1st grade cgi problem solving
TRANSCRIPT
CGI = Cognitively Guided Instruction
Thomas Carpenter and Elizabeth Fennema defined different problem types. “If we want to give children the
opportunity to build their understanding from within, we need to understand how
children think about math.” -Carpenter, et. al. (1999)
3 strategy types for problem solvers:
1. Modeling strategies 2. Counting strategies 3. Facts strategies
Carpenter, et. al. (1999)
Problem Types
Join & Separate Problems
*Both involve an action that causes a change.
*Natural starting point for children.
*Use direct modeling.
Join Problems
1. Join Result Unknown John had 5 cookies. Maria gave him 5 more. How many does he have now?
2. Join Change Unknown John has 5 cookies. How many more cookies does he need to have 15 cookies?
3. Join Start Unknown John had some cookies. Maria gave him 10 more cookies. Now he has 15.
How many cookies did John start with?
Separate Problems
1. Separate Result Unknown John had 15 cookies. He gave 5 cookies to Maria. How many cookies does he
have now?
2. Separate Change Unknown John had 15 cookies. He gave some to Maria. Now he has 5 cookies. How
many cookies did John give to Mary?
3. Separate Start Unknown John had some cookies. He gave 5 to Maria. Now he has 10 cookies. How
many cookies did John start with?
Part-Part-Whole Problems
*The whole is the sum of the parts and the parts make up the whole.
Part-Part-Whole Mats
Part-Part-Whole Problems
1. Part-Part-Whole, Whole Unknown John has 5 sugar cookies and 10 chocolate chip cookies. How many
cookies does John have?
2. Part-Part-Whole, Part Unknown John has 15 cookies. Five are sugar and the rest are chocolate
chip. How many chocolate chip cookies does John have?
Compare Problems
*Often the most difficult type, because the problem solver must infer
an action to solve the problem.
Compare Problems
1. Compare Difference Unknown John has 15 cookies. Maria has 5 cookies. How many more cookies does John
have than Maria?
2. Compare Quantity Unknown Maria has 5 cookies. John has 10 cookies more than Maria. How many cookies
does John have?
3. Compare Referent Unknown 4. John has 15 cookies. He has 10 more cookies than Maria. How many
cookies does Maria have?
Resources for you! *IXL website *Voki.com *Thinkingblocks.com *SMART Exchange *Educreations (free app)
“I now realize that I must be very patient, because the growth of young
children as problem solvers is anything but steady and continuous. Beginning problem solvers seem to ‘bump along,’ and then one day they ‘jump’ to a much higher level of
understanding.” -Buschman (2003)