# Math Program

The purpose of this math program explanation is to clarify math placement in the Middle School. It includes course descriptions, information on how placement decisions are made, and indicates how the progression of math classes functions (table above).

We believe building a strong foundation in algebra is essential for success in subsequent mathematics courses. Algebra is the turning point from using arithmetic skills to solve basic math problems with specific numeric values, to creating generalized formulas for equations that use variables that represent more than one value. The abstract reasoning and analytical thinking skills required for an in-depth understanding of algebra is both difficult and developmental. Students entering the Upper School as freshmen who do not demonstrate this foundation of knowledge and do not take or review Algebra I in 9th grade will find themselves struggling when they take later courses, such as Pre-Calculus. Therefore, all Middle School math courses focus on skill-building, problem-solving, and algebraic thinking. We know these are the critical elements of a strong mathematics foundation.

#### What is Math 6?

Math 6 is a course designed to solidify, strengthen, and deepen foundational math skills. In addition, the course emphasizes creative problem-solving strategies and generalizing patterns to push the growth of each student’s abstract thinking and logical reasoning ability. The beginning of algebraic thinking is woven throughout the curriculum. The students are also introduced to computer programming during our gender-based grouping.

#### What is Math 7/Pre-Algebra?

Math 7/Pre-Algebra is a course designed as a continuation of the topics in Math 6 with the goal of extending student understanding of basic math facts and skills. Application of this knowledge to problem-solving situations is expanded, logical reasoning skills are strengthened, and foundational concepts are explored. Emphasis is placed not only on math proficiency, but also on building the habits of learning that are critical to understanding in a math environment. Pre-Algebra topics are incorporated into the course.

#### What is Pre-Algebra?

Pre-Algebra is a very broad term used to describe courses that prepare students for the study of algebra. This course includes topics that involve arithmetic review and the introduction of skills and concepts for algebra, geometry, and statistics. Our program emphasizes mastery of the facts and skills of mathematics and the development of abstract concepts, logical reasoning, and application of skills through problem-solving challenges.

#### What is Algebra?

Algebra courses vary greatly from one school to another in terms of their depth and rigor. At Catlin Gabel, our vigorous program emphasizes abstract thinking and logical reasoning. Topics covered in algebra include evaluation and simplification of algebraic expressions, solving and graphing linear equations, linear systems, operations with polynomials, radical and rational expressions, and factoring. Four dimensions of understanding are emphasized to maximize performance: skill in carrying out various algorithms; developing and using mathematics properties and relationships; applying mathematics in realistic situations; and representing or picturing mathematical concepts.

#### What is Algebra 1A?

This course allows students to complete the study of Algebra over two years to ensure a thorough understanding of the topics and to build a strong foundation for higher-level mathematics.

#### What is Accelerated Pre-Algebra and Algebra?

The accelerated version of these classes move at a quicker pace, which allows time for additional extensions and greater emphasis on conceptual understanding and abstract reasoning.

#### How are math placements decided?

We strive to place students in a class that will meet their individual needs as learners. To ensure a fair process, objective measures are relied upon heavily and subjective opinions are introduced only for unusual circumstances. Although there are courses and typical math paths, we recognize that students change, mature, develop more abstract reasoning and improve their critical thinking abilities, hence a student may be moved up or down over the course of the year to best serve their learning needs.

In 6th grade, the first weeks of school are used to assess each student’s basic math skills, abstract thinking, problem-solving ability, and spatial reasoning. Several placement assessments are used during this time, including 5th grade teacher input, standardized tests, pre-algebra readiness assessments, and baseline exams. In 6th grade, the great majority of the students are placed in Math 6, a vigorous math curriculum reviewing and solidifying elementary math skills, deepening the conceptual understanding of these topics, extending these skills to more complex number sets, and exploring new topics. In addition, abstract thinking and problem-solving strategies are stretched and expanded. Students who place in the 99th percentile on standardized tests with Independent School norms will be placed in an advanced math class. This is a small group of students who have demonstrated mastery over the 6th grade math curriculum and whose intuitive learning style cannot be accommodated in a heterogeneous group.

Between 6th and 7th grades, students are further grouped by math proficiency and learning pace. For our current students, placement into 7th grade math classes happens at the end of 6th grade. The placement includes the cumulative work over the course of the year, final assessments of content and problem solving, and teacher input. For new students, we review teacher recommendations from the admissions process, SSAT scores, and consult with former teachers as necessary.

Between 7th and 8th grades, the groups continue along the same lines as 7th grade. The placement includes the cumulative work over the course of the year, final assessments of content and problem solving, and teacher input. For new students, we review teacher recommendations from the admissions process, SSAT scores, and consult with former teachers as necessary.

#### What is the difference between the terms accelerated and advanced, because I see the Middle School uses both?

Accelerated means the pace of the class is faster. The students in those courses understand new concepts quickly and are facile with abstract ideas. The teacher is able to move quickly, minimize direct instruction, present broader concepts, and deepen abstract thinking.

Advanced means the content of the class is at a different level of mathematics. Our advanced math classes are essentially one year ahead of the scope and sequence of our grade-level offerings. These courses are not designed simply for strong math students, but for those who are clearly outliers and already have mastered the content of that year’s math class. In addition, the content and instruction are adapted for the intuitive learning style of these outliers.

#### Is there movement of students during the course of the year?

Yes. If a teacher assesses a student is not able to meet the expectations of a course or is far exceeding the expectations of a course, the student will be moved to a more appropriate placement.

#### What if I have questions about my child’s math placement?

Parents are always welcome to contact their child’s math teacher, or Barbara directly, to discuss placement decisions and their child’s math progress.