Using National Diagnostic Report as a Professional Developmental Tool for High School Mathematics Teachers

USING NATIONAL DIAGNOSTIC REPORT AS A PROFESSIONAL DEVELOPMENTAL TOOL FOR HIGH SCHOOL MATHEMATICS TEACHERS

FACULTY OF EDUCATION

PhD (Mathematics Education)

A research proposal by:

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Date: 2018

SUPERVISOR:Statement of originality

I declare that, to the best of knowledge and belief, this is my original work, that all sources have been properly acknowledged, and that it contains no plagiarism

AbstractThe study will describe professional development intervention strategy on teaching and learning for high school mathematics teachers and its impact on teachers use of NDR during instruction. The focus of the study will be to support teachers in embedding error analysis in their instruction, encouraging teachers to use NDR for their lesson preparation, and make use of concept of cartoon in summarising identified errors. Teacher and learner performance data will be collected on participating teachers, controlled teachers and their learners during the study period. This professional development intervention will have an impact on teachers lesson preparation, instruction and approaches as well as performance of their learners.

Keywords:

National Diagnostic Report

Professional Development

Concept Cartoon

Error analysis

CHAPTER 1

Introduction/ Overview

Recent studies on misconception and errors in mathematics education has led to recognition of this learning barrier in a way not previous attended to, hence the need to interrogate error analysis at professional development level of mathematics teachers. GeorgeWalker and Keeffe (2010) argue, recognition of the need to change the way in which mathematics is taught and learned is international in scope. Research evidence from other countries indicates that professional preparation of teachers is significantly related to students achievement (National Mathematics Advisory Panel, 2008). Moreover, the recent reports of the international TEDS-M study indicate that rigorous mathematics instruction in schools and demanding programs in the preparation by the university teachers in countries like Taiwan and Singapore accounts for their teachers having better knowledge of mathematics and its teaching.

This study discusses the need for the preparation of mathematics teachers in South Africa, the institutional arrangements that exist, the context that guides the priorities, efforts that have been made, the challenges that continue to limit gains, and possible ways forward. The discussion will largely focus on the mathematics teachers at the school level. There is recognition of the need for specialised training and preparation of teachers at the tertiary level of education beyond the regular university education. Teaching is a very complex and demanding profession and at the same time extremely challenging. As Shulman (1986) said: "The person who presumes to teach a subject matter to children must demonstrate knowledge of that subject matter as a prerequisite of teaching". Nevertheless, this is insufficient. Teachers need to possess a wide range of skills and various types of knowledge and abilities (Christensen et al., 2011 p23). For instance, they need pedagogical knowledge concerning available teaching materials and methods; knowledge and abilities for adapting teaching approaches to specific subjects and the reasons thereof, and knowledge and abilities for designing lessons. In addition, they need to know and initiate asking questions and presenting problems; knowledge and abilities about students: difficulties, misconceptions they have, and the ways students construct their knowledge; knowledge and abilities of being reflective: ways of analysing what the teacher did, how and why the teacher did it.; knowledge and abilities of communicating and interacting with students.

Statement of Problem

The purpose of the study is to determine the relationship between use of national diagnostic report on high school mathematics and it applicability as a tool for professional development for mathematics teachers in Chris Hani west Municipality, South Africa. In addition, the study will focus on examining how the report can be used effectively to enhance teaching of mathematics in high schools.

Research Questions

Main research question:How can National Diagnostic Report be used as a tool for professional development of mathematics teachers?

Quantitative questions

What is the association between the use of National Diagnostic Report and professional development of mathematics teachers?

Ho: There is an association between use of National Diagnostic Report as a tool for professional development for mathematics teachers and their performance

HA: There is no association between use of National Diagnostic Report as a tool for professional development and their performance.

Qualitative questions

The purpose of this study is to explore the association between national diagnostic report and professional development of mathematics teachers.

Do teachers have access to the national diagnostic report?

Do teachers make use of national diagnostic report to inform their teaching?

Is the national diagnostic report effectively used?

Is the national diagnostic report relevant to teaching and learning?

Objectives of the Study

Using national diagnostic report as a source for professional developmental of mathematics teachers

Developing a framework from the national diagnostic report for professional development of mathematics teachers

Significance of the study (Purpose and its Application)The purpose of this study is to determine the feasibility of using national diagnostic report as a professional developmental tool for mathematics teachers as well as developing a framework from the National Diagnostic Report to enhance teaching and learning of mathematics.

Universities: universities will adopt the error analysis in national diagnostic report to inform study guides for teacher training education. The university study guide materials should have an in-depth knowledge of current misconceptions and error patterns to incorporate possible strategies to minimize these learning materials in the study materials.

Department of Education: The national diagnostic report will be used to inform planning of teacher training workshops.

The Department of Basic Education (DBE) will also use national diagnostic report to inform curriculum planning.

Textbook Publishers, Educational NGO and other related stakeholders will also adopt national diagnostic report to inform their planning.

Chapter 2

Literature Review

This study will illuminate the claims that feedback from error analysis plays an important role in professional development of mathematics teachers. Such claims stem from recent studies on error analysis that examines its relevance on professional development of mathematics teachers (reference). Scholars researching on errors and misconceptions in Mathematics contents have also advocated for the need to incorporate feedback from error analysis in developing teachers for mathematical quality instruction (Baumert et al., 2010 p133).

National Diagnostic Report

The National Diagnostic Report is a report that gives an in-depth analysis of National Senior Certificate candidates performance to aid teachers, Subject Educational Specialist (SES) and Curriculum planners in their planning for improved and quality teaching and learning. The report gives account of question-by-question analysis of all the key subjects: Mathematics; Accounting; Geography; Economics; Physical Science; Mathematical Literacy; Business Studies; History, First Additional Language; Life Science. The report also discusses candidates misconceptions and associated errors with suggestions to stakeholders to minimize such learning barriers. The findings of the report also inform intervention programs organised by the department of Basic Education (DBE) to continuously develop teachers for improve quality teaching and learning.

Misconceptions

According to constructivists, misconceptions happen because the new idea has no link with existing knowledge; as a result, assimilation or accommodation becomes impossible. Misconception leads to serious learning difficulties in mathematics, since learners try to make use of their previous inadequate teaching informal thinking or poor remembrance. Drews et al. (2005:18) defined a misconception as a misapplication of a rule, an over or under-generalization. Misconceptions may also be referred as an alternative conception of an idea, which differs from expert understanding (Baumert et al., 2010 p133). Research on misconceptions suggests that repeating a lesson to emphasize a point does not help learners who have acquired alternative conceptions or misconceived (Champagne, Klopfer & Gunstone, 1982; McDermott, 1984; Resnick, 1983). Learners tend to be attached to their misconceptions because they actively constructed them and gives them smart solutionsCITATION Nas14 \l 2057 (Naseer & Hassan, 2014). Identifying misconceptions and employing diverse and effective strategies to re-educate the learner in order to correct this learning barrier is probably ideal.

Gay, Mills, and Airasian (2011:109) suggested that changing the conceptual framework of learners is one ideal way of repairing mathematical and science misconceptions. He expounds that it is not usually successful to explain the errors and misconceptions to the learners. This is because misconceptions should be changed internally partly through the learners belief systems and partly through their own cognition. Creswell (2013:12) also affirmed the constructivist view that learners do not come to the classroom blank; rather they come with informal theories constructed from everyday experiences.

Geary (2011:1539) described learner errors are the symptoms of misconceptions. Generally, misconceptions manifest through errors. The challenging issue concerning misconceptions is that many people have difficulty correcting misconceptions because the false concepts may be deeply ingrained in the mental map of the individual. Some people do not like to be proven wrong and will continue clinging to a misconception even if they have been proven wrong (McDonald, 2010). This view is consistent with that of Hammer (1996:99) who thought students misconceptions:

Are strongly held, stable cognitive structures: This means that the learners formed misconceptions are solidified cognitively and become intricately difficult to eradicate.

Differ from expert understanding; when evaluated by someone with a strong knowledge base, they find that the learners perceptions of mathematical constructs are incomprehensible due to weakened concept images.

Affect in a fundamenta...