Mathematics

Elementary Mathematics

At the heart of mathematics education for elementary grades lies the fundamental belief that students should develop a deep and meaningful understanding of mathematical concepts. This understanding is best achieved through hands-on exploration and interaction with manipulatives.  Rather than focusing solely on rote memorization of procedures, students should engage in activities that allow them to discover, explore, and internalize mathematical ideas.  Through the use of manipulatives such as blocks, counters, geometric shapes, and measuring tools, students can develop a deeper understanding of numbers, operations, geometry, and measurement.  Activities that involve sorting, grouping, patterning, and spatial reasoning not only enhance mathematical skills but also promote critical thinking and problem-solving abilities.  Math should be taught in meaningful contexts that are relevant to students' lives and interests. Real-world applications and problem-solving scenarios help students connect mathematical concepts to their everyday experiences, making learning more engaging and meaningful.  Recognizing that students have diverse learning needs and styles, instruction is differentiated to accommodate various learning preferences.  Building mathematical understanding is a gradual process that requires scaffolding. Teachers should provide structured guidance and support as students progress from concrete manipulative-based activities to more abstract representations and problem-solving strategies.  Assessment should focus on understanding students' conceptual grasp rather than just procedural fluency. Observing students' interactions with manipulatives, their ability to explain their thinking, and their application of mathematical concepts in different contexts provides valuable insights into their mathematical understanding.

Middle School Mathematics

In middle school mathematics education, the integration of technology plays a crucial role in fostering discovery-based learning and nurturing conceptual understanding, particularly in the realm of algebraic thinking.

Middle school students are at a developmental stage where they are curious, exploratory, and eager to make sense of the world around them. Therefore, the philosophy of math education for this age group emphasizes discovery-based learning, where students actively engage in exploring mathematical concepts, making connections, and discovering patterns and relationships on their own.

Technology, such as interactive simulations, graphing calculators, mathematical software, and online resources, serves as a powerful tool to support discovery-based learning. These tools provide dynamic visualizations, interactive activities, and simulations that allow students to experiment, investigate, and test hypotheses, leading to deeper conceptual understanding.  Technology can also support differentiated instruction by offering adaptive learning platforms, personalized feedback, and interactive learning modules tailored to individual student needs. As one example, a hallmark of the early middle school experience at TMS is in the flipped classroom model we offer in Math 6 or Math 7 Advanced. Click here for more details.

Algebraic thinking is a central focus of middle school mathematics, and the philosophy of education in mathematics for this age group targets the development of conceptual understanding in algebraic concepts. Rather than focusing solely on procedural fluency, students are encouraged to explore the underlying principles, properties, and patterns in algebraic expressions, equations, functions, and transformations.

High School Mathematics and Computer Science

The Mathematics Department of Tenafly High School offers a dynamic sequencing of courses designed to provide students with the opportunity to complete four years of mathematics.  While the New Jersey Department of Education's graduation requirements include three years of mathematics, all students are strongly encouraged to complete four years of mathematics during their high school studies. Our mathematics curriculum is designed to provide all students with the appropriate rigor and depth necessary to build a strong foundation in mathematics, both conceptually and procedurally.  Enrollment in mathematics courses is a sequential, traditional progression. The courses students enroll in from one year to the next are dependent upon their completion and success in previous classes. Therefore, it is critical to understand that placement in mathematics classes is reliant upon course sequence not grade level. All students must complete an Algebra I class to advance in the mathematics sequence that is appropriate for their high school program.

Students in Kindergarten through fifth grade are enrolled in general grade-level math courses based on the New Jersey Student Learning Standards (NJSLS) for Mathematical Content and Practices.  Within each grade-level, teachers differentiate the learning experience for students to extend and/or scaffold concepts and skills based on the individual readiness with which students present.

Differentiated course placements begin in grade 6.  Students in grade 6 are enrolled in either Math 6, the standard grade-level course or Math 7 Advanced, an accelerated course aligned to the Grade 7 NJSLS-Math.  Course sequences follow these placements as shown in the chart below:

Grade Level	Sequence 1	Sequence 2	Sequence 3
6	Math 6	Math 6	Math 7 Advanced
7	Math 7	Math 7 / Math 7 Advanced	Algebra 7
8	Math 8	Algebra 8	Geometry 8

 

Following Grade 8, students typically follow one of the high school sequences shown below:

Grade Level	Sequence 1	Sequence 2	Sequence 3
9	Algebra 1	Geometry	Algebra 2
10	Geometry	Algebra 2	Precalculus
11	Algebra 2	Precalculus or Trigonometry	Calculus
12	Precalculus or Trigonometry	Calculus or Statistics	Statistics

 

Please note, this is a simplified chart offering our most common sequences, though there are many other options and possibilities available to students.  Please see the THS Program of Studies for more details.