Teachers at the Perry Elementary School are deepening their understanding of math by studying a theory of learning called Cognitively Guided Instruction (CGI). CGI increases teachers’ understanding of the knowledge their students bring to the math-learning process by learning how students connect their own informal or intuitive knowledge of math with the formal mathematical concepts and operations presented in the classroom.

Developed by education researchers Thomas Carpenter, Elizabeth Fennema, Penelope Peterson, Megan Loef Franke and Linda Levi, CGI is guided by two major premises. The first claims children come to school already equipped with a rich informal system of mathematical knowledge and problem-solving strategies, and this knowledge can serve as the basis for developing formal mathematics instruction in primary school. This premise leads teachers to look closely at how students solve problems.

The second premise is that math instruction should be based on the relationship between computational skills and problem solving—that is, between abstract rules and their concrete application—which leads teachers to emphasize problem solving in the classroom and the repetition of number facts, for example, practicing the rules of addition and subtraction.

According to Perry Elementary School Principal Kelly Schloss, CGI is "all about making sense of mathematics. Students use speaking and writing skills to describe their thinking in finding solutions. The goal for teachers is to uncover students’ level of understanding, so that they can either remediate or extend their thinking."

A common misconception about CGI is teachers are telling students there is no right answer. "This is untrue," Schloss said. "The conversation that teachers are really having with students is, How do you know that? and Tell us how you got the answer."

Terra Webb, third grade teacher at Perry Elementary, sees promise in the CGI approach. "Clearly what we have been doing for the past 20 some years isn’t working," she said. "Once common core standards are fully rolled out, the expectations will be much higher than they already are. It’s time we start looking at best practices and using the power of standards to influence our instruction."

Unlike rote instruction—the mechanical repetition of rules—CGI requires students to be responsible for their own learning, Webb said. "When they use their own strategies to solve problems and are asked to justify their strategies and understanding, we see a much more positive disposition toward learning math in general," she said. "With STEM initiatives on the rise and the demand for young mathematical minds at its greatest, this seems to be a simple solution, right?"

CGI on ESL: intended for instruction designed to help students grow in both academic content knowledge and applicable English language skills. If these are not addressed together, in a way that matches individual student needs, then the student is not served. It is not equitable to offer cookie cutter curriculum and instruction and expect all students to do equally well.