A partnership for teachers, children and education
Home Curricular Support Resources Bookshelf Forums E-courses Contacts
Environmental Studies
  * Ourselves
  * Living Things
  * Weather & Seasons
  * Universe
Mathematics
  * Numbers
  * Operations
  * Geometry
language
  * Development
  * Comprehension
  * Expression
  * Grammar
   
    Teaching Mathematics

1. Planning the curriculum
Since Mathematics is hierarchical in nature, it has to be constructed like a building where the work proceeds level by level. All the different kinds of work needed to complete a level have to be completed before moving to the next level. A spiral coverage of curriculum is better than a linear coverage.

As commonly practiced, it is roughly an annual spiral. A spiral coverage completed every term would be more effective. In such a scheme, learning and revision get integrated.

2. Using the Textbook
Due to many non-academic compulsions, the topics in a Mathematics textbook are arranged linearly. For implementing a spiral coverage of the curriculum, the textbook will have to be used in a different way.

3. Sustaining the intrinsic motivation of children to learn
We wrongly concentrate on teaching 'ability' without ensuring that the necessary 'motivation for learning' is also nurtured.

Here are two strategies for sustaining motivation.

  1. Promote autonomy among students. Encourage students to make their own problems and to check their own answers. Provide them multiple ways of approaching a problem. Let students adopt the method they are most comfortable with. Let students feel that they have a control over their learning and efforts.
  2. Encourage exploration.
    Mathematics has many areas where students can conduct open-ended explorations with surprise patterns and endings. These will make learning Mathematics 'fun' for children.

4. Teaching Concepts

  1. Provide enough experiences leading to concept formation before introducing definitions and terms related to the concepts. For example, provide experiences in equal sharing before introducing the concept of division and the words associated with division.
  2. Less emphasis on verbal explanations. Since language itself can become a barrier to learning, purely verbal explanations may not result in true understanding.
  3. Enable formation of mental images and patterns. Concepts are stored in our mind in the form of images and patterns. Our teaching methods should assist children in this process.
  4. Move from the concrete to semi-concrete to abstract.
    Concepts are abstract ideas. Children should be helped to construct these in their minds by starting with concrete experiences and then move on to semi concrete experiences and then to abstract experiences.
  5. Relate concepts to learners' experience and previous knowledge. New concepts are integrated into our existing knowledge. Sometimes, new concepts that do not agree with our existing knowledge, may cause the restructuring of our existing knowledge to accommodate the new knowledge. This takes thinking on the part of the learner.
  6. Plan activities, if necessary, with 'designed' activity materials. Many mathematical concepts may be related to experiences that a child may not have had. In such cases activity materials should be designed so that children can play with them and internalize the related concepts.
  7. Encourage peer group interactions. Concepts have to be constructed in the mind in a continuous process of formation and adjustment. For this it is very important to discuss your ideas, defend them and where necessary correct them. This has to be facilitated in a non-threatening and non-combative atmosphere. Encourage peer group interaction and cooperative learning.
  8. Less emphasis on writing while trying to understand concepts. Writing Mathematics is very easy as the language of Mathematics has very few alphabets. If too much writing is involved while learning a concept, there may not be sufficient time for understanding the concept.
  9. Design Concept Worksheets. Design 'Objective-Type' or short answer worksheets mainly to test concepts. These worksheets should not test computational skills.



 
    Number Games
   
 12 With Four Three's
 
The number 12 can be very easily expressed with four three's:
12 = 3 + 3 + 3 + 3
It's more of a problem to obtain 15 and 18 using four three's:
15 = (3 x 3) + (3 + 3);
18 = (3 x 3) + (3 x 3);
And if you were required to arrive at 5 in the same way, you might not be very quick
5 = (3 + 3)/3+ 3

Now think of the ways to get the numbers 1, 2, 3, 4, 6, 7, 8, 9, 10.



Click here for the solution



Next Last
 Problems 1 of 36

 

Source: Numeracy Counts !, Anita Rampal, R Ramanujam and L S Saraswati, N L R C, LBS National Academy of Administration, Mussoorie.

 
Content developed by S. Sundaram, Principal, Atul Vidyalaya, Valsad, Gujarat.