# Misconception series: Class 5 Maths, Basic Shapes, Geometry and Visual Estimation

### (1) Why was the question asked in ASSET test?

This question checks whether students recognize quadrilateral shapes based on their properties.

### (2) What did students answer?

Around 27% of the students have chosen the correct option A, and almost 50% have chosen the most common wrong answer, option C.

Possible reason for choosing B:P and Q are shapes which students are familiar with as quadrilaterals, and they may feel that shape T is more or less similar to a rectangle, with just a small bend at the top on both sides.

Possible reason for choosing C:These students could have looked only for the regular shapes which they have learned as examples of quadrilaterals i.e. square, parallelogram, rectangle etc. R did not “look like” any of these examples.

Possible reason for choosing D:Very few students have chosen this option and may be making a random guess.

### (3) Learnings

In the course of their learning, students see the same kinds of shapes which are called as ‘quadrilateral’ or ‘triangle’, and they associate the name with the usual shapes they see. They don’t give importance to the fact that a shape is defined by its properties, and not by its visual appearance alone. Thus when they see a figure, which is different from the ones they are used to seeing, they are unable to identify it, based on the defined properties. Students need to understand which properties are ‘essential’ to a certain shape, and which properties are ‘incidental’. In the case of the quadrilateral, the essential properties are that

• It should be a closed figure

• It should have 4 sides

• All sides should be straight line. In contrast, the sides being equal, or parallel are ‘incidental’ properties, and do not determine if a shape is a quadrilateral or not. A clear understanding of these basics is essential to study geometry and other higher topics in Maths.

### 4) How do we handle this?

The key to developing this kind of understanding is to expose the students to a number of hands-on activities and not just memorizing formulae and definitions. Before introducing the name and properties of a shape for example, the teacher can give the students a number of cut-outs representing the shape being taught, and ask them to identify what is common to all of them. This way the students learn to identify essential and incidental properties. When teaching a concept the teacher should provide correct and incorrect examples, in as many different variations as possible (different orientations, different sizes etc.).

She can ask the students to distinguish between correct and incorrect examples and discuss why some are considered incorrect. For example, while teaching quadrilaterals, the teacher could draw shapes like the ones shown in figures S and T and ask why these are not quadrilaterals. Which specific property is violated?

Following is a suggested activity to teach children to recognize shapes by property and not by visual appearance alone.

• Prepare cards, on one side of all of which, are drawn distinct shapes in different orientations. On the reverse describe the properties of a shape other than that drawn on that card.

• Distribute the cards one each to a student. The student who starts, reads out the description on his card.

• The student who has the card with the matching figure holds up the card and names the figure. Now he reads out the description on his card.

• The game continues until the first student gets to show the figure on his card.

You may also look up the other teacher sheets (M4–0608–01, M6–1008–15) which contain other activities to help students understand shapes.