By The Numbers will focus on what needs to be changed in Math education to help students be prepared for their future outside the classroom.
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
Curriculum & Instructional Specialist
Go down deep enough into anything and you will find mathematics. ~Dean Schlicter