Rectangles ARE Long

So, we did indeed attend (and present at) our annual early childhood conference (MNAEYC/MNSACA) last Friday.  See previous post for details about our Dodge presentation; it was well received and standing room only, yay!  I also had a chance to attend a few presentations too, and one in particular made an impression on me, and teaching buddy, Joey.

I won't go into too many details about the presentation in question; suffice it to say, it was about teaching geometry to young kids, and, in particular, emphasizing definitions of specific shapes in your practice with kids.  The presentation addressed a concern (underscored by some studies based on elementary school testing outcomes), that there is a "math gap" between early childhood and grade six.  Testing seems to indicate that kids are not learning to label geometric shapes in these years.  Apparently, kids fall down on tests when they can't label a shape with a specific and correct word, like "rhombus" or "parallelogram."  The remedy, as presented, is to use correct and very specific terminology in the early childhood classroom:

"When teaching about rectangles DO SAY:
-A rectangle has 4 sides with opposite sides the same
-A rectangle has four right angles or corners
-All sides are connected and straight
-A square is a special kind of rectangle where all the sides are the same

DO NOT SAY:
-Rectangles are long
-Rectangles have two long sides and two short sides
-Rectangles are like any 3-D shapes such as a shoe box"

--Mary Ann Hannibal, Young Children Developing Understanding of Geometric Shapes.  1999.

Hmm.  I do not take issue with the presenters; they were very professional, very prepared and very open to discussing their recommended approach at length.  However, I do bristle a bit at the notion that three, four and five-year-olds absolutely must use shape-specific vocabulary when they are handling blocks or doing anything else (in the early childhood classroom we emphasize using language, period, instead of say, hitting; it seems a bit much to quibble with a three-year-old about their observations about a rectangle.  Hurrah if they are making verbal observations at all!).

Because we do what we do here at Dodge, day after day, I can say, without hesitation, that the most age-appropriate method for learning the definition of a triangle, circle, oval, parallelogram or anything else, is to encounter it in the world and work with it.  This approach goes back to the thesis of our Dodge presentation (and my previous post) that nature+creativity=inquiry.  Day in and day out, we see kids making terrific strides through experience, through hands-on experimentation.  Later, when children are ready, after they have a concrete, physical understanding of a shape and it's properties, then we can give them vocabulary.  Kids are more likely to apply the vocabulary consistently and correctly to something they truly understand.  When you observe the differences between a cat and a dog, you can apply the terminology of differentiation, right?

One would think that it can't necessarily hurt to give a young child the vocabulary alongside the experience.  But, I would argue that while it might not hurt, it could seriously get in the way of learning.  If, when a child is in a frenzy of block and ramp building, I intercede with a lot of language--"Triangles may vary in orientation, size, symmetry, or pointedness"-- I might actually interrupt the child's creative process and their "scientific thinking;" I might be a distraction, if not a turn-off if I try to correct a technically incorrect observation like, "triangles have a point in the middle," with "Actually, triangles have three points or corners."  If a child is doing what hope they will do--experimenting with materials and collaborating with peers while doing so--it seems counter-intuitive to interject with formal language.  Interject with supportive language, maybe, like, "Right, and also a point here and one here.  Cool."

Now, I am a big proponent of naming things, of giving kids real language for any situation.  Naming feelings is very important, for instance.  If kids are interested, giving them descriptive taxonomy when you are out in the field can also give them a sense of control and mastery, and help them differentiate.  Readers will recall our mushroom exploits last fall here at Dodge.  First came the experience of the fabulous and varied fungus.  Kids spied, touched and talked about mushrooms.  We encouraged them to note differences like "sticky," "yellow,"  "stinky," etc.  We took pictures of mushrooms, drew them, made them out of clay, ate them, dried them, magnified them-- you name it, we did it with mushrooms.  And here is the thing, we applied vocabulary when kids were interested and we needed to.  The big white mushrooms?  Those are puffballs.  The stinky, slimy, nasty looking ones?  Those would be stink horns.  The less mature kids might not have been as interested in mushrooms, and they were surely less interested in their taxonomy.  And the vocabulary and taxonomy only served to underscore the things they had already learned about the flora:  size, shape, smell...all the properties had already been experienced first hand.  The naming really came last.  If you tell teachers to emphasize that geometry vocab in the early childhood classroom, I really worry they are going to miss the point of focusing kids on experience.  Hands-on experience.  Nothing like it.  Nothing like it for cognitive development; nothing like experience for social, emotional and physical development.  And in the scheme of things, when we are talking about early childhood education, social and emotional development always wins, always comes first.  As my favorite conservative (yes, I actually have one) David Brooks recently said,

"...getting the academics right is not going to get you far if millions of students can't control their impulses, can't form attachments, don't possess resilience and lack social and emotional skills."

--from Brook's Jan. 23rd OP-ED in the NYT, "It Takes a Generation" 

more important than calling a rhombus a "rhombus"

more important than calling a pentagon a "pentagon"

more important than calling a hexagon a "hexagon"

more important than knowing the definition of a "quadrilateral"

still more important than knowing the definition of  a "quadrilateral" 

more important than knowing what the difference is between a "pentagon" and a "regular polygon"

There is a lot of talk about the importance of early childhood education right now, but "quality early childhood education," can mean very different things to different entities.  In this case, I'm with Brooks.  The rhombus takes a backseat to impulse control.  I'm not sure a rhombus will keep you out of prison (but it could literally keep you in).

My concern is that if teachers are told to apply geometry vocab whenever children learn about shapes, they will wind-up focusing on the wrong thing.  Not only might they ignore the import of social and emotional development, their practice might not be developmentally appropriate in terms of cognition. If a kid plays with blocks every day and is allowed to be creative with them, to build again and again, to practice trial and error, she will arrive at implicit knowledge about shapes before she needs to name them.  I would argue that the child who has spent a good deal of time building forts, creating sculptures or working on carpentry projects will do much better in geometry class down the pike, because she's had all that hands-on experience with concepts that can seem wildly abstract if you haven't learned them physically.  One day, the kid who plays with blocks all the time will create a square, pardon me, a cube (or maybe a rectangular prism), out of four triangle blocks.  She's learned a great deal about the properties of those shapes through play and experimentation.  Her attention span has lengthened as a result of all this time with the material and she has matured enough to manipulate the material with a degree of control and skill.  If you sit a three-year-old down at a table and present her with four triangles and teach her how to make a square with them, you aren't doing anything too bad, but you are missing the big boat of age-appropriate skill development.  What if you invite a kid to that table who can't yet sit still or maintain focus on this triangle/square task?  You are setting that kid up for anxiety or failure, and taking control, autonomy and creativity away from them, and all because they have not yet built the skills to be ready to understand the definition of "triangle" and "square."

I think a teacher should strive to support, and challenge, children; when you know a young child well, you can make an educated guess about what is appropriate for them.  Your educated guess about what to do next, about how to challenge a kid or extend inquiry is based on your experience with that child; teachers, of young children at least, must rely on hands-on, real time experiences with their students more than any codified curriculum requirements.  Threes, fours and fives need to practice life skills most of all.  I can tell you that the bulk of early childhood curriculum is based on toileting, washing, waiting, and using words to express feelings.  Life skills are the challenges for young children; the rest, frankly, is gravy.  If you refuse to wipe your own bottom, it is likely that I will challenge you to do so.  If, after wiping your bottom, you join us at group time and observe that "triangles have a flat bottom, like me," I am not going to pause and, as The Creative Curriculum Approach suggests, correct you and say, "That is not true because triangles can be three dimensional."  No!  I am going to applaud the fact that you took care of your own bottom and positively rejoice that you also observed a similarity and made a comparison.  I might even ask your assembled classmates, "What else has a flat bottom?"

Healthy kids are fairly driven to explore; we need to make sure we focus on the most important details, and sometimes we even need to get out of the way.  There is a time and place for applying vocabulary and taxonomy.  And really, if we are most worried about kids falling down on math vocabulary on a sixth grade test, aren't we really missing the point?  Maybe there is bigger issue about how we are teaching, and testing, around math.  If we need to raise a generation of creative thinkers, should we really be worried about what we call a triangular prism in the preschool classroom?  I'm with Brooks on this.  Wouldn't it be better if we understood the properties of a triangular prism and how we might use one?  Every year, people fall and hurt themselves, trying to shovel snow off of triangular prisms.  The triangular prism shape can be found in the roof of a house, and in a Toblerone chocolate bar (which you should also exercise caution with, but for different reasons).  Why is it hard to walk on a triangular prism?  Why are roofs shaped like triangular prisms?  A kid who plays and plays with blocks, or rain barrels, might be able to tell you (Dodge kids do both).  Sir Isaac Newton used a couple of actual triangular prisms to figure out that the sun's light can be refracted into an spectrum of colors, and then reunited in white light.  They are used in rear view mirrors and in spectrascopes, which reveal information about stars, helping people analyze the elements that compose the atmosphere of those stars.  Triangular prisms are used in color television cameras and computer-generated triangular prisms help scientists solve electromagnetic problems.  It turns out that triangular prisms are a lot more than just a shape, and that is cool.

So I'm not beating up on my geo vocab enthusiasts, just suggesting that we all have some bigger fish to fry, in preschool, and beyond.  Read that Brooks OP ED; I don't agree with everything he has to say, but when he says, "If you really want to make an impact, you've got to have a developmental strategy for all the learning stages, ages 0 to 25," I'm in full agreement.  Developmentally appropriate, useful practice every step of the way.