This academic paper is based on the reflection of co-teaching experiences in a community based school in Karachi, Pakistan. The author taught in grade V along with the co-teacher Jaweria (pseudonym) who was a veteran Mathematics teacher. A number of situations surprised him and made he reflect deeper into the situation with the help of suitable literature. The importance of Mathematical vocabulary, teachers' Pedagogical Content Knowledge and appropriate text book are highlighted.
Table of Contents
1. Context
2. Content Analysis
3. Student Thinking
3.1 Least Common Multiple
3.2 Square
4. Teachers Knowledge, Thinking and Instruction
4.1 Prime Factorization
4.1.1 Teaching
4.1.2 Planning
5. Conclusion
Objectives and Topics
This paper aims to reflect on the author's co-teaching experiences in a grade five mathematics classroom in Karachi, Pakistan, focusing on the critical role of teacher knowledge and pedagogical content understanding in addressing student misconceptions.
- The impact of traditional teaching methods on student comprehension.
- Identifying and addressing student misconceptions regarding mathematical terminology.
- The importance of pedagogical content knowledge for teachers to predict student errors.
- Challenges associated with language barriers in mathematics instruction.
- The necessity of meaningful connections within mathematical concepts.
- Evaluating the role and relevance of textbooks in a specific socio-economic context.
Excerpt from the Book
Square
When I had to co-teach the concept of square as an exponent I planned to give the concept by linking it with the area of the geometrical square. I started the lesson by asking them the definition of square, hoping that they would come up with the definition of geometric square as well. Surprisingly, the students initially only told me the definitions of the exponent square. On deep probing they finally told me the definition of the geometrical shape as well. I asked them if there is something similar between the geometric square and exponent square. They told me no, the common response for geometric square was“woh shape haijo geometry mein hota hai” (it is a shape which is present in geometry) and for exponent square was “woh number mein hota haijo do dafa multiply karne sey aatahai” (it is present in number which is obtained by multiplying a number twice).
I expected them to tell me that the square shapes is the multiple of length of its two equal sides and the arithmetic square is refers to a number being multiplied twice. The above scenario struck me because I was not prepared for these responses. Pedagogical content knowledge is very important for teachers to possess because it gives information about students thinking on specific areas and it prepares the teacher to predict student errors (Lau & Yuen, 2012; Peng, n.d). Shulman (1986) argues that through pedagogical knowledge teachers can identify students’ misconceptions. I was not aware that the students will not be able to make the connections between the different branches of mathematics. Bosse (2003) says that connections in mathematics help students to use and remember a larger number of thoughts. Students can merge those thoughts in to connected mental componentsfor easy handling later.
Summary of Chapters
Context: The author describes the educational environment in a grade five classroom in Karachi, Pakistan, noting the traditional teaching methods employed.
Content Analysis: This section explores the mathematical concepts of factors and multiples, emphasizing their connection to divisibility and higher-order thinking.
Student Thinking: The author analyzes student responses to concepts like Least Common Multiple and Square, highlighting common misunderstandings and the impact of vocabulary.
Teachers Knowledge, Thinking and Instruction: This chapter examines the necessity of teacher expertise in prime factorization, specifically focusing on teaching methodologies and lesson planning challenges.
Conclusion: The author summarizes the findings, asserting that mathematics teachers require strong pedagogical and subject-matter knowledge to enhance student learning.
Keywords
Mathematics education, pedagogical content knowledge, co-teaching, student misconceptions, prime factorization, Least Common Multiple, geometry, arithmetic, teaching methodologies, teacher training, factor trees, conceptual understanding, Pakistan, educational context, student engagement.
Frequently Asked Questions
What is the primary focus of this research?
The paper focuses on the author's reflections on co-teaching mathematics in a fifth-grade classroom and the vital importance of teachers possessing deep subject-matter and pedagogical knowledge.
What are the main thematic areas covered?
The work covers student misconceptions in mathematics, the role of pedagogical knowledge, the importance of mathematical connections, and the influence of textbook content on student learning.
What is the central research question?
The research explores how teacher knowledge and instructional choices directly affect the ability of students to grasp mathematical concepts and identify connections between them.
Which scientific methods are utilized?
The author utilizes reflective practice and qualitative observation of classroom interactions to analyze teaching strategies and student learning patterns.
What topics are discussed in the main body?
The body discusses the teaching of Least Common Multiple, the geometric versus arithmetic concepts of a square, and the challenges of teaching prime factorization in a traditional environment.
Which keywords best characterize this work?
Key terms include mathematics education, pedagogical content knowledge, student misconceptions, and prime factorization.
Why did students struggle with the term "Least Common Multiple"?
Students struggled because the term was often abbreviated as "LCM" in class without adequate discussion of the vocabulary behind the individual components, leading to confusion with terms like "long."
What was the specific misconception encountered during the "Square" lesson?
Students could not identify the connection between the geometric shape of a square and the arithmetic process of squaring a number, viewing them as entirely unrelated concepts.
What issue arose during the prime factorization lesson?
The author observed that the textbook language was too complex for the students' language proficiency level, causing them to fail to grasp the definition of decomposition.
What is the core takeaway regarding teacher qualifications?
The author concludes that mathematics teachers must be academically qualified and reflective practitioners to effectively translate complex concepts into relevant, student-centered knowledge.
- Arbeit zitieren
- Asma Mamsa (Autor:in), 2014, Least Common Multiples and Squares. Reflections on co teaching Mathematics in a community based school, München, GRIN Verlag, https://www.grin.com/document/1001524
