Staying on that general theme, I've recently reviewed a math curriculum called Number Worlds™. The authors conceived an imaginary math universe with five different Lands, where young students can explore and develop what math teachers call "number sense".
I am a big fan of alternative worlds (Star Trek, Narnia, Oz, Middle Earth, The Borrowers) and I publish math curriculum, so I read on with interest. Here's my take on it:
Object Land is a world of tangible objects.
Children manipulate and talk about one or more objects. They begin with 3-dimensional things they can touch, talk about and compare, then move to 2-dimensional items (pictures / diagrams), which prepare them for numbers. The activities and language that children encounter create a foundation for math.Picture Land depicts quantities by groups of dots on dice, dominos or playing cards
Number words are connected to items with dot patterns (half-way between real objects and abstract symbols / numbers). Kids build a mental understanding of the relationships between sets. For example, they may notice that a domino with 5 spots is similar to one with 4, but with one extra dot in the center. Numerals appear in this Land as an alternative way to represent quantities.Line Land is marked by numerals appearing along a horizontal path; farther to the right usually means more (a ruler)
Numbers represent both a sequence of positions along an ordered path (ordinal), and names given to set sizes of different magnitudes (cardinal). Kids discover that addition or subtraction of objects is equivalent to movement forward or backward along a line. They also move from small countable objects to abstract numbers and numerical operations.Sky Land is a place where numerals appear along a vertical path; higher usually means more (a thermometer)
Students discover movement up and down in a vertical rather than horizontal plane. They use the language of height (increased size). Right/left, backwards/forwards, up/down are eventually connected to greater/lesser.Circle Land is the home of numbers that appear in a circular arrangement; clockwise usually means more (a clock)
Many natural processes are cyclical: waking and sleeping, the rising and the setting of the sun, the waxing and waning moon, etc. This Land introduces a cycle, or path that returns to itself. Students develop spatial understanding and get hints of geometry.
This all sounds very logical. And fun. I'm getting into it. I'm imagining those worlds. I'm wishing I had thought of this! But then suddenly!
Woe is me!
I read the fine print, and I lose heart.
Sigh. Groan. Gnashing of teeth.
The publisher declares: A prevention/intervention curriculum for Pre-K to 1st grade kids who have fallen 1-2 grade levels behind their peers.
What are they saying? These worlds aren't real? They're imaginary AND remedial?
Suitable only for students who by age 5 are already 2 grades behind their peers? How can that be?
Imagination = Intervention? versus Pragmatic, practical, real = Advanced Placement?
That is so wrong! C'mon kids - let's go. Beam us up, Scotty, we gotta get out of this place.