I LOVE patterns. I love how they are evident in almost everything and anything that we look at each day. Many patterns that we see today are physical patterns, whether it's your patio stones and the way they interlock together to make a pattern, or an embroidered pattern on some fabric, or the pattern the windows in a high rise building create. Growing up as a kid, I loved being creative. At summer camp, my favourite activity was arts and crafts, because I got to create patterns of my own through friendship bracelets, mirrored images, stamps, and more. I got to create the patterns myself and explore what it meant to me.
This is where my love for patterns started, with the physical patterns, but patterns have always continued to excite me when it came to numbers as well. Number patterns are a different "breed" compared to physical patterns. Number patterns are so delicately put together and have so much depth to them. Hm, this isn't that easy to explain...let me provide you with an example.
Pascal's Hex has always been a neat pattern for myself. The way it forms itself by adding two numbers together to get the number below it (for example, in row 2: 1+1 = 2, which becomes row 3). As the rows continue, the numbers get larger and "more complex", but the pattern and the steps toward each row is exactly the same. Being primarily a primary/junior teacher myself, patterns begin fairly mundane and easy. Square, traingle, circle, square, triangle, ( circle ). Students get to draw in that the next answer is square (because obviously, the question was in 2D shapes, not words like I use). Advancing into intermediate levels of mathematics, I have noticed in the curriculum that it becomes much more than shapes and an understanding of order/repetition, but it becomes about applying the knowledge and being able to create their own patterns (more complex patterns) and being able to describe them using variables and in algebraic terms. Patterning in the older grades is about compounding the way you describe a pattern (the curriculum provides this example, take the number patterns 3,5,7,9...the general term is the algebraic expression 2n+1; evaluating this expressiong when n=12 tells you that the 12th term is 2(12)=1, which equals 25). Instead of simply saying, each number goes up by 2, they create an expression that helps them determine the 12th, 24th, etc. term without having to write out 12 or 24 numbers themselves. Oooooh how it all works and is beautiful!
Patterns are a beautiful thing, and something that students can relate to if you present it in the right way for them. It's less complicated then can sometimes be described (and I admit, I don't think I did a great job of explaining it here...SORRY!). Let the kids explore, give them an example and let them off their leashes to try it themselves and see how much success and fun they have with patterns!!
As I like to sign off with...Happy Math Teaching!
Taking a topic and then giving examples of that topic is another great use of a blog post. Even though I had never heard it referred to as Pascal's Hex, it is still a great pattern. So many different patterns are hidden in there. I like the way you asked a question. One way you could do that to have it more interactive is to put a bracket in the text with the answer in the bracket. Next make the colour of the font the same as the background. Now you won't be able to see the text unless you highlight it with your mouse (I can't show you how to do that in the comment section though).
ReplyDeleteI put in your suggestion of the "invisible text" - thanks for the suggestion - I always forget about things like that while blogging!!
DeleteI love that patterns are everywhere, too! I have obsessions with numbers (like, I do whatever I can in multiples of 2, volumes have to be at multiples of 2 or 5, etc.), so patterns make me very happy. And it's true that they're all around us! I find it trickier, though, of finding "physical patterns" to use in intermediate classes. But I guess you could always show them a pattern and have them represent it with numbers and then try to find an equation to represent that pattern. This would actually be a really fun intro activity to each class (especially in high school, where you don't want your class interrupted by late students). You can always start the class off with an "eye opener" that's more at their level. Patterns would be cool to do, too, since students could make their own and challenge each other.
ReplyDelete