Making Sense of Partitive and Quotitive Division: A Snapshot of Teachers ’ Pedagogical Content Knowledge

Responses to an item intended to assess teachers ’ Pedagogical Content Knowledge (PCK) are discussed. The item examined 92 teachers ’ capacity to name the two forms of division, provide a simple representation and story problem for each, and explain which form helps to make sense of dividing a whole number by a decimal. Teachers appeared more familiar with partitive than quotitive division. Apparent understanding of quotition with whole numbers did not always transfer to division with decimals. Some findings from the broader PCK research are also shared. Theoretical Background Since Shulman (1986) first identified the more general pedagogical content knowledge that all teachers bring to their profession, researchers have attempted to conceptualise and measure teachers ’ mathematical knowledge for teaching (Ball & Bass, 2000; Chick, 2007