The Problem With Math Textbooks

I have some reservations about the use of math textbooks for the primary classes (k-5). The reservations come out of certain perspectives of what constitutes effective teaching of math in these classes.

You could either contest my perspectives themselves or the validity of the conclusions drawn from these perspectives.

'My perspectives'

1. The children are still in the concrete-operations stage of cognitive development and find it difficult to understand abstract ideas. Listening to a teacher’s lecture is an abstract activity.

2. They learn best through activities which require physical movement, role play, relating to their life experiences and playing with physical objects.

3. Hence less “lecture” and more “activities” to connect concepts to their classroom & life experiences is essential.

4. There should be many opportunities for independent explorations & group project work. “Math talk” and discussions in the class are important.

5. Children can easily “memorise” and also easily “forget”. Hence all the above activities related to any topic should be deliberately repeated several times over a period of time so that children can internalize the understandings & skills. There should be a spiral implementation of the curriculum.

6. All concepts & skills should be learnt through activities where the essential focus is not on writing. After several such activities, students can assess/ document their understanding through a worksheet. This helps the concepts & skills to be “anchored” through writing and also serves as a reference document for parents.

7. All the concepts & skills they have to learn are vital. Hence these should be reduced to the critical minimum. All children should score at least 80 to 90% learning in these. A 40% pass is meaningless.

'My reservations'

1. In our education system a textbook promotes the idea for teachers & hence to students, that it contains “all that needs to be learnt”. The difference between a curriculum & syllabus is lost. It also reduces the importance of reading beyond the textbook.

2. Many textbooks, particularly for the primary, are designed by educators who do not seem to have any experience with teaching in primary school.

a. The syllabus and hence the textbooks contain many topics which are unnecessary & unsuitable for students in the primary classes. They contain concepts and procedures which cannot be understood by students in the “concrete operations” stage. The topic of large numbers & Indian & International number systems are an example.

3. Such topics reduce the time available for teaching topics which are very essential for building a good foundation. A weak foundation in primary school, hinders math learning through higher classes.

4. Textbooks contain too much of textual explanation which cannot be comprehended by students who are also struggling to learn the basics of English. No Primary student uses the textbook for learning. It is a convenience for teachers & a good business for textbook publishers & school managements

5. Textbooks “force” teachers to cover the syllabus is a linear fashion which is not very suitable to mathematics. We have seen that the best way to teach mathematics is through a spiral curriculum which revisits the topics again and again at increasing levels of complexity.

6. The problems provided at the end of the chapters makes

a. teachers forget the art of writing word problem &

b. denies students the skill of writing word problems

7. Parents think that the textbook has to be covered, in the classroom, from the first page to the last. They get even paranoid about any question in the test paper which is slightly away from the textbook. This defeats the very purpose of teaching mathematics which is for developing HOT skills.

8. At the same time, textbooks also do not contain essential concepts which are necessary for a good foundation. The topic of operation metaphors is an example. (By metaphors I mean the life situations which mirror arithmetic operations. For example “put together” and “more than” are the 2 metaphors for the addition operation.)

'My proposal'

1. The math textbooks should be in 3 parts

a. Work & Activity book for students

b. Assessment Book for students (Up to Class 3, (a) & (b) could be combined into one book

c. Teacher Handbook which

i. Explains the syllabus for that grade & suggests learning objectives

ii. A framework for implementing a spiral curriculum

iii. Has frameworks for designing activities & problems (including word problems)

iv. Frameworks for continuous assessment of the students through the year

2. All the topics should be “taught” through activities, role plays & discussion of life experiences

3. After 5 to 6 activities for the same topic, students can be asked to do a worksheet which documents as well as anchors their understanding of the topic

4. There should be an effective & continuous teacher development system which will enable a teacher implement this new approach.