Concept mapping
- 1. Modern Instructional Strategies: Concept mapping 1 By, Sandhya J Mathematics
- 2. 2 INDEX Contents Page number Introduction 3 Concept mapping 4-8 Conclusion 8 References 8
- 3. 3 INTRODUCTION A mathematics teacher has a variety of strategies available for use in teaching mathematics. The selection of a suitable strategy depends on the objectives of the needs of the learner and the nature of the content. In a traditional classroom, instruction is teacher-centered and group-paced. It caters to the needs of ‘average’ students and does not make allowances for the vast individual differences found in the classroom. Students differ in their interest, aptitude, attitudes, and intellectual abilities and in a number of other aspects such as pace of learning, learning style, cognitive style and so on. Nowadays teachers are following the modern instructional strategies. These include pragmatic, associate and lecture approaches. Modern instructional strategies are those strategies which are constructed on the basis of the interest, or aptitude of the students in classroom. Different modern instructional strategies are : Cooperative learning strategies Collaborative learning Concept mapping Gradation Simulation From these, concept mapping is discussed here.
- 4. CONCEPT MAPPING Concept maps (knowledge maps or mind maps) are graphical tools for organizing and representing knowledge. Concept mapping is the individualized technique of summarizing the relationship among different ideas in graphs while engaged in learning activity. It is developed by Novak in 1972. A concept map is a diagram showing the relationships in between concepts. 4 According to Novak, “A concept map is a visual representation of the hierarchy and relations among concepts within an individual’s mind.” In a concept map(C-map), the concepts, usually represented by single words enclosed in a rectangle (node), are connected to other concept boxes by arrows (arcs). A word or brief phrase, written by the arrow, defines the relationship between the connected concepts. Shortly, a concept map (mind map) is a knowledge model, represented as a labeled set of nodes and arcs used to summarize a body of knowledge on a topic, much like an outline. Characteristics of Concept mapping 1. Concept map is a tool for organizing and representing knowledge in graphs.
- 5. 2. It is a graphical method of taking notes. 3. It visualizes relationships between different concepts. 4. It is a special form of a web diagram for exploring knowledge and gathering and sharing information. 5. Concept maps connect multiple words or ideas. 6. A concept map presents the relationship among a set of connected concepts and ideas. 7. It is a pictorial representation of concepts in different hierarchies. 8. It consists of nodes (vertices) and arcs (links). Nodes represent concepts and arcs represent the 5 relations between concepts. How to develop concept maps? Concept maps are graphical tools for organizing and representing knowledge. They include concepts, usually enclosed in circles or boxes of some type, and relationships between concepts indicated by a connecting line linking two concepts. Words on the line, referred to as linking words or linking phrases, specify the relationship between two concepts. The following are the steps involved in drawing concept maps: 1. Select: Focus on a theme and then identify related key words or phrases. 2. Rank: Rank the concepts (key words) from the most abstract and inclusive to the most concrete and specific. 3. Cluster: Cluster concepts that function at similar level of abstraction and those that interrelated closely. 4. Arrange: Arrange the concepts into a diagrammatic representation. 5. Link: Link concepts with linking lines and label each line with a proposition. Example: Polygon family tree from the class IX Topic: Polygons Concept: Growing shapes
- 6. 6 Polygons Triangles Acute Obtuse Isosceles Right Equilateral Scalene All angles are less than 90° One angle greater than 90° One angle 90° All angles are equal No sides are equal Two sides are equal Quadrilaterals Parallelogram Trapezium Both pairs of opposite sides are parallel and congruent. One pair of opposite sides are parallel and congruent Diagonal bisect each other. Exactly one pair of opposite sides are parallel Exactly two pairs of consecutive angles are supplementary Rectangle All the properties of a parallelogram Has a right angle Rhombus All sides are congruent Diagonals are perpendicular Square All the properties of parallelogram, rectangle, rhombus Other polygons Pentagon (5-sided) Hexagon (6-sided) Heptagon (7-sided) Octagon (8-sided)
- 7. 7 Another example: Nature of the solution of second degree equations Standard : X Topic : Second degree equations Concept : Discriminants 풂풙ퟐ + 풃풙 + 풄 = ퟎ Solution Greater than zero equal less than zero to zero 푥 = −푏 ± √푏2 − 4푎푐 2푎 Discriminant 풃ퟐ − ퟒ풂풄 Two solutions No solution One solution
- 8. 8 Importance of concept maps The following are the important uses of concept maps in classroom learning: 1. The implementation of concept maps in the classroom allows both the teacher and the student discovering and describing meaningful relations among the concepts. 2. A concept map helps to connect new ideas to knowledge that the learner already have. 3. They are a handy way to take notes during lectures and are excellent aids to group brainstorming. 4. They assist in planning studies and also provide useful graphics for presentations and written assignments. 5. A concept map can be used not only as a learning tool but also an evaluation tool. CONCLUSION A concept map is defined as a graphic representation of a person’s knowledge of a domain. They help the learner to refine his creative and critical thinking. Concept mapping provides a framework for organizing conceptual information in the process of defining a word. If we allow the students to create their own concept maps in classroom it will result in the enlargement of their cognitive structure. REFERENCES (1) Psychological bases of Education- Dr.N.K.Arjunan (2) Teaching of Mathematics – Dr. Anice James (3) Kerala Reader – Mathematics Std X and Std IX