(1) Why was the question asked in ASSET test?
This question checks if students are able to integrate what they have learned in different topics, and apply it to solve a non-routine problem.
(2) What did students answer?
Only 25% of the students have answered it correctly, and 56% have opted for A, the most common wrong answer.
Possible reason for choosing A: The way the triangle is superimposed on the circle in option A probably ‘looks the most like an answer’ to students, and they may not have looked at the other alternatives. Or if they did, D did not ‘look like an answer’ to them.
Possible reasons for choosing B & C: Very few students have chosen these options and are probably making a random guess.
Very few students have chosen options B and C. That shows that most of them know what an equilateral triangle is. They may also know what the radius of a circle is. Yet a majority has not been able to answer this problem. This points to the fact that students are not able to bring together the isolated concepts that they learn, and apply them as a whole to solve a problem. Also when faced with an unfamiliar problem, they don’t seem go about solving it methodically. It is quite likely that many students did not even draw the radius or mark the side/ radius as 5 cm, which would have helped them to visualize or understand the problem better.
4) How do we handle this?
The following points are essential to solve this problem.
• An integrated view of concepts learned and not as separate sections with exercises to do.
• A systematic approach to solving problems.
• A through understanding the ideas involved- here radius of a circle and what an equilateral triangle is.
The first of these can be addressed by exposing the students to solving problems that require application of multiple skills. A number of such problems can be found in the link 2 below.
When faced with non-routine questions, students may follow these basic steps to solve it.
• Understand the problem: Identify what is given and what is to be found out.
• Represent the given details pictorially if possible, or write them out clearly.
• Identify connections between what is given and what is to be found out.
• Use these to find out the unknown.
• In addition, when solving a multiple choice question students should be trained in a good elimination strategy. The following is an analysis of this ASSET question in this light.
Problem – The given ASSET question. Solutions:- Step1: Identify that, we are given a circle of radius 5 cm and an equilateral triangle of sides 5 cm Step 2: Required to place the triangle inside the circle. Step 3: Represent the given data on the diagrams. Mark the sides of the triangles in the options, and the radii of the circles as 5 cm. Step 4 : It will be clear that the radius of the circle in option A and the side of the triangle cannot be 5 cm at the same time. Also some sides of the triangles in options B and C cannot be 5 cm. Step 5: With Options A, B and C eliminated the possibility is D. Check that it indeed satisfies the requirements.
The teacher can pick out other problems from the link below, appropriate to the class, and follow a similar analysis.
Also she should verify that the students have really grasped the different concepts involved in solving the problem and are not repeating without understanding.