Above image shows some data related to a walk. It says that the person has walked a distance of 7.05 km in 1 hour 8 minutes 49 seconds. Average pace shown here is 9 minutes 45 seconds per Km and the time taken in different kilometers are given just below that. This average pace can be simply computed by dividing the total time (1 hour 8 minutes 49 seconds) by the distance walked (7.05 Km) and doing the required conversions between hour, minutes and seconds. This means, if I walk each of the 7 Kms at the same pace completing them in exactly 9 minutes 45 seconds then the total time taken by me to walk 7.05 Kms would be 1 hour 8 minutes 49 seconds. In the last .05 Km too, the pace has to be same.  Time taken in each of the 7 Kms are given in the image. Let us check, whether the walking pace was higher or lower than the given average in the last .05 Km. Before reading further, pause a bit and think about the process you would like to follow to do this. I plan to check whether the given a

  L et us talk about this Cycle. Those who know how to ride it know how easy and enjoyable it is to go for a long ride in nice weather and location. They can also recall;  how difficult it was to even hold it when they were not knowing how to ride them. Most likely, they didn't become comfortable with cycle immediately. They might have fallen few times, might have struggled to balance and might have even lost motivation to learn cycling. But  now they might be looking for opportunities to ride a cycle. Learning Mathematics is similar to learning cycling. You make errors, struggle to get the concept, lose interest and it becomes more difficult. But once you overcome these, it becomes a favorite subject. Solving Mathematics problems can even become stress buster. When someone is training you how to cycle, he may make you familiar with a cycle. He will tell you about seat, handle, peddle etc. He will tell you about how to sit on the seat, keep the foot on the peddle, hold the handle,

  Here, we are taking an example to demonstrate how students are answering the questions right, getting good marks, letting the concept level problem continue and getting stuck in their studies or career at later stage. We also discuss, what approach can help in making learning right.  I hope, readers are aware of linear equations in one variable. Something like 15x+5=90, or 3x+5=2x+9.  Let, a student is asked to solve the 2nd equation 3x+5=2x+9. It's easy for most of the students. He solves this equation using right method and gets the answer as 4. Correct and full marks. Does it mean that he knows the concept of linear equations in one variable good enough?  Why should he solve such equations? Where can these concepts be used? Can he frame a question based on real life scenario where such equation may be needed? Can he visualize the impact of change in coefficients or constant values on the nature of the equation? If he is not clear about all these, then solving large number of s

  Here, we take a question and create three learning environments. You can check yourself, which environment offers what benefits. We talk about a formal learning environment where student is a part of school/ college/ coaching/ tuition etc. and is helped by the teacher in learning various topics as per the prescribed syllabus. These learnings are immediately helpful in getting marks in the examination but are also highly required in various applications and competitive examinations at later stage. So, learning them right at the time they are being learnt is necessary to avoid various blockages that can restrict the growth later. Let us take 3 scenarios: Scenario A:  Student asks a question. Teacher answers that. Student is now able to answer that question. Scenario B: Student asks a question. Teacher also asks few questions to understand why the student had to ask it. He determines the area of difficulty for the student and helps student to answer the question by addressing the proble