At Westside, we love how engaged our parents and guardians are with their children's learning. Some of the more common questions we receive are about how and why we teach math the way we do. Math education looks different today than it did when many of us were in school. In recent decades, there has been significant research into how our brains are wired for learning, as well as the impact of mindset on learning. Our approach to teaching math at Westside is rooted in this research, as well as state and national guidelines for best practices in math education.
Research on Math Instruction
The National Mathematics Advisory Panel's most recent comprehensive study of math research and education indicates that a teacher-directed, stand-and-deliver, algorithm-based approach, which many view as "traditional" math instruction, is not the most effective. Rather, high-quality math instruction requires a combination of student-centered and teacher-directed approaches. Washington State's Mathematics Content Philosophy echoes and furthers this thought and states clearly that best instructional practices in math should focus on reasoning rather than computation and memorization. It states, "...this vision of mathematics education requires students to reason and model with mathematics, be problem solvers, and interpret data. Mathematics programs that emphasize only computation and memorization should be updated or replaced with curricula designed to develop these areas of mathematical thinking." In addition, both recommend a focus on the depth of math learning rather than speed.
Research also tells us that the most robust learning occurs when we use different pathways within the brain. The left side of our brains handles factual and technical information and is called upon with math work that focuses on procedures and calculation. The right side of our brain handles visual and spatial information and is often more involved in conceptual understanding and problem-solving. An equal focus on both components of math education - concepts and calculation - requires greater communication between brain areas, which enhances learning.
Research on Mindset in Math Education
Jo Boaler, a mathematics professor at Stanford University, has done a great deal of research into the impact of mindset in math education. She believes that all students can be mathematical thinkers and that math education that encourages a growth mindset rather than a fixed one is essential. She states that "In the early years of school, we develop a system whereby students are required, from an early age, to learn many formal mathematical methods, such as those used to add, subtract, divide, and multiply numbers. This is the time when students stray from mathematical mindsets and develop fixed, procedural mindsets. This is the time when it is most critical that teachers and parents introduce mathematics as a flexible conceptual subject that is all about thinking and sense-making."
From Research to Practice
So, what does this research look like in practice? At Westside, our math program aims to develop students as mathematical thinkers and reasoners. While students learn formal mathematical methods, which we often refer to as the standard algorithm, they are also challenged to manipulate and reason with numbers in ways that go far beyond these formal methods. We do not focus on skill-and-drill instruction - a practice that most schools are moving away from. Rather, we work to balance the conceptual and computational skills that students need in order to be successful mathematicians, all while supporting the development and maintenance of a growth mindset.
Thank you for taking the time to learn more about our robust math program at Westside. Please click on the following links to commonly asked questions to learn more.
Catey Roe, Director of Teaching and Learning
Commonly asked questions:
How do I know what my child will be learning in each grade?
An overview of content at each of Westside's grade levels is available through the Teaching and Learning section of our website. Like other public and independent schools in Washington, our curriculum is aligned with Common Core State Standards for Mathematics.
What math resources does Westside use?
In the lower school, our teachers use the Bridges in Mathematics curriculum and many other resources, including web-based tools such as IXL. In middle school, our teachers pull from a variety of print curricula, including the Connected Mathematics Project and Prentice Hall mathematics, as well as Khan Academy and other web-based tools.
Is math at Westside rigorous? Is my child being challenged enough?
Washington State's Office of Superintendent Public Instruction states that a rigorous math program should "pursue conceptual understanding, procedural skills and fluency, and application with equal intensity." Rigor is not indicated by the amount of time spent on math work or the number of problems a student is given and completes.
Westside's math program follows Common Core State Standards at each grade level and uses many of the same curricular resources as other local public and independent schools. While we differentiate to ensure that each student's needs are met, the majority of our students are working at or above grade level.
Should my child have more math homework? What about tutoring?
Research indicates that when a student learns a new idea in math, it is most helpful to reinforce it by using it in different ways. Jo Boaler writes, "Worksheets that repeat the same idea over and over turn students away from math, are unnecessary, and do not prepare them to use the idea in different situations." Research also shows that the mere presence or absence of homework has minimal or no effect on student achievement. The types of problems and habits of mind encouraged by homework are far more important than the amount. While math homework at Westside may include some worksheets, it will likely also include other types of activities that focus on the application of concepts, such as family games.
When a student needs support with a particular concept or area of mathematical thinking, additional support outside of school may be useful. Westside does not recommend skill-and-drill tutoring approaches that focus more on quantity than quality. If you have concerns about your child's math skills, reach out to your classroom teacher for support.
What about math facts?
Math facts can be learned more effectively through conceptual engagement than through rote memorization. For example, there are many simple partner games involving dice that allow students to construct, solve, and practice math facts without the pressure of flashcards or timed exercises. On their own, facts are only a small part of math and are best learned through the use of numbers in a variety of ways and contexts. Additionally, when students have strong number sense and math reasoning skills, memorization of facts can become unnecessary.
Boaler writes, "I grew up in a progressive era in England…I was not presented with tables of addition, subtraction, or multiplication facts to memorize in school. I have never committed math facts to memory, although I can quickly produce any math fact, as I have number sense and I have learned good ways to think about number combinations…."
How does Westside address math anxiety in our students?
One of the ways we work to tackle anxiety is by working with students to develop a growth mindset. Research shows that many students who experience anxiety around math have a fixed mindset rather than a growth mindset. When a student has a fixed mindset and generally experiences success in math, they tend to give up more quickly when they encounter an obstacle than those with a growth mindset. Jo Boaler writes, "Students with a growth mindset see math as something to work at. When it gets difficult, which it will, they persevere."
In math classrooms that build and support a growth mindset, mistakes are celebrated as a way to grow your brain, questions are encouraged, and there is a core belief that math is about learning, not performing. Creative thinking, connections, and communication are valued, and there is a focus on depth over speed.
Another way we address math anxiety can be seen in our approach to both classwork and homework. Many teachers will assign work that is time-limited rather than requiring students to complete a certain number of problems. This allows students to focus on doing good work at their own pace rather than experience the pressure to complete a full set of problems.
Does Westside track in math? Do we differentiate?
Westside, like many other schools both regionally and nationally, has moved away from ability grouping, or tracking, in math. Instead, we focus our energy on differentiation within our math program. Across grade levels, our learning specialists partner with our core math teachers to help with access to curriculum, as well as ways to support and stretch students so that each is being appropriately challenged.
International research shows that the most successful countries in math performance are those who group by ability (or track) the latest and the least. Countries like Finland and China, which top the world in math performance, reject ability grouping. In New York City public schools, tracking was recently eliminated. All students were taught at or above grade-level math in heterogeneous groupings. The first cohorts of these students have been followed through high school and beyond, and research found that students took more advanced math, enjoyed math more, and passed the state test a year earlier than those who were tracked. Additionally, when students are tracked, particularly in middle school, they miss exposure to a wide group of peers who approach topics differently.
How do Westside students compare to other students?
One of the ways we monitor progress is through our twice-yearly MAP testing for grades 3-8. MAP is a nationally normed test that allows us to see how our students compare to students nationally in both public and independent schools. MAP's most recent norms were generated in early 2020, just prior to the pandemic.
Our most recent MAP data shows that each Westside grade has an average RIT score that exceeds the national average for students at that grade level. Overall, Westside 3-8th graders' mean RIT score is 8 points higher than the national average. 81% of Westsiders are above the 40th percentile or above average.
Are Westside students prepared for high school math?
Our eighth-grade math curriculum covers major concepts from both Math 8 and Algebra 1. As a result, many of our students enter high school at a level beyond Algebra 1, which may be Geometry or Algebra 2, depending on the school. A recent survey of our alumni indicated that 44% of respondents took honors math their freshman year and that approximately two-thirds placed above grade level as ninth graders. Both through formal surveys and anecdotal feedback, we repeatedly hear that our alumni feel prepared for high school and continue to thrive mathematically after Westside.