Learning Difficulties SOME SOURCES OF LEARNING DIFFICULTIES 1. STUDENT’S PROBLEM * Student’s perception and attitude toward mathematics and mathematics teacher * The nature of mathematical thinking * The student’s ability to learn mathematics 2. TEACHER PROBLEM * The presentation of mathematics in the classrooms * The nature of the teaching methods and strategy used by the teacher 3. CURRICULUM * The non-flexibility of the curriculum * The nature of the syllabus * The use of resources that is not fit to the individual student 4. CLASS ORGANISATION * Difficulties Attribute to school or Class organization * The environment that is not supporting the student to learn 5. THE SUBJECT ITSELF * The written form of mathematics * The abstract nature of mathematics * The complexity of the concepts * The hierarchical of the mathematics concepts * The formal notation 6. etc. DR. IDA KARNASIH, SEAMEO RECSAM
PM – 6522 Integrating Constructivism and Meaningful Learning In Student-Centred Primary Mathematics Classroom 31 March – 25 April 2008 Facilitator : Dr. Ida KArnasih Conception and Misconception in Primary Mathematics
What is a Concept? (John son & Rising,1972) A Concept is mental abstraction of common properties of a set of experience or phenomena Ausubel (1968) – concept formation Concept as abstraction from experience involving examples of concepts Hunt, Martin, Stone (1966) – concept assimilation A concept is a decision rule which, when applied to the description of an object, specifies whether or not a name can be applied. Henderson (1970) Verbal concepts are those for which a conventional name or designating expression exit, they are learned by concept assimilation or by definition – e.g. rhombus, polygon, variable, mean Non-verbal concepts are learned by concept formation or by abstraction from example – e.g. number, time, color, space
Kinds of Concepts Concepts can represent: • Objects • Acttivities • Living things Concept can also represent: • Properties, such color, size • Things that are abstract • Relations (for example: better that, smaller than, bigger than)
Forms of Concepts: • Concrete concepts • Abstract concepts • Verbal concepts • Non-verbal concepts • Process concepts
CONCEPTION • The ability to form or understand mental concepts and abstractions. • Something conceived in the mind; a concept, plan, design, idea, or thought
Concept, idea, image, notion, perception, thought. exists in the mind as the product of careful mental activity
How Concept can be developed 1. Markle’s model (1969) The building up of concept can be seen as the result of the learner making separate discriminations related to the concept and classifying them as an example or non-example 2. Skemp’s Model (1971) • Primary concept are derived from sensory and motor experience • Secondary concept are derived from previosly abstract concepts – (verbal concepts) • Hence , “ hierachical order” of concept is postulated where the highest order concepts are those furthest removed from the primary concepts
Problems in Learning of Concept • Students’ Cognitive ability • Language factor • Abstract Nature of Mathematics • Complexities of Mathematical concepts
Misconception Misconception are crucially important to learning and teaching, because: • Misconception from part of pupil’s conceptual structure that will interact with new concepts, • Misconceptions influence new learning, mostly in a negative way, • Misconceptions generate errors.
Slips, Errors and Misconception • Slips are wrong answers due to planning • Errors are wrong answers due to a planning. Errors are the symptoms of underlying conceptual structures that are the cause of errors; • Misconceptions: Beliefs and principles in the cognitive structure that are the cause of systematic conceptual errors.
Group tasks 1. Get some manipulatives, think of activities, or living things 2. Try to find out as many as concepts you can from activity 1 (concrete, abstract, verbal, non verbal, formation, and assimilation concepts) 3. Think of the possibility of students’ misconceptions in learning those concepts (if any) 4. Think of how to re-educate/ help students’ away from those misconceptions 5. Discuss your results in front of our class.