Meeting the Needs of Advanced Learners

Over the next several weeks, the blog will feature a series of articles on meeting the needs of advanced learners. We begin with an article written by Crystal Davis, who is starting her 3rd year as K-12 Math TOSA for Tumwater School District in Tumwater, Washington. She also taught algebra, algebra II, and precalculus for four years at Black Hills High School.

Meeting the Needs of Advanced Learners

by Crystal Davis

High school mathematics requires students to think about non-routine problems, explain their reasoning, and make connections between concepts and mathematical representations. It is sad to say that too often I have had students unable to think and do mathematics in this way. And too often my "advanced" students are the most uncomfortable.

Students who are gifted and talented in mathematics learn patterns, skills and algorithms quickly. In fact, that's part of what makes them gifted and talented in mathematics. That's what makes it so ineffective to challenge them by teaching them the next skill or showing them another algorithm and having them practice. It is ineffective to borrow the math book from the teacher in the room next door and push them into content from the next grade level. All that is accomplished is to perpetuate the idea that learning mathematics consists of learning and practicing a rule. And it never challenges them or teaches them to think mathematically and problem solve. The consequence is they come to high school mathematics with the expectation that the teacher will show them exactly what to do. If I select a non-routine problem that they have the skills to solve, they don't know how to start. And if I ask them to explain their reasoning, they falter and exclaim "I just know." Those students who should be the most capable of going deeper into a concept and finding alternative solutions or strategies, struggle the most.

The solution is simple. Through mathematics education (and starting in kindergarten) ask them questions such as "Why?" or "How do you know?" and have students justify their thinking. Ask them questions such as "Will that always work?" or "Can you find another way to solve it?" and have students look for patterns and connections. In short, go deeper into the mathematics and ask students to tackle non-routine problems, explain their reasoning, and look for connections. The payoff is huge; they'll be challenged every step of the way and they'll be ready for high school mathematics when they get there.