Mental Math Index Calculation

Blog on Brain Training

# Mental Math Index Calculation

2012-08-28 10:40:06

Creating the mental math exercise I needed a way to measure the progress user achieved. Some kind of mental math index that can be tracked over the time and can be compared to the other users index.

It should have taken into account the number of digits in numbers being operated. It should also have taken into account different complexity of the multiplication and addition operations.

In the computer science the complexity of addition/substraction operations is O(n) and multiplication/division is O(n^2). It means that addition complexity is directly proportional to a number of digits in an operand and multiplication - to a 2-nd power.

After doing some tests I've created a mental math user index formula. For addition/substraction operations it is n + m - where n and m is the number of digits in the first and second numbers. For multiplication/division it is ( n + m ) ^ 2.

To calculate a index of a specific set we take the type and level of it and add a success rate divided by 100. So, for example, you have completed a set with level 2.2 and type multiplication. You've answered 8 of 10 trials correctly, so your success rate is 80%.

Your mental math index for this set is: ( 2 + 2 )^2 + 80 / 100 = 16.8

For a set with the same parameters but addition operation it will be: ( 2 + 2 ) + 80 / 100 = 4.8