Top Three Common Errors for Maths…And How to Avoid Them
1. Calculation
Calculation errors cause a domino effect to the entire question. Get one wrong value and subsequent values are all impacted.
Example : Find the price after GST for a $200 t-shirt
Calculation Error
GST amount = 7% of $200 =7% x $200 = $140
Total amount = $140 + $200 = $340
Proper Working
GST amount = 7% of $200 =7% x $200 = $14
Total amount = $14+ $200 = $214
OR
Total amount = 107% of $200 = 107% x $200 = $214
How to Avoid Calculation Errors?
Oftentimes, students are reluctant to go a step back to check consistency of the values achieved. The above error can be easily corrected if one asks the logic of such an answer i.e. can 7% of $200 be having such a high value of $140 when 50% or half of $200 is $150?
If given a calculator, use the calculator to re-calculate at least once more. If your child is not allowed a calculator, then do the steps once more in a manual manner.
2. Careless
Writing the steps too fast? Not paying close attention to key words and numbers? Then careless errors may occur.
Example: Simplify 3 -(-4)
Careless Mistake
3 – 4 = -1
Proper Working
3 + 4 = 7
Careless Mistake may be result in ignoring signs i.e. + becomes – or x becomes +.
How to Avoid Careless Errors?
Slow down. Oftentimes, rushing into a problem causes high chance of errors. Instead, employ a step by step checking approach. Check steps before moving on to the next step by asking if this step fits the question. Is it logical? Does the number match the question’s information?
Highlight important key words and write values down in diagrams to avoid missing out on crucial information.
3. Conceptual
These are errors due to a lack of understanding of fundamental concepts and are most dangerous because it signals a gap in the child’s Maths understanding. Even if the child is careful and calculates everything correctly, not understanding the basics leaves students clueless about the question and he/she will write whatever that comes to mind.
Example : The total value of donation collected is $6000. The same number of men and women donated. However, each women donated twice more than each men. What is the total amount donated by the women?
Conceptual Error
2 units = $6000
1 unit = $6000 / 2 = $3000
Proper Working
Using Grouping method, since I am given total value, I group men and women into a group of values.
In 1 group, there is 1 man and 1 woman, since there are equal number of men and women who donated.
In 1 group, value of donation is $1 + $2 = $3
Number of groups = $6000 / $3 = 2000
Total amount donated by women = 2000 x $2 = $4000
How to Avoid Conceptual Errors?
Ensure mastery of concepts before exposing student to question types. This can be done by providing numerous similar examples. These examples are best guided first to provide student with relevant skills before getting them to try on their own.
Teach concepts more than one way. Students learn best with visual methods. Provide real life examples and draw diagrams where possible.
Have self-administered mini tests to examine conceptual understanding i.e. select questions from Grouping and tweak values.
Ultimately, Maths is never an impossible subject. There is however no magic pill or formula. Just magic processes to follow and stick to on a consistent basis.
All the best !