Purpose and Design

Complementary Mathematics / Purpose and Design

As the name implies, Complementary Mathematics (CM) is designed to complement the math program currently used in your district, school, or home. Based on the five strands of math proficiency (reasoning, applying, understanding, computing, and engaging) as described in the National Research Council’s “Helping Children Learn Mathematics”*, this CM website consists of specific sets of activities, assignments, assessments, and instructional videos (both created and selected) designed to ensure content achievement across all five proficiency strands. Each component of CM is clearly defined and objectively measured. The math topics addressed are those most typically associated with the respective grade levels including those from the Common Core State Standards for Mathematics.

The CM structure is built upon the tenets of brain science and how students learn mathematics (see Brain Science and Learning Math under the research heading). One key takeaway from this document is the absolute necessity of reinforcement and repetition when building deep understanding and facility within a given topic. Think of the focused repetition applied by musicians, dancers, athletes, or anyone who wants to master a complex task. Unfortunately, many of today’s math programs have embraced the mantra of “no drill and kill,” never realizing the “drill” is actually the essential practice necessary for mastery and the “kill” is merely an unfortunate classroom approach. When presented as prescribed, students grow to enjoy the challenge of mastering each level of discipline. By blending the science of learning and the art of teaching, each and every math understanding or skill can be mastered and appreciated.

To ensure adequate practice opportunities, the first two CM activities—Fluency Anchors and 1-Page Grade Level Overviews—are presented through several parallel forms of each expectation. This provides the opportunity foreach  student to learn, practice, polish, and become proficient in that expectation. Student activities are supported by short narratives and/or primitive YouTube videos.

The recommended progression of learning the CM materials begins with deep and ongoing discussions of the topic under consideration by all students. The discussion and development of understanding should never be hurried or pressured, and ample opportunities to assimilate the full understanding of the topic must always be available. Rushing through math materials and moving on before true understanding is attained serves as the chief cause of frustration, confusion, anxiety, and general dislike of math class. At the other end of this learning continuum, following a set of gradual transitions, each student becomes proficient and confident across the math expectations.

Unlike most math programs, CM provides recommended time expectations for the activities listed under the computing and understanding proficiency strands as a measure of the “flexibly, accurately, efficiently, and appropriately” language of the NRC. Even more specifically (page 11) the NRC states, “Students need to compute basic number combinations (6+7, 17-9, 8X4, and so on) rapidly and accurately.” And while these time expectations are not set in stone, they are based on the experiences of thousands of students across several decades. At first take, most teachers will feel the time expectations supplied are unrealistic and overly aggressive; however, after utilizing the program as described, these same teachers typically report that the time expectations are too generous and that they should be decreased.

The recommended methodologies associated with the applying and reasoning proficiency strands are included within the problem solving and extended responses headings of this website.
*https://www.nap.edu/catalog/10434/helping-children-learn-mathematics