I noticed a tutor working with a student at a Starbucks. I’ve brought my own kids to such places for tutoring help. Nothing like a beverage to ignite academic thinking. Long division was the focus of the student. She looked to be a tween or young teen, and she looked stressed.
“I don’t get it,” She said pointing to the math problem on the paper. “Why do I only deal with the first two digits, and not the entire number?”
The tutor reassured her that the rest of the number–4 digits–should be ignored until the first step was completed. Only then would the address the next digit. For example, if the problem was divide 25 into 8050, just divide 25 into 80, and. . . well you get the idea. If not, please try the Khan Academy video at the end of this blog.
The tutor was doing what most of us would have done–Teach the system step by step. Math in the U.S. tends to be about the steps. Memorize the math facts like multiplication and learn the steps to solving problems. This was documented in a TIMSS study which is explained in Education World– “Math Education in the U.S., Germany, and Japan: What Can We Learn from This?” The trouble with this approach was that the student’s question was not being answered:
“Why do I only deal with the first two digits, and not the entire number?”
She needed to understand the concepts that underlined the meaning and purpose for long division. Maybe explaining how division is about finding how many groups of “something” there are. For example, dividing 850 by 25 gives me 34 “somethings”. Or to put into context, if I have 850 mini candy bars and 25 tables to divide the sweets amongst, my calculations would lead to placing 34 candies on each table.
Once the student understands the concept of division as finding how many “somethings” in a group, she might be on her way to having context for the steps. Of course she might understand even better if she could see a visual of the description and possibly do some work with manipulatives.
A concept-based approach increases students’ understanding of facts and skills in a context for “Why.” This approach can liberate curriculum and instruction of standards. Unpacking standards for the core concepts enables teachers and students to find relevant connections to their lives, and that of a community. For example, a 4th grade team of teachers took required curriculum around the early explorers of the Americas, and transformed it into having students investigating the value of exploration of the solar system and/or the Earth’s ocean depths. By understanding the motivations, characteristics, and successes of explorers in ancient history, students will look at the concept of exploration as it applies to contemporary needs. The teachers soon realized that by focusing on Exploration as a concept, students could consider how they are explorers when visiting a new place, and how scientists explore the microorganisms world when seeking cures for diseases and maladies. In the course of the 4th grade team’s exploration, they tied together Social Studies and Language Arts, with the possibility of incorporating Math and Science curriculum.
The team of 4th grade teachers proved what I’ve often seen. Using a concept-based approach builds connections for helping students understand “Why” so that they can do the steps and see how they can use them in meaningful ways in their lives.
When I left the cafe, the students looked unconvinced by the tutor’s assurances. “Keep pushing the question, Why,” I silently encouraged her. Keep pushing the question, and maybe she or the tutor would explore a different path to explaining the steps through a concept that made clearer sense.
Note: Two places where you might explore Concept-Based Learning are…
Lynn Erickson – Stirring the Head, Heart, and Soul: Redefining Curriculum, Instruction, and Concept-Based Learning
Grant Wiggens and Jay McTighe – Understanding by Design
Great way of explaining why it’s so important to answer the question the student is actually asking.