Head of School Blog "Math at Orchard and The Elephant Challenge"
Dear Orchard Community,
Here is one of my favorite word problems: An elephant climbs a mountain at 5 miles per hour and returns down at 9 miles per hour. What was the elephant’s average speed during its round trip? The impulse is to answer 7 but that is incorrect. I will not give you the answer in this blog but am happy to explain it to you if you ask in person (this is a social experiment proving that math can connect people). The point of sharing the problem of the wayward elephant is that the solution requires one to think deeply about what is being asked and to apply algebraic thinking rather than quickly jumping to a hasty answer.
Here is one of my favorite word problems: An elephant climbs a mountain at 5 miles per hour and returns down at 9 miles per hour. What was the elephant’s average speed during its round trip? The impulse is to answer 7 but that is incorrect. I will not give you the answer in this blog but am happy to explain it to you if you ask in person (this is a social experiment proving that math can connect people). The point of sharing the problem of the wayward elephant is that the solution requires one to think deeply about what is being asked and to apply algebraic thinking rather than quickly jumping to a hasty answer.
This type of problem requires a much deeper level of thinking than worksheets that are designed to plug and chug the same algorithm over and over again in a stupor inducing drill and repeat cycle. I think Orchard students would relish contemplating the elephant’s journey and, because they have been taught to apply what they know, extrapolate, and have been required to think through multiple steps, they would be able to solve this brain teaser.
At Orchard, there is more emphasis on problem solving, alternate solutions and being able to model and explain one’s mathematical thinking. This last summer the middle school math department and many of the middle school science teachers attended the Anja S. Greer Conference on Mathematics and Technology at Phillips Exeter. This is an outstanding conference designed to challenge educators, keep them informed about cutting edge teaching practices and techniques and provide an opportunity for the deepening and refining of knowledge and skills in the company of exemplary colleagues and cohorts in the field. Our teachers returned feeling affirmed in our approach, inspired by the facilitators and the topics at the conference and confident, as they dialogued with many math teachers from flagship high schools, that Orchard graduates are on track not only to be prepared but to flourish and lead in math and science classes at the next level.
In the elementary school, we have adopted the Bridges math textbook series, which is an inquiry based approach to math congruent with the main tenets of the National Council of Teachers of Mathematics. According to the NCTM, learning in math is a combination of "factual knowledge, procedural facility, and conceptual understanding" is necessary for students to use mathematics. While they state that "learning the 'basics' is important",the NCTM does not consider the most simplistic forms of memorization by repetition to be sufficient achievement in mathematics. A good student not only understands how and when to use facts, procedures, and concepts, but he or she also wants to figure things out and perseveres in the face of challenge. Bridges also provides a common baseline for all teachers and guarantees a stepwise and thorough scope and sequence to our curriculum. Additionally, we have gradually shifted the focus of the academic support positions in 2nd, 3rd, and 4th grades from language arts to specialists in math and science, bringing us Molly Carroll, Nate Mylin and David Oyama.
The other day one of our youngest students was astounded when her teacher declared that the Earth was not flat, it rotated on its axis and orbited the sun at a very high speed. “I don’t believe it. It looks flat and, anyway, if we were spinning then why doesn’t this spot move out from under me when I jump in the air?” These questions are astoundingly astute. What is of equal importance is that her teacher took her questions seriously and spent the next few days exploring and trying to prove that the Earth is round, spinning and orbiting. What is wonderful is that the ideas of this young thinker were not casually dismissed; they were honored and if that happens over her years at Orchard she will grow to be a confident young woman secure in the notion that her ideas and observations matter. So, we are not merely fostering good mathematical thinking, we are encouraging creative, independent thinking.
Back to the peripatetic pachyderm problem: please send me your elegant solutions. I am interested in the ways you think mathematically and hope that this small taste of what we offer your children each day in math and science classes at school will inspire you to enthusiastically support what we are doing in these areas at Orchard.
Truly,
