Making Math Count
Michelle Sullivan sits on the floor with a group of first graders at The Summit Country Day School’s Lower School. Before them are the empty squares of a 10-frame mat. She fills in some of the empty spaces with dots. The six-year-olds must figure out how many more dots are needed to make 10.
As a math specialist educated at the Massachusetts Institute of Technology, Mrs. Sullivan is being intentional about how she teaches math from concrete, to pictorial, to abstract in a curriculum called Conceptual Math developed at The Summit’s Lower School. This particular exercise teaches students to think algebraically about adding, or subtracting, groups of numbers. “This understanding is critical to the foundation of algebra,” Mrs. Sullivan says. “Even though they are in first grade, we are thinking ahead to sixth and seventh grade where they manipulate numbers to solve equations using this inverse operation concept.”
Mrs. Sullivan is also trying to reach students whose personal learning styles vary. “We say the math, read the math and write the math – engaging students in the three main modalities of learning, visual and auditory being the primary learning modality of more than 90 percent of people. Including the kinesthetic targets the remaining population of learning styles. It also keeps little hands engaged, and thus their minds and ears, too.”
Mrs. Sullivan is part of a team of educators in The Summit’s Lower School who are committed to helping students build a mathematical foundation that can endure a lifetime and prepare them for the rigorous coursework ahead. The upwardly spiraling curriculum has produced math scholars who have skipped grade levels in the Middle School and taken college-level math classes in the Upper School.
“For the past five years, Lower School teachers have been accepted into the Professional Learning Community (PLC) at Xavier University and have attended monthly workshops to learn best practices from educational leaders,” says Curriculum and Instruction Director Kirstin McEachern, who has a Ph.D from Boston College. At school, teachers meet regularly with Math Specialist Julia Almaguer, a specially trained math coach who has a bachelor’s degree from Duke University and Masters in Education from Ohio State University.
“Their meetings center around the questions that guide PLC work,” says Dr. McEachern. “What mathematical concepts do we want our students to know? How will we know if they know them? How can we support students who do not know them? How can we extend the knowledge of students who already know them? When you put grade-level teachers together in a room to analyze student math work with these questions in mind, students get a personalized approach that improves their learning.”
Professional development extends beyond what teachers get locally. This year, two math teachers are attending the National Council of Teachers of Mathematics conference. Three faculty members are attending the national Professional Learning Community Summit because of the conference’s math focus. Lower School teachers usually engage in prescribed summer reading, too. Last summer, all the math teachers read Accessible Mathematics | 10 Instructional Skills that Raise Student Achievement by Steven Leinwand. “We have high expectations for our students and our teachers, and we give them both the tools and experiences they need to achieve them,” says Dr. McEachern.
The Summit aims for each student to develop a conceptual mathematic foundation that can endure for a lifetime. “The style of teaching math in the Lower School is to use best practices to provide children with enduring understandings,” says Mrs. Almaguer. The curriculum exceeds national standards for each grade level by drawing upon research-based pedagogy, years of successful experience from specially trained faculty and globally recognized best practices. Teachers are not limited to using a single textbook or textbook series for the curriculum. Materials-rich classrooms are equipped with many hands-on learning tools to physically demonstrate the mathematic principles. Promethean SmartBoards and wireless student-response clickers turn classrooms into a 21st Century learning environment which allows teachers to monitor individual progress and tailor instruction to each child’s needs.
“Some math programs at other schools are extremely scripted,” says Mrs. Almaguer. “You teach this exact lesson on the 31st day of school using prescribed manipulatives. We’re not like that. We have a curriculum with deliberate academic goals layered into each lesson plan for every unit in first through fourth grades. Because our strength is the ability to personalize instruction to meet each student’s needs, teachers can decide which activities, manipulative tools and online resources are most effective. Educational assistants and two math specialists add manpower to the classroom. So teachers can drill down to individual math skills that need to be mastered and have different groups working on different skills at the same time.”
Teachers at The Summit have been trained to meet each student where he or she is and target instruction. Using testing data to identify each child’s specific needs and with the help of educational assistants in the classroom, teachers can create needs-based small groups to focus on skill sets. While one group works on mastering one part of a unit, another group can work on other skills.
Mrs. Almaguer helps teachers identify additional classroom and technological resources. She and Mrs. Sullivan also work with students individually or in groups to develop better foundational understanding or leap forward to advanced practice.
Key aspects of Conceptual Math include explicit instruction that follows a natural progression of conceptualizing math from concrete, to pictorial, to abstract; developing an enduring understanding about a math foundation in every unit; algebraic thinking; pre-assessment and post-assessment of each unit of study in order to personalize instruction to each student; writing about math to help students to organize, clarify and reflect on their own understanding of mathematical concepts; and 21st Century Math, a math lab which generates excitement about the real-world applications of what they have learned. Led by fourth grade math teacher Ellen Valentine, the math lab immerses students in explorations of economics, Science, Technology, Engineering and Math (STEM) and the stock market. Mrs. Valentine also moderates an after-school Robotics Club.
“We routinely apply math knowledge to real world topics because using math in this way helps children develop a sense of numbers, a sense of how to use math,” says Mrs. Valentine. “In real life, math isn’t just a rote mechanical practice of how to apply a formula or how to factor a number. In a very real sense, we are teaching children how to get from here to there – how to think critically and solve real world problems.”
Students from the Lower School move into a challenging Middle School curriculum that moves them forward according to their math aptitude – offering a variety of courses at each grade level to ensure each child is being appropriately challenged. Students are assessed at the end of each course to ensure proper placement from year to year. Students progress through College Preparatory or Honors Algebra I over the course of two years in the Middle School. This makes it possible for most Middle School students to take Calculus in the Upper School without a year of doubling up math classes. This year, eight eighth grade students who took high school-level Algebra I during their sixth and seventh grade years were able to take Algebra II as eighth graders in the Upper School.
Data show the school’s math program is working. In this year’s high school placement math test, 21 of the 25 top scorers in the freshman class were Summit students entering from The Summit’s Middle School. Perhaps even more of the top scorers would have been Summit students if not for the fact that Summit Middle Schoolers who took Algebra II did not have to take the placement test. About 45 percent of the freshman class came from other schools. “Students at The Summit have a real advantage relative to students in K-8 schools because the advanced students can take courses in the high school,” says Rich Wilson, Head of School. The foundation which was laid in the first grade at the Lower School made this outcome possible.
See a video about The Summit’s signature Conceptual Math program at www.summitcds.org/ConceptualMath.