I have been conflicted lately about a word that seems to have no defintion (in the mathematical world, at least) but, like the oval, is a widely acceptable shape. It’s the diamond. I have grown up my entire life with the understanding that a diamond is just a square with compressed, opposite vertices. I think I may have also accepted that a 45 degree rotation of a square magically creates a diamond. I probably would have fallen for this marketing scheme:
Why did my teachers lie to me and tell me that a diamond was a shape? I never learned about rhombi (or rhombuses). Was it just a cruel joke? Are some teachers genuinely misinformed? Doing a simple Google Shopping search for “shape posters” will provide a number of hits of products that perpetuate the myth of the diamond shape. Here is one sample:
Maybe I learned (incorrectly) that a diamond was a shape on playing cards. Everyone accepts that one of the four shapes in a deck of cards is diamond, right? I don’t remember ever dropping down the Queen of Rhombi. It’s Hearts, Clubs, Spades, and DIAMONDS!
As a child, I enjoyed downhill skiing. What was one warning I learned early on? Stay away from the Double Black Rhombus runs. Nope! I wasn’t afraid of the blue square runs; they were intermediate level. But rotate that square 45 degrees, pinch it in from the sides, and paint it black and I wanted nothing to do with it! Those were DIAMONDS and they scared me!!!
Just this morning I was eating a bag of chips (yes…breakfast of champions!). On the back of the bag was the company’s quality assurance symbol. What was it? A black diamond. Ironically, the very “shape” that scared me on the slopes was the same shape that comforted me into knowing that I was eating a high quality chip.
I think I can justify why I have always considered a diamond to be a valid shape, worthy of a definition. But now I have a higher degree of knowledge. I now know I’ve been looking at rhombi all this time. I’m kind of bummed because I really think I would have loved to use the word “rhombi” throughout my life. Those are childhood opportunities that are lost forever.
But what about our students now? Should we perpetuate this lie or should we travel on a crusade as anti-diamondites, attempting to abolish this mathematically impure practice? If we ignore the word “diamond” and replace it for the more appropriate term “rhombus” we may just be creating a generation who won’t recognize quality chips, who won’t heed the warnings of the daunting shapes of the slopes, or who won’t be able to appropriately play with a deck of 52 cards.
Maybe telling them that there aren’t diamonds is the greater lie…
Reflective Questions (You can add any thoughts in the comments section):
- Even though a diamond doesn’t have a mathematical definition, can we still consider it a shape?
- Do teachers of young children know the difference between a rhombus and a diamond?
- When and how do we handle the teaching of these two items and the accompanying confusion?