A Holistic and Integral Presentation
The temptation of using a textbook is to jut from one mathematical axiom to the next, with little-to-no explanation of why one is engaging in such problem-solving, how it applies to the greater mathematical goal, what skills are being used and built upon, or why a topic is important. This would not only be improper but destructive; a student would not only digress in his ability to see mathematics as a holistic subject but he would quickly lose his joy for learning. Mathematics is a holistic and culminating subject —what we learn in Form 1 is a foundation built upon even in Form 5 and beyond. It is essential that students are taught not only the how but also the why behind instruction and practice if we expect them to reason in math and all other subjects. Mathematics is a study that operates in tandem with other studies— oiling the analytical engine of mathematicians and historians alike. Lorien Wood students are led in this belief, learning math as a language rather than an arduous obstacle course of ones and zeros. Whenever an instructor is able, they should strive to incorporate historical, artistic, and scientific connections to further enrich a student’s understanding. Mathematics is not solely an instruction of hard skills but a lens with which we see the world— and it is in the mastering of this lense that students find purpose in their education.
The Joy of Analysis
There are instances where answers must be freely given to students and moments where leading a student to the answer is appropriate. For the most part, however, a student learns the how from being shepherded in the way they should think. In addition to the aforementioned factors, an essential aspect of learning mathematics is a child’s ability to discover the answer on their own. Analyzing in math is truly an art that may be learned through practice and should be applied to all other subjects. This often looks like an instructor illustrating a concept, giving students opportunities to demonstrate the topic with the instructor’s observation, and then, individual work to practice the concept in question. Though catchy phrases can at times help students remember certain actions, an instructor’s demonstration should reveal the why behind the concept and should illustrate step-by-step problem-solving. With this technique, students learn to break down impossible problems into achievable steps. In the words of Gottfried Leibniz, they come to understand,“[w]hen a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached.” The student then experiences the satisfaction of coming to a conclusion on their own and pulling on their cumulative knowledge to do so.
The Foundation of Mathematical Instruction at Lorien Wood School, Part 1
Mathematics is often seen as an exception— the one subject that cannot be taught holistically, conceptually, or creatively because of its seemingly rigid nature. At Lorien Wood, we challenge this perspective and believe absolute theorems and conceptual, innovative thinking are not mutually exclusive. In fact, a long-lasting ability to solve mathematical queries and prove axioms depends on one’s ability to critically think and analyze, not just on one’s ability to memorize or answer quickly. While memorization is important and at times essential, if a student can learn how to think critically about mathematics, he may approach all other subjects with a unique ability to reason and discern, and a keen awareness of his abilities and how to use them. A proper Mathematical instruction depends on a few key factors, all working in tandem to teach students the language of mathematics, a language which informs how they see the world.
The Teacher and Not the Textbook
Lorien Wood is founded on the importance of living ideas— thus much of our curriculum centers around excellent literature, written by those with such a profound and thorough knowledge of a subject that they are most able to holistically impart essential truths. Math textbooks are not profound displays of living ideas, as helpful as they may be. Though they are exhaustive displays of theorems and mathematical topics, textbooks are bland illustrations of the patterned, ordered, complex, and beautiful subject at hand. An instructor, having become an expert on the subject himself, is better suited to illustrate mathematical complexities differentially and understandably than a standard textbook. Mathematical instruction, according to Charlotte Mason, “depends upon the teacher and not the textbook” mainly because of an instructor’s knowledge of each child’s learning preferences and their ability to “give the inspiring ideas, what Coleridge calls the ‘Captain’ ideas, which should quicken imagination.” While textbooks are excellent resources, it should be the instructor’s desire to present truth in such a way that it comes alive to each student. Mathematics comes alive when it is presented to students imaginatively, integrally, and holistically— as a small part of a grand design.