Top 8 Reasons to Use CGI to address the New Generation Standards (CCSS)

I just came home from working with a district that has chosen to use Cognitively Guided Instruction (CGI) as their research-based strategy to improve math education.  The last day of our three-day training we took time to look specifically at the 8 mathematical practices from the common core and looked closely at several unpacking documents from Arizona, North Carolina, and Ohio.  During this time teachers began seeing many connections between the new Common Core Standards and Cognitively Guided Instruction.  When asked, why a district would choose to use CGI as a district strategy in relationship to the Common Core Standards the list below is what the group created.

1.     The first mathematical practice insists that students make sense of the problems and persevere in solving them.   This also includes students to monitor and evaluate their progress and change course if necessary.  Younger students may rely on using concrete objects or pictures to help conceptualize and solve a problem and check their answer to see if it makes sense.  Students, when allowed to solve problems that make sense to them from a young age in one premises of CGI.  Students are given a variety of word problems, asked to solve them in ways that makes sense to them, and to share their thinking.  Some students may be direct modelers (using a variety of tools), others may use counting strategies, and others may use derived facts (doubles + or - one, sums of ten, etc.) to solve the problem.  The one thing that tends to be very common amongst CGI students is that they believe they can solve the problem, they make sense of the problem, and they preserve in solving the problem.

2.     The second mathematical practice requires students to reason abstractly and quantitatively and to create habits of using a variety of properties and to work flexibly with numbers.  Students who have had the opportunity to directly model problems from an early age begin to abstract those ideas into numbers and symbols.  These experiences allow students to explore the mathematical properties of numbers and operations.  For example:  Adding 53 + 38 a student may solve by adding 50+30 to get 80 and then adding 3 + 8 to get 11, then adding the 80 + 11 to get an answer of 91.  This student has the understanding that 53 is made up of 50 plus three.  It is also clear that the commutative property is being explored.  Another student may say 53 plus 40 is 93 but then I need to take off 2 because 40 is two more than 38.  This student has the ability to round and compensate for numbers. 

3.     The third mathematical practice states that mathematical students can construct viable arguments and critique the reasoning of others.  In other words, communication is key for a student to be successful.  The variety of strategies that students come up with in CGI is a perfect platform for developing dialogue and discussion in the math classroom.  Not only do students need to understand their thinking a skilled CGI teachers will ask students to compare strategies.  How might two strategies be similar, what was this student thinking when they solved the problem this way, Is there another way to solve that problem.  The questioning of skilled CGI teachers allows students to clarify, listen to arguments of others, and decide whether they make sense.  This modeling of good questioning then transfers to students to ask meaningful, useful questions to improve their understanding and arguments.

4.     The fourth mathematical practice is titled model with mathematics, although the component of this standard includes that students can write an equation to go with the situation.  CGI contains several different types of problems.  When students are expected to write the equation to go with the problem, this mathematical practice is met.  For example:  John has some apples, he picks 12 more apples, John ends up with 25 apples in his basket.  How many apples did John have to begin with?  A + 12 = 25 represents this situation.  Young students often begin by writing a box in place of the variable "A", but as students progress-writing variables to represent the situation are appropriate.

5.     The fifth mathematical practice is suing tools appropriately and strategically.  Students in CGI use a variety of tools to solve problems.  Even when solving the same problem some students may use number lines, others hundreds chart, others unifix cubes, others base ten blocks, or tens frames, etc...  The tool that makes the sense to the story problem and to the student is appropriate.  Using math tools allows students to visualize the problem at hand.

6.     The sixth mathematical practice asks students to communicate precisely to others and explain their own reasoning.  CGI students are constantly sharing and explaining their ideas to each other, to the teacher, and to the class.

7.     The terminology that is used in the Common Core Standards to describe the different problem types matches the actions in CGI problems.  In CGI students learn about different join, separate, part-part-whole, compare, multiplication, and division types.  The similarity between the Common core and CGI is amazing.

8.     CGI also suggest that multiple strategies are used.  Not all students think about the problem the same, nor do they solve the problem the same.  The common core encourages this type of flexible thinking.