At Avenues, we see mathematics as a language—one that expresses the laws that shape the world we live in and through which we can think critically and creatively. In addition to graduating students who are “accomplished in the academic skills you would expect,” our math program teaches students to ask incisive questions, collaborate to find solutions and develop an approach to problem solving that will serve them throughout their lives. Over the course of their time at Avenues, students come to appreciate both the practical application of mathematical thinking and the beauty of mathematics as a source of reasoning.
In nursery and pre-kindergarten, foundational math concepts–counting, patterns, measurement, addition and subtraction–are introduced through a variety of multi-sensory play-based experiences and activities in both English and the immersion language (either Chinese or Spanish). Like other areas of cognitive development, numeracy is measured along a continuum of growth, allowing children to experience success and satisfaction at every stage of their learning.
From kindergarten to 7th grade, the Avenues math curriculum utilizes Singapore math, which is based on the framework developed by the Singapore Ministry of Education. Avenues selected the Singapore math program for two reasons: firstly, it encourages inquiry while developing fluency and flexibility with numbers (what educators refer to as “number sense”); and secondly, it is an unparalleled tool for developing strong problem-solving skills, a necessary foundation for our distinctive 8th–12th grade math program. Singapore math draws on best practices from around the world and takes problem solving and bar modeling as the basis of mathematical learning. Lessons often begin with a concrete, tactile experience with blocks or counters. After that, students use pictures, symbols and diagrams to visualize mathematical concepts and then create representations based on the pictures in their minds. Known as the “concrete–pictorial–abstract” sequence, this methodology is highly effective for developing a holistic conceptual understanding of math.
By 5th grade, students have become comfortable with abstraction–the third phase of the sequence. They begin to make discoveries using new (and more demanding) concepts. By 6th grade, students are thinking in terms of fractions, decimals, ratios, percentages and measurement, and beginning to appreciate how these tools can be used to understand the world. In 7th grade, having developed a robust number sense, students tackle fundamental topics in algebra and work on problem sets that foreshadow the challenges of 8th grade math and beyond.
In all units of study, students practice using mathematical language to explain their reasoning. In addition to developing traditional mathematical skills, we place emphasis on improving student beliefs and attitudes about math. In keeping with the Singapore math framework, our faculty is dedicated to promoting a positive mathematical mindset and instilling a belief in our learners that all students can excel and thrive in math.
As part of Avenues’ commitment to interdisciplinary studies, students make strong connections between math and other subjects. Math is integrated into coding and creative computation, World Course, music, arts and real-world problem solving in STEAM projects.
Beginning in 8th grade, students transition to a discussion- and problem-based approach to mathematics that emphasizes collaboration and encourages students to take active ownership of their learning. Before class, students are given a set of problems to work on. The problems are designed to draw upon students’ prior knowledge but usually require them to apply that knowledge in a new context. In class, students present solutions and discuss their approach, concept and alternative ways of arriving at a solution. The teacher makes connections from these problems to previous material, introduces new ideas and skills, guarantees that knowledge is presented accurately and elegantly, and if necessary, provides extra practice immediately. In 9th, 10th and 11th grade students take Integrated Math 1, 2 and 3 respectively, with the option of an elective in statistics in 11th grade. In 12th grade, math is taught through advanced electives in calculus and statistics. In addition, college-level math classes on topics such as linear algebra and multivariable calculus are offered according to student interest and background.
In these math classes, students learn perseverance, collaboration and an approach to problem solving that can be applied to any area of life. As Cem Inaltong, global academic dean and upper grades math teacher says, “This is about making multiple attempts to solve a problem and realizing that failure makes each attempt better than the last. This is about appreciating the value of making mistakes and having the grit to keep going. These skills transcend the simple acquisition of math formulae; students become lifelong learners who can tackle any problem.”
The Upper Division math program is underpinned by the following ideas:
1) Mathematical thinking begins with intellectual stimulation and engagement, not with the memorization of formulae. Drawing on previous learning, and with guidance from the teacher, students discover and formulate solutions and develop tools to solve future math problems. At the same time, students develop an aesthetic appreciation of mathematics.
2) Students are encouraged to take risks and embrace failure; teachers guide them to learn from their mistakes in a safe and supportive environment.
3) We encourage and expect students to develop a sense of ownership and responsibility for constructing their mathematical knowledge and skills. By adopting a discussion-based approach and requiring active participation by every member of the class, we put student voices at the center of the learning process while purposefully and thoughtfully disrupting the traditional teacher-student hierarchy.
4) Technology is seamlessly integrated into the work that students do in and out of the classroom. Important math software such as Geometer’s SketchPad, Geogebra, Desmos and the TI family of calculators are used as part of the curriculum. Faculty members are encouraged and supported to develop innovative ways of integrating technology into their day-to-day teaching practice.
September 20, 2018
At Avenues, we have a tendency to think of high-intensity practice as belonging solely to the HIP Thinking program. However, shifting from HIP Thinking to Face Your Fears made it clear to me how essential the methods we’ve developed in the HIP program can be to helping students quickly develop competency in discipline-based skills as well.
September 14, 2018
As a culminating experience in nursery, the Whales and Peacocks headed down to the Battery Urban Farm to explore the different sights, sounds, textures, tastes and smells.
September 7, 2018
Here are some tips from an Avenues librarian for next time you aren’t sure what to read next!
September 6, 2018
Last spring our 7th and 8th grade Chinese classes went on a field trip to Flushing, Queens, which is one of the largest and fastest growing Chinese communities outside of Asia.
August 30, 2018
Students are always surprised to hear that that I have other passions besides mathematics. I am often involved in art projects outside of school and Minimester provided me with the opportunity to spend a week creating art with middle grades students.