It's been a busy few weeks with stacks of papers to read, student teachers to observe in their solo weeks and conference presentations to make. It's also been a busy week for the St. Michael's Teaching Gardens where a new, large stone was installed faced on one side with a chalkboard. It looks like the first person to take advantage of this chalky mode of expression was a math person (although maybe not as members of the SMC Math Department have assured us that the expressions don't make a whole lot of sense). It's fun to write on a chalkboard again as they finally disappeared from school classrooms with the advent of computers which are allergic to chalk dust.
The conferences I presented at were quite different but there was a common theme of mathematics education. The first was the annual Massachusetts Down Syndrome Congress in Worcester, Mass. on November 3, where I presented a paper on teaching math to students with Down Syndrome. The presentation comprised four parts; some theory, some math, some Andrew and some applications. These four aspects of teaching are based on the idea that you have to make connections between your theoretical understanding of math, your knowledge of the student you are working with, and the available applications for helping the student interact with the math.
The second presentation was yesterday at the annual ATMNE (Association of Teachers of Mathematics in New England) conference and focused on the application of the idea of the referent unit in elementary school math. It's something we often don't think about but has a significant impact on the way children develop their ideas of quantitative literacy. For example, in 1/2 x 1/2 = 1/4, what is the 1 (the referent unit) of each fraction if we are asking what is half of the first half of a football game? No wonder operations with fractions is so difficult.