Having a far reaching standard can intimidate even the strongest educator, student, and parent. However, setting proximal (short term) attainable goals is the path to insuring success, and taking steps towards building self efficacy.
The common core is a systematic approach to learning that inspires the educator to help even the youngest student set realistic goals that can be reached in a shorter period of time. It allows us to individualize instruction, and manage the input of information through systematic approaches to learning.
The first time I heard the term “cognitively guided instruction”, I wished someone had known this effective strategy during my years of mathematics instruction. In all the years of meaningless memorization no one ever asked me how I arrived at the answer. Considering the correct response is a very small part of what makes children think logically, I often wonder why we don’t ask children who respond incorrectly how they arrived at their responses. Piaget did this always asking those he tested to explain to him how they arrived at the “wrong” response. A key ingredient of mathematics reasoning, and the common core encourages us to look beyond the response and into the mathematical reasoning of all children.
The link video provides a better example than I could explain of what CGI looks and sounds like. Note the teachers input and the students response. Notice how he words the questions to motivate the student to share with him the process by which she came to what appears to be a simple mathematical solution. By incorporating this method into mathematics instruction we are investigating the processing instead of the response.
(1) CGI 1: http://www.youtube.com/watch?v=y-0b15nhO0s
(2) CGI 2: http://www.youtube.com/watch?v=UAaTZB_3-7c