The Sparhawk Formula, A Mosaic of Teaching and Learning Styles
by Louise Stilphen, Headmaster & Founder
David Hawkins, Professor Emeritus from the University of Colorado, developed a model using symbols to represent three levels of teacher interaction with students. His basic model is valuable in describing the cognitive component of a typical day at Sparhawk’s Lower School, so it is used and, with his permission, expanded on in this article.
CIRCLE
Represents those activities that children undertake spontaneously in either a prepared environment or a natural one. The teacher’s role is to observe and reflect.
TRIANGLE
Represents a choice by the teacher to intervene and focus children’s spontaneous activity or to provide “scaffolding” that fosters discovery. For example:
• by adding materials
• by asking questions designed to inspire further investigation • with a demonstration or suggestion
• by modeling
• by suggesting that the child initiate documentation
• by asking the child to become the expert and find out more • by encouraging the application of core skills to find an answer
SQUARE
Represents reliance on authoritative sources. Teachers plan curriculum that supports the acquisition and refinement of academic skills and an evolving knowledge-base.
• information given; questions answered • practicing and internalizing basic skills • books, films, artifacts, etc. • strategies for problem-solving
• lectures, dialogue
The Sparhawk Formula describes a mosaic of teaching and learning styles. The component parts of the Sparhawk model, the circle, triangle, and square are, in real life, fluid and interactive -an integrated whole in practice. They also evolve with each developmental stage. Where elementary school is a balance of all three, middle and high school curriculum design mostly involves square and triangle levels.
As students learn the mechanics of reading, writing, and mathematics, they are acquiring what are called academic skills, and when they are taught new information in a specific subject area and memorize facts, they are increasing their academic knowledge base. This ”square”, or convergent style of instruction is the one traditionally associated with schooling. As important as this type of teaching and learning is, it is insufficient because it does not, by itself, foster students’ evolving ability to ponder, formulate questions, hypothesize, solve problems or to think conceptually.
“To instruct someone...is not a matter of getting him to commit results to mind. Rather, it is to teach him to participate in the process that makes possible the establishment of knowledge. We teach a subject not to produce little living libraries on that subject, but rather to get a student...to take part in the process of knowledge-getting. Knowing is a process not a product.”
- Jerome Bruner
“Circle” and “triangle” experiences, engage children in a process of inquiry. They provide opportunity to fashion information meaningfully, rather than just memorize it, and they naturally require the application of emerging skills, including those from the square level, in the context of important rather than solely rote work. Circle and triangle stages encourage divergent thinking. They activate children’s natural curiosity and enable them to develop questions, seek their own answers, and they tend to result in the most sustained interest and satisfaction. Here is where children gain confidence in their ability to generate knowledge. As clay is not a sculpture until the artist acts upon it, humans must construct meaning from what they learn in order to contour their understanding. The triangle and circle levels foster this experience.
“When a room is dominated by predigested materials, the message
is implicit: others have done the thinking, you memorize.”
–Francis Hawkins
The function of the “square” level is to formalize a lesson, give facts, or confirm hunches. Here, teachers direct the study process with curricular goals in mind. Activities are convergent and their design is intentional. Their purpose is to advance students’ learning along established scope and sequences and to stockpile information from authoritative sources. It is an effiicient way to deliver large amounts of information and to integrate experience through the lens of facts and theories, in other words, to sum-up findings from the triangle and circle levels. For students in the early grades, the square level has greatest value if it is a posteriori, that is, combined with, or deriving from, observations or experiences at the circle and triangle levels. Unless learning is meaningful to young children, unless it is proceeds from what they already understand about the world and what interests them, and unless it is useful, it will not be retained in any significant way.
Circle, square, and triangle levels may occur in any sequence or operate separately and they may represent either planned or spontaneous interactions. They also apply to all curriculum content areas for each has discovery and mastery aspects. Everything, from art to science and music to math, even recess experiences, has all three levels, as we will demonstrate.
At Sparhawk’s Lower and Middle Schools, the teacher’s job is to prepare and maintain a rich learning environment and to observe at each level and then decide on interactions that optimize individual learning at all levels.
