# School of Education

## Research Student: Innocent Tasara

### How do teachers of mathematics teach calculus?

**Submission Date: October 2018**

My doctoral study seeks to investigate aspects of teacher practice for calculus teaching with the aim of contributing to the knowledge base that seeks to improve, not only the teaching and learning of calculus in secondary schools, but also the teaching and learning of mathematics teaching in teacher training programmes. The study will conducted in England secondary schools that provide post 16 or advanced level mathematics.

The study will focus on tools and representations that teachers use for teaching differentiation because tools (Vygotsky, 1978) mediate the object of the teaching activity (Engeström, 1993). Not only will this study investigate what type of tools and representations teachers use, but more importantly, how they use them in teaching differentiation. These tools could be internal or external to the teacher, physical or symbolic, textual or digital resources (Adler, 2012). The mathematical representations could be described in terms of language and notation, numerical, geometric or graphical and algebraic or symbolic forms and contexts, used by the teachers (Zimmermann, 1991; Hughes-Hallett et al., 1994; Tall, 1996). The following research questions will form the basis of that investigation:

- What tools/resources do teachers of mathematics use for teaching differentiation, and why?

Data collection will involve the use of interviews and lesson observations. The primary participants will be teachers who, at the time of data collection, shall be teaching post 16 mathematics classes. This is a qualitative research in which a combination of deductive and inductive approaches to thematic data analysis will be adopted in deconstructing the teachers’ narratives.

### Background

My name is Innocent Tasara. BSc(Hons), Dip(Ed), PGCE, MA(Ed), FHEA. I am a Lecturer in Mathematics Education and a Fellow of the Higher Education Academy (FHEA). I am the leader for Post Graduate Certificate in Education (PGCE) Secondary Mathematics and the MA in Education at the University of Leeds. Since 2013, I also taught and coordinated the Teaching Advanced Mathematics (TAM) course for post 16 teachers of mathematics, in conjunction with Mathematics in Education and Industry (MEI).

Prior to joining the University of Leeds in 2012 I was a teacher of mathematics in the secondary schools in Yorkshire (England) having completed BSc (Hon) Mathematics and PGCE Secondary Mathematics in 2008, and MA in Mathematics Education, subsequently; all from the University of Leeds. However, my mathematics teaching career dates back to 1999 when I obtained my first teaching qualification, and taught mathematics in secondary schools in Zimbabwe. I have experience of working with and teaching students from diverse backgrounds of varying degrees of attainment.

I am a full time lecturer in Mathematics education who is currently studying a PhD in mathematics education on a part-time basis at the University of Leeds.

### What motivated me to undertake PhD study?

My prime motivation in this research topic stems from my previous personal experience as a secondary school teacher of mathematics for four years, and my recent and current experiences as a mathematics teacher educator at the University of Leeds. The majority of the mathematics student teachers on my PGCE course have Advanced Level mathematics and mathematics university degrees. I quickly realised that the majority of these students could only demonstrate some standard methods for calculus, thus procedural understanding but very limited conceptual understanding of calculus. Calculus is first taught post16 in secondary schools in the UK. I wondered how introductory calculus was being taught in secondary schools, hence my choice of the topic for research.

My secondary motivation came from exploring past research studies on the teaching and learning of calculus (Tall, 1990, 1992; Orton, 1983, 1986). The study by Orton (1983) reveals that many students are introduced to differentiation “as a rule to be applied without much attempt to reveal the reasons for and justifications of the procedure” (p8). Now in the 21^{st} century, how secondary school teachers of mathematics teach calculus, became the subject of my doctoral study with a particular focus on differentiation.

### What makes me passionate about my subject?

I am very passionate about the teaching and learning of mathematics in our schools, and the teaching and learning of mathematics teaching. I am a lecturer in mathematics education whose primary interest is rooted in mathematics teacher education. I believe that this study will be invaluable for my professional learning and development as a researcher, and as a mathematics teacher educator. Ultimately, understanding how teachers teach calculus is crucial to finding more meaningful and effective ways to uncovering what students need to know and be able to do in order to understand calculus.

### What are my plans once I have completed my PhD?

- To successfully complete the research project:
*The early take-up of Core Mathematics: successes and ch*allenges. This is a Nuffield Foundation funded (£250K plus) project (Joint Applicant with Matt Homer -*Associate Professor in Quantitative Methods and Assessment*). The research will start in 2017 and run for three years. - Continue contributing to the academic intellect of the School of Education by conducting or participating in research which will enhance the University of Leeds reputation as a research-led teaching institution, and a Russell Group university.
- My ultimate career aspiration is to become a professor in mathematics education through producing high quality teaching programmes; high quality research and high quality publications, as well as quality leadership.