1. Why might children from low-income backgrounds have less mathematical knowledge before preschool than children from middle-income families?
2. What do the terms 'counting-all' and 'counting-on' mean? Who might use the 'counting-all' method and who might use the 'counting-on' method?
3. In what ways do elementary school-aged children find the answer to division problems? By the time they are middle school-aged, what is the predominant method? Why might this method become predominant?
4. Why is working memory so important for people to solve mental multi digit arithmetic problems? How can the constraints of working memory be solved to help with mental calculations?
5. Why might 4 to 5 year old children be able to implicitly understand commutativity without being able to formally state why a problem such as 3+14 = 14 +3 works?
6. Why is it easier to learn addition than subtraction and multiplication than division?
7. Explain the differences between the Chinese and the American children in solving algorithms and what may cause the differences.
8. What are hte different levels of understanding that researchers have attributed to children in understanding hte principles of associativity and commutativity?
9. Why do you think mastery of algorithms is dependent on procedural memory while the acquisition of arithmetic facts and understanding of them are in long-term memory?
