The fundamental purpose of teaching is to pass on knowledge to new generations. But that purpose is often obscured by the material needs of contemporary students. The exact definition of knowledge likely varies among people and institutions. The school’s slogan, “preparing boys for life,” suggests a priority on the overarching concepts of education, rather than minute, insignificant details.
By focusing on larger ideas, teachers at Haverford strive for deeper understanding. Few people have spent more time contemplating the meaning of this deeper understanding than upper school pre-calculus teacher Mr. Nathan Bridge.
“I’m trying to really provide the students with an opportunity to demonstrate to me what they actually know and understand about the mathematical material,” Mr. Bridge said. “So when I design an assessment, I want to eliminate any factors or variables that might interfere with that communication.”
“If I want to know what students understand, it quickly becomes evident that we can’t put all the emphasis of the problem on getting the correct answer.”Mr. Nathan Bridge
For Mr. Bridge, getting the correct answer is only a portion of the understanding he wants from his students.
“Even if they don’t get the right answer, they still have plenty of opportunity to communicate all their thinking about the problem. If I want to know what students understand, it quickly becomes evident that we can’t put all the emphasis of the problem on getting the correct answer,” Mr. Bridge said.
Students in his class are appreciative of the multiple opportunities to demonstrate their knowledge.
“I think it’s really interesting the way that he grades it using so many different rubrics,” Fourth Former Luke Putter said. “There are just so many different ways that you’re able to get your grade up.”
Mr. Bridge has spent countless hours perfecting these different rubrics to optimize the growth potential for all of his assessments.
“In my class, knowledge and understanding means making sense of the problem and understanding what it requires, getting the right answer, using valid techniques, and having evidence of conceptual awareness,” Mr. Bridge said. “So you need to understand not just the techniques of how to do it, but also the concepts behind them, and why they’re appropriate for the given problem.”
As a result of these additional elements to the rubric, students obtain more information every time they step into the classroom.
“It’s a lot of fun taking his class because it’s very engaging, and I feel like I’m learning a lot more underneath the concepts,” Fourth Former Dawson Baker said.
Fully grasping the concepts is certainly important in mathematics, but the notion can also be applied to history courses.
Baker said, “Just memorizing dates can be utterly useless, to be completely frank. It’s a lot more important to know why something happened and everything that comes with it, rather than just a strict set of events.”
“Concepts and contents are on a spectrum. I try to teach the concepts into the content.”Mr. Jeremy Hart
Ancient and Modern World History Teacher Mr. Jeremy Hart often preaches the importance of learning concepts as opposed to content, hoping that students will be able to acquire knowledge from his courses rather than just memorize it.
“Concepts and contents are on a spectrum,” Mr. Hart said. “On one end you have the larger ideas and principles, and on the other you have the real specifics of an item. I try to teach the concepts into the content.”
With this philosophy in mind, Mr. Hart designs his tests to evaluate his students’ conceptual understanding, hoping that they will prove their knowledge of the content along the way.
“Part of the way I assess is, I say, ‘Give me the idea’ or ‘Explain the concept to me.’ And by proving they understand the concept, they also show that they know some of the content that’s tied to it,” Mr. Hart said.
This pedagogy can enhance the teacher and student relationship.
Mr. Hart said, “The whole idea of Haverford is preparing boys for life, and I think when students understand the concepts, they are able to have a critical eye for some of the bigger questions in life.”
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