I recently had a session with a grade 10 math student that made me think back to when I was in high school. I was going through a test with him that he didn’t do well on, and it was clear from the test that he had a fairly good understanding of the unit, but he had lost too many marks due to careless mistakes.
He said to me, “I feel like I’m going too fast when I’m solving a problem.”
I could easily identify with what he had said because I went through the exact same thing when I was in school. I would often lose marks because of careless mistakes. There was a point when I came to realize that I’m prone to making certain mistakes, so I started to be a lot more aware when answering questions. I started to identify the most common mistakes that I was likely to make, and so I would slow down when carrying out operations in which I knew that I was prone to making mistakes in order to double check what I was writing. Using this approach allowed me to start getting much better marks on my tests.
I recommend to my students to make a list of the most common mistakes that they make, so that they become more aware of them and, thus, will be less prone to committing them in the future. Moreover, it is especially important for students to check over their answers if they have time left after they finish writing a test. I emphasize to all of my students the importance of double-checking solutions.
The most common mistakes that I see on a regular basis and which can be easily avoided are those that involve adding and subtracting integers; students often end up with the wrong sign or number because they are not comfortable working with integers. I’ve also noticed that a lot of mistakes that students make are linked to them being too reliant on a calculator. Students are so accustomed to using a calculator that they accept any value that the calculator gives back to them even if it is incorrect because they are so used to it being a crutch. I discourage students from using a calculator during tutoring sessions. A calculator often leads to more harm than good.
Every year I meet high school students that tell me that they don’t know how to multiply and divide numbers by hand. It is very disconcerting to me to see what affect technology has had on the math skills of students. Using a calculator for every simple operation leads to students being slower when completing tests and for that reason having to rush to finish, which makes them even more prone to making mistakes.
The path to improvement in math starts with improving one’s mental math ability and reducing the frequency of careless mistakes. It is imperative for high school students to know their times tables perfectly. Apart from possessing mental math skills, a student also needs to have a good foundation in working with fractions, decimals, integers, roots and exponents. Once a solid foundation is in place a student is ready to start improving his or her problem solving skills by learning to use a problem-solving framework.