Learning DifficultiesSOME 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 – 6522Integrating Constructivism and Meaningful Learning

In Student-Centred Primary Mathematics Classroom

31 March – 25 April 2008

Facilitator : Dr. Ida KArnasih

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 assimilationA 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

The ability to form or understand mental concepts and abstractions.

Something conceived in the mind; a concept, plan, design, idea, or thought

CONCEPTION

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

1. Students’ Cognitive ability

2. Language factor

3. Abstract Nature of Mathematics

1. 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 tasks1. 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.