ethanporcaro/eric-fulltext-meta huggingface dataset:
A Teacher&apos;s Engagement with Learner Errors in Her Grade 9 Mathematics Classroom
Author: Gardee, Aarifah
Date: 2015-00-00
Type: Journal Articles
Subjects: Teacher Participation,Teacher Student Relationship,Error Patterns,Grade 9,Mathematics Instruction,Misconceptions,Mathematics Teachers,Calculators,Faculty Development

How errors are dealt with in a mathematics classroom is important as it can either support or deny learner access to mathematical knowledge. This study examines how a teacher, who participated in a professional development programme that focused on learner errors, engaged with mathematical errors in her Grade 9 classroom. Data were collected over a two-year period in the form of videotapes and were analysed qualitatively. Our findings illustrate that this teacher dealt with four types of mistakes: slips, errors derived from misconceptions, language-related errors and errors that occurred from the incorrect usage of the calculator. She dealt with these by correcting, probing or embracing them. We found that, over time, this teacher dealt with more errors and corrected and embraced errors in different ways. We recommend that teachers use their professional knowledge to decide when, why and how it is appropriate to correct, probe or embrace errors in light of their knowledge of the content and their learners.
Exploring Boot Camps for &apos;Gatekeeper&apos; Service Courses in Mathematics
Author: Campbell, Anita
Date: 2015-00-00
Type: Journal Articles
Subjects: College Mathematics,Introductory Courses,Tutorial Programs,Engineering Education,Student Improvement,College Freshmen,Foreign Countries,Program Effectiveness,Instructional Design,Student Attitudes,Tutors,Teacher Attitudes,Mathematics Instruction

Pressure to increase the throughput of university students in ethical ways has been a catalyst for innovations to improve learning and student success. Student dropout occurs mostly in the first year of study and poor performance is a major contributor to dropout even if the underlying reason for the poor performance is not academic under-preparedness. This article discusses the design and implementation of a mathematics tutored reassessment programme (TRP or 'boot camp') to improve the pass rate of students writing supplementary examinations for first year engineering mathematics. Interviews with students and tutors suggest that the TRP cultivated positive affective changes in students. A notable result from this case study was that students who qualified for a reassessment with marks in the range 40%-44% (and who would not normally have been granted a supplementary examination) outperformed students qualifying with marks of 45%-49%, for whom attendance at the TRP was optional. Theoretical motivations for five principles guiding the design of the TRP are discussed.
Developing a Model for Problem-Solving in a Grade 4 Mathematics Classroom
Author: Nieuwoudt, Susan
Date: 2015-00-00
Type: Journal Articles
Subjects: Models,Problem Solving,Mathematics Instruction,Grade 4,Student Attitudes,Foreign Countries,Mathematics Teachers,Elementary School Students,Elementary School Teachers,Elementary School Mathematics,Mathematics Activities

The teaching of problem-solving through the development of a problem-solving model was investigated in a Grade 4 mathematics classroom. Learners completed a questionnaire regarding their knowledge of mathematical problem-solving, their attitudes towards problem-solving, as well as their experiences in solving problems. Learners' responses revealed overall negative beliefs towards problem-solving as well as a lack of knowledge about what problem-solving in mathematics entails. The teacher then involved the learners in a structured learning programme where they worked in cooperative groups of six on different kinds of mathematical problems to solve. The groups regularly engaged in discussions about the different strategies they were using to solve a specific problem and eventually succeeded in formulating a generic problem-solving model they could call their own. The model was effectively used by the learners to solve various mathematical problems, reflecting their levels of cognitive development to a certain extent.
Student Mathematical Activity as a Springboard to Developing Teacher Didactisation Practices
Author: Biccard, Piera
Date: 2015-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Mathematics Activities,Mathematics Teachers,Teaching Methods,Elementary School Teachers,Elementary School Mathematics,Grade 5,Grade 6,Faculty Development,Foreign Countries

This article is part of a larger study on teacher development. The main study investigated teacher development within primary school Mathematics teachers' classrooms to determine if teaching practices could be enhanced through a didactisation-based programme. It sought to develop teachers within their own environments and classrooms. Design research (both designing the conditions for change and studying the results of those conditions) enabled the researchers to design a programme that was congruent with teachers' own needs and experiences. The programme ran for a period of a year with regular contact between the teachers and the researcher conducting the programme (the first author). The programme set out nine didactisation practices: active students, differentiation, mathematisation, vertically aligned lessons, accessing student thinking and ideas, probing student thinking and ideas, connecting student ideas, assessing students and reflecting on practice. One practice, student activity, is the focus of this article. It was found that by initiating discussion and cognitive conflict in teachers by using modelling problems, and further allowing teachers to observe pupils working in groups with modelling problems, teachers were starting to incorporate the didactisation practices within their own classrooms. This article documents specifically the fundamental role of student mathematical activity and the importance of improving student mathematical experiences, both for teacher development and for student mathematical learning. The study may be valuable in structuring and planning further effective teacher development programmes.
Teacher Narratives in Making Sense of the Statistical Mean Algorithm
Author: Lampen, Erna
Date: 2015-00-00
Type: Journal Articles
Subjects: Personal Narratives,Mathematics Instruction,Statistics,Mathematics Teachers,Mathematical Concepts,Foreign Countries,Problem Solving,Arithmetic

Teaching statistics meaningfully at school level requires that mathematics teachers conduct classroom discussions in ways that give statistical meaning to mathematical concepts and enable learners to develop integrated statistical thinking. Key to statistical discourse are narratives about variation within and between distributions of measurements and comparison of varying measurements to a central anchoring value. Teachers who understand the concepts and tools of statistics in an isolated and processual way cannot teach in such a connected way. Teachers' discourses about the mean tend to be particularly processual and lead to limited understanding of the statistical mean as measure of centre in order to compare variation within data sets. In this article I report on findings from an analysis of discussions about the statistical mean by a group of teachers. The findings suggest that discourses for instruction in statistics should explicitly differentiate between the everyday 'average' and the statistical mean, and explain the meaning of the arithmetic algorithm for the mean. I propose a narrative that logically explains the mean algorithm in order to establish the mean as an origin in a measurement of variation discourse.
An Exploration of Learners&apos; Theorems-in-Action Used in Problems on Ratio and Proportion
Author: Mahlabela, Patisizwe T.
Date: 2015-00-00
Type: Journal Articles
Subjects: Problem Solving,Mathematical Concepts,Mathematics Instruction,Secondary School Students,Secondary School Mathematics,Grade 9,Foreign Countries,Multiplication,Mathematics Teachers

The purpose of this study is to explore Grade 9 learners' understanding of ratio and proportion. The sample consists of a group of 30 mathematics learners from a rural school in the province of KwaZulu-Natal, South Africa. Data were generated from their responses to two missing value items, adapted from the Concepts in Secondary Mathematics and Science test set in the United Kingdom over 30 years ago. The study utilised Vergnaud's notion of theorems-in-action to describe the learners' strategies. It was found that the most common strategy was the cross multiplication strategy. The data reveal that the strategy was reduced to identifying and placing (often arbitrarily) three given quantities and one unknown in four positions, allowing the learners to then carry out an operation of multiplication followed by the operation of division to produce an answer. The study recommends that the role of the function underlying the proportional relationship should be foregrounded during the teaching of ratio and proportion.
Understanding Students&apos; Misconceptions: An Analysis of Final Grade 12 Examination Questions in Geometry
Author: Luneta, Kakoma
Date: 2015-00-00
Type: Journal Articles
Subjects: Misconceptions,Grade 12,Geometry,Foreign Countries,Mathematics Instruction,Geometric Concepts,Problem Solving,Error Patterns,Mathematics Tests,Secondary School Students,Secondary School Mathematics,Secondary School Teachers,Mathematics Teachers

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.
The Effectiveness of a Teacher Professional Learning Programme: The Perceptions and Performance of Mathematics Teachers
Author: Ndlovu, Mdutshekelwa
Date: 2014-00-00
Type: Journal Articles
Subjects: Teacher Attitudes,Mathematics Teachers,Faculty Development,Mathematics Education,Grade 7,Grade 8,Grade 9,Secondary School Teachers,Program Effectiveness,Knowledge Base for Teaching,Foreign Countries,Teacher Competencies

The purpose of this article is to report on an investigation of the perceptions and performance of mathematics teachers in a teacher professional learning (TPL) programme based on realistic mathematics education (RME) principles, which included a topic on transformations, undertaken by the researcher. Forty-seven Senior Phase (Grade 7--9) teachers took part in the mixed-methods study in which they answered a questionnaire with both closed and openended items. Fifty teachers took an achievement test at the end of the programme. The TPL programme used the RME approach in the design and delivery of mathematical tasks intended to enhance teachers' mathematical knowledge for teaching. The sessions were conducted in a manner that modelled one way in which RME principles can be adopted as a teacher professional development strategy. The significance of the study is that continuing TPL is acknowledged to contribute to improvement in teaching and learning to address the concern about unsatisfactory learner achievement in mathematics. The responses suggested that the majority of teachers experienced the sessions positively in relation to all but one of the six RME principles. The teachers reported that they took an active part both as individuals and in small groups and expressed their willingness to adopt the type of activities and materials for their classrooms, which is an essential first step in Guskey's first level of evaluation of a teacher TPL programme. The teachers' average performance in an achievement test at the end of the topic was 72% which was indicative of modest learning gains at Guskey's second level of TPL effectiveness.
An Examination of the Pediatrician-Prescribed Gaming App-Based Exercise Prescription: A Pilot Study
Author: Yli-Piipari, Sami
Date: 2019-03-19
Type: Journal Articles
Subjects: Physical Activities,Intervention,Obesity,Hispanic Americans,Children,Pediatrics,Educational Games,Computer Oriented Programs,Exercise,Outcomes of Treatment,Instructional Effectiveness

This study examined the effectiveness of a physical activity (PA) intervention among obese Hispanic children delivered by a free mobile phone game application (app) recommended by a pediatrician. A sample of 40 (age M=10.16[2.01] years) children participated in this pilot study. Pre- and posttest data were collected on participants' PA attitudes, intention, and objectively measured PA. The intervention was a game-based exercise prescription to engage in at least 20 minutes daily for seven days in moderate-to-vigorous PA (MVPA) delivered by their primary care pediatrician. The results showed a statistically significant decrease in sedentary time (SED) (t(26)=3.03, p=0.007, d=0.66) and an increase in moderate PA (MPA) (t(26)=3.19, p=0.005, d=-0.69), vigorous PA (VPA) (t(26)=-5.74, p&lt;0.001, d=-1.25), and MVPA (t(26)=-9.09, p&lt;0.001, d=-1.89). In addition, the study showed increase in PA attitudes (t(26)=-3.63, p&lt;0.001, d=-1.10) and PA intention (t(20)=-3.13, p=0.001, d=-0.94) after the intervention. This study provides evidence that a mobile app gaming-based exercise prescription may help to engage obese Hispanic children in health enhancing PA.
Item Difficulty Analysis of a High-Stakes Mathematics Examination Using Rasch Analysis
Author: Jacobs, Mark
Date: 2014-00-00
Type: Journal Articles
Subjects: Foreign Countries,Mathematics Tests,Test Items,Difficulty Level,High Stakes Tests,Item Analysis,Grade 12,High School Students

The National Senior Certificate examination is the most important school examination in South Africa. Analysis of learners' performance in Mathematics in this examination is normally carried out and presented in terms of the percentage of learners who succeeded in the different bands of achievement. In some cases item difficulties are presented -- item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics, such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study that, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked scripts of the candidates who wrote the National Senior Certificate examination in Mathematics in November 2010. Rasch procedures were used for the analysis. The findings indicate that learners perform differently on subsections of topics, herein referred to as items, and that focusing on scores for full topics potentially mask these differences. Mathematical explanations are attempted to account for difficulties learners exhibit in these subsections, using a hierarchy of scale. The findings and our analysis indicate that a form of measurement-driven testing could have beneficial results for teaching. Also, for some items the difficulty obtained from the work of examinees runs counter to the commonly perceived wisdom that an examination ought to be structured in such a way that the less difficult items are at the start of a topic. An explanatory device anchored around the construct of 'familiarity with problem types through repeated productive practice' is used to account for the manifested hierarchy of difficulty of the items.
Towards an Understanding of Students&apos; Thinking in Learning New and Unfamiliar Concepts: Focus on the Factorial Function
Author: Maoto, Satsope
Date: 2015-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,College Freshmen,Cognitive Processes,Mathematics Skills,Problem Solving,Experience,Teaching Methods,Preservice Teachers,Methods Courses,Mathematical Concepts,Concept Formation,Mathematical Logic

This study used participant observation to explore students' thinking when learning the concept of factorial functions. First-year university students undertaking a mathematics methodology course were asked to find the number of ways in which five people could sit around a circular table with five seats. Using grounded theory as a qualitative research strategy, we analysed student responses and written reflections according to the sequence of their experiential realities: practical and textual experiences. This was followed by an analysis of their reflections on both experiences in a pedagogical context. We found that the way basic mathematics operations are learned impacts on the student's ability to experience components of new problems as familiar. Consequently, they encounter these problems as new and unfamiliar. At the same time we found that engagement with practical experience does allow for the emergence of representations that have the potential to be used as foundations for learning new and unfamiliar concepts. The blending of practical, textual and teaching experiences provoked students' thinking and ultimately their understanding of a given new and unfamiliar mathematics concept.
The Development, Validation and Standardisation of a Questionnaire for ICT Professional Development of Mathematics Teachers
Author: Leendertz, Verona
Date: 2018-00-00
Type: Journal Articles
Subjects: Information Technology,Faculty Development,Mathematics Instruction,Mathematics Teachers,Foreign Countries,Test Validity,Test Reliability,Questionnaires

This article reports on the development of a custom-made questionnaire. The questionnaire was developed with the aim to compile guidelines for the professional development (PD) of mathematics teachers for the pedagogical use of information and communication technology (ICT) integration in teaching and learning. During the standardisation and validation of the questionnaire it was distributed to 179 schools and 300 teachers in eight educational management districts in the Western Cape, South Africa. The extracted factors had a reliability level higher than 0.8, which indicates the items in the questionnaire are significant to address the research problem and the questionnaire is valid for ICT PD.
The Effect of a Group Approach on the Performance of High School Mathematics Learners
Author: Dhlamini, Joseph
Date: 2013-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Secondary School Mathematics,Secondary School Students,Instructional Effectiveness,Problem Solving,Grade 10,Experimental Groups,Control Groups,Mathematics Tests,Achievement Tests,Foreign Countries

In this study, we investigated the effects of a group approach versus a non-group approach on the mathematics performance of learners. A group approach refers to an arrangement in which learners sit together to discuss and solve mathematics tasks. We studied a convenience sample of low-performing Grade 10 mathematics learners using a quasi-experimental design with a non-equivalent control group. The experimental group was taught using a group approach and the control group using non-group approach instruction. To measure the effects of teaching approaches, we administered a Financial Mathematics Achievement Test (FMAT) before and after the experiment. Using a one-way analysis of covariance (ANCOVA) the study found that learners in a group approach learning environment performed significantly better than learners taught through a non-group teaching mode (p &lt; 0.05). The theory of cognitive load was used to interpret the results. The results suggest that a group approach may be effective when teaching certain mathematics topics in Grade 10 classrooms.
The Merits of Teaching Mathematics with Variation
Author: Mhlolo, Michael
Date: 2013-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Foreign Countries,Mathematics Teachers,Secondary School Mathematics,Secondary School Teachers,Grade 11,Teaching Methods,Theory Practice Relationship,Numbers,Mathematical Concepts

There is a general perception that the South African curriculum statements for mathematics create polarity between the 'old' and the 'new', which does not benefit both the teachers and the learners. The new curricula demand a radical shift from the traditional teacher-led approaches that teachers are familiar with, yet does not provide a model of what it might mean to teach for conceptual understanding. This article aims to provide such a model by examining the potential of teaching with variation, which is viewed as an important mathematics teaching and learning style. Proponents of the theory of variation claim that how teachers make available the object of learning to their students has been neglected yet it has a critical influence on learners' learning. This is important for educators as they struggle to make sense of the seemingly contradictory requirements of the new curriculum. In this article a discernment unit comprising four variation patterns is used as a tool to analyse a seemingly rich teacher-led approach to teaching that was observed in one South African Grade 11 mathematics classroom. The results of the analysis and implications for theory and practice are then discussed.
&apos;They Say We Are Crèche Teachers&apos;: Experiences of Pre-Service Mathematics Teachers Taught through the Medium of isiZulu
Author: van Laren, Linda
Date: 2013-00-00
Type: Journal Articles
Subjects: Preservice Teachers,Mathematics Teachers,Language of Instruction,Foreign Countries,Native Language,Numeracy,Higher Education

Language of instruction, both in schools and higher education institutions (HEIs), is a contentious issue in South Africa. At our university in the KwaZulu-Natal province of South Africa a language policy was approved in agreement with the &quot;Language Policy for Higher Education,&quot; recommending promotion of isiZulu as a medium of instruction for teaching and learning. In complying with this policy the School of Education of our university offered three education modules (Numeracy, Life Skills and Literacy) in the Foundation Phase (FP) Postgraduate Certificate in Education (PGCE) through the medium of isiZulu. Against this background we conducted a qualitative study with 16 FP PGCE pre-service teachers selected purposefully from the 2011 cohort who completed the FP numeracy education module in isiZulu. Participants were generally positive about their experiences of being taught in isiZulu, but highlighted challenges related to isiZulu as a medium of instruction for academic concept explanations, translation of teaching and learning materials, and the status of isiZulu as an instruction medium at a HEI.