Sherry Mantyka says she wants students to know that, as downtrodden and defeated as they might feel when they face first-year math courses at Memorial University, they're fully capable of working out the numbers themselves.
Mantyka, an associate professor of mathematics and statistics at Memorial and the director of its Mathematics Learning Centre, says there are fundamental issues with students' math skills when they begin their post-secondary education — and it's largely not their fault.
She says it's due to a shift in the math curriculum that they've being taught in grade schools in Newfoundland and Labrador.
The most recent changes to the curriculum came about when education stakeholders outlined a need for a better balance between the study of math basics and a more conceptual understanding of how math processes work.
This prompted the province's Department of Education (and many other Canadian jurisdictions) to conduct a major review of its math curriculum in 2007.
The department then developed the Excellence in Mathematics Strategy, which included the implementation of a new math curriculum (the same one being used in other parts of Canada), in 2008.
While kindergarten to Grade 10 students in the province are already being taught this new curriculum, Grade 11 students will be introduced to it this fall, and high school seniors won't see it until September 2013.
CBC reporter Caroline Hillier recently caught up with Mantyka to discuss her issues with the K-12 math curriculum and how she helps first-year students fill the gap in their math knowledge.
CBC: What are some of your issues with this new math curriculum?
Mantyka: The philosophy that's underlying both the Western and Northern Canadian Protocol (WNCP) [which is being implemented] and the Atlantic Provinces Educational Foundation curriculum, which was in place from 1995, is based on the National Council for Teachers of Mathematics standards document from 1988. That document suggested a move away from so much drill and practice and skills-based curriculum activities, towards more problem solving.
But these curriculums, with the interpretation of that document, have been quite extreme. So the focus is predominantly on investigations and problem solving. The investigations are designed to expose children to conceptual models of mathematics, and in problem solving, you use the conceptual models. So there's very little emphasis on developing efficient skills in the use of algorithms, and so a lot of students are not able to do mathematics.
CBC: Are students in the primary grades not getting the proper foundation of these basic skills?
Mantyka: That's right. They're learning strategies for computing multiplication facts, instead of just knowing them. So given that multiplication facts are only one tiny piece of problem solving, when you're trying to figure out how long it's going to take you to drive to Clarenville at 90 kilometres per hour, it really slows your reasoning down. It handicaps students when they're not required to move beyond conceptual models for figuring stuff out.
CBC: What other foundations should students be getting besides basic math skills?
Mantyka: They really need to come out of primary knowing their addition and multiplication facts. They also need to know the laws that apply to the link between multiplication and addition. For example, 2 x (5 + 7) is the same as 2 x 5 + 2 x 7. And they should know that automatically without having to really think: "OK, what's the conceptual model underlying this?"
And then moving on, into Grade 4 and beyond, there's an introduction to fractions. So they need to know efficient algorithms for working with fractions and the order of operations, like when you have a string of numbers connected by arithmetic signs: addition, subtraction, multiplication, division, brackets, and powers. You need to know what order to do those arithmetic operations in, and you need to know that automatically.
CBC: What are the issues or the challenges that students face when they enter their first-year math courses at Memorial University?
Mantyka: We give [students] a series of diagnostics when they start their program. So they've written the math placement test, and they haven't gotten a score which is high enough to put them in a credit course. If they want to do a credit course, they're required to come [to the Mathematics Learning Centre] and do an upgrading program. The first thing we do is look at the way they approach all of the core skills that were assessed on the math placement test. What we're finding is that they're using strategies to do things that they should know algorithmically.
The 'aha!' moment
CBC: Do any of the students that you see at the Math Learning Centre have their "aha!" moment, when they realize they should be using a different strategy?
Mantyka: Well, the students are 18 years old, and they've had 12 years of math teachers telling them that they were doing OK, so the first sense they have of being [at the centre] is distrust ... Once they start working with us and they see that they can do things quickly, and they have a better understanding of the big picture of mathematics — not the big picture of problem solving, but the big picture of how all the bits and pieces of math work together — that's when they have an "aha" moment.
That's when they start feeling confident about themselves being able to do it. So it's a really big roller coaster ride for them. Not passing the math placement test is devastating ... The students who do complete what we ask them to [at the centre] can successfully move on through their MUN courses, and can do very well at university .... But they have to be prepared to do what we ask them to do, which is really just put more structure into the learning.
CBC: What would you like to say to parents whose children are struggling with math?
Mantyka: I want parents to know that it doesn't mean that their children are unable to do math. The lack of structure in the curriculum really interferes with the students' ability to become procedurally competent enough, so when they're challenged with higher level math, their working memory overloads, and they're completely confused and can't cope. But it's not because the children are stupid or unable [to do it]. It's just that the structure of the learning experience has been too casual.
Sherry Mantyka produced the video below to help explain the Learning Centre's approach to teaching math.