85-121 How Children Learn Math Midterm 1 Study Questions
1. Some authorities have argued that the prefrontal cortex is particularly crucial in making human beings human. Do Dehaene's descriptions of prefrontal functioning in math support or contradict this view? How so?
2. Why do you think children fail number conservation tasks, when they have other types of understanding about numbers? Why do they fail class inclusion tasks (six tulips, two roses, more tulips or flowers)? How can we reconcile infants' and toddlers' competence in some aspects of numerical understanding with much older children's lack of competence in other aspects?
3. In his conclusion, Dehaene says that biology probably plays a part in great mathematical achievement, but then says that they "do not weigh much compared to the powers of learning, fueled by a passion for numbers." Is it purely a matter of a supportive environment whether a person develops a passion for numbers? Might biology play a role there too?
4. Is the comparison to multiplication of the arbitrary facts on p. 127 a persuasive one? What is the difference between learning multiplication facts and learning the logical statements on p. 127?
5. Why did base 10 become the most common system in widely dispersed societies? Why not base 2, 5, or 20?
6. Why is it important to present a specific event within event-related potential research, rather than just watching the brain functioning (p. 223)?
7. What does it mean to say, "understanding numbers occurs as a reflex" (p. 78)?
8. What are distance and magnitude effects? Why do you think they're so widespread among animals (including people)?
9. Great mental calculators almost always calculate from left to right. Why do you think they do this?
10. Why was the invention of 0 so important?
11. Does the frequency of subtraction bugs indicate that, "the child's brain registers and executes most calculation algorithms without caring much about their meaning?" (p. 133)? What alternative explanations can you generate?
12. Dehaene argues that relying more on calculators, rather than practice with arithmetic facts, would lead to better understanding of mathematical concepts. What is his logic? What logic would lead to the opposite prediction?
13. What are the implications of the Clever Hans story for interpreting difficult to understand modern claims, such as those regarding ESP (extra sensory perception), seers such as Jean Dixon, and 1- and 2-year-olds' learning to read and do math from being presented flashcards?
14. What is the SNARC effect? In what way does it provide evidence for spatial representations of numbers?
15. What is the logic of split-brain studies; what have they told us about processing of numbers in each hemisphere? Why might findings from them not be generalizable to people with intact brains?
16. Should the long looking time in Wynn's experiments and other habituation paradigm studies on the dishabituation trial be viewed as indicative of surprise? Can you think of other reasons why babies might look for a long time at certain displays even if they were not surprised?
17. What are the advantages of brain imaging technologies over studying the thinking of brain damaged patients? Do we gain any valuable information from studying brain damaged patients that we do not gain from neuro-imaging studies?
18. What role do fingers serve in children's learning of arithmetic?
19. What are neural net models? Why are they frequently used to model thought processes?
20. As Dehaene notes on p. 157, the larger sizes of certain brain areas relevant to musical performance in musicians is as likely due to their experience playing their instrument as to any innate difference in their brains. Design an experiment to determine if there are innate differences in the brains of musicians independent of their musical experience? Don't worry about the expense of the experiment.
