Mastery Integration Wonder

Challenges abound in education today, compelling thoughtful educators to search for new teaching methods and solutions for the classroom. Private schools, charter schools, and homeschools have freedom to implement the changes that will actually improve education and increase student achievement. 

So where do we start in science and math?

What is needed is nothing short of a paradigm shift in the way we teach and in the ways we expect students to learn.

Centripetal Press founder and author John D. Mays has identified three areas of focus that have proven to be true game changers for student academic achievement: Mastery, Integration, and Wonder. These three core principles are at the heart of all Centripetal Press textbooks.
Teacher in lab coat talks to students wearing goggles


The first step toward improving academic performance is to change how we define success in our classes. The method most students use is what we call the CramPassForget cycle.

cram-pass-forget with a no sign over itIn this futile cycle, which is ubiquitous in schools and colleges across the nation, students cram for their tests, pass them, and then soon forget most of what they learned. Success in such an environment revolves around jumping through hoops, not genuine learning. Students are bored by this regimen, and teachers are demoralized by the results.

By contrast, we promote teaching methods and curriculum materials designed to promote a LearnMasterRetain cycle. This first involves culling down the bloated curriculum so popular today. A reduced-scope curriculum enables students to learn a reasonable amount of material deeply, instead of giving shallow attention to scores of topics that they will neither comprehend nor remember. Students who learn this way typically outperform their peers as they move to higher level classes.

Second, leading students to mastery and retention requires teaching methods designed to produce these results. The standard approach used today involves teaching a chapter and giving a test on the chapter. By contrast, pedagogy designed for mastery and retention involves continuous review, ongoing accountability for retention of previously studied material, and embedding of basic skills into new material. Of course, an effective method includes innovative strategies to enable students to master course content.



A second major aspect to the needed paradigm shift is that instruction must be integrative. A method of integrated teaching begins with eliminating the habit of  compartmentalizing disciplines of learning that today pervades everything from problem assignments to lesson presentations to test design. Instead of isolating science and math content from everything else, critical points of effective integration must be developed. These integration points should include:

  • frequent use of mathematical skills in science classes, and frequent science applications in math classes;
  • maximizing opportunities to develop good written expression on exams, lab reports and papers;
  • developing key historical connections that serve to enhance understanding; and
  • treating, in addition to basic skills, the nature of scientific and mathematical knowledge, and the roles these play in leading us toward truth, goodness and beauty.

Naturally, for integration to be effective, specific learning objectives must be developed, explained to students and incorporated into assessments.



We believe that appreciation of—and care for—the natural world begins with a sense of wonder at the exquisite complexity and balance we see everywhere in nature. Students too easily grow up today spending most of their time indoors instead of exploring the nature in outdoor activities. One or two generations ago, it was common for students to spend much of their leisure time outdoors biking, playing in the woods, exploring creeks, camping, hiking, fishing, and the like. Today, we must proactively help our students develop a love for the natural world. As this love is cultivated, students will be more interested in studying nature in their science classes, and they will be more inclined to develop healthy attitudes toward caring for and preserving the earth and its millions of species of living creatures.

Centripetal Press texts strive to instill in students a sense of wonder and fascination with the natural world. This is not difficult, since nature is loaded with beautiful and amazing creatures, formations, and processes. It is our hope that as students pick up on our enthusiasm for the amazing world around us they will be stimulated to learn more about it, and that this knowledge will enhance their enjoyment of the natural world and lead to an increased desire to help care for the earth.