Recently I attended the Kansas Association of Teachers of Mathematics Conference. While at KATM, I presented Cognitively Guided Instruction and the Common Core: How do they Connect? I began the discussion with background information on CGI. Cognitively Guided Instruction is a research-based instructional strategy developed by Thomas Carpenter, Elizabeth Fennema, Linda Levi and others in the late 1980s. It was funded by the National Science Foundation and the work occurred at the University of Wisconsin at Madison
The premise of CGI is to find out exactly what children can do on their own when immersed in problem solving. The research found that children intuitively solve word problems by modeling the action and relations described in them. In the training, teachers learn how basic concepts of addition, subtraction, multiplication, and division develop in children and how they can construct concepts of place value and multi digit computational procedures based on their intuitive mathematical knowledge. Teachers also gain knowledge of math problem types and children’s solution strategies.
So why is CGI, an instructional strategy developed in the 80’s, so relevant today?
By looking at the 8 Mathematical Practice Standards from CCSS we can see the intersection between CGI and Common Core.
Mathematical Practice #1: Students will make sense of problems and persevere in solving them. The connection here is obvious….that is the premise of CGI.
Mathematical Practice #2: Students will reason abstractly and quantitatively. When students are involved in problem solving they are seeing numbers in context and they are required to attend to the meaning of quantities.
Mathematical Practice #3: Students will construct viable arguments and critique the reasoning of others. This occurs on a daily basis in a CGI classroom as students share their solution strategies and their answers to problems. If disagreements occur, student are encouraged to engage in discourse with their classmates.
Mathematical Practice #4: Modeling with Mathematics. In CGI classrooms, students are encouraged to represent their mathematical thinking with different representations. This varies from using tools, to drawing pictures but eventually leads to equations.
Mathematical Practice #5: Using Appropriate Tools Strategically. CGI students will do this naturally. When presented a word problem, CGI students choose any method and tool that makes sense to them.
Mathematical Practice #6: Attend to Precision. CGI students are required to communicate their mathematical reasoning precisely. They are asked to attend to units and labels and use vocabulary and symbols accurately.
Mathematical Practice #7: Look for and make use of structure. CGI students naturally pay attention to the structure of a problem. They follow the sequence of the word problem and by using tools that make sense to them, they are able to solve complex problems. Many of these problem types are ones teachers might not believe young children are capable of understanding.
Mathematical Practice #8: Look for and express regularity in repeated reasoning. Students in these classrooms look for patterns, and through discussion teachers can encourage all the known solution methods and help students look for shortcuts. Children are also encouraged to continually check for reasonableness.
Final thoughts that I shared at the KATM session were, although there might be a few concepts in elementary mathematics that do not lend themselves to word problems, most concepts do. This is why CGI is a natural fit with the Common Core State Standards.
For more information about CGI: http://ncisla.wceruw.org/publications/reports/RR00-3.PDF