My cat Mia is a snugglin' and lovin' cat. She loves to play and won't let me sit down without her sitting on my lap. I loved thinking about what she sees. She spends her time watching out the windows, napping behind the couch, or sitting on my lap. According to some of the sites I visited, domestic cats see mostly shades of blue or green, so my photos have been retouched to reflect that.
Dice (or number cubes) are used in our classrooms to explore numbers. We use them for games, for examining patterns of random numbers, and more. A die (traditionally) is a cube with circular "pips" on each side representing a number. The pattern on dice is the same so people learn to associate the pattern with the number. Each value on a die is equally likely to appear (as shown by our repeated activity called Dice Roll and Tally.) So we practice counting, equally likely outcomes, and many other "number sense" concepts with these tools. Another exploration we use regards the patterns of totals that two dice can represent. It is interesting to hear their theories of the "shape" of this chart before and after we begin!
Here is a little ditty that we use to remember
even and odd numbers from our Everyday Mathematics program: 0, 2, 4, 6, 8 Being even is really great! 1, 3, 5, 7, 9 Being odd is just fine! As I teach the concept of even and odd, the analogy of the odd numbers not having all pairs is a powerful one. My post with the visual patterns of odd and even highlights this idea. Here is my attempt at poetry to show that the odd numbers are lonely! I'm the odd one, the odd one out. I'm hardly ever allowed to pair up with a partner an odd one just like me I'm so looooooooooonely To the tune of "You're a Mean One, Mr.Grinch" Of all the stretching my mind is doing this semester, these two skills win the prize for challenging me the most! I am certainly someone who can appreciate the simplified abstract ideas that I deal with every day and I revel in a good analogy, but appreciating some of the deeper abstract ideas and the skills presented in artistic ways is really tough for me.
I've seen abstract images in museums, in books, and online. Some of them are simply abstract, where the creator is attempting to grasp the essence of the object or concept he or she is representing. Others use analogies, highlighting the similarities between the object or concept with a seemingly unrelated object or concept. Being able to create these works shows a deep level of understanding that comes from reflecting upon the meanings and properties of the subject. Abstractions are so simple that they can be difficult to notice. In fact, there were many abstractions in the chapter that I didn't realize were abstractions! The example in the book that spoke the most clearly to me was Picasso's bull. I actually hadn't seen that example before, but I never would have guessed he did so many drafts, gently paring away more and more each time, to arrive at the abstract idea he ended with. This is the example that hooked me and opened my mind to abstract ideas, which you'll see below is very difficult for me! I was reminded as I read of my own personal disbelief in the atom as my 6th grade teacher sat behind his desk and related the concept to us. I remember thinking he was crazy, because I could not even imagine something so tiny moving around yet being a "solid." Even now, I would not understand them as well without the analogies. I enjoy abstract ideas in math and science but am frustrated by poetic and artistic abstractions. They challenge me because I never seem to understand the point the author or artist is trying to make until someone lays it out for me. I found the literature classes during my undergraduate years to be difficult because of this. And to be perfectly honest, sometimes I disagree with the professor's interpretation entirely! (If I still had my B+ paper for Engl 272 I would post it here to prove it - I really thought I was right!) Personally, I think I can work to be more open to someone's abstract ideas. When looking at a painting that I formerly dismissed, I can look deeper and spend more time In my classroom, we use abstracting within many of our practices. My class has a twitter account, and even though twitter is blocked at school, we tweet from our smartphones and the class helps compose the tweet. We also do a lot of analogizing in K and 1st as we make connections with our reading and ourselves, other texts, and the world. I laugh as I think of the "Daily Oral Analogies" book in my cupboard that uses simple abstract pictures to teach analogies and I think I should dig that book out to see if it is teaching the kinds of relationships that my students should be exploring, too! But as the book says, meaningful analogies are tough to come up with, so as I am working to develop a more inquiry-based curriculum, I am thinking about asking my students to help connect ideas through analogy. For example, we just studied wind as part of their weather exploration. I wonder, especially after this week of windy storms, what they would come up with if I asked "what does the wind remind you of?" As with any of the creativity strategies we have explored so far, it comes down to time (for me at least). Time to think and play with ideas is critical. I have found it very hard to carve out these chunks of time for myself in my busy, harried, life. It is equally difficult to find time for my students to use this kind of creativity. I look forward to my school's implementation of the new common core standards, which I believe will allow these I work with first graders to learn the difference between odd and even numbers. Here is a typical way we will demonstrate that odd numbers have an "odd man out" and the even numbers have "all partners." But we can also examine when odd and even numbers come up when we are counting with other patterns. I haven't done this before, but I think combining the concept of counting patterns with odd and even patterns could build understanding even better! It is interesting to see that counting by 5s yields another odd/even/odd/even pattern while counting by 2s yields all even numbers. (This is an association I have previously shared as a fact, rather than allow students to explore and discover this for themselves.)
PatternsWe recognize patterns when we realize a connection between things we didn't previously associate. And to recognize these patterns, we use multi-sensory observation and conceptual analysis. (99) The world is full of them, in fact they are in a lot of places I never considered, until reading two chapters in sparks caused me to expand my definition of patterns.
I think I'm great at finding patterns. In fact, I'm so good at it that I don't even recognize that I am finding them. Jokes are patterns? Poets use patterns of syllable-foot relationships to make the poetry sound the way it does? I never realized the science behind these things I naturally recognize and appreciate! I had this revelation while reading the myriad of examples that the Root-Bernstein's include in the chapters regarding patterns. So many examples led me to think back to my summer classes in the MAET program, when Punya Mishra discussed the process of making the familiar unfamiliar, of reversing my natural inclination to recognize the patterns in the world. Now I identify them as patterns, which adds a new element of appreciation for them. As an early childhood educator, I am introducing children to some of the most basic yet complex patterns, especially regarding letters, sounds, words, numbers, and pictures. We have had some pretty teacher-directed curriculum regarding math and phonics in the last five years, in which we are revealing the patterns to students. Actually, in phonics I think the program is leading to better reading because although we teach what the patterns in words are, we still are asking students to find them and code them. In math, however, I think we have a lot of students who can tell you which numbers are odd and which are even, but not what makes them that way. We have students who can count to high numbers but can't compose and decompose numbers fluently. In fact, some of our teachers are excited about the new core curriculum standards that are coming because it will free us to explore and let students take time to find the patterns in letters and numbers. In fact, just last week, I thought about this as I was teaching my math groups and discovered that they could do some of the work, but didn't understand the patterns of the numbers enough to make it easy for them. This chapter has motivated me to include more time to talk about the patterns in the world with my students. They are great "noticers" so if I just give them time and format to notice, I think we'll discover some pretty amazing things! Assignment:
Look for hidden images within our everyday world. These can be found in wood grain patterns, water stains, brush strokes on walls, asphalt, clouds, hair swirls, or any other place you can think of finding unintentionally hidden pictures. |