Susan Watson was drawn to the little girl who sat by herself, silently reflecting on the math problem she had quickly solved. Some of the girl's classmates huddled around the teacher at a nearby table, working through the problem a second time in hopes that they, too, would solve it.
Sitting next to the girl, Watson asked the student to show how she arrived at the answer. After seeing her steps and pressing her for explanations, it became apparent to Watson that although the girl had the correct answer, the student didn't understand why she had arrived at it.
This much is obvious: mathematics education is changing.
Memorizing multiplication tables and algorithms are no longer the key to success in classroom mathematics. Now, Washington's State Learning Standards in math ask students to understand how a formula works or why they need to use a specific algorithm to compute the area of a triangle, for example.
It isn't so much about the content--in general it's the same multiplication and algorithms that teachers have been teaching for years. The difference is the eight learning standards referred to as Standards for Mathematical Practice. These standards describe what students should understand about mathematics at each grade level. For example, the first standard--MP1--says simply: Make sense of problems and persevere in solving them.
"There has been a shift in teaching," said Watson. "We want students to be able to get the right answer, but also explain the why behind the math. It's about teaching mathematics for enduring understanding."
What isn't so obvious is what Battle Ground Public Schools is doing to help educators implement teaching strategies that help students understand the why of mathematics practices. "Changing the standards is the easy part," said Paula Koehler-Martin, Battle Ground's executive director of curriculum, instruction and professional development. "Changing the instruction to achieve the standards is going to be harder, and that is what Susan is doing."
"Job embedded professional development is effective," Watson said. "The closer to the classroom that the professional development happens, the greater the impact on teacher practice and student achievement. It's all about the kids learning. We work on teaching practices to impact student achievement."
Watson helps educators shift their math lessons to focus on student understanding through a process she learned during her fellowship with the Teachers Development Group, a nonprofit focused on increasing the effectiveness and efficacy of math instruction in schools. The group funded the fellowship with a grant provided by the National Science Foundation.
The process begins when Watson meets with a teacher to create a lesson plan. As the teacher implements the plan, Watson conducts a classroom visit during which she studies what students say and write during the lesson. She uses these clues to determine whether students understand the why of solving the lesson's math problems. After the classroom visit, Watson meets with the teacher again to discuss what worked and what didn't and how the lesson could be changed (for example, more small group discussion about solving a problem) to help students understand the math. This best practices training "gives teachers a framework of how to teach for understanding," Watson said.
Take the example of the little girl who arrived at the correct answer without understanding why. Watson said in that case, she might put an example of the girl's work on a projector for the class to examine and then let the students discuss it in teams. The goal, as the first learning standard for mathematical practice suggests, is to persevere until students achieve understanding. "Everyone can learn mathematics with the best instruction and right mindset," Watson said.