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16 Jun 2008
How I Become a Better Math Tutor
Frank Ho
Canada certified math teacher and founder of Ho Math and Chess
After spending most of my life on consulting and teaching and tutoring for over 30 years, I felt a bit depressed last few months since I was puzzled on why some kids would not make progress despite I have tried so many different strategies and made efforts to teach them. As an educator, I have constantly remind myself not label children since their potential is perhaps unknown to us and just because they are not good at math it does not mean they are going to have the dead end in their life. But still I was at loss to try to find some solutions to the following of my observations.
1. I was teaching a child how to convert from km to m and then to cm and mm. He just could not get it. I drew picture of stairs to remind him that to find lower unit is to time by 10 and divide by 10 when going higher unit but he could not get it. Finally I was totally stunned when I asked him this simple question “if 1 cm is 10 mm then how many cm is for 10 mm?” He gave me answers like 100 or even thousands. Then I changed the question to “If one dime is 10 cents then how many dimes is for 10 cents?” He immediately answered one dime so I told him the relationship between 1 cm to mm is just like 1 dime to 10 cents and he replied ”Oh! I get it”. He got this money question right but still could not do the conversion. It was 8 p.m. so we all had to go home.
2. I was preparing a girl for grade 10 final exam and despite I have taught her how to factor trinomials she looked at me as if I had never taught her the method and her day school had never taught her any method, what happened to her? After some reviews and also showed her two ways of factoring, she told me that she simply forgot. She saw me once a week so what can I do as a tutor if she just forgets what she had learned?
3. I was so surprised when one of my day school students told me that his day school math teacher told the whole class that 6 minus 1 and 2/3, the answer should be 6 minus 1 and then add 2/3. This is a grade 7 teacher who is teaching kids at a public school. More amazing is the boy told me that some kids actually got the right answers but was told it is wrong when in fact the teacher is wrong! Equally shocking is some math tutors perhaps should not be math tutors, I list the following examples used by some math tutors who were trying to tech children how to convert a fraction to % and how to solve an equation.
Convert 40/3 to a percent. The tutor told the student to get decimal 13.33 and then it is converted back to fraction as 13 33/100 = 1333/100 and then the answer is 13.33 after 1333 is divided by 100. The second example is to find x of 4 x^2 – 19 = 45, 4x^2=64, 4x^2 – 64= 0, (2x + 8) (2x – 8) = 0, so x = + or – 4. The tutor has completely forgot the equation can be reduced as x^2 = 16 and from here an answer is very easily got by using perfect square.
Facing these problems, how do I educate myself to be a better tutor? I started to research the relationship between math IQ and students’ math performance and the results is very educational for me and this has led me to produce an integrated worksheets of math, IQ puzzles, chess puzzles and word problems all combined as one worksheet.
I observe that just by helping students’ school work; for some students it will not be enough to bring up their real math strength. I also discovered this type of integrated worksheets is most effective to use when the child is young. By continuing stress the importance of thinking skills and by continuing giving students the highorder thinking problems the students are able to make progress in improving their problem solving ability.
I also discovered that how wrong it is to think elementary math has 2 parts that is one part is for computation and does not train problem solving skills and the part has word problems which train problem solving or thinking skills. This kind of thinking is perhaps a mistake in making or producing math worksheets for kids and this has made kids feel the computation practice is boring and not satisfying. By producing math worksheets in a different and “outofbox” approach, I was able to use my own students to conduct the experiment to see the difference and I was so moved when I witness the results were so much different and see the children were much happier.
My worksheets are developed from the “mention sensor” angles instead of “spot light” direct angle approach in that students see the relation between operations in wide different angles. For example, a student will not just practice 3 + 2, 6 + 1, 8 + 4. 7 + 4, instead they are asked to do exercises so that they see how 3 + 2 is the same as 2 + 3. They learn orientation, spatial relation, logic, and learn how to gather information and analyze it and how to do information retrieval. There are all kinds of visual stimuli built into worksheets so that they can reinforce what students learned and also to find the answers after going through a few steps just like going through the same thinking process as they would work on a word problem. I feel to develop the computation worksheets in such a way that they require students to “think” is a very innovative idea and is very different from conventional wisdom that computation is just from top to down or from left to right and aligned with numbers or sometimes with miss numbers.
By observing how others teach, by producing new and innovative worksheets, and by observing how children learn, I feel that I have become a better tutor on how to teach children math.
Frank Ho
