In this monthly column, we speak with a notable member of the Western Canadian mathematics education community about their past, present, and future work, and about their perspectives on the teaching and learning of mathematics. This month, we had the pleasure of speaking with Diana Sproat, Mathematics Consulant of Greater Saskatoon Catholic Schools.
Diana Sproat has been employed by Greater Saskatoon Catholic Schools for the past 22 years as a teacher, Teacher on Assignment, and most currently as the Mathematics Consultant. She completed her Masters of Education at the University of Saskatchewan with a focus in the area of mathematics and as a member of the Math Cohort. Diana was honored to receive the Saskatchewan Mathematics Teachers’ Society Math Service Award in 2014.
First of all, thank you for taking the time to have this conversation in the full swing of the school year! Could you tell our readers a bit about the work that you do as the Mathematics Consultant for the Greater Saskatoon Catholic School Division?
I have been the Mathematics Consultant K-12 for Greater Saskatoon Catholic Schools since 2011. I believe I have the best job at the board office! This role allows me to continue to stay close to the classroom as I work with teachers to plan, model, and co-teach. I also have many opportunities to collaborate with school teams to assist in working toward setting learning improvement plan goals and monitoring strategies. Being a part of a team of consultants and coordinators allows me to learn and to expand my vision outside what is happening in my area to the broader goals of the division. The ability to collaborate with Student Services, the First Nation and Metis Education Unit, the Literacy team and many other professionals brings richness to my specific area. I am also fortunate to be a member of a Provincial Math Group, who will be developing resources and supporting teachers across the province.
In recent years, there has been much public interest in the teaching and learning of mathematics in our country and province’s schools. Many parents, in particular, have expressed concern in newspapers, on the radio, and social media about recent changes in mathematics curricula and approaches to teaching. As a mathematics consultant, do you communicate with parents as well as teachers? If so, what kinds of misconceptions or misunderstandings do you hear, and what do you want parents to understand about these changes?
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]The most common misconception we hear about the “new math” is that the strategies used do not make sense and that students are not learning the basic facts in school.[/perfectpullquote]In my role as math consultant I do have the opportunity to communicate with both teachers and parents. The most common misconception we hear about the “new math” is that the strategies used do not make sense and that students are not learning the basic facts in school. To address the questions, concerns, and curiosity parents have, our schools and Catholic School Community Councils offer Math Parent Information Nights, which I am often invited to lead. This is a wonderful opportunity to engage parents in “doing the math” by providing a problem solving task for them to work through collaboratively.For example, in one task, parents were asked to build a rectangular pig pen for a pet pig using 22 meters of fencing. They were challenged to find as many ways the pen could be constructed and to identify which pen would provide the largest enclosed area. The goal, a grade 5 outcome, was to discover that different rectangles with the same perimeter have different areas. Parents were given geoboards, elastics, grid paper, and pencils. Some created the pig pens with elastics on the geoboard, others drew pens on the grid paper, and some worked systematically using a table to ensure all possible side lengths were considered. The beauty in this task was that in recording the side lengths and the resulting area, the formulas for calculating perimeter and area were also revealed. In another task, we ask parents to do some mental math, describing the strategies used to solve questions such as 36 + 48 or 114 – 98.
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]The approach and the timeline may look different, but all of the skills that parents want their children to develop continue to be components of balanced mathematics programming.[/perfectpullquote]These tasks highlight that not everyone solves problems in the same way, and that a variety of strategies may work to solve the same problem (some strategies being more efficient than others). It is also important to relay to parents the balanced approach provided by the curriculum, which is designed to first build conceptual understanding followed by practice to increase procedural fluency. The approach and the timeline may look different from how some parents were taught in the past, but all of the mathematical skills that they would want their children to develop are there and continue to be components of balanced mathematics programming.In your view, why has the public interest in mathematics education increased? Do you see an end to the “math wars,” and if so, what role will teachers play?
I believe there will always be those who hold strong views on either side of the “math wars,” as we all have lived experiences in the education system. Our role as teachers will be to join both camps in seeing the need for a balanced education, providing excellent mathematics programming for all students that emphasizes both conceptual understanding and procedural fluency.
The public interest in mathematics education, it seems, crosses not only provincial but also national borders, and comparisons are frequently made to countries such as Japan and Singapore (who typically perform well on international mathematics assessments) during the “math wars” debates. In your 2009 article for vinculum (the journal of the Mathematics Teachers’ Society), you discussed the strengths of Singapore’s system of teaching mathematics. This was also a topic that was discussed at the most recent Saskatchewan Teachers’ Association convention. What aspects of the approach to the teaching and learning of mathematics do you feel can (and should) be adapted to our local context? Are there aspects that would not “cross over” well?
I first encountered Singapore Math when my son, then in grade 3, showed me a bar model that he said he could use to add and subtract. He then asked if I could figure it out! I soon realized that he was using a key component of the Singapore Math approach, Bar Model Drawing. The pictorial representation provides the bridge students need as they move from concrete to abstract understanding. Model drawing can be used by students as a powerful tool to represent, understand and solve complex problems. In our local context, this key component of the Singapore system may become part of a repertoire of personal strategies students use for part-whole calculation, comparison, rate and proportion problems.
Years later, I had further opportunity to investigate the Singapore Math through work done with the Saskatchewan Teachers’ Federation. I offered a few summer courses for teachers to learn the model drawing approach to solving problems, which could be easily implemented into existing curricula. During that time, we were in the process of renewing the provincial mathematics curriculum, and some changes that occurred in the Saskatchewan renewal are reflective of the Singapore system, including a narrowing of the outcomes at each grade level to allow for deeper understanding and the introduction of algebra at an earlier age.
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]A key strength in the Singapore system is the emphasis on teacher education. [/perfectpullquote]Another key strength in the Singapore system that we could benefit from is the emphasis placed on teacher education. In Singapore, mathematics teachers are carefully selected, expected to demonstrate mathematical skill at a high level, and receive 100 hours of professional development each year. In contrast, one aspect that would not “cross over” well from the Singapore system would be the streaming of students at an early age into mathematics programming that suits their “ability,” as measured by a public exam. New brain research around learning and the brain’s ability to change, adapt and grow tells us that everyone, with the right teaching and the right attitude, can be successful at math and achieve at the highest levels.Singapore, of course, has been a top performer in well-known international assessments such as the Programme for International Student Assessment (PISA) and Trends in International Mathematics and Science Studies (TIMSS). Although there have been questions about the validity and reliability of such assessments, the results (in particular, the rankings) are often taken to heart by journalists and policy makers. Do you feel that teachers and policy makers in Saskatchewan should be concerned about Canada’s standing in such assessment? If so, what can they learn from the results?
Although there is information and trends that can be disseminated from large scale assessment, these assessments are only one component in a comprehensive assessment system. In measuring the achievement of our students, assessments based on provincial curriculum give us a better indication of the learning of our students and is more readily used by teachers to guide their instruction, change practice, and increase their own professional learning and outcomes for our students.
Switching gears for my last question. As a mathematics consultant, you must be an expert in the resources that are available for mathematics teachers at the elementary and secondary level who are looking to improve their practice. Could you share your top few resources with our readers, perhaps a few from each level, and say a little about how they can help improve teachers’ practice?
I do have some favorites that have made it onto my bookshelf in the past year or two.
- Number Talks, Grades K-5: Helping Children Build Mental Math and Computation Strategies by Sherry Parish and Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4 – 10 by Cathy Humphreys & Ruth Parker – I love the simple and highly effective framework that teachers can use to build students’ number sense and computations skills while they mentally solve problems and discuss their strategies.
- Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching by Jo Boaler – Incredibly interesting research applied to create strategies for use in the classroom that can improve students’ mindsets and learning outcomes.
- High Yield Routines by Ann McCoy, Joann Barnett, Emily Combs – This book features easy-to-implement activities to infuse math into daily routines and to enhance students’ mathematical understanding.
- Math Work Stations: Independent Learning You Can Count On by Debbie Diller – I found this to be a very practical book to help teachers in all elementary grades (although it is meant for Grades K-2) set up their classrooms to give students opportunities to work on instructional materials that further their mathematical understanding and to allow the teacher to provide differentiated and small group instruction.
- Solving for Why: Understanding, Assessing, and Teaching Students Who Struggle with Math, Grades K-8 by John Tapper – This book is a valuable resource for all educators who look for ways to close the gaps for students who struggle.
Two recently purchased, but still unfinished:
- Principles to Actions: Ensuring Mathematical Success for All by the National Council of Teachers of Mathematics – I picked this book up while attending the NCTM Annual Meeting and Exposition in San Francisco in April. Many of the conference sessions focused on one or more of the 8 specific teaching practices that, according to the book, are essential for a high-quality mathematics education for all students.
- Intentional Talk: How to Structure and Lead Productive Mathematical Discussions by Elham Kazemi – The title says it all!
Thank you, Diana, for taking the time to discuss your work and expertise with our readers. We look forward to continuing the discussion in the future.
If you would like to get in touch with Diana Sproat, please email DSproat@gscs.sk.ca.
Ilona Vashchyshyn