Synthesis

We have been learning about the Cognitive Guided Instruction (CGI). The key components of CGI, observed from two in class videos, happened to be that students are using their own methods to arrive at a solution, the students are explaining step-by-step their methods, the questions are open ended, and the students are capable of higher level thinking when solving the problems. The assumptions that go along with this teaching style are that the students are capable of explaining themselves clearly, there are multiple approaches to solving a problem, and that students have the knowledge to find their own methods for solving a problem.

We have learned about addition, subtraction, multiplication, and division using this teaching style. The addition and subtraction are placed together are given different categories. There is join, separate, part-part-whole, and comparison for the main categories of the types of problems. Join problems are generally addition problems, and separate problems are generally subtraction problems. Compare can be subtraction or addition, but are saying that "y" has more of "n" than "x". Part-part-whole problems are usually involving a problem that seems it could be a fraction or ratio. There are three different subcategories for each problem and are the same for three of the four categories. The three subcategories are result unknown, change unknown, and start unknown. Part-part-whole has two subcategories, those being part unknown and whole unknown.

For the multiplication and division portion of CGI, There are four categories of the type of problem and then three categories for the problem. The three categories for the problem are multiplication, measurement division, and partitive division. The first category obviously deals with multiplying, and the last two obviously deal with division. Multiplication deals with the missing total for the problem, measurement division deals with one missing group within the problem, and partitive division deals with missing objects in a group. The four problem types are grouping/partitioning, rate, price, and multiplicative comparison. Grouping/partitioning is dealing with students placing items into a group and figuring out the answer from grouping. Rate deals with time and distance, normally miles per hour. Price is dealing with the unit price or price per pound/gallon. Multiplicative comparison is saying that something is some many times taller, longer, wider, etc. than another like object/person.

I like how easy this teaching style seems to be for students, and we are asking students to do something most are naturally able to do, such as grouping objects together or using drawings to figure out the answer to a problem.