# Learners’ Beliefs & Conceptions About The Role Of Mathematics In Physics

## Abstract

Mathematics is an essential part of what we call physics. It plays an important role in physics research as well as in learning physics. It can be a useful tool or a barrier too high to overcome for some of our students. Only recently this aspect of learning physics has been given more attention. The study presented here makes a contribution to this field of research by providing a first view on students’ conceptions about the role of mathematics in (learning) physics. These beliefs are functioning as filters for perception and processing and therefore have an important impact on our students’ learning processes.

To know about students’ conceptions can inspire teachers to create more adequate learning environments for our students and help them to be more efficient. German learners grade 10 and 12 as well as physics teacher students in their 4th semester have been surveyed. Quantitative methods have been applied – structural equation modeling (sem) to ensure one-dimensional measures as well as measurement invariance across groups and a general linear model approach (glm) to test for within-subjects effects (distal vs. proximal beliefs and graphical vs. algebraic representations), between-subjects effects (group, achievement, sex) and interaction effects. The results encourage further in depth research.

## Chapter One

### Introduction

#### 1.1 Background of the Study

Federalism Mathematics plays an important role in doing and learning physics. There are studies and publications dealing with philosophical aspects, attempts to model math use in physics and studies focusing on the learners’ perspective in terms off attitudes and conceptions towards mathematics or science (see Krey 2012 for a review). The motivation for research on students’ prior knowledge, attitudes etc. is, that all of these intuitive theories influence the learners’ way in which things are perceived, information is processed, and new things are learnt (eg. Pehkonen & Törner, 1996; Köller et al., 2000). or for teachers’ beliefs Pajares (1992) This instrumental reason for studying beliefs is complemented by a substantial one – namely, these beliefs are core components of what we call mathematical or scientific literacy, e.g., the relevance of nos-knowledge, which should include conceptions about the role of mathematics for scientific (e.g., physics) research and science (e.g., physics) learning. While there are a few philosophical approaches towards exploring the role of mathematics in physics, there is a lack of empirical findings about students beliefs in this field, although there are first attempts to close this gap (eg. Bing, 2008; Krey, 2012). While a few interviews have been conducted within the scope of this study, its main focus lies on developing an instrument with which a quantitative approach becomes possible. Research on the nature of science as well as common sense, suggest, that it is necessary to distinguish between proximal and distal beliefs (Hogan, 2000, 52): “Distal knowledge of the nature of science refers to students’ knowledge about […] the professional scientific community. Proximal knowledge of the nature of science refers to students’ understanding of and perspectives on the nature of their own science knowledge-building practices and the scientific knowledge they form or encounter.“ Based on first interviews conducted with grade 10 students, I assumed that in general it would make a difference whether students are confronted with mathematical representations in graphical or algebraic form. When I use the term “graphical representation” I am referring to a graph in a coordinate system (see Friel, Curcio, & Bright, 2001 for an overview), while “algebraic representation” refers to equations that need to be constructed and interpreted when learning physics (Sherin, 2001). The purpose of this research project was to collect data that help to describe the learners belief system about the role of mathematics in physics. A complete description of an individual learners’ belief system was not intended. For this purpose a few fields of interest have been nominated and operationalized. These fields include the students’ self-feeling when dealing with mathematical representations, their beliefs about aesthetics of mathematical representations, epistemological aspects and their beliefs concerning relatively non-controversial functions that mathematics fulfils in physics (e.g. Fischer, 2006; Frey 1967).

Mathematics is at the heart of many successful careers and successful lives for societal development, particularly in the extraordinary and accelerating change circumstances. However, in reality, most people in general and students in particular dislike mathematics. The review of school-based educational research has revealed that the majority of school students find mathematics as the most difficult, abstract, tedious, deadly, and boring subject (Ernest, 1996; Wong, Lam & Wong, 2001; Nardi & Steward, 2003; and Kirsti, Grevholm & Lepik, 2005). Moreover, research studies show that students in primary schools enjoy mathematics but when they move to secondary school their interest towards the subject declines (Lazim, Abu & Wan, 2003; Dossey Mullis, Lindquist & Chamber, 1988 cited in Ocak, 2006; Barber, 1994 cited in Chambers, 1998). The negative conceptions of mathematics have a major impact on students’ achievement, enrollment in higher education and their future career decisions (Sam, 1999). Generally, students’ views of mathematics are developed based on their school learning experiences (Schoenfeld, 1989; Ernest, 1996) and how the public image of mathematics is portrayed in the society (Sam, 1999). To elaborate, in general it is believed that males are born with innate capabilities of making sense of abstract ideas and as mathematics is also an abstract level subject boys can do well as compared to girls (Walkerdine, 1998, Halai, 2006). Some of the other viewpoints students hold about mathematics include: mathematics problems have one and only one answer and they can be solved in a particular way; mathematics is a solitary activity, done by individuals in isolation; mathematics requires good memory and is only for clever ones. In order to facilitate students to possess a positive image of mathematics there is a need to explore their existing conceptions and attitude towards the subject. Once we are aware of their conceptions then we can address their alternative conceptions through designing appropriate mathematics teaching and learning programmes. In physics studies students have been found to struggle with explanations and the solving of physics problems when they need to relate theoretical models to real world phenomena, especially while using mathematics, i.e. combining mathematical operations with conceptual reasoning about physical phenomena – realising that equations can express a supreme meaning (Kuo et al., 2012; Michelsen, 2006; Tuminaro & Redish, 2007; Uhden et al., 2012). Solving of “standard-problems” (often appearing in the end of a chapter in physics textbooks) is traditionally a central part of physics teaching in upper secondary school in Nigeria. This is emphasised in a study by Due (2009) where students state that to succeed in physics, it is necessary to put a lot of effort into solving physics problems. Teachers often take for granted that students, who are able to solve standard problems, also have a good understanding of physics concepts and models. However, research show that this is not necessarily the case. Students can solve the problems without really understanding the concepts and models used (t.ex. Maloney, 1994; Hobden,1998). An explanation to this is that beginning physics students tend to search for a formula that fits the numbers/variables given in the problem (Larkin et al., 1980). In summary we know from earlier research that the solving of physics standard problems is not a guarantee that students focus on the relationship between models/concepts and the “real world”, as stated above as central for physics. Instead students in this situation often focus on putting numbers into formulas or combinations of formulas, manipulating them mathematically and getting the right answer. In this study we want to broaden the perspective on how the relations between the real world – Theoretical models – Mathematics (e.g. manipulations of formulas) are communicated in different kinds of situations (not only problem solving) in the teaching of physics. The research in this area is so far scarce.

#### 1.2 Statement of the Problem

To succeed in physics, it is necessary to put a lot of effort into solving physics problems and physics problems are solved using mathematics. Learning of mathematics starts from when we begin to learn how to count. Then, we use mathematics in our everyday lives, sometimes without even realising. In these situations, what is needed to be learned – the ‘basic numerical concepts’ (Ansari, 2004) – was nothing but a way of expressing ourselves (in a language), in order to communicate with and relate to others. Mathematical skills develop as we grow and become involved in more and more activities, for example, measuring flour while making cakes or maybe rushing to “the sale” calculating (in our head) how much money could be saved. What we need in these occasions is mostly common sense, a practical approach towards obtaining a solution and some prior experience. From infancy to preschool, children develop a base of skills, concepts and understanding about numbers and mathematics. However, as children learn mathematics in a formal setting (the school curriculum), the sense they make of what they are presented with can differ from what the teachers might expect. The concepts can be counterintuitive and they do not understand the fundamental ideas or basic concepts covered in the mathematics class.

#### 1.3 Objective of the Study

This study was conducted with the following objectives:

- To explore the role of mathematics for physics teaching and learning in upper-secondary school through investigating relations made during physics lessons.
- To find out conceptions students hold about the nature of mathematics and attitude towards physics in the federal collage of education Zaria, Kaduna state?
- To find out if the effective teaching of mathematics, mathematical concepts and reasoning used impacts and inspire students during physics lessons.

#### 1.4 Research Hypotheses

##### Hypothesis One

**Hi:**Mathematical concept of students affects their expectations of and attitudes to physics**Ho:**Mathematical concept of students does not affect their expectations of and attitudes to physics

##### Hypothesis Two

**Hi:**Effective teaching of mathematics, mathematical concepts and reasoning impacts and inspire students in physics.**Ho:**Effective teaching of mathematics, mathematical concepts and reasoning does not impact and inspire students in physics.

#### 1.5 Significance of the Study

It is hoped that the finding of this project work will not only add to the vast knowledge about the beliefs and conceptions of learners about the role of mathematics in physics. It will also be useful to the Government and relevant policies makers in the educational sector by taking necessary measures to ensure the necessary steps are taking to improve the concept of learners on the roles of mathematics in physics.

#### 1.6 Scope and Limitation of the Study

This study is primary concerned with the role and conception of learners on the role of mathematics in physics. This study covers the federal college of education in zaria, Kaduna state. The researcher encountered some constraints, which limited the scope of the study. These constraints include but are not limited to the following.

##### a) Availability of Research Material:

The research material available to the researcher is insufficient, thereby limiting the study

##### b) Time:

The time frame allocated to the study does not enhance wider coverage as the researcher has to combine other academic activities and examinations with the study.

#### 1.7 Definition of Terms

##### Physics:

The branch of science concerned with the nature and properties of matter and energy. The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.

##### Mathematics:

The abstract science of number, quantity, and space, either as abstract concepts (pure mathematics ), or as applied to other disciplines such as physics and engineering

##### Student:

A person who is studying at a university or other place of higher education.

#### 1.8 Organization of the Study

This research work is organized in five chapters, for easy understanding, as follows

- Chapter one is concerned with the introduction, which consist of the (overview, of the study), historical background, statement of problem, objectives of the study, research hypotheses, significance of the study, scope and limitation of the study, definition of terms and historical background of the study.
- Chapter two highlights the theoretical framework on which the study is based, thus the review of related literature.
- Chapter three deals on the research design and methodology adopted in the study.
- Chapter four concentrate on the data collection and analysis and presentation of finding.
- Chapter five gives summary, conclusion, and recommendations made of the study

## Chapter Five

### Summary, Conclusion and Recommendation

#### 5.1 Introduction

It is important to ascertain that the objective of this study was to ascertain a critical analysis of learners’ beliefs and conceptions about the role of mathematics in physics.

In the preceding chapter, the relevant data collected for this study were presented, critically analyzed and appropriate interpretation given. In this chapter, certain recommendations are made, which in the opinion of the researcher will be of benefit in addressing the challenges of learners beliefs and conceptions about the role of mathematics in physics

#### 5.2 Summary

This study aimed at having a critical analysis of learners’ beliefs and conceptions about the role of mathematics in physics. Three objectives were raised. These objectives include: To explore the role of mathematics for physics teaching and learning in upper-secondary school through investigating relations made during physics lessons. To find out conceptions students hold about the nature of mathematics and attitude towards physics in the federal collage of education Zaria, Kaduna state? To find out if the effective teaching of mathematics, mathematical concepts and reasoning used impacts and inspire students during physics lessons.

#### 5.3 Conclusion and Recommendations

Based on the above findings pertaining to the objectives of the study the following conclusions are drawn. From the collected and analysed data, it can be concluded that Mathematical concept of students affects their expectations of and attitudes to physics

Effective teaching of mathematics, mathematical concepts and reasoning impacts and inspire students in physics.

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