Today, we’re back with an another part of the long-running series ‘MISCONCEPTIONS’, which features, ‘CLASS 4 MATHS, BASIC SHAPES, GEOMETRY AND VISUAL ESTIMATION’.
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(1) Why was the question asked in ASSET test?

This question was asked to check the students’ understanding of shapes, and their ability to recognize them, irrespective of the orientation or size.

(2) What did students answer?

A little over 37% of the students have answered the question correctly & almost 49% have chosen the most common wrong answer, option A.
Possible reason for choosing A: These students have a mental image of what a square should look like, and have gone by the overall appearance of this image. The square faces of the cube in option A matches this mental picture and option C does not ‘look’ like a square on account of its orientation.
Possible reason for choosing B: These students are aware that a square is not a three dimensional object, and B fits their idea of a square better than the shape in C.
Possible reason for choosing C: Very few students have chosen this option and may be making a random guess.

(3) Learnings

We observe that the visual appearance of the figure has had a stronger impact on the students than their knowledge of the properties of the shape. Although they may be aware of the properties of a square in terms of definitions, they have not been able to set aside irrelevant details like the orientation of the figure to get to the essential properties.

4) How do we handle this?

This can be handled by taking the students through hands-on activities involving sorting, identifying and describing various shapes, rather than the teacher drawing a shape on the board and defining its properties to children. A few activities are suggested below and links to a few sites giving such activities are also provided.
Activity 1: Cut out a collection of shapes from a thick cardboard sheet, consisting of a number of rectangles, triangles, etc of different sizes. Ask the students to pick out shapes which are similar to a given shape chosen at random. Encourage the students to describe the underlying similarities . One can even ask them to draw another shape which is similar to the given one.
Activity 2: The teacher can engage the class to play a “Who am I” game like the following. Call a student to the front of the class and pin a shape to his back, so that he does not see it. He has to guess what it is. He can ask his class mates questions like
• How many sides do I have?
• Do I have some sides equal?
• How many of my sides are equal?
• Do I have right angles?
• Are all my angles equal?
Encourage the students to try to guess with the minimum number of questions, prompting them about the essential properties and telling them something like “Does that help you?” when irrelevant details are given importance. The teacher can lead the students to identify shapes by their essential properties rather than appearance.
Activity 3: Have the children fold a sheet of coloured paper many times over, and cut out a shape say a triangle from the folded sheet. They get a number of identical triangles. Now have them paste these triangles in their notebooks in different orientations. Lead them on to the observation that though the triangles “look “different on the note book, they are all essentially the same, since they were cut out to be so. This way, the children learn to disregard, irrelevant aspects when dealing with shapes.