A Brisbane-based mathematics education expert is determined to highlight the significant contribution women have made to mathematics in the lead up to International Women’s Day – 8 March.
ORIGO Education co-founder Dr Calvin Irons, who has been involved in mathematics education for more than 50 years, believes one woman in particular, Ada Lovelace, should be acknowledged in the year where people are being asked to #ChooseToChallenge.
In the history of machine computing there are only two computer languages named after people – Blaise Pascal (1623 – 1662) and Ada Lovelace (1815 – 1852). Both of these are before the era of electronic computing and are often lost in the emphasis on inventions of the 20th century. Pascal’s machine was a very simple device that could add by turning dials one way and subtract by turning in reverse. On the other hand, Lovelace’s contribution was much more significant and she is correctly described as the first computer programmer.
In 2013, James Essinger published his work “A Female Genius” where he describes the life and contributions of Ada, the countess of Lovelace. Based on her mother’s influence, Ada studied arithmetic, music, and French. Her father, Lord Byron, influenced Ada’s interest in literature and poetry. Lord Byron called his wife, “the princess of parallelograms” so it isn’t difficult to imagine that Ada’s mother was indeed an influence on her daughter’s later mathematical pursuits.
The family was very active in the London social scene of the mid-1800s. At one of these events, Ada met Charles Babbage who shared his thoughts about a machine that could complete the tedious and often erroneous calculations in tables of data. Babbage had the ideas for the machine and Ada saw how mathematics might be used to ‘program it.’ Their initial efforts were intended to involve the preparation of accurate mathematical and astronomical tables as well as tide charts.
A machine could be used to calculate data for the tables that were related to patterns. In particular, predictable patterns generated by equations. The easiest patterns were mathematical tables of values from polynomials such as y = x2 + 3x – 6. Ada used what she knew and built on her mathematical knowledge of patterns to create the ‘programs.’ At a basic level, the mathematics involved differences. As an example, consider the sequence of square numbers in the first row below that would arise from one of the simplest polynomials, y = x2. The pattern of square numbers is growing. The differences between the square numbers also grows, but less quickly. The second sequence of differences are equal, or constant.
Ada essentially programmed the machines to begin with the first few values and then work back from the constant differences to determine the values in the row of First Differences and then the beginning row of square numbers. Ada had determined that constant differences at the second level meant the greatest value for an exponent in the polynomial was called 2. This called a polynomial of second degree.
Because the mathematical analysis involved differences, the first machine was called a Difference Engine, shown at the right after it had finally been built and proven to be operational. Babbage thought a machine should be able to do the calculations. But Ada was the person that analysed and applied the mathematics that was necessary so that it could work. The machine was never built during the 1800s, but it was constructed by the British Science museum in the 1990s and in their words, “worked flawlessly.”
The Difference Engine wasn’t built because Ada developed further mathematical ideas so the pair started work on a more advanced computing machine called the Analytical Engine. This device could do more than work with differences and calculate values for complex equations.
Unfortunately, Ada died at a very young age. Dr Irons said it was interesting to theorise what might have happened if she had been able to make further contributions to mathematics.
The term ‘computational thinking’ is appearing with greater frequency in educational documents. This is the content that today’s computer scientists suggest should be taught to equip students with future skills.
“It’s important to acknowledge the work of individuals who had already completed much work in the discipline of computational thinking before it even had a name,” said Dr Irons.
“This could include mathematicians such as Leibniz who argued for a binary system, Pascal who created one of the first calculating devices or Ada Lovelace who wrote innovative programs for the first ‘computers.’”
Dr Irons and his co-founder of ORIGO Education James Burnett will soon release a STEM Investigations series of readers for primary school students. These new books, which weave computational thinking across fresh activities, will be presented in a friendly research format for young learners.