I took almost half a year break last year as my daughter is born late june. This year, i had several new sec 3 and sec 4 students when i restart my classes.
Careless mistakes – my most hated bug in the classroom. I realise several students i have this year tend to make a lot of maths careless mistakes.
This is frustrating for both me and the kids. I know they do not mean it (seriously, who likes to make silly mistakes and do corrections?) So its a habit that we must BREAK!
I started reading online for methods. And did some suggested observation on my students. Below are some of the general guidelines to combat the careless mistakes bug.
1) Pls do not be ‘lazy’ or ‘prideful’ and do too many steps at once.
Many careless mistakes are caused by trying to skip several steps. For example, this is one scenario where an error often occurs:
3(y + 5) = 20
3y + 5 = 20
3y = 15, therefore y = 5. Wrong
In the above, multiplication was not applied to the ‘5’ in the brackets – a common mistake. One way of avoiding this is to insert a BRACKET to remind you to apply the multiplication to all items in the brackets, i.e.
3(y + 5) = 20
(3*y + 3*5) = 20
3y + 15 = 20
3y = 5, there y = 5/3 Correct
2) Dont assume and identify common tempting incorrect expansion.
(x+y)^2 is the same as x^2 + y^2 is an especially tempting error. WRONG. From sec 2, students should know that (x+y)^2 = (x+y)(x+y) = x² + 2xy + y²
To students who make this mistake:
“Why did u assume??
Maths is about accuracy. Dont assume.”
You’re trying to do too much mentally at one time. It actually takes a lot less effort and YES LESS time to just pen down each thought, that means to write one methodical step at a time.
In other words, you can achieve both speed and accuracy by taking small quick steps, rather than taking large slow ones. Imagine you are walking. Make sense now? We must train to breakdown our processing thoughts into smaller, easier to manage pieces by penning them down fluently.
3) Use units.
Most students find writing units too trival and hence they cant compare correctly. 1000m is suddenly 10cm² (instead of 10cm) in the working. Especially for map-scale and mensuration questions, you better write your units along with your calculations in the working.
In my maths tuition classes, for topics like map scale, mensuration and circular measure, I make sure my students write their units. This is because it is so easy to make careless mistakes like keying 2.6rad as 2.6degrees in the calculator (meaning student forget to change to rad mode when they didnt write units). The units serve as a REMINDER to our brain which quantity we are dealing with at which step of the working. Please be prudent and convert all rates and quantities to the same units before attempting to solve the problem.
4) Check your workings intermittently.
Hone this skill to check things fast.
Yes yes i know students barely have time to check your answers after finishing your exam papers. Thats why I DO NOT encourage only checking your work after finishing your paper. I cant stress the important of cultivating the habit to carry out intermediate checks as you work through your maths problems. And if this habit/skill is honed, you are able to identify your errors VERY FAST.
For instance, during treasure hunt games – would you only check your map once at the start and once at end of the journey (provided you get there in the first place), or would you be checking your map intermittently throughout the journey to make sure you are going in the correct direction? This is the same logic for checking your answers!
5) Be familiar with common Check Tools you can use.
I also stress on ‘check tools’ during my maths lessons – you can read about them online,
– Sanity Check ( i.e, if the question ask for length and if your result is negative, you better check your workings)
– Reverse Check (Check that the signs of the algebraic groups change when they cross over the equal sign)
– Loop Check ( i.e substitute in your answers into the equation. This is especially useful for simultanous equations. )
6) Use calculator to help you check.
There are also ways to make use of certain features available on the latest approved scientific calculator like mode 3,3 to find the solutions of quadratic and cubic equations.
I really hope the above tips and explanations on why we need to do them can help students cultivate good working habits and minimise careless mistakes.