The first test will be primarily on CGI research about how students learn addition and subtraction. Problems that are likely to appear on the test will fall into the following categories:
- Identifying the CGI type of a given problem (for example, see the retakeable CGI types quiz)
- Writing a problem of a given CGI type
- Determining which of a pair of given problems is more difficult. Problems might be more difficult (see lesson 5) because they are:
- of a more difficult problem type (JRU, SRU easier than PPW-WU which are easier than PPW-PU and JCU which are easier than CDU, and all of them are easier than JSU, SSU, CQU and CRU. CQU is easier than CRU. I don't know how CQU and CRU compare to JSU and SSU).
- of the same problem type, but with a continuous context (harder) rather than a discrete context (easier)
- of the same join or separate problem type, but with the information given out of time-dependent order (harder) rather than in order (easier)
- JCU set in the past (harder) rather than a how many needed (easier)
- Explaining some of the differences in problem types discussed in the lessons. Specifically, you might be asked:
- Why do some children find PPW-WU problems more difficult than JRU problems (what is it that they find difficult or confusing)?
- What makes CQU problems easier than CRU problems?
- Is it a good idea to tell children to add when they see the word "more" and subtract when they see the word "fewer" or "less"? Why or why not?
- How are Join and Separate problems similar in a way that is different from PPW and Compare problems?
- Describing how children solve word problems by direct modeling. Specifically, you should be able to describe the most typical way that students solve each each of these problem types by direct modeling:
Additionally, there will be a few related questions about counting strategies. In particular, you should know and be able to explain:
- What is the difference between direct modeling and a counting strategy? Is counting all a counting strategy?
- Know what counting strategies are most likely to be used with the problem types:
- Describe a the process of using the counting strategies:
- counting on
- counting back
- counting up to for subtraction
- Describe a the a teaching strategy, lesson or game for teaching:
- counting on
- counting back
- counting up to for subtraction
The test will be shorter than it would appear from the above list, and it will be given during the last hour of Saturday's class.
The test is closed book and notes. I will provide a table with the names of the CGI types and the similar CCSS type names. The table will look a lot like this.