Basic theory of educational neuroscience for mathematics teachers – a review

This paper is a review of how the knowledge of educational neuroscience by teachers of mathematics and its inclusion in mathematics teacher education curricula can enhance our understanding of how students learn mathematics. It is premised on studies that point to two of the obstacles that teachers of mathematics face, that is we know almost nothing about how people do mathematics and we almost know nothing about how people learn how to do mathematics. Teachers’ understanding and knowledge of what goes on in the brain and mind as learners grapple with mathematical concepts and facts could enhance the way we teach and disseminate mathematical information. Teachers’ knowledge of educational neuroscience will also dispel neuromyths - a presentation of facts with little or no scientific bases about the science of the brain, memory and learningInstitute for Science and Technology Education (ISTE

Towards validation of a rational number instrument : an application of Rasch measurement theory

Abstract: The rational number knowledge of student teachers, in particular the equivalence of fractions, decimals, and percentages, and their comparison and ordering, is the focus of this article. An instrument comprising multiple choice, short answer and constructed response formats was designed to test conceptual and procedural understanding. Application of the Rasch model enables verification of whether the test content was consistent with the construct under investigation. The validation process was enabled by making explicit the expected responses according to the model versus actual responses by the students. The article shows where the Rasch model highlighted items that were consistent with the model and those that were not. Insights into both the construct and the instrument were gained. The test items showed good fit to the model; however, response dependency and high residual correlation within sets of items was detected. Strategies for resolving these issues are discussed in this article. We sought to answer the research question: to what extent does this test instrument provide valid information that can be used to inform teaching and learning of fractions? We were able to conclude that a refined instrument applied to first-year students at university provides useful information that can inform the teaching and learning of rational number concepts, a concept that runs through mathematics curricula from primary to university. Previously, most research on rational number concept has been conducted on young learners at school

An evaluation of secondary school mathematics textbooks in light of sustainable education in Zimbabwe

Mathematics plays a major role in overcoming future challenges, and mathematical skills as well as problem-solving skills might help provide apt solutions to existing and upcoming economic, social and environmental challenges. Textbooks play a major role in mathematics lessons, and they influence how concepts are taught and learners’ understanding of the concepts. The article analysed secondary school mathematics textbooks to find out how they were aligned with sustainable development goals. Content analysis was used to analyse four textbooks that are mainly used in the teaching and learning of mathematics at the secondary school level which are forms one to four in Zimbabwe. The aim was to present how education for sustainable development related content is addressed in the textbooks. According to the findings of the study, the three dimensions (economic, social and environment) of sustainable development goals were reflected in the four mathematics textbooks. Most of the sub-contents in the three dimensions were covered in the textbooks except for climate change, human rights, peace and security, sustainable consumption and narrowing the gap between the rich and the poor

Towards improving learner performance in the national senior certificate examination - script analysis research report

This summary report includes a) a summary of findings across subjects, b) the main findings from each subject area analysis, and c) a background section which describes the purpose, rationale and research approach

Foundation phase teachers’ (limited) knowledge of geometry

This study is about student teachers’ conceptual understanding of shapes. While the National Curriculum Statement stipulates that by the time learners exit high school they should have grounded knowledge of basic geometry and know shapes such as polygons and polyhedrons and their properties, this study finds that the majority of student teachers have limited knowledge of basic geometry and require not remedial, but re-learning of these basic concepts. The Van Hiele levels of geometric thought model is used as a lens to gauge and understand students’ knowledge of geometry. A cohort of 128 first-year students registered for a foundation phase programme took part in the study. It was found that while Grade 12 learners are expected to operate at levels 3 and 4 of the Van Hiele’s levels, the majority of the participants in the study were operating at level 1, the level of the learners they will be teaching when they complete the course. Suggestions are made for how to address this problem

Understanding students’ misconceptions: An analysis of final Grade 12 examination questions in geometry

The role geometry plays in real life makes it a core component of mathematics that students must understand and master. Conceptual knowledge of geometric concepts goes beyond the development of skills required to manipulate geometric shapes. This study is focused on errors students made when solving coordinate geometry problems in the final Grade 12 examination in South Africa. An analysis of 1000 scripts from the 2008 Mathematics examination was conducted. This entailed a detailed analysis of one Grade 12 geometry examination question. Van Hiele levels of geometrical thought were used as a lens to understand students’ knowledge of geometry. Studies show that Van Hiele levels are a good descriptor of current and future performance in geometry. This study revealed that whilst students in Grade 12 are expected to operate at level 3 and level 4, the majority were operating at level 2 of Van Hiele’s hierarchy. The majority of students did not understand most of the basic concepts in Euclidian transformation. Most of the errors were conceptual and suggested that students did not understand the questions and did not know what to do as a result. It is also noted that when students lack conceptual knowledge the consequences are so severe that they hardly respond to the questions in the examination

Examining the teaching strategies of high-performing mathematics teachers in solving challenging 3-dimensional (3D) trigonometry

 In this article, we discuss teaching strategies that high-performing mathematics teachers use to assist learners in solving challenging 3-dimensional (3D) trigonometry concepts more effectively. High school learners often find 3D trigonometry challenging. For this study, a purposively qualitative research design was chosen. Five mathematics teachers were interviewed, and 381 scripts of the learners were analysed with the mathematical language error, procedural error, conceptual error, and application error (MPCA error) analysis protocol. Results from this study showed that using concrete models to illustrate the dimensions of 3D concepts was helpful for high-performing schoolteachers. The mathematical knowledge and the quality of mathematical instructions used by the teacher to unpack the 3D trigonometry concepts were found to play a pivotal role in the learners’ understanding. The teachers’ in-depth knowledge of error analysis was valuable, while the teachers’ ability to implement blended learning was crucial for learners. When a misconception occurs amongst learners, it should be challenged or contrasted with the correct conception. An understanding of learners’ errors in 3D trigonometry helps teachers minimise learners’ errors

Implementation of an Intervention Program to Enhance Student Teachers’ Active Learning in Transformation Geometry

Active learning strategies are purported to be effective in enhancing students’ understanding of concepts that would otherwise be difficult to master through other strategies of mediating learning. This study forms part of a bigger study where pre-service teachers’ errors and misconceptions in transformation geometry were identified, analyzed and then addressed. The focus of this current study is on exploring the implementation of a van Hiele phase-based instruction to address the students’ misconceptions through the facilitation of active learning. The instructional program was implemented with 82 pre-service teachers (student teachers) and field notes, observations and informal conversations with students were used to collect data during the implementation. A test was then given at the end of the intervention to determine the effect of the intervention on student performance. Findings suggest active learning can be promoted, through the use of van Hiele phase-based intervention program, to address effectively students’ misconceptions

Mentoring as professional development intervention for mathematics teachers: A South African perspective

Only a small percentage of mathematics teacher professional development activities in South Africa include pedagogy and instruction approaches required to teach the content. In the light of the poor mathematics results, it is of pertinent importance that teachers need to be developed in terms of the mathematics they teach and the pedagogical component of it. A teachers’ professional development programme that used mentoring as one of the interventions was investigated where the mentor conducted classroom observations and had post–observation conferences with the teachers. The data from the observations, post observation conferences and interviews of both the mentors and the mathematics teachers was used to inform the off-site workshops on mathematics content and the instructional skills required to effectively teach the content. Mentoring supported the teachers in terms of mathematics content and instruction, team teaching and lesson preparation. The teachers’ individual content and instructional needs were also assessed and supported. The study revealed that mentoring that takes cognisance of teachers’ content and instructional needs enhanced their lesson preparation and understanding of mathematics as well as the skills required to teach it effectively. The study recommends mentoring as an effective intervention in professional development programmes especially when it is informed by the teachers’ instructional and content needs

Exploring students’ usage of an online Interactive program

Abstract : This study explored students’ usage of an online interactive program which was designed to improve their mastery of mathematical procedures. The aim was to examine students’ mastery of mathematical procedures through repetitive practice of procedures relating to simplification of exponents. A purposive sample of 42 first - year extended engineering students was selected. This quantitative and qualitative study was conducted in one of South Africa’s public universities located in the Gauteng province. Sources of data for the study included students’ online reports and an open-ended questionnaire. The findings indicated that some students made use of the program successfully by showing mastery of mathematical procedures. However, other students only attempted exercises requiring skills with which they were already familiar and comfortable