Preschool Problem Solvers: CGI Promotes Mathematical Reasoning

This article discusses CGI, or Cognitively Guided Approach, for students at the preschool age. It suggests that manipulatives give students the ability to think and group data when asked a question. The CGI approach includes direct-modeling, counting strategies, and number fact strategies (Shumway, J.F, & Pace, L., 2017). Direct-modeling is when children solve a problem using manipulatives or fingers to count. Counting strategies is when students realize they can count up or down from a number to get the start of the result of the question. Number fact strategies is when children apply their knowledge of number facts to problems (Shumway, J.F, & Pace, L., 2017). The CGI method makes students think past the one-to-one correspondence to focus on a representation of the whole answer of a problem.

There are two different types of problems. Joint-result-unknown compared with joint-start-unknown. With the joint-result-unknown, they know the two factors going into the result, but need to figure out the result. With joint-start-unknown, they know the result but need to figure out what the person in the word problem started with (Shumway, J.F, & Pace, L., 2017).

CGI focuses on opportunities to extend their knowledge of numbers past the basic concept of it. It allows students to make basic number operations and understand simple concepts (Shumway, J.F, & Pace, L., 2017). It fits easily into a play-based curriculum, meaning teachers can ask math questions in a way that does not seem like math while students are playing. Preschool students are able to engage in word problems constantly, because they are always playing with figures and different amounts of toys. Students can have small group time or individual time to analyze problems. The teacher asked one student in February of 2017 about having 5 bags of apples with 2 apples in each. The student added 5+2 and answered 7. That May, the teacher asked the student the same question. Using CGI, the student was able to correctly count 2 apples 5 times and add them up, equaling 10. The second example given was a joint-result-unknown with the numbers 3, 3, and 6. The students got a plate cut to a semi-circle with an empty middle. They also got 6 beads. They were asked the question about having a necklace with certain beads on it, whether they were 3 beads plus 3 beads or certain colors and asked for the total. Each student was able to answer the questions with the beads being a model of representation for the necklace. Finally, there was a problem about 4 caves with 2 bears in each cave. One student immediately used her fingers to count and the other made a drawing. Then, they were asked if three of the bears went into hibernation, how many would be left? The girl put down three fingers and answered five. The other student crossed out, 3 circles which represented bears, answering 5. Each student in all situations had a different approach to solving the problems. They used models to attain their answer.

Shumway, J. F., & Pace, L. (2017). Preschool Problem Solvers: CGI Promotes Mathematical Reasoning. Teaching Children Mathematics, 24(2), 102-110. doi:10.5951/teacchilmath.24.2.0102