A Cambridge Correspondence Course in Arithmetic for Women

Abstract

The unprecedented increase in remote learning compelled by the COVID-19 pandemic has led to increased interest in effective strategies for distance teaching. One may wonder how contemporary distance education compares with that of the past. We focus on an example of distance learning provided to women in England in the late nineteenth century, when the Cambridge Examination for Women was established to verify the qualifications of women in pursuit of a teaching career. A resulting benefit of such an exam was greater emphasis on the preparation of women who wished to become teachers. One means of support to prepare for the examination was a series of “Lectures for Women” sponsored by the Association for Promoting the Higher Education of Women in Cambridge. This effort was complemented by a series of correspondence courses offered to women who lived in remote areas devoid of suitable teachers and to governesses who did not have sufficient control over their time to permit them to attend lectures. We highlight a correspondence course in arithmetic offered by W.H.H. Hudson in which candidates received a set of mathematical problems at fortnightly intervals. After forwarding their answers, students read related material and prepared for the next problem set while the instructor read over their work and returned it with comments. Hudson’s correspondence, illustrating his educational philosophy, and tips on how to prepare for the examination, are illuminated.

Appendix

For the interested reader, we offer an opportunity to try your hand at the 1873 Higher Local Examination arithmetic problems. As there were no hand calculators in 1873, a good score depended on one’s fluidity with arithmetic operations. The ability to work flexibly and strategically with properties of arithmetic was an advantage. In addition, ready recall of English weights, measures, and currency was essential.

Arithmetic Higher Local Examination

Tuesday, June 17, 1873 9 to 11 A.M.

• 1. Multiply three hundred and seventy-two million four hundred thousand and forty-six by itself and express the result in words.

• 2. Reduce to tenths of a penny the difference between five guineas and eighty-nine half crowns.

• 3. If 17 acres 3 rods and 33 poles cost £1236. 6s., how much will 50 acres 2 roods 21 poles cost at the same rate?

• 4. Find, by practice, the cost of 94 lbs 10 oz. 18 cwts. 6 qrs. at £3. 6s. 8d. per ounce.

• 5. Multiply together the sum and difference of $\frac {11}{18}$ and $\frac {5}{27}$ and divide the result by the product of 5$\frac {1}{7}$ and 1$\frac {31}{84}$.

• 6. Reduce $\frac {5}{256}$ to a decimal. What decimal of £5 is £12. 16s.? Find the value of 0.01625 of a ton, and shew that when divided by 0.0175 it becomes 18 cwts. 2 qrs. 8 lbs.

• 7. Find the interest on £875. 10s. for 3$\frac {1}{2}$ years at 5 per cent.

• 8. A cubic inch of gold is made to cover an acre of metal. Find the thickness of the gilding, and the weight of one square yard of it, assuming that gold is nineteen times as heavy as water, and that a cubic foot of water weighs 1000 oz. Avoirdupois.

• 9. Reduce $\frac {11}{56}$ to a circulating decimal and 0.631$\bar {8}$ to a vulgar fraction.

• 10. Extract the square root of 88.604569 and of $1 + \frac {1}{9} + \frac {1}{4-\frac {1}{10}}$.

• 11. There are three speculations which bring in respectively 5, 7, and 9 per cent on the money invested. Compare the average interest on their capitals obtained by two speculators, one of whom invests an equal sum in each, and the other invests such sums that he obtains equal income from each.

• 12. A person buys an article and sells it at a profit of 2s. 7d. On calculating his profit he finds that if he estimates it as a percentage on his outlay, it is one-fifth as great again as it would be if he estimated it as a percentage on the selling price. What did he give for the article?

• 13. The cost of a ton of coal in London is four times the cost at the pit’s mouth, and half of the latter goes in the miners’ wages. If a rise of 20 per cent in miners’ wages be accompanied by a rise of 20 per cent of coals in London, what proportion of the cost of coals must have been due to carriage that the profits of those engaged in the coal trade may be only three times as great as before? (The cost of carriage is supposed to be unchanged.) (Shaw 1887a)

Answers (Shaw 1887b)

• 1. The product is 138,681,794,260,802,116. In words, the value is one hundred thirty-eight quadrillion six hundred eighty-one trillion seven hundred ninety-four billion two hundred sixty million eight hundred two thousand one hundred sixteen.

• 2. The difference is 14,100 tenths of a penny. The astute solver might realize that 5 guineas is equivalent to 21 crowns, or 42 half-crowns. Then the difference is easily determined to be 47 half-crowns. One half-crown is equivalent to 30 pence, and the remainder of the calculation is straightforward.

• 3. £3899. 2s.

• 4. £3796. 7s. 6d.

• 5. $\frac {2107}{43740}$

• 6. (a) 0.01953125; (b) 2.56; (c) 1 qr. 8.4 pounds; (d) 18 cwt. 2 qrs. 8 lbs.

• 7. £145. 18s. 4d.

• 8. (a) $\frac {1}{6272640}$ inch; (b) $\frac {83125}{40144896}$ oz. Troy.

• 9. $\frac {139}{220}$

• 10. 1 $\frac {1}{19}$

• 11. The average interests are to one another as 143 is to 135.

• 12. 12 s. 11 d.

• 13. $\frac {53}{60}$ of the cost is due to carriage.