Notes
- In order to get full credit in the open ended questions, you need to spend some time reflecting upon and writing your answers. In most of these problems, the probability that a one-sentence answer will get full credit is close to 0 (and so will be what you learn from the exercise)
- Make sure you show all your work on the problems that require it so. Otherwise, even if you give a correct answer, if you do not explain how you obtained it, you'll get very little or no credit.
- It would be great if you discussed ideas with your classmates. The write-up, however, must be done individually.
- These questions are designed to exercise your amazing human mind. Unless specifically allowed, please do not use AI (ChatGPT or similar) to answer them.
- Recall that the slides of the lectures can be found here.
Problems
Example Problem 6
Topic: The beginnings of counting
Bibliographical information:
Barras, Colin. "How did Neanderthals and other ancient humans learn to count?" Nature 594, no. 7861 (2021): 22–25.
Link: https://www.nature.com/articles/d41586-021-01429-6
Answer:
This paper discusses different hypotheses about the invention of numbers. It is useful because it tackles exactly what my topic is about. I know that it is peer-reviewed because Nature only publishes peer-reviewed articles, and the Stony Brook Library website also marks it as peer-reviewed.
Note: Problems 4 and 4 are adapted from the Roger Cook's book
History of Mathematics: A Brief Course, by Roger Cooke, 2005, Wiley-Interscience.
Grading Rubric
Problem 1: Mathematics Definition Quotation (10 points)
| Component |
Points |
Criteria |
| Quotation provided |
3 |
Clear quotation with source identified |
| Interpretation |
4 |
Explains what the definition means |
| Critical analysis |
3 |
Takes a clear position with reasoning |
| Total |
10 |
|
Problem 2: Ishango Bone Hypothesis (10 points)
| Component |
Points |
Criteria |
| Creative hypothesis (Part A) |
4 |
Hypothesis matches bone patterns |
| Historical context (Part B) |
3 |
Connects to known math history of the period |
| Reasoning |
3 |
Logical connection between evidence and hypothesis |
| Total |
10 |
|
Problem 3: History of "x" as Unknown (10 points)
| Component |
Points |
Criteria |
| Correct answer |
3 |
Identifies when/who first used x |
| Complete citation |
4 |
All required elements present (author, title, etc.) |
| Source credibility |
3 |
Explains why they believe the source is correct |
| Total |
10 |
|
Problem 4: Calendar Development (10 points)
| Component |
Points |
Criteria |
| Method explanation (Part A) |
4 |
Clear method for determining days in a year |
| Calendar uses (Part B) |
4 |
Two distinct uses for ancient societies |
| Historical reasoning |
2 |
Shows awareness of ancient societies' needs |
| Total |
10 |
|
Problem 5: Exact Values & Irrational Numbers (10 points)
| Component |
Points |
Criteria |
| Conceptual understanding |
4 |
Understands difference between exact and approximate |
| Practical consequences |
3 |
Discusses real-world implications |
| Extension to π and e |
3 |
Meaningful discussion of other irrational numbers |
| Total |
10 |
|
Problem 6: Peer-Reviewed Source (10 points)
| Component |
Points |
Criteria |
| Topic provided |
1 |
Topic clearly stated |
| Complete citation |
2 |
All required elements present (author, title, journal, volume, year, pages) |
| Working link |
1 |
Link works and leads to the source |
| Source appropriateness |
2 |
Source is peer-reviewed and relevant to topic |
| Content explanation |
2 |
Clearly explains what source is about |
| Relevance justification |
1 |
Explains why source is useful for their topic |
| Peer review evidence |
1 |
Shows understanding of how they identified peer review |
| Total |
10 |
|