The Great Canadian Math Debate, Pt 6: Math prof. Anna Stokke responds to Alberta Education
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Intro to The Great Canadian Math Debate
In a series of posts we dig into the debate around teaching math to elementary school students. The series kicks off with how Dr. Nhung Tran-Davies, a small-town mom and family physician, discovered her 8-year-old daughter Kenya hated math, even as she was a top student in the subject.
Tran-Davies dug in to the issue and found what she saw as a major problem with the new and unconventional way kids are now being taught math, a method that has slowly but surely taken over our curriculum and classrooms in the past decade.
In response to this issue, Dr. Tran-Davies started a petition asking for Education Minister Jeff Johnson to return elementary math education to a system where children are directly taught the best and standard practices in addition, subtraction, multiplication and division, and where they are asked to practice and master this work. Thousands of parents and educators have signed the petition. A number of university math professors also signed. The Journal’s Andrea Sands and numerous other media outlets wrote stories and the petition movement spread to Ontario and B.C.
Tran-Davies has also been asking questions of Education Minister Jeff Johnson and Amaya Ortigosa, team leader for mathematics K-9 with Alberta Education.
Journal city hall and board of education columnist David Staples (yes, me) followed up an exchange of emails between Tran-Davies and Ortigosa with questions of his own to Ortigosa. Here, in Part 6 of the Great Canadian Math Debate is that exchange, along with a follow up response from University of Manitoba math professor Anna Stokke on Alberta Education’s response to date.
Letter from David Staples, Edmonton Journal, to Amaya Ortigosa, Alberta EducationMs. Ortigosa:
I’ve read your reply to Dr. Nhung (Tran-Davies) with great interest and will be writing a follow up article on your conflicting positions.
Before I do that, I’d like to clarify a few of your positions.
You state: “In the current mathematics program of studies, students are expected to know and master number facts as they develop number sense. How students attain this mastery may differ; memorization may work for some students, but should not be at the expense of understanding”
You seem to be asserting that the memorization of math facts can harm understanding of math. How can the memorization of times tables by K-6 students harm understanding of numbers? Why do you say this? What proof do you have of this notion?
Don’t you have to understand math, or at least the best practice for simple multiplication, to be able to do your times tables and, subsequently, to memorize them?
Also, what studies are there that prove discovery math — this focus on students writing out many strategies for solving a problem — actually leads to greater understanding of math?
What I’m hearing from parents, many educators and a number of math PH.Ds is the opposite, that this focus on discovery math is doing the opposite by depriving K-6 students of the classroom time needed to master best practices in math. It’s essentially cluttering their minds with ineffective strategies, instead of teaching them and having them master the best practices for basic addition, subtraction, multiplication and division.
What do you think of this critique of discovery math? And, again, if there are a number of conclusive studies that show this discovery math has had great results in increasing student understanding of math, I’d like to see them.
Secondly, there’s some concern that the Nelson math textbooks now used for K-6 are not written by educators who have university level degrees in math, but were written by educational professors. Is this the case? Can you tell me the math training of those who wrote the textbooks used in Alberta K-6? Did anyone who worked on the project have a PH.D. in math? If not, why not? If the main writers of our math textbooks aren’t university-certified math experts, why are we buying their textbooks?
Cheers, David Staples
The Edmonton Journal
Response from Rohit Sandhu, Alberta Education communications, to David Staples
Thank you for your questions, for which you will find responses below (highlighted in your original email).
We know that curriculum is the fundamental basis for learning and teaching in K-12 education.
Opportunities for future math curriculum:
Recognizing that the questions at hand speak to the current mathematics curriculum, it is important to note that Alberta Education is currently leading a Curriculum Redesign initiative that will help build Alberta and bring the vision of Inspiring Education to life. Curriculum Redesign involves revising our provincial curriculum (programs of study, assessments, and learning and teaching resources). Math is one of the subjects included as part of Curriculum Redesign, with new programs of study expected to be developed by March 2016.
Recognizing that curriculum is an expression of expectations: the attitudes, skills, knowledge that society values and wishes children and youth to achieve and demonstrate, we will be looking to what Albertans are telling us as well as the latest research to help inform the development of Alberta’s new mathematics curriculum. This will include a review of recent topics raised by some Albertans relative to the current mathematics curriculum: the place of number facts and memorization with understanding in math education.
Current math curriculum
Ms. Ortigosa:
I’ve read your reply to Nhung with great interest and will be writing a follow up article on your conflicting positions.
Before I do that, I’d like to clarify a few of your positions.
You state: “In the current mathematics program of studies, students are expected to know and master number facts as they develop number
sense. How students attain this mastery may differ; memorization may work for some students, but should not be at the expense of understanding”
You seem to be asserting that the memorization of math facts can harm understanding of math. How can the memorization of times tables by K-6 students harm understanding of numbers? Why do you say this? What proof do you have of this notion?
Thanks for the opportunity to clarify: Memorization does not necessarily harm understanding of math. That being said, memorization in the absence of understanding does not promote retention or transfer and application of knowledge that will allow students to learn more complex math.
Don’t you have to understand math, or at least the best practice for simple multiplication, to be able to do your times tables and, subsequently, to memorize them?
Yes. The Alberta mathematics programs of study emphasize understanding math concepts. This emphasis on deeper understanding of the concepts and processes of math enables students to learn the concepts better, remember them longer, and build upon them to learn more complex mathematics.
Students are still expected to know basic number facts through an understanding of numbers. There are mandatory learning outcomes throughout grades 2-6 that address the understanding of addition, subtraction, multiplication and division, with an emphasis on mental mathematics. Specifically, by the end of grade 3, students are expected to add and subtract 2-digit numbers as well as multiplying to 5X5. By the end of grade 5, students are expected to multiply and divide to 9X9. In other words, all Alberta students are expected to know their math facts to 9X9 by the end of grade 5. During the coming months, Alberta Education will be examining ways to clarify this expectation in the current math program with students, teachers and parents. We will also, as previously stated, be reviewing the mathematics program as part of Curriculum Redesign.
Also, what studies are there that prove discovery math — this focus on students writing out many strategies for solving a problem — actually leads to greater understanding of math?
The WNCP Mathematics Research Report (March 2004) helped informed the development of Alberta’s current math programs of study. The programs of study encourage students to learn strategies for solving problems. Strategies focus on why a procedure works. Students can develop or adopt an efficient strategy to solve a problem. What is important is that students understand the strategy they use.
What I’m hearing from parents, many educators and a number of math PH.Ds is the opposite, that this focus on discovery math is doing the opposite by depriving K-6 students of the classroom time needed to master best practices in math. It’s essentially cluttering their minds with ineffective strategies, instead of teaching them and having them master the best practices for basic addition, subtraction, multiplication and division.
‘Discovery math’ is not a term used by Alberta Education to describe the Alberta mathematics programs of study. Teachers are expected to address the diverse learning styles, cultural backgrounds and developmental stages of all students through a variety of approaches. The intent of the mathematics program is that students master efficient and accurate practices for basic addition, subtraction, multiplication and division. Students are exposed to many strategies and are expected to choose one strategy that they understand and that is efficient for solving the problem.
What do you think of this critique of discovery math? And, again, if there are a number of conclusive studies that show this discovery math has had great results in increasing student understanding of math, I’d like to see them.
Secondly, there’s some concern that the Nelson math textbooks now used for K-6 are not written by educators who have university level degrees in math, but were written by educational professors. Is this the case? Can you tell me the math training of those who wrote the textbooks used in Alberta K-6? Did anyone who worked on the project have a PH.D. in math? If not, why not? If the main writers of our math textbooks aren’t university-certified math experts, why are we buying their textbooks?
In Alberta, under the School Act, local school jurisdictions have the responsibility for the selection and approval of the resources teachers use in their classrooms. School boards may choose among the resources on Alberta Education’s authorized resource list (http://www.education.alberta.ca/apps/lrdb), or they may develop or choose other resources that support the provincial programs of study. Generally, teachers are responsible for selecting resources to use in their classrooms, in alignment with approval policies set by their school and jurisdiction. For questions about the authors of specific resources, we would encourage you to contact the publishers.
Additional background:
Further to your previous comments regarding the results of the Programme for International Student Assessment (PISA), please note that Alberta students who wrote the 2012 PISA assessment learned their basic number facts based on the former math program. Since there is no PISA data from students who have learned number facts in the current program, the latest PISA results cannot be attributed to the change in approach.
University of Manitoba math professor Anna Stokke’s response to exchange between David Staples and Alberta Education
“By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development.”
“There is to be a balance among mental mathematics and estimation, paper and pencil exercises, and the use of technology, including calculators and computers. Concepts should be introduced using manipulatives and be developed concretely, pictorially and symbolically.
Pg. 13 (Grade 5 outcome)
3. Apply mental mathematics strategies and number
properties, such as:
• skip counting from a known fact
• using doubling or halving
• using patterns in the 9s facts
• using repeated doubling or halving
to determine, with fluency, answers for basic
multiplication facts to 81 and related division facts.
Demonstrate, with and without concrete materials,
an understanding of multiplication (2-digit by
2-digit) to solve problems.
And that’s the end of multiplication (with whole numbers). How are they supposed to multiply with 3-digit numbers, you ask? Here’s the answer:
Pg. 15 (Grade 7 outcome)
Demonstrate an understanding of the addition,
subtraction, multiplication and division of
decimals to solve problems (for more than 1-digit
divisors or 2-digit multipliers, the use of technology is expected).
The techniques they teach kids are very limited in the size of numbers they can be used for.
There is no mention of using the standard (vertical) algorithms anywhere in your curriculum. It is evidently not a requirement to teach them at all and since they don’t work with numbers larger than 2-digits it’s not obviously necessary to teach them.
We insisted that the phrase “standard algorithm” be listed in the revised MB curriculum and students are required to be able to work with larger numbers, without calculators.
What difference does it make if they use the phrase “discovery math” in the curriculum or not? They know what we’re talking about – multiple strategies, unguided instruction, deemphasis on practice and pencil-and-paper math.
He is also setting up a false dichotomy between understanding and skills. None of us want to see ONLY skills taught. We all want to see kids both understand math and be fluent with calculations. However, there are a fair number of consultants would do not think it’s important for kids to be fluent with calculations.
A couple of other things.
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