Exercises: Math
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Some of these exercises are intended explore the notions of "data", classification and "properties" of a group or "class" of objects. Working with this information -- and your "re-worked" information -- may reveal some interesting and important aspects of socio-economic life and may help you with your investigation of the Lowland Clearances. This is a simple example of using Mathematics as a tool in the social sciences.


Math Lesson One: Classification and Properties of a Class of Objects

Refer to the following pages as your "input evidence":

  1. Education
  2. New Math: "The Practical Figurer" (This is a subset of the total list of subscribers)
  3. Mathematicians
  4. Philanthropy
  5. Industry
  6. Age of Enlightenment
  7. James McCowan's Library
  8. Glossary
  9. And a good dictionary for any other unfamiliar words!


Exercises for Math Lesson One

Discuss the evidence and explain your answers in some detail.

  1. Who was Lord Dumfries?
  2. How many Ayrshire women subscribed to "The Practical Figurer"? Compare the number of female subscribers to the number of male subscribers. Express as a ratio. Why do you suppose this is the case?
  3. What do you think was Mrs. Culbertson's occupation at Dumfries House?
  4. How many subscribers to "The Practical Figurer" lived at Dumfries House in Cumnock? For each of these, write their name and their occupation in a small table. Classify these people into one "Occupational Group" and give the group a name. Class Discussion: List some "properties" of this group (ie traits or attributes that are basically common to all of the occupations in this group).
  5. Do you think that each of the subscribers at Dumfries House purchased their own copy of The Practical Figurer? If not, who purchased each of the copies and why? Class Discussion:  Discuss this issue in the overall context of the entire set of subscribers.
  6. How many different occupations are represented in the complete table of subscribers (as shown on the page New Math)?
  7. Why are so few farmers listed?
  8. List those occupations that only occur once or twice in the table.
  9. Class Discussion: Propose a way to classify occupations into ten groups and then even into five larger groups. (Tip: Use the Glossary and your dictionary.)
  10. Which of your ten groups do you consider to be occupations of the lower class? Why?
  11. Which of your ten groups do you consider to be occupations of the middle class? Why?
  12. What is the ratio of "Upper Class Subscribers" to "Lower + Middle Class Subscribers"? Class Discussion: How do you explain this ratio and what do you think it means? Do you think this is a fair comparison in terms of the raw data? If not, why not?
  13. Class Discussion: Discuss any "gray areas" or limitations in your classification system. Make a list of the criteria that could or should or should not be used in such a classification system. Discuss the relevance and acceptability today of such a classification.
  14. Mary Fairfax, age 12, was visiting Dumfries House with her father. While her father and Lord Dumfries discussed military matters, Mary explored the mansion. She found Mrs. Culbertson reading "The Practical Figurer" in the kitchen as she prepared a special cake. Mary asked Mrs. Culbertson why a book about arithmetic, quantities and calculations was important in the kitchen. They struck up a conversation most enlightening for the girl -- you write the dialogue, say, 100 words. How did this conversation prepare Mary Fairfax for a distinguished career in mathematics?
  15. Class Discussion: Refer to the summary, "Overall Distribution of Place of Residence of the Subscribers". Discuss this summary. Of the 309 total subscribers to the book, how many do you think actually lived in Ayrshire. How many do you think were farmers? Do you think your findings in Questions 2, 6 and 8 to 13 above would be significantly different if you could see all 309 records of the subscribers and their occupations?
  16. Who was William Halbert? Be sure to refer to two particular input pages listed above. Write a short argument that the author of "The Practical Figurer" in 1789 was the same person as the Cumnock Teacher in 1761. What additional evidence would you like to have?
  17. Consider this statement: "The list 'Overall Distribution of Place of Residence of the Subscribers' is a rough measure of the relative dispersion of Ayrshire folk due to agricultural change and the industrial revolution". Do you agree or disagree with this statement? Explain your position. (For some additional reference material on this web site, go to "The Lowland Clearances" and linked pages.) What other information would you need in order for you to agree with the statement or at least with part of the statement?
  18. Class Discussion: Discuss the author's purpose in writing "The Practical Figurer"? Do you think he had any particular audience in mind? What would you need in order to make a more thorough assessment?
  19. Consider this statement: "Most of the subscribers to 'The Practical Figurer' were former students of Mr. Halbert". Is this a reasonable statement? Explain your answer.
  20. From each of the first seven "input pages" shown above, pick at least one element or idea that seems important to you. Link each of these elements together into a theme and compose a 200 word essay entirely in your own words. Choose any theme you like for your essay.

The Scarboro Heights Record V12 #12


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