Misconceptions found in Measurement, Data Interpretation/Analysis: Averages and Graph Reading of Class 7 students

1. Student Misconception Series –MATHS (Part 4)

2. Do your Student Learn or Mug up ? Students of all ages seem to have a mind of their own when it comes to responding to any situation or performing any task. As teachers, most of us go back home thinking that our students have understood every concept that we teach them. It is only when we test them that we find that some concepts have not been understood as clearly as they should have been. It is this desire to understand student thinking that prompted us to examine ASSET questions of the past rounds, in Maths, examining the most common wrong answers to understand what could have made students select the options they did.

3. Measurement,DataInterpretation/Analysis: Averages and Graph Reading Class 7

5. Why was the question asked? This question tests if students are able to interpret data presented in the table and answer questions based on it. What did student answer ? 36% of students have correctly chosen A and 30% have chosen the most common wrong answer, C. Possible reason for choosing B: These students may have found the difference between the times in the departure column corresponding to Vadodara and Ratlam. Possible reason for choosing C: These students may have found the difference between the times in the arrival column corresponding to Vadodara and Ratlam. Possible reason for choosing D: These students may be subtracting times as normal numbers. They may have subtracted 1:30 from 22:10, smaller number from the larger one, in both hours and minutes and arrived at the answer 21:20.

7. Computing time differences in the case of 24 hour representation of time. (Students seem to be subtracting times as if they were ordinary numbers.)It is quite important that students master concepts, to be able to apply them in real life situations. It is good to ingrain the attitude of seeing the applications of Maths in day-to-day activities, among students.

8. In order to solve a problem like this, students should be able to: • Understand what the given table is about and identify what data is given there. • Understand the question, and identify what data is needed to solve it. • Be able to extract the required information from the given table and do the necessary manipulations. Students should be encouraged to look at the various column headings in the table and identify what is given in each column. In the given question, help the students identify what exactly is asked. The question asks for the time interval between the train leaving Vadodara, and reaching Ratlam. So ask them to point out the entries in the table between which the time interval is to be calculated. Have students draw arrows in the table, highlighting when the train leaves a station and arrives at the next station. If students draw vertical lines within 1 column, ask them what the times in the other column indicate, and help them appreciate the data. Observe if students are able to find the interval between the 2 times. Let them count the hours out and realize that they cannot find the difference between 2 times, as though they were ordinary numbers. Pose other questions from the same table, and help them identify the relevant data needed to solve the question. For example - • From where does the train start, and where does its journey end? • What is the total time taken by the train to travel from Mumbai to Delhi? (Which entries in the table are needed to solve this?) • How long does the train halt in Kota? • What is the maximum duration between two halts during the train's journey? Students may be encouraged to come up with other questions which can be answered from the given data. Also help them identify where they apply Mathematics in their daily life and have them do a project on one of these like a comparison of electric bills in a colony, study of average rainfall in a place over a period etc.

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