New technologies and global interaction have changed the way the world communicates. Math has become a universal language, one that shares the basic semantics of numbers and doesn’t discriminate according to gender, class, faith or age. No matter what cultural, linguistic or geographical differences we might have, we always have numbers in common. We all participate in commerce, communicate through the Internet and use some form of transportation—these things are all part of the equation. Then why is it that with all the patterns and problems of math surrounding us, we don’t think we can speak math? According to Ivars Peterson, the director of publications for journals and communications at the Mathematical Association of America, “To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.”

This fear of numbers is affecting the education of our children. Current studies and data, like the Trends in International Mathematics and Science Study (TIMSS) 2003, places Canadians below average. John A. Van de Walle, a mathematics educator and researcher, reflects on the results of the study and students’ performance. “Canadian children are above average in Grade 4, below average in Grade 8 and significantly lower than average [on world standings] by the time they reach Grade 12. They are doing more homework and receiving more hours of mathematical instruction and scoring lower on the international stage.”

It is unfortunate to think that one of the world’s most influential forms of communication for the future is such a challenge for our youth and prospective workforce. Asks Jennifer Armstrong, principal of BSS’s Junior School, “Where else is it possible to say, ‘I don’t do writing. I don’t do speaking?’ Nowhere. Nowhere else in school is that acceptable and yet over time it has become acceptable to say ‘I don’t do math.’” That is about to change.

After careful contemplation of the North American student standings in TIMSS, Ms. Armstrong and her enthusiastic staff rallied to make changes and tackle a somewhat daunting question: How do you separate mathematical thinking from mathematical proficiency? The solution seemed obvious and yet contradictory. They would find the current algorithm and challenge its list of closely defined instructions. Ms. Armstrong is candid in her confidence. “There is an algorithm for everything. But first, we want to understand why?”

Improving the math skills and international test scores of North American children will take a lot of work on the part of parents, faculty and students. But you have to start somewhere, so BSS chose the Junior School. The Junior School applied its concern to the mediocre and below average standings in Canada and the United States, and invested in the professional development of its staff.

Four years ago the BSS Junior School began a lesson study with Van de Walle’s text, Elementary and Middle School Mathematics: Teaching Developmentally, a resource and reference to help in the process of teaching ‘math thinkers and doers.’ At this time, the school also encouraged JS faculty to participate and enroll in Math Additional Qualifications (AQ) courses. By creating a staff of enthusiastic and strong mathematical thinkers, the Junior School could “ensure that all the teachers at BSS have the deep conceptual knowledge and understanding to share with their students,’’ says Ms. Armstrong.

“The comfort level that comes from detailed discussions, classroom observations, and intensive study and discussion also provides teachers with the understanding of how a child’s thinking evolves.”

Today, there are two teachers in the Junior School well on their way to completing their AQs, one certified specialist, and two more teachers entrenched in further study this summer. This is not common in all junior schools. Often, math specialists teach at the senior school level or are employed in industry.

There is also a shift underway in BSS’s Senior School. Teachers have increased their work with conceptual frameworks and the evolution of mathematical thinking. There is an increase in inquiry-based environments using tools such as Harkness tables, and real-world problems being introduced to provide depth in the classroom. It is only after a certain level of confidence in the student’s ability is reached that educators teach process and procedure pieces.

Junior School Vice Principal Patti MacDonald explains the BSS approach to JS mathematics and a natural correlation with the Reggio approach to education. “We are not discarding mathematical proficiency. The skill, fluency and accuracy are tools that help students work through math more quickly, but they are not replacements for mathematical thinking. And we want to give our girls the understanding of math from the beginning of their education. It is hard for them to move backwards and grasp the concepts and frameworks when they know they can get the answer with an algorithm. We are teaching them to have that understanding from the start.”

At the Junior School level, there are also many math-rich activities that the girls tackle daily. The administration believes that changes in the Junior School program have been necessary for success. It would be a lot easier to just drill students on basic math facts and fill all math periods, as traditional North American schools have since the industrial age, with basic addition, subtraction, multiplication and division. The assessment would be simple and the curriculum repetitive and established. That is not the approach that a school that prides itself on innovation and an understanding of girls’ learning can be satisfied with. If the student has just memorized a formula, and they don’t have a deeper understanding of what two is, and how two twos go together to make four, then they can’t recognize an equation or find a solution out in the real world.

Instead, the Junior School has taken some really big ideas and made them manageable by focusing on six key principles derived from top mathematics programs in Singapore, South Korea, Japan, Hong Kong, the Netherlands, Czech Republic and Austria. These places had the highest scores of the TIMSS 2003. With strong examples of teaching, four years of lesson study and an in-depth research and professional development program, BSS has shifted its classroom focus to curriculum, equity, teaching, learning, assessment and technology.

Visit a Junior School class and the positive changes are evident. No longer is it common practice to see girls work on problems in isolation. Instead, the classroom has become a mathematics community where the use of logic, mathematical evidence as verification and mathematical reasoning connect ideas and applications.

“The goal is to provide an atmosphere where all students can succeed, not just the students who understand something like fractions from the get-go,” says Ms. Armstrong. “The concept goes back to the Reggio vision of the child. The assumption is that students are capable and that every single one of them has the potential and ability to do complex mathematics and do it well. To expect any less is just shortchanging the system and shortchanging the person.”

According to Susan Hislop, Grade 1 teacher and co-developer of the Junior School curriculum, several changes that have been implemented in the school have improved teaching and learning. “The Japanese have perfected the art of carefully planned and well-organized blackboard use. They call it ‘Bansho.’ We have adapted this method in Grade 1, incorporated technology with the Promethean Board, and used it to produce math journals. The documentation of our lessons are then used as reference and built upon.” This is a strong example of how the teachers and staff are benefiting from new techniques and technology, coupled with substantiated best practices—one result of the lesson study.

“The study brings a group of people together around a specific concept,” says Ms. MacDonald. “A lesson is planned and researched from a conceptual framework and then the lesson is taught. During this time there is an army of observers that watch the lesson, watch the students and critique it and analyze it, then look at the evidence of student-thinking and determine if the result was what the lesson was assigned to produce.” In this case, the Promethean Board, a whiteboard with unlimited writing surfaces and interactive tools, suits the task perfectly because it keeps a record of the lesson and helps students remember what they need to do. It also helps them work collaboratively and see connections between different lesson strings.

Ultimately the focus of this change ensures that every child comes out of the Junior School with a deeper understanding of mathematical concepts. It is also important to realize that socially constructed learning is essential for everybody. According to Ms. Armstrong, “the ability of a group of girls to sit around a table with a really complex math problem is significant because girls like to talk. They process information through talk and make it legitimate as a learning tool. I think that because this is the girls’ vehicle, this approach honours who they are.”

This is why the school has moved away from repetitive memorization and “plug-in” formulas. Putting a task in front of each child and asking them to sit at their desk and figure it out alone does not produce the same complex understandings that emerge when a group discusses the problem together and each one scaffolds the others’ understanding.

Ms. Armstrong is proud of the successful changes in the Junior School. “It was lovely for us to be able to say that girls love these tools. Clearly the mathematicians are preaching that this is what we should be doing and that no one should be learning mathematics in isolation. But it is even greater to see that, for girls, this really works!”

Posted July 20, 2008 at 10:01pm

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