3 Creating compare and contrast activities – making small changes to existing practice

Reading about new teaching ideas might be exciting and desirable, but how does it fit in with existing practice? Like the teachers in the case studies, you could use the activities from this unit or from other sources and adapt them to fit with your teaching practice. At times, small changes can also be made with great effect on the quality and efficiency of learning.

The next activity is a planning activity that focuses on making small changes to the existing practice of textbook use. It requires a little extra lesson preparation time but it can actually save considerable teaching time because exercises from the book are used more efficiently and focus on what can be learned. A good start is to have some questions to hand that will lead students to compare and contrast, perhaps written down on a piece of paper and stuck to your desk or displayed on the wall. These questions can be used repetitively at any point in any lesson. Some simple though good questions are:

  • What is the same and what is different?
  • Can you make up another question like this?
  • Can you make up a hard question and an easy question?
  • How do you know?

Activity 3: Planning to adapt questions in textbooks

In the textbook you use, look at exercises about working in different number systems.

  1. What is the same and what is different in these questions?
  2. How could you make small changes to these questions so that it would allow you to compare and contrast?
  3. How could you introduce these questions to your students, so that it would allow them to compare and contrast?
  4. Make notes to use when you are teaching these lessons. Sharing your ideas with other teachers will build up a list of suggestions for different lessons.

You can find an example of adapted textbook questions in Resource 6.

Case Study 3: Teacher Anand reflects on using Activity 3

I teach secondary classes in a rural government school, where class sizes are about 80 students per class. I usually have a careful look at the questions given in a particular exercise of a chapter in the textbooks before I teach this to the class. I had never considered looking at the questions in the way suggested in the activity. It looked very simple. I did not expect to notice much because I think the books are good and introduce mathematical ideas gradually, step by step, to the students. However, my returning frustration is that the students find it difficult to remember what they did last lesson, last week, last month or last year, and often they do not do as well in exams as I would like them to! Why do they not notice the differences between the different number systems, for example?

So on this occasion, I looked at the chapter ‘Number system’ for Class IX, in particular at Exercise 9.3 of the NCERT textbook. I thought about what was the same and what was different in these questions: I noticed that Question 1 involved conversion of fractional form to decimals; in Question 3 the opposite was asked. I decided to make a small change and combine these two questions. The students were now asked to convert 65/100 and 13/99 to decimal form and then convert the decimal forms back to fractional forms, instead of doing this in two separate exercises with another question in between. I thought this would help them to correlate the concept of decimal and fractions, to make connections and not think of these two concepts in isolation.

This seemed indeed to be the case. Moreover, by asking the students the questions ‘What is the same, what is different?’ and ‘How do you know?’, the students were able to compare and contrast terminating and non-terminating decimals, and explain how they are different.

On reflection, I think it is important to take a critical view of the questions in the textbooks. By asking myself simply ‘What is the same and what is different?’ I could see the difference in structure in the questions and the learning opportunities they offer.

Pause for thought

Identify three ideas that you have used in this unit that would work when teaching other topics. Make a note of two topics you have to teach soon where those ideas can be used with some small adjustments.

2 Working on visualisation