To achieve this goal, this study had to determine learner perceptions before and after the incorporation of the history of mathematics into the lessons on the Pythagorean Theorem. From the inclusion of the history of mathematics it also seemed as if learners learned that failure is part of the learning process.
INTRODUCTION
BACKGROUND TO STUDY
This research attempted to bring life back to mathematics in classrooms through the integration of the history of mathematics. This study postulates that the students' perception of the subject by using the history of mathematics can be improved or reversed to some extent.
THE RATIONALE
For example, Carter, Dunne, Morgan, and Smuts (2006, p. 8) illustrate the ancient Indian numerals used in the eastern part of the Arab Empire in the years between 969 and 1082. Although these textbooks and the curriculum statement contain historical fragments, the history of mathematics does not appear to be much anchored in practice.
PURPOSE OF STUDY
RESEARCH OBJECTIVES This study sought
CRITICAL RESEARCH QUESTION
In this study, it is envisioned and argued that when learners have the right perspective on mathematics, the eagerness to learn will grow and thus ignite an inquisitive mind in the learner which is a prerequisite for success in mathematics . Which aspects of using the history of Pythagoras' Theorem have the most influence on learners' perceptions.
AN OVERVIEW OF UPCOMING CHAPTERS
CONCLUSION
REVIEW OF LITERATURE
- INTRODUCTION
- THE HISTORY OF MATHEMATICS AND MATHEMATICS EDUCATION
- ASPECTS IN THE USE OF THE HISTORY OF MATHEMATICS
- The use of historical narratives within mathematics classrooms
- The use of discovery learning within mathematics classrooms
- The use of technology within mathematics classrooms
- GEOMETRY IN MATHEMATICS EDUCATION
- THE STORY OF GEOMETRY: THALES TO EUCLID
- LEARNING GEOMETRY
- PEDAGOGY AND GEOMETRY
As such, it was for this reason that I incorporated technology as an aspect of the history of mathematics. In his research, Yevdokimov (2006) investigated the use of e-books in incorporating the history of mathematics.
THEORETICAL FRAMEWORK
- INTRODUCTION
- OPTING FOR A DIFFERENT LENS – THE GENETIC APPROACH
- THEMES FROM CONSTRUCTIVISM
- THE CONCEPTUAL FRAMEWORK - PERCEPTIONS AND UNDERSTANDING This conceptual framework presents concepts I considered critical in this study. The close
- Nature of perceptions
- How perceptions change
- Factors affecting perceptions
- Importance of perceptions
- CONCLUSION
With this insight, this study sought to determine students' perceptions of the Pythagorean Theorem before and after exposure to some Pythagorean Theorem lessons that included the history of the Theorem. I believed that the formation of students' perceptions of the Pythagorean theorem was influenced by their experiences, attitudes, and interests in the learning context.
RESEARCH DESIGN AND METHODOLOGY
- INTRODUCTION
- Research approach
- Research paradigm
- RESEARCH METHODOLOGY
- DATA COLLECTION
- Setting
- Sampling
- Data collection methods
- DATA ANALYSIS
- Data transcription
- Organising and coding of the data generated
- ETHICAL CONSIDERATIONS
- RESEARCH TRUSTWORTHINESS
- CONCLUSION
Understand and interpret students' perceptions and perspectives of the Pythagorean theorem before and after the inclusion of the history of mathematics in their lessons. The interview questions were formulated to gather students' perceptions and perspectives on geometry prior to the inclusion of specific aspects of the history of mathematics in learning. The discussion went to the students' perspectives and perceptions of geometry and the Pythagorean theorem, before the history of mathematics was included in the content of the sentence.
The aim of this dialogue was to determine (i) whether the inclusion of the history of mathematics in their lessons had any impact on their perceptions and perspectives on the Pythagorean Theorem and geometry and (ii) what aspects of the use of the history of the Pythagorean Theorem had the greatest impact on students' perceptions and perspectives. The focus of this dialogue was the students' perceptions and perspectives on teaching and learning methods. this is the genetic approach) used in teaching the Pythagorean Theorem in which the history of mathematics was involved.
CHAPTER FIVE
FINDINGS, ANALYSIS AND INTERPRETATION
INTRODUCTION
ABOUT THE PARTICIPANTS
Data on number of years in the same grade and ability level are based on year-end (2014) 10th or 11th grade student grades. Four participants repeated the 11th grade because they did not meet the requirements for promotion to the 12th grade. The policy for progression in Further Education and Training (FET) is that a student would not be eligible to progress to the next grade if they did not have a home language, life orientation or more than two subjects they were studying.
In this study, in terms of ability, below average means that the end of year marks for the learner were below thirty percent.
Learners’ profiles
One of my fascinations is ancient Egyptian work and I would like to be an archaeologist as a hobby in my spare time. My name is Sbu Xulu, a student at Warrenview Girls High School and I am currently in 11th grade. My name is Phume Mkhize, sixteen years old, I am in grade 11 at Warrenview Girls High School.
I would like to become a nurse when I finish my studies because I enjoy helping old and sick people. I made this choice because when I grow up, I would like to be a doctor or have a career in health sciences so that I can help people who are sick like me.
LEARNER PERCEPTIONS OF THE PYTHAGOREAN THEOREM
- Learner perceptions of mathematics
- Learner perceptions of geometry
- Learner perceptions of the Pythagorean Theorem
In the next section (5.3) I address the first research question: what are learners' perceptions of the Pythagorean Theorem. It was my view that there was a possibility that perhaps learner perceptions of the statement were also derived from their perceptions of mathematics. Maxine's contribution confirms the perception that the learners at WGHS had similar perceptions of geometry and mathematics.
It was surprising to note that despite all the negativity about learners' perceptions of mathematics and geometry, grade 11 learners at WGHS had a positive view of the Pythagorean Theorem, a topic in geometry. It was the learners' view that the Pythagorean theorem was easier because they knew the formula and did not change it.
INFLUENCE OF THE HISTORY OF PYTHAGORAS’ THEOREM ON LEARNERS’
- The use of historical narratives within mathematics classrooms
- The use of discovery learning within mathematics classrooms
- The use of cooperative learning within mathematics classrooms
- The use of technology within the classroom
It was my finding that the history of the Pythagorean Theorem awakened in the learners a desire to know more about the history of the mathematicians and their achievements. This meant that her perspective of mathematics was broadened by using the history of Pythagoras' Theorem. Discovery learning involving the use of the history of Pythagoras' Theorem is fun as claimed by the participants of WGHS.
Through the revealing lesson of incorporating the history of the Pythagorean Theorem, the tests were no longer scary for the students, but interesting and fun. It was my interpretation that the inclusion of the history of the Pythagorean Theorem, augmented by the use of appropriate technology, had led to change in the students as they showed an interest in proofs of the Pythagorean Theorem.
ASPECTS OF THE HISTORY OF MATHEMATICS THAT HAD THE MOST INFLUENCE ON LEARNER PERCEPTIONS
- The use of historical narratives in the teaching and learning of mathematics
- The use of cooperative learning in mathematics classrooms
- Technology integration in teaching and learning
Integrating the history of mathematics through cooperative learning on proofs of the Pythagorean theorem had a great impact on students' perceptions of the theorem because students, working as a team in small groups, shared ideas and discussed the requirements of each activity. Through collaboration, as an aspect of the history of mathematics, they realized that they did not have to work in isolation, but had their peers critically analyze their ideas and work. It can be concluded that incorporating mathematics history using cooperative learning has had a significant positive impact on students' perceptions of tests by helping them overcome their fear of tests and reduce math anxiety (Marshall, 2000).
Feryn (Journal Entry, 28 July 2015) was of the opinion that group work activities were more. At this stage, let me hasten to say that although technology is not a direct aspect of the history of mathematics, its integration with the history of the Pythagorean theorem had a tremendous impact on students' perceptions of geometry.
CONCLUSION
Discovery learning involving group work activities, a principle of the genetic approach to learning, presented a somewhat informal work environment for students. Within this collaborative environment students seemed more inclined to learn and as a result their perception of the Pythagorean Theorem was positively affected in some way. The students appreciated the use of technology as we are in the age where technology is the order of the day.
The use of technological devices in learning the Pythagorean Theorem in which its history was incorporated was simply to bring their favorite devices into the lesson. This had an impact on their perception of the lesson as learners repeated that bright colors resonated with them.
CHAPTER SIX
CONCLUDING REMARKS, IMPLICATIONS AND LIMITATIONS OF STUDY
- INTRODUCTION
- CONCLUDING REMARKS
- IMPLICTIONS OF STUDY’S FINDINGS
- Implication for practice
- Implications for educators
- Implications for policy makers
- Implications for future research
- LIMITATIONS OF STUDY
- CONCLUSION
It seemed that by including the history of mathematics the students had learned that failure is part of the learning process. Considering the findings of this study, it is imperative that the history of mathematics be considered as a tool in mathematics education. The inclusion of the history of mathematics in this study brought about positive changes in students' perceptions of mathematics, geometry and the Pythagorean theorem.
Incorporating the history of mathematics into the mathematics curriculum could have similar benefits to those identified in this study. Future research may need to explore the theoretical aspects of integrating the history of mathematics.
Turnitin report
Parental and participants consent letters
I have been fully informed about the research and know that I can contact the researcher at any time for information or explanation. My child/ward's participation in this study will involve participating in recorded interviews in which she will be asked a question that will later be transcribed. Her participation in this study is completely voluntary and she may withdraw from this study at any time without giving a reason.
Her participation will be treated confidentially and all information will be kept anonymous and secure. I am free to discuss any questions or comments I wish to make with the researcher's supervisor.
Learner’s Letter of Consent
- Group interviews’ Guide (video recorded)
- Questions before Task 1
- Questions after Task 1
- to 1.9 will be repeated excluding question 1.8
- Questions after Task 2 Question 1.8 will be repeated
- Journal (Kept by learners for the entire duration of data collection) Today’s lesson
- Reinventing Pythagoras’ Theorem
If you were given the chance, what would you change about the way you were taught the Pythagorean Theorem. Was your understanding of the Pythagorean theorem changed in any way by discovering the theorem yourself and learning about some of the mathematicians who proved it. Did your new understanding of the sentence affect the way you solved Exercise 2 problems.
How has the historical information about the mathematician Pythagoras influenced your understanding of the theorem? Has there been any change in your perception of the Pythagorean Theorem after attending these classes?
BEHOLD!”
BHASKARA
Learners work in groups of five. (Cut and paste activity)
Cut and paste activity)
- Using your findings from (g) and (h) show that a 2 + b 2 = c 2
What is the ratio of the areas of the horizontal and vertical rectangles in the last diagram. Is there a relationship between the sum of the areas of the interior components and the area of the large exterior square? Considering the 4th diagram in the 2nd row of the 1st column, find the area of the inner square with respect to c.
If all triangles have right angles, find the area of one of the triangles. What is the size of each of the sides of the square (in terms of a and b) at the center of the diagram.
Euclid’s proof of Pythagorean Theorem
If you have combined these results and the results previously determined from (1.6.1 and 1.6.2), write an equation that shows the relationship between the areas of rectangle BDLM and triangle ABD. Write another equation to illustrate the relationship between the areas of rectangle BDLM and triangle FBC. Given the two equations in (1.6.4. and 1.6.5.) write an equation to relate the areas of the rectangle BDLM and the square ABFG.
Combining these results and the previously established results from (1.6.7 and 1.6.8), write an equation that shows the relationship between the areas of the rectangle CELM and the triangle ACE. Write another equation to illustrate the relationship between the areas of the rectangle CELM and the triangle BCK.
NAMING OUR INVENTION
- Show that the above equation can be simplified to c 2 = a 2 + b 2
- Discovering Pythagoras’ Theorem – If a square is draw from each side of any right angled triangle, the sum of area of the two smaller squares is equal to the area of the larger square.(Lesson of about 120minutes)
- General application of Pythagoras’ Theorem (60minutes)
- Discovering the distance formula (120 minutes)
Set the area of the trapezoid equal to the total area of the three triangles and simplify. Theorem by bringing to their attention that which they discovered, just like the mathematicians of ancient times, which is called the Pythagorean Theorem. A quick review of the work on measurement and then learners get Task 2.2 as homework.
