattern analysis and rectification or correction techniques (Gardee & Brodie, 2015) which they could regularly apply in the classrooms, the students could have made less errors.…”

“…Error analysis should not just end at the 'analysis' level, but as suggested by Peng (2010) cited in Shalem, Sapire and Sorto (2014), it should include all the steps of identifying, addressing, diagnosing and correcting the errors. Thus two more steps could be added to the seven above.…”

Ensino De Sequências Numéricas: Uma Investigação Com Professores De Matemática

“…Uma classificação dos tipos de conhecimento do conteúdo de professores de qualquer disciplina e nível de ensino foi estabelecida por Shulman (1986). O autor distingue três categorias: conhecimento do conteúdo da disciplina, conhecimento pedagógico do conteúdo e conhecimento curricular.…”

“…As ideias de Shulman (1986de Shulman ( , 1987 sobre as categorias de conhecimento do professor, bem como a classificação nelas baseada, realizada por Ball, Thames e Phelps (2008), têm influenciado muitos pesquisadores no Brasil e no exterior (HILL; BALL, 2009;MANDARINO, 2010;JAKOBSEN;RIBEIRO, 2013;SHALEM;SAPIRE;SORTO, 2014, entre outros). São revisados esses pressupostos teóricos para, em seguida, apresentar os procedimentos metodológicos da pesquisa e seus resultados.…”