CGI Ch.1-3 Reflection

After completing this weeks selected readings from Cognitively Guided Instruction I found many concepts to be both helpful and extremely interesting. One of my greatest fears as a future educator has been my own confidence and knowledge of strategies to teach to children to utilize when solving mathematical equations. According to Ch. 2 of our text, however, it states, "All of the strategies we have described come naturally to young children. Children do not have to be taught that a particular strategy goes with a particular type of problem. With opportunity and encouragement, children construct for themselves strategies that model the action or relationship in a problem." While I questioned whether or not this could really be true, I reflected back upon experiences I have had within my own classroom. While I have never explicitly seen my CT teach the children any one strategy to use when solving mathematical equations, there still seems to be a wide array of techniques put to use by the children. For example, on one particular day there was a story problem written on the overhead projector that read " Jill has eight library books. She returns 5 of them to the library. Now how many library books does Jill have?" As I walked around the room to observe how each child chose to solve the problem, I was amazed at the wide array strategies that were being used. While some children obtained physical objects, or manipulatives, from the shelves, others were drawing pictures, writing equations, counting on their fingers, etc. As our textbook suggests, this is because children are intuitive and hard wired to develop a plethora of problem solving strategies independently. I find this to be both interesting and exciting because it enables children to become invaluable resources for each other.

I was also very interested in reading about the variety of ways to word a story problem in order to truly capture a child's cognitive ability. While we discussed in class how important the wording of a story problem is and the various benefits that differentiated wording ensues, I couldn't help but wonder HOW to do this. The reading, as well as the charts and graphs provided within the text, discussed in detail each specific type of problem and what that problem was testing. On page 12, figure 2.2. we are given a chart inclusive of eleven diverse ways to present the same exact story problem! Personally, I find this to be an excellent point of reference for me to continuously refer to in the future and fully intend on taking advantage of this information.

Lastly, though I do not have any questions regarding the reading, I do have a few questions regarding our class discussion about standards presented in Thursdays class. One of my classmates brought up the issue of private schools and wondered what standards they were required to adhere to. Having gone to private catholic school from k-12th grade myself, this was a topic I have also been curious about. Do national and state standards only apply to those schools which are governmentally funded? And if that is the case, then who creates and enforces standards within private schools? Also, there was never a special education program present within my schooling but it seems that nearly all public schools are inclusive of this. Is this also something that is mandated by the state for public schools? These are just a few questions I have had for some time now and our discussion on Thursday seemed like a perfect segue for me to present these ideas and gain some insight!