Math & Sciences

Cognitively Guided Instruction (CGI) is an approach to teaching mathematics that fosters the development of students’ mathematical thinking.

 

It helps teachers guide students’ understanding of mathematical concepts as they learn about their students’ thinking and the ways in which they solve problems. At the core of this approach is the practice of listening to children’s mathematical thinking and using it as a basis for instruction. Research based frameworks of children’s thinking in the domains of addition and subtraction, multiplication and division, base-ten concepts, multi-digit operations, algebra, geometry and fractions provide guidance to teachers as they listen and work to understand the thinking of their students.

 

Teachers use a variety of practices to extend children’s mathematical thinking. It’s a tenet of CGI that there is no one way to implement the approach and that teachers’ professional judgment is central to making decisions about how to use information about children’s thinking. Children are able to solve problems without direct instruction by drawing upon informal knowledge of everyday situations.

 

Teachers and students pose problems that are relevant and that people encounter in their everyday lives. Students solve the problems alone and collaboratively; and the teachers and students facilitate a conversation around selected solutions as a means to understand more deeply the mathematical concepts embedded within the problem.

 

Novel and diverse approaches deepen mathematical content knowledge of the students and teachers and lead to efficiency in algorithmic thinking and automaticity with facts.

 

In addition to problem solving aligned to the Common Core State Standards, the teachers also engage the students in a series of warm-ups that foster reasoning, number sense, and fluency with facts. Warm-ups may serve to deepen understanding or they could be used to introduce students to patterns and structures that may assist them in solving the problem for the day.

 

The beauty of CGI is in its relevance to children’s everyday lives and its ability to strengthen the understanding not only of the students but also of the teachers.

 

For a better understanding of CGI as an approach, you can watch three LAUSD Teachers in action and see Dr. Megan Franke of UCLA in her work with district leaders on the District’s mathematics branch’s website.

 

The first dimension, Crosscutting Concepts, helps students investigate within the four domains of science, including Physical Science, Life Science, Earth and Space Science, and Engineering Design. When the concepts within these domains, such as “cause and effect”, are clear for students, students can develop a coherent and scientifically-based view of the world around them. They act and think like scientists.

 

The second dimension, Science and Engineering Practices (SEP’s), detail what scientists do to explore the natural world and what engineers do to design and build systems. There is inherent inquiry in these practices that help develop the range of cognitive, social, and physical practices that they require. Students investigate and ask questions to build, deepen, and apply their knowledge of core ideas and crosscutting concepts.

 

The third dimension, Disciplinary Core Ideas (DCIs), is a set of key ideas in science that have wide-ranging importance within or across multiple science or engineering disciplines. These core ideas are cumulative as students move through grade levels and are clustered into the following four domains: Physical Science, Life Science, Earth and Space Science, and Engineering.