This is the first in a two-part conversation with Lower School Principal John Heffron and Curriculum Director Chris Bezsylko. Part II will be published in next week’s Friday Folder.
Mr. Heffron and Mr. Bezsylko got together recently to discuss the math curriculum and the new primary resource in the lower school, Investigations in Numbers, Data, and Space. The discussion was framed around the National Council of Teachers of Mathematics (NCTM) Principles for School Mathematics. The Principles for School Mathematics describes a future in which all students have access to rigorous, high-quality mathematics instruction, knowledgeable teachers have support and ongoing access to professional development, the curriculum is mathematically rich, and students have access to technologies that broaden and deepen their understanding of mathematics.
The NCTM principles establish a foundation for school mathematics programs by considering the issues of equity, curriculum, teaching, learning, assessment, and technology. Part I of this two-part series focuses on the first three principles: equity curriculum, and teaching.
The Equity Principle states that all students must have opportunities to study and to learn mathematics through a coherent, challenging curriculum. Here at HIS, what does this look like?
Mr. B: “The equity principle does not mean that all students should be treated the same. In fact, it asks us to meet each individual student where they are and to provide them with a pathway to mathematical understanding that is developmentally appropriate and aligned with high expectations. At HIS that means differentiation, our ability to provide students with different avenues to acquire content and to develop teaching materials and assessments that allow all students in a class to learn effectively, regardless of differences in ability. While all students are held to high grade-level standards at HIS, we understand that some students need remediation and other students need additional resources to keep them challenged and engaged. The Investigations math program supports differentiation by providing a variety of activities for practicing a concept – referred to as Extension, Practice, and Intervention activities. The Investigations math program requires teachers to open up their instruction to each student’s original ideas, and to guide each student according to his or her own developmental level and way of reasoning.”
The Curriculum Principle states that the mathematics curriculum needs to introduce concepts in such a way that they build on one another, instead of seeing math as a series of disconnected topics. It also states that the curriculum should prepare students for continued study and solve problems in a variety of school, home, and work settings. How does the HIS program build on itself and prepare students for higher learning?
Mr. B: “Our approach to mathematics is directly aligned with the rigorous standards of the Educational Research Bureau (ERB). While these standards are differentiated within the grades, the key concepts across the grades are number sense and operations, geometry and spatial sense, measurement, data analysis, statistics and probability, patterns and functions, and Algebra. Because of the many interconnections among these concepts, instructional units often revolve around two or three related areas. In each unit, students explore these interconnected concepts through a series of investigations that allow students to build on the concepts they have already mastered and to learn about new concepts they have never encountered. Rather than presenting skills and concepts in isolation, learning is scaffolded both within and across the grades by using prior knowledge to access new learning.
As for preparing students for higher learning, NCTM’s publication Focus in High School Mathematics: Reasoning and Making Sense offers that simply exposing students to topics is not enough. Nor is it enough for students to know only how to perform procedures. NCTM points to research which indicates that students are more likely to have a positive disposition towards learning mathematics and to retain mathematical concepts through a program that emphasizes reasoning and sense making, rather than mathematics that is presented as a set of isolated skills and procedures. Investigations challenges students to use a variety of strategies to solve problems, then explain, justify, listen, evaluate, and reevaluate their solutions. This is intentionally different than rote instruction. Rather than simply being asked to apply a formula to several virtually identical math problems, students are challenged to find their own solutions to an identified problem and to justify their reasoning to their peers and the teacher. This interactive work has a major impact on students’ learning. Not only are students learning specific ways to solve problems, they are also increasing their knowledge of the fundamental concepts of mathematics.”
The Teaching Principle talks about teachers needing to increase their knowledge about mathematics and pedagogy, learn from their students and colleagues, and engage in professional development and self-reflection. How is this happening at HIS?
Mr. H: “We started our school year off with professional development from a Pearson trainer on our new Investigations program and we will be having a Pearson consultant back for another day of training later this month. As Principal, I am in classrooms daily, observing the teaching and learning that takes place. After these observations, I have conversations with teachers individually, at grade-level, and across the division focusing on how we are teaching mathematics and developing different strategies that we can and should be using to help students engage in and master our math curriculum. Additionally, grade-level teams have a dedicated meeting time each week to plan and coordinate math instruction.
As for learning from their students – one of the exciting things that happens in Investigations is that children will often make use of their natural intuition to invent ways to solve problems or get to a correct answer. This out-of-the-box thinking from students not only expands the horizons of their peers, but of the teacher as well.”
Part II of this conversation focuses on the final three NCTM Principles of Mathematics – learning, assessment, and technology. It will be published next week.