A favorite New Yorker cartoon of mine is by Sidney Harris.
Two men stand in front of a chalkboard. Their demeanor indicates they are mathematicians. Scrawled on the chalkboard to the left of them is step one, a complicated mathematical formula. To the right of them, step three, is the solution to that complicated formula. In the center of these numbers and symbols,one of the men is pointing to the phrase, “THEN A MIRACLE OCCURS…”.
Under the cartoon is the caption spoken by one of the mathematicians: “I think you need to be a little more explicit here in step two.”
There are so many scenarios that could be explained by this cartoon, but lately I have been thinking about how this cartoon represents the process of education. The missing “step two” is the miracle of how a teacher helps a student to learn, since by definition, a miracle is an extremely outstanding accomplishment. Good teaching is that miracle that blends both science and art. The science formula here is the diagnosis of student needs and the application of strategies that address these needs. The art is the manner in which a good teacher does both.
This blend of science and art is necessary since each student learns differently. Students’ brains are different. Students’ personalities are different. There are differences in how students mature physically and emotionally, and students’ learning styles are different. A great deal of time and energy has been expended in researching the science of teaching to address these differences.
For example, at the beginning of the 20th Century, researchers noted that those students who performed well on one type of test, say mathematics or verbal fluency, were also successful on other academic tests, while those who did poorly on one test tended to do poorly on other tests as well. British psychologist Charles Spearman, put forth a theory that a student’s mental performance across different could be consolidated in a single general ability rating, the g factor. In 1983, American developmental psychologist Howard Gardner countered with his Theory of Multiple Intelligences. He suggested that a measuring student’s intelligence should also include the following considerations:
Visual/Spatial – Involves visual perception of the environment, the ability to create and manipulate mental images, and the orientation of the body in space.
Verbal/Linguistic – Involves reading, writing, speaking, and conversing in one’s own or foreign languages.
Logical/Mathematical – Involves number and computing skills, recognizing patterns and relationships, timeliness and order, and the ability to solve different kinds of problems through logic.
Bodily/Kinesthetic – Involves physical coordination and dexterity, using fine and gross motor skills, and expressing oneself or learning through physical activities.
Musical – Involves understanding and expressing oneself through music and rhythmic movements or dance, or composing, playing, or conducting music.
Interpersonal – Involves understanding how to communicate with and understand other people and how to work collaboratively.
Intrapersonal – Involves understanding one’s inner world of emotions and thoughts, and growing in the ability to control them and work with them consciously.
Naturalist – Involves understanding the natural world of plants and animals, noticing their characteristics, and categorizing them; it generally involves keen observation and the ability to classify other things as well.
Gardner’s theory has been adopted by educators, including Sir Ken Robinson, an English author, speaker, and international advisor, who has stated that,
Many highly talented, brilliant, creative people think they’re not — because the thing they were good at at school wasn’t valued, or was actually stigmatized.
He has noted that organizing students by birthdate is not the best determiner of learning saying,
Students are educated in batches, according to age, as if the most important thing they have in common is their date of manufacture.
Robinson advocates accounting for student differences in an educational system that has been standardized for ease of delivery, an educational system of definitions and measurement. Balancing these forces of measurement and definition in the science of good teaching demands another great force, the art of good teaching.
Good teachers practice the art of teaching in accounting for student differences in maturity, in personality, and in interest. Good teachers practice the art of teaching by choosing how to challenge or aid a student with new content. Good teachers practice the art of teaching when they distinguish between the look of confusion from a look of comprehension and respond appropriately. The art of teaching is knowing how to address the needs of the individual learner.
While there is a degree of science used in the “miracle” step two of the cartoon, the degree of art is trickier. Science is valuable to education as measuring the student; art is valuable to education because the art of teaching has an effect on the student that cannot be measured. The miracle of good teaching is a blend of the two, a blend of science and art for each individual student.
As to those mathematicians in the cartoon who need to be more explicit in step two? They should ask a teacher about performing miracles.