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MTES 3243 AND 3273 Interactive Activity 1 Activity 2 - Coggle Diagram
MTES 3243 AND 3273
Interactive Activity 1
Activity 2
Misconceptions and Errors in Integer Operations: A Study in Preservice Elementary School Teachers (PGSD)
Emphasizes the importance of mathematics learning, specifically in developing competencies such as pattern tracking, creativity, communication, and problem-solving.
Highlights the significance of understanding mathematical concepts, particularly integers, as a basis for success in advanced mathematical topics.
Identifies common difficulties students face in solving problems related to integers, indicating a low mastery of the integer concept.
Defines misconception as a type of error in understanding mathematical concepts and problem-solving
Methods
Describes the research as a qualitative study conducted in November 2019 with 45 prospective elementary school teachers as subjects.
Subjects are given a test to detect misconceptions about integer calculations, categorized into Careless errors (Ca), Concept errors (Co), and Careless and Concept errors (Ca and Co).
Data analysis involves counting correct and incorrect answers on each question, with a focus on wrong student answers.
Results and Discussion
Presents variations in misconceptions or errors among students, with a particular focus on questions related to subtracting negative numbers.
Highlights that 69% of students made mistakes in questions 3 and 4, indicating a lack of understanding of negative numbers and possible confusion caused by the use of number coins.
Analyzes types of misconceptions: Careless errors (Ca), Concept errors (Co), and Careless and Concept errors (Ca and Co).
Identifies specific misconceptions, such as writing incorrect symbols, miscalculating operations, and misinterpreting negative integer subtraction.
Discusses the challenges faced by students in using number coins as a representation tool for integer operations.
Conclusion
Categorizes misconceptions into three types: Careless errors (Ca), Concept errors (Co), and Careless and Concept errors (Ca and Co).
Reports that 10% of students made Careless errors, 53% made Concept errors, and 9% made Careless and Concept errors out of the total questions.
Highlights the most common mistake as Concept errors, indicating a lack of understanding of rules and principles in positive and negative integer operations.
Concludes that misconceptions in integer operations among prospective elementary school teachers involve both carelessness in reading and rewriting questions and conceptual errors in completing operations.
Sources and Possible Causes of Errors and Misconceptions in Operations of Integers
Basic operations of integers appear simple but lead to confusion among students.
Lack of conceptual understanding due to abstract teaching methods.
Importance of solid fundamentals for advanced mathematical topics.
Problem Statement
Teachers emphasize memorization of rules, leading to confusion among students.
Students apply rules without understanding, resulting in errors.
Investigation needed to understand teachers' approaches and knowledge in teaching integers.
Method
Year 7 students in public Malaysian schools observed and interviewed.
Eight classes selected from different states using cluster sampling.
Interviews conducted with teachers and students.
Instruments: Interview protocols, observation checklist.
Results - Student Interviews
Carelessness
Some students misinterpret symbols (e.g., multiplication sign as addition).
Confusion between division and addition symbols.
Poor Knowledge
Errors due to weak understanding of basic concepts (parenthesis, factorization).
Weakness in multiplication and division.
Can't Assimilate Concept
Students treat integers as whole numbers, ignoring negative signs.
Inability to grasp the concept of integers.
Rule Mix-Up
Students apply rules without understanding when adding or subtracting integers.
Majority of students commit this error.
Surface Understanding
Some students unable to explain how or why they solve certain problems.
Correct answers provided without understanding.
Observation Data
Lacks Multiple Representations
Teachers use 2-3 representations, lacking concrete examples.
Real-life representations (analogies) used by only a few teachers.
Lacks Cooperative Learning
No evidence of cooperative learning observed.
Teachers prefer simple activities to save time.
Lacks Creative and Critical Thinking
Teachers use number line approach, focusing on memorization of rules.
No room for creative and critical thinking.
Teachers' Interviews
Parenthesis Misapprehension
Students struggle with understanding the function of parenthesis.
Teachers emphasize rules but students still make mistakes.
Poor Knowledge of Basic Concepts
Errors in addition and subtraction due to confusion with symbols and values.
Students struggle with operational symbols and negative signs.
Calculator Hooking
Dependency on calculators, hindering conceptual understanding.
Students prioritize getting correct answers over understanding.
Superficial Understanding
Students struggle with questions beyond those covered in class.
Lack of understanding of symbol and negative value concepts.
External Limitations
Time constraints and mixed-ability classes impact teaching approach.
School activities, holidays, and natural disasters affect lesson progress.
Discussion
External limitations (time constraints) identified as the main cause of errors.
Lack of emphasis on multiple representations, cooperative learning, and critical thinking in classrooms.
Dependency on calculators hinders conceptual understanding.
Conclusion
Emphasis on teaching for understanding.
Recommendations for active learning, cooperative learning, multiple representations, and creative lessons.
Proposed teaching framework to address errors and misconceptions in integers.