Fragments to Mosaic: The Art of Teaching Math to Shape Critical Thinking and Problem Solving Skills

Our sincere hope is you have found this book to be transformative—perhaps even revolutionary. ClearMath® represents a paradigm shift in terms of pedagogy. It creates a different learning culture, resulting in a different kind of student—in-depth thinkers. Many are the voices calling for raising the standards for content. Relatively few are calling for raising the standards for pedagogy. But that is the bigger need. Since teaching is the mother of all professions, perhaps we need to begin saying, “Those who cannot teach should not.” School administrators need to be willing to tell prospective teachers, “Maybe you should look for work elsewhere. Your pedagogy is not up to our standards.” Sadly, some teachers may not even know what pedagogy means, even though it is literally their craft. ClearMath® is pedagogy—a method of teaching. Above all else, the pedagogy impacts the learning. ClearMath® lessons are shaped in real time and are fitted to the needs of the student. This is opposed to highly scripted lessons that may or may not fit. Programs and templates just do not suit this pedagogy. Hunting and probing for ambiguity through dialogue is the major teacher-directed activity. Through dialogue, the teacher discreetly exposes missed percepts, missed concepts, misperceptions, and misconceptions, in order to make the lesson fit the student through discovery, correction, clarification, and development of connections. An integrated approach, immersed in the language of math, is used in the presentation of the lesson. “Big” is better for making connections. Specifics and details are learned in more depth when they are first seen or heard in context with the Big Picture. Connected concepts promote holistic understanding. Holistic understanding facilitates application. The teacher spins a web of knowledge, creating a mosaic of understanding. ClearMath® is perceptual teaching®. ClearMath® emphasizes conceptual connections for holistic understanding, leading to creative applications. So what is the missing piece? It is you! If you want math lessons to be understood and retained, try ClearMath®. It is efficient, and it works! —Don White and John Lowder PS. I am still looking forward to teaching my next lesson. I think it is going to be my best! I have not taught my best lesson yet . . . neither have you.