Happy April Fools’ Day everyone. Guess which gang of fools is gonna get fooled, and guess which gang of fools is gonna do the fooling.
We have already written on Mister Wisdom’s Keynote address to the Christian Schools National Policy Forum, and De Carvalho’s cute reference to ACARA’s manufactured Joint Statement as his sole example of the “public conversation”. We noted the key nonsense of his address, and most else is not worthy of comment, just the standard ACARA fluff dipped in De Carvalho’s wading pool philosophy. But, mirroring another of his gems, De Carvalho takes a moment to consider a mathematical example in pseudo-depth. We’ll make it a WitCH, so we don’t have to do any work and can get an early start on the vodka.
In his address, De Carvalho spouts the standard nonsense on ACARA’s supposed “refining, realigning and decluttering” of the Curriculum. Readers will recall that ACARA achieved this magnificent tidying by ramming the general capabilities – the “critical and creative thinking” and whatnot – into the curriculum itself, making the entire thing an impenetrable, inquiry-infested swamp.
To make his point, De Carvalho notes “the false dichotomy between factual knowledge and the ability to think creatively and critically”. Skipping over the questionable grammar, we then have De Carvalho distinguishing “the ability to recall facts” from “”knowledge”. It is at this point that we get to De Carvalho’s example, with “knowledge” somehow sliding into “genuine understanding”:
So the ability to recall facts from memory is not necessarily evidence of having genuine understanding.
A student might, for example, memorise the formula for calculating the volume of a prism but do they understand why that formula works every time and when they should use it to solve some real-world problem? The process by which a student arrives at that point of understanding, with the assistance of the teacher, is what makes learning exciting.
De Carvalho has an unerring gift for creating the anti-example. What does De Carvalho mean? What are students supposed to be taught so that they “understand” the formula for the volume of a prism and its “use”?
To add context, below is the relevant content and associated elaborations from Year 7-9 of the (only visible) draft curriculum. Make what sense of it you will. Or, just give up and go straight for the vodka.
YEAR 7 CONTENT
Apply computational thinking and digital tools to construct tables of values from formulas involving several variables, and systematically explore the effect of variation in one variable while assigning fixed values for other variables
experimenting with different sets of tables of values from formulas, for example, using volume of a rectangular prism = length × width × height, and specifying a fixed width and equal length and varying the height
YEAR 7 CONTENT
establish the formula for the volume of a prism. Use formulas and appropriate units to solve problems involving the volume of prisms including rectangular and triangular prisms
packing a rectangular prism, with whole-number side lengths, with unit cubes and showing that the volume is the same as would be found by multiplying the edge lengths or by multiplying the height by the area of the base
developing the connection between the area of the parallel cross section (base), the height and volume of a rectangular or triangular prism to other prisms
connecting the footprint and the number of floors to model the space taken up by a building
representing threefold whole-number products as volumes, for example, to represent the associative property of multiplication
using dynamic geometry software and prediction to develop the formula for the volume of prisms
exploring the relationship between volume and capacity of different sized nets used by Aboriginal and Torres Strait Islander Peoples to catch different sized fish
exploring Aboriginal and Torres Strait Islander Peoples’ water resource management and the relationship between volume and capacity
YEAR 8 CONTENT
choose and justify the appropriate metric units for solving problems involving perimeter, area, volume and capacity. Solve practical problems involving the volume and capacity of prisms and converting from one metric unit to another
YEAR 9 CONTENT
solve problems involving the volume of right prisms and cylinders in practical contexts and explore their relationship to right pyramids and cones
investigating the volume and capacity of prisms and cylinders, to solve authentic problems
determining and describing how changes in the linear dimensions of a shape affect its surface area or volume, including proportional and non-proportional change
solving problems involving volume and capacity, for example, rain collection and storage, optimal packaging and production
experimenting with various open prisms, pyramids, cylinders and cones to develop an understanding that pyramids and cones are derived from prisms and cylinders respectively and that their volumes are directly related by a constant factor of 1/3