Kohila Sivas started tutoring friends and family in math 17 years ago and now has her own businesses doing so, bridging a gap that concerns many in Canada.
Sivas has her own math tutoring business in Maple Ridge, and helps students across the country. Her business is one of many popping up across the city, including Sylvan Learning, Mathnasium of Maple Ridge, Math4me and Kumon Math and Reading Centre.
She started her business seven years ago with 30 clients. Now she tutors online as many as 65 students across the country. She even has clients in England and is currently in the process of hiring and training new math coaches to work with her.
Sivas attributes the growth of her business, MathCodes, to students having no clear picture as to why they are learning the math that is given to them in school.
“They just do it as a requirement. They’re just doing it, there’s no motivation for learning it,” she said.
A major problem, Sivas adds, is that there is a lack of understanding in the earlier grades that becomes compounded as students progress. She doesn’t fault the teachers because they have to deliver the curriculum for the grade they are teaching.
“Every grade they teach is some new thing and that gets applied in the next grade,” explained Sivas, giving an example of factoring.
“Factoring needs to be mastered as if you were adding one plus one. But a lot of kids come to Grade 12 without even knowing how to factor or what is factoring,” she said.
The new math curriculum in B.C. means that the traditional algorithmic approach to the subject, where children memorized rigid formulas and times tables, have been pushed aside for an inquiry or constructivist approach.
The Foundation Skills Assessment is an annual province-wide assessment of all B.C. students’ academic skills in Grades 4 and 7.
The Fraser Institute, a Canadian public policy think tank and registered charity, published a report card on elementary schools in B.C. based on FSA scores between the years 2013 and 2017.
In general, the report shows that numeracy scores during this time frame have been slowly slipping, including those in Maple Ridge and Pitt Meadows.
The average Grade 4 numeracy score in all schools across B.C. was 490 in 2013 compared to 486 in 2017, and in Grade 7 the average score went from 481 in 2013 to 476 in 2017, according to The Fraser Institute report.
The Fraser Institute also looked at the average scores on the Foundation Skill Assessment tests during the 2011/12 and 2015/16 school years and found the average numeracy score for Grade 4 students in the public school system was 484, compared to those in non-elite independent schools that averaged 554 the average score of 611 in elite independent schools.
In Grade 7, the average scores went from 471 in the public schools, to 538 in the non-elite independent schools and 595 in the elite independent schools.
Average marks on the Provincial Required Exams for foundations of math and pre-calculus 10 during the same school years demonstrated the same gap in performance.
Students in public schools averaged 69.1 per cent, non-elite independent school averaged 72.3 per cent and students in elite independent schools averaged 81.3 per cent.
In Alberta, the provincial government decided that, after years of declining math scores and growing frustration with a math curriculum that parents said was too focused on discovery, analysis and group work, to return to focus more on basic math skills – memorizing number facts and learning keyboarding skills early as part of the updated K-4 curriculum, released by the provincial government in October.
In September, the Ontario provincial government released a new guide for teachers and parents to help students in Grades 1-8 learn traditional formulas and memorization techniques in mathematics.
Sivas got into the tutoring business because she once struggled with math.
“I was looking at other people and thought, ‘Why are they all getting it, why am I not getting it?’”
She credits one really good teacher who took the time with her to explain what she was doing.
“It just made sense. And I started looking at it as if I were just solving a puzzle, right? Math became a puzzle and I looked inside of it and there was a lot of patterns and puzzles. And one method that you would use on one question could be translated into another,” said Sivas.
Retired Whonnock elementary teacher Zdena Novy also sees trouble with the new curriculum in B.C.
She said students must understand the basics of math before moving on, and that is accomplished by repetition.
“If you don’t get the basics, how can you build on something you don’t understand,” Novy asked.
“It is not done on the computer or calculator because your brain doesn’t work. You have to make [your brain] think.”
She went from failing math to excelling in the subject by the time she entered Grade 12. She attributes her success to her Grade 10 math teacher at Daniel McIntyre high school when she lived in Winnipeg.
“He taught math completely different,” explained Novy.
“He never got excited. When he taught us, he was very calm, very quiet and very persistent,” she said, adding that there was tons of homework, but he always gave students time to do it.
Novy said her teacher also made his students show all of their work and taught them how to correct the answers themselves.
She excelled in mathematics and took calculus at the university level.
Novy received a Bachelor of Education from the University of British Columbia and a Masters of Education in 2009 at Simon Fraser University and taught at Whonnock elementary until she retired in 2015.
When Novy was teaching, she used a math program called Journeys, where lessons were on the left side of each page of the textbook and the right side was practice. It was consistent, grade by grade.
“It was directed, it had specific instructions,” she said.
But, she added, students must have homework in math in order to understand.
“A calculator is awesome if you want to check your answer. But if you don’t understand … how are you going to check it?”
She taught the skills to check work without a calculator.
“Because you should know it.”
Novy added, if you have a group of Grade 7s entering Grade 8 who have been introduced to all new concepts, but they don’t have the basics, what are you going to do?
“You’re going to have to go back and you’re going to have to start from scratch,” said Novy.
Hugh Burke, headmaster at Meadowridge School, a private, International Baccalaureate school from Kindergarten to diploma, has been teaching the inquiry-based model at the school for the past 15 years.
He believes there is a gap in understanding in what the schools are trying to accomplish in math.
“Are we trying to get kids who can get the right answer to a well-defined problem that we give in the form of a test or are we getting kids who can apply mathematical thinking to a variety of real life and scientific problems and use mathematical understanding to help solve them,” he asked.
Burke said the inquiry or constructivist approach means that children are taught how to approach ill-defined questions with mathematical thinking. Both approaches, he adds, require the ability to add, subtract, multiply and divide and to understand what signs mean and the order in which they should go.
However, he said, when you get into the real world, mathematics is messy and requires mathematical thinking.
“Algorithmic teaching depends on memory and application. The discovery method depends upon inquiry, resolving the question and after providing multiple and potential answers,” said Burke.
Burke said that the easiest approach to math in the classroom is algorithm because it is definable and easy to teach and score. And parents understand it because it is the way they were taught.
But, he said, the National Council of Teachers in Mathematics determined years ago that teaching that approach is why we had very few mathematicians in Canada.
“Because once you get into real math, simple algorithm does not work.”
Burke noted that participation goes down in math in Grades 11 and 12 because they get frustrated and give up.
“If we teach children mathematical understanding, they tend to do much better as they get older and as they go to university and further,” he said.
“The problem is that it is more difficult, it takes more time and feels more complicated,” he said of the inquiry-based approach.
Burke gave an example of a problem given to students regarding the division of a property. At first, they were given a simple outline of the property and told to divide it in two.
“They had to find a parallelogram and the formula for dividing it. That was algorithm,” he explained.
But he said when the students visited the property, mathematically the division became much more problematic because there was a tree-house in the middle that they wanted to save and a slope that caused drainage issues.
“We had, I think, 20 kids in our classroom. They came up with 11 different solutions, all of them correct,” he said.
“And, all of them taking into account a much more complicated life situation.”
Maple Ridge-Pitt Meadows union head Suzanne Hall, who was a math specialist at the elementary school level, is excited about how the teaching of the subject has changed over the past decade.
“To be good in math when I was little was to be fast at doing computation. To be good at math now is to understand and be able to apply patterns,” explained Hall.
“One of the things we do a lot of with kids in primary are using Base Ten Blocks.
When they add and subtract, they can see what carrying and borrowing mean.
Concrete representation of math processes is a powerful way for children to understand those steps that they learn to do actually represent something, she said.
“And they can apply it a lot better.”
She agrees that there is some truth to what Sivas is saying about some students advancing without mastering their previous year’s studies.
Hall said teachers have stopped failing children out of courses because it doesn’t make them more successful. Instead, a school is more likely to put a student in summer school to boost up their understanding or put them in the next grade with a support teacher that they have access to once a day to help them pick up any areas that they are weak in.
She added more math tutoring business are opening up in town partly due to the shift of the school curriculum over to a conceptually based, deeper understanding of math, that is an uncomfortable concept for a lot of adults who still have that view that math is being able to do computation quickly.
“There is actually nothing wrong with having a good fast recall of your facts and being able to automatically go through processes. Unless the kids don’t understand how that links to anything real,” said Hall.
“So we have moved away from defining success for good understanding as quick computation to deeper understanding,” she added.
Ultimately, Hall said, there are lots of parents who are not comfortable with the new curriculum and think their children are not good at math because they, “can’t show them 18 flash cards and they have them answered in 20 seconds.”
“But, really, we now have spell check, we now have grammar check, we have word processing so we can go back and edit really easily and we have calculators, that are completely useless if you don’t actually understand what the math means.
But they take care of a lot of that computational drudgery,” she said.
“Because life does not say to you, ‘Here is a math problem you need to multiply.’ Math says you’ve got 23 people in your family and the cruise costs $1,364, what’s the total cost going to be,” Hall said.
“You need to understand that’s a multiplication situation. A calculator does nothing for you if you don’t actually understand that.”