AoK1: Mathematics -- Lesson 1

Guiding questions to Lesson 1:

1. What is mathematics?
2. How and why is mathematics an important area of knowledge?

Stimuli used to consider guiding question 1 include:

• What do you know about maths?
• 'To speak freely, I am convinced that it [mathematics] is a more powerful instrument of knowledge than any other…'. (Rene Descartes, 1596-1650)
• 'Everything that can be counted does not count. Everything that counts cannot be counted.' (Albert Einstein, 1879-1955)
• 'The mark of a civilised man is the ability to look at a column of numbers and weep.'(Bertrand Russell, 1872-1970)
• 'Survival' maths' vs. Maths 'believed necessary' in society.

We began addressing guiding question 2 by considering:

• its Greek etymology (máthema) = learning, study, science.
• its main concepts -- namely, 1) quantity, measurement (e.g. numbers – mass, time, distance, heat); 2) structure (e.g. set theory, proof theory); 3) space (e.g. geometry); 4) change (e.g. calculus)
• the differences between 'pure' and 'applied' mathematics.

Homework -- to be completed by January 14th and 16th

Read carefully the Ian Stewart (1996) article given out in class, 'Is mathematics the grand design for the universe, or merely a figment of the human imagination?' Stewart starts with the question that is in its title and lies at its heart: "Where does mathematics dome from?" Though he opens by saying that mathematics is both "already out there [in the physical world], waiting for us to discover it" (p. 1) and "in the mind of the beholder" (p. 1), waiting to be invented, he goes on to suggest that neither "discover" nor "invention" "adequately describes the process" (p. 2) that, for him, is mathematics. Stewart argues his case in four main sub-sections: Nature's patterns, Baking bread, Herd of elephants, Lottery illusion.

For this week's blog posting assignment, you are to pick two of these four sub-sections to focus on. In particular, you are:

• to summarise the main point(s) made in each sub-section you've selected (hint: what does the heading itself suggest?)
• to consider carefully the evidence Stewart uses in each sub-section to convince readers of his point of view (hint: identify the evidence -- e.g. appeal to sense perception, language, reason, emotion, another area of knowledge? does it convince you -- why? why not?)
• to discuss what you have learnt about mathematics in each sub-section.

Each of your two sub-section treatments should be about 125 to 175 words long (i.e. 8-12 sentences); you may want to group the 'summarise'/'consider carefully' foci into one paragraph, and make the 'discuss' focus its own and separate paragraph... which means that each sub-section treatment should be two paragraphs long.

Please contribute your post to the blog by Monday, January 14th.

Please comment on someone else's post by Wednesday, January 16th. Choose posts that DO NOT treat the same two sub-sections you have focused on (if one of two is the same, that's fine... but both is not). Your comment should:

• retell (i.e. summarise their post's point);
• reflect on what you've learnt by reading it -- feel free to agree and/or disagree with them; and
• relate it to your developing understanding of mathematics as an area of knowledge).

Reminder: Please bring coloured pencils to the next lesson!