“Young children reinvent arithmetic. Spontaneously or by imitating their peers, they imagine new strategies for calculation. They also learn to select the best strategy for each problem. The majority of their strategies are based on counting, with or without words, with or without fingers. Children often discover them by themselves, even before they are taught to calculate.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics
How can teachers understand children's number sense trajectories?
Cognitively Guided Instruction Interviews
Cognitively Guided Instruction (CGI)
Cognitively Guided Instruction (CGI) is a professional development program for teachers eager to build students' number sense and computation skills through problem solving. On this page, you'll read about our experiences conducting CGI Interviews.
Daisy Gomez
AJ Barnes
Ava is in the eighth grade. She easily solved problems involving unit price and rate. She also demonstrated an understanding of division as multiplication by the reciprocal. Ava showed fluency working with multi-digit and decimal numbers. The one problem that Ava was not able to confidently report an answer for was a measurement division problem with a remainder. She performed long division to divide 29 by 3, but was unsure about how to use the quotient and remainder to answer the question of how many groups there would be in a teacher’s class. She finally stated that there would be a total of 10 groups, but she did not explain that 9 of these groups would contain 3 students each, and one group would only contain 2 students.
Since our interview was virtual, I was not able to see if Ava used manipulatives. However, based on her self-reporting, she solved most of the problems without the use of any tool. For some of the more complex problems, she used paper and pencil to perform long division.
Jay Trueheart
This video shows a written summary of a CGI interview with a fourth grader. The write up includes the word problem, problem type, student's response, and analysis of the response. This is repeated for a series of 10 word problems. The final segment of the video shows an overall summary and analysis of the student's number sense and mathematical thinking.
