Week 4 "Patterns don't go anywhere?" (February 6 - 12)


This week's topic is PATTERNS. It was one of more popular themes the syllabus the participants created

We can all think of some wonderful elementary tasks about making patterns. But there is a big argument among teachers, math curriculum developers and researchers about the value of these tasks. Sure, opponents say, patterns are fun and kids play with them gladly and notice some vaguely mathematical properties. But these activities "don't go anywhere" in terms of developing formal, abstract mathematics.

For example, my math club kids explored consistency and change with growth pattern activities, as shown in this photo:

But they really struggled to translate this into formal math of any sort. They consistently added five counters per leaf, for example, but weren't even aware, initially, of the number 5 (let alone the skip-counting by fives), just focusing on the visual design. I think this struggle led to valuable insights, but some people think it's a waste of time and effort.

THE TASK

Do you think pattern activities are worth the time spent on them, or too slow and too far removed from what mathematics is all about? If you think patterns are worth it, how can you help kids to abstract math out of them? I would love your thoughts, examples, blog finds and wild ideas for this ongoing argument!

Video intermission (a relevant tangent):

http://www.youtube.com/watch?v=zDZFcDGpL4U

Task Discussion


  • Keisha   13 februari 2012 02:48

    I don't think math patterns are a waist of time for children to learn math. I think it's great way to introduce math to younger kids. Here are a couple activities and webites I found:

    http://www.kindergarten-lessons.com/kindergarten-pattern-activities.html .....This website gives you tons of activities for children that will teach kids pattern block vocabulary.

    http://www.learner.org/teacherslab/math/patterns/ ....Here's another website that talks about the different patterns in math: Logic, Number, and Word.

    http://en.wikipedia.org/wiki/Pattern ...Here's the wikipedia for patterns.

    After doing some research this got me thinking about the worksheets I did in elementary school that were about patterns. I  never knew it had anything to do with math until I got older. I just thought is was cool to color in. None of my teachers took the time to explain the shapes and the pattern that they were in. Here's what I'm talking about.... http://geometrip.com/ We used to get these a lot in class during free time or to take home and do for fun. There were only a few times we did them in class as a large group.

    I think a great way to teach children math patterns are to use what's around us. I have these pj's that have a polka dot pattern on them. A lot of clothes nowadays have many different patterns on them, especially kids clothes! We can use their outfits to teach them number patterns and shape patterns. I'm going to try this on my little cousins and see how it works.

  • Julia Brodsky   11 februari 2012 17:33

     

    Richard Feyman describes (1999: 174-175) his first mathematical experiences at the hand of his father:

    …when I still ate in a high chair, my father would play a game with me after dinner. He had bought a whole lot of odd rectangular bathroom floor tiles from someplace in Long Island City. We set them up on end one next to the other, and I was allowed to push the end one and watch the whole thing go down. So far so good.  

    Next the game improved. The tiles were different colors. I must put one white, two blues, one white, two blues and another white and then two blues… You recognize already the usual insidious cleverness; first delight him in play, and then slowly inject material of educational value!   Well, my mother, who is a much more feeling woman, began to realize the insidiousness of his efforts and said, “Mel, please let the poor child put a blue tile if he wants to.” My father said, “No, I want him to pay attention to patterns. It is the only thing I can do that is mathematics at this earliest level.” If I were giving a talk on “what is mathematics?” I would have already answered you. Mathematics is looking for patterns.    

    Feynman, Richard P. (1999) The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman. Perseus, Cambridge, MA.

  • Kathy Cianciola   11 februari 2012 18:16
    Reageer op:   Julia Brodsky   11 februari 2012 17:33

    Julia,

    This is interesting. It seems like floor tiles wouldn't be the safest thing for a young child to play with, but sometimes parents are desperate to find activities to occupy their children. I like the part where he says, "You recognize already the usual insidious cleverness...First delight him in play and then slowly inject material of educationlal value."  This is a perfect explanation of  what I refer to as "back-door learning."  I think that Dads can sometimes be a bit pushy when it comes to teaching their children, but they mean well.  

  • Carolyn Lesser   11 februari 2012 17:26

     

    I believe that patterns are very important to learn and definitely worth the time and effort. Patterns are part of our daily lives. Learning how to decipher them at a young will help us later in life to figure out more complex patterns. Patterns are evident in children as young as toddlers.  This website, http://www.learner.org/teacherslab/math/patterns/more.html, listed how prevalent patterns are at all ages and how they progress as we get older. Here some of the patterns they listed:

    ·         The toddler separates red blocks from blue blocks. The separation is a pattern: the reds go here, the blues go there.

    ·         The kindergartner learns to count: the numbers are a pattern.

    ·         A first grader makes a pattern with stamps or stickers: tree, turtle, tree, turtle.

    ·         The fourth grader notices that multiples of five end in five or zero—another pattern.

    ·         Sixth graders make tessellations: patterns that cover a plane.

    ·         High school students learn that mathematics from algebra to calculus is all about function, which is the pattern of how one number changes into another.

    ·         The college chemistry major studies how symmetry in a molecule—a pattern in space—affects its infrared spectrum.

    ·         The stock trader looks for trends—patterns—in the stock market.

    ·         Designers of all kinds create beautiful and functional patterns, ranging from the pattern in fabric to the way rooms are arranged in a house to the order of images in a TV commercial.

    ·         And the physician does her best to decide who is well and who is ill, and recognize the patterns of health.

    To learn how patterns work, we really have to start simple and work our way to more complex ideas. Without learning the simple patterns we may never reach the ability to see patterns in a job that we have later in life. 

  • Amanda Graf   11 februari 2012 16:12

    I think that patterns can be very effective in math, and goes along great with our previous theme of integrating art and math. Diagrams like this one:

    Uses art and patterns to display triangles; it's combing three different concepts (art, patterns, shapes) into one theory.

    Patterns are also important to learn from an early age because patterns are relevant all through one's educational career. Once a student is older, they use patterns in various ways, such as with multiplication. "2, 4, 6, 8" is a pattern of counting by 2's and also explains multiplying by 2. So, learning in Kindergarten that "red" comes next in a "red, blue, red, blue" pattern, progresses into a very useful skill later in your education.

    Patterns also apply to one's daily life, in a non-mathematical way. Having a set routine, (or a "pattern"!) is a very beneficial way to organize one's day. A child usually operates better when they know what to expect. So in school, if they know the schedule is journal time, circle time, snack time, recess, art, lunch, circle, reading, snack, seat work, and that's a daily routine, or pattern, the day will flow more smoothly because kids, like adults, like to know what to expect.

    Patterns are also a great segway into learning semetry. For example, if you have a circle, circle, square pattern, and a student knows that next comes a circle, circle, square, you can then invert the second half to segway into semetry. Obviously the student would have to have patterns down really well or the semetry vs. patterns will confuse them, but it's a good follow-up to patterns!

  • Kathy Cianciola   8 februari 2012 12:12

    Departing slightly from the theme of patterns as discussed in the context of visual patterns, I wanted to bring up teaching patterns involving movement, sound and music.  There are some great children's audio music CDs and music videos out there to accompany movement. Moving in rhythm to music is a great concept to assist in learning.  You could incorporate clapping, drumming etc. with any of these music Cds.  It could be a great diversion for the children after sitting for hours in the classroom, yet they will be hearing and learning along with the music.  Repetitive movements plus repetitive lyrics help the students solidify ideas embedded in the songs. It's kind of a sneaky way of teaching. I think they call it "Back Door Learning."

    Numbers in the Teens They start With a One

    http://www.youtube.com/watch?v=S5eaBjKI8xQ

    The Number March

    http://www.songsforteaching.com/happalmer/numbermarch.htm

    Handful of fingers

    http://www.songsforteaching.com/intellitunes/s/handfuloffingers.mp3

  • SandyG   7 februari 2012 20:14

    I do see the benefit in teaching patterns.  If for no other reason, I think teaching patterns can help students become more aware of their environment.  For some children with special needs, schedules and routines are very important.  It is the regularities in their environment that help them move throughout their day.  First, though, they must be able to spot these patterns or consistencies.  "Organization, order and patterns. We all crave the familiarity that they provide in everything we do. The music we listen to, the movies we watch and the books we read all contain recognizable features and conventions. An ostensibly chaotic world when examined more closely shows patterns and logic in nature and is an indication that the tendency to seek out routine is hard-wired into us at birth" http://www.education.com/magazine/article/preschool-math-patterns/.
     

    Working on patterns does translate into the real world.  In teaching patterns in math, I think students can sharpen their ability to predict, and it strengthens asumptive, high-level thinking. Here is a short article about teaching pre-school pattern lessons: http://www.education.com/magazine/article/preschool-math-patterns/

  • Laura Haeberle   7 februari 2012 18:28

    I believe that patterns are very much worth the effort, and I'm surprised that many teachers would disagree. To me, patterns are one of the core foundations of mathematics. They were such a part of my childhood, and a fantastic way to reinforce critical math concepts. For example, I can't imagine learning multiplication without the handy multiplication chart.

    The chart is, in essence, a series of patterns. Having a basic understanding of patterns is key to making sense of how math works. And it's difficult to try creating any sort of graph without knowing number patterns. Patterns give way to the general understanding of how to treat numbers, and why certain actions will cause specific reactions everytime.

    Moreover, patterns are everywhere around us. Patterns are the backbone of architecture, decorations, even clocks rely on the consistency of the numbers. Moreover, I believe that children who work with numbers early on will begin to feel some control over the numbers; they know what's supposed to happen everytime. That control will lead to confidence in math skills, an important part of any childhood. I think that teachers could create lessons based on patterns easily. For example, a pattern activity that involves counting out a specific number of items reinforces the numbers, and gives children an understanding of the size of numbers. Children can begin to see what certain operations do to numbers, recognizing more complex patterns as they grow older. I think that patterns should be a very important part of an elementary classroom, simply because patterns are a crucial element in mathematics.

  • SandyG   7 februari 2012 20:00
    Reageer op:   Laura Haeberle   7 februari 2012 18:28

    I agree, Laura.  I'm surprised that any teacher would be disagreeable to teaching patterns.  I never considered the multiplication chart a form of pattern teaching, but of course it is.  Thanks for helping me make that connection!

  • Denise   8 februari 2012 10:31
    Reageer op:   Laura Haeberle   7 februari 2012 18:28

    Here's a really nice multiplication table pattern:

    http://thegriddle.net/handouts/mult_color.pdf

    Other options available here.

  • Kathy Cianciola   8 februari 2012 10:47
    Reageer op:   Denise   8 februari 2012 10:31

    Very pretty, and functional at the same time.

  • Carolyn   9 februari 2012 18:01
    Reageer op:   Laura Haeberle   7 februari 2012 18:28

    My mind goes all over the place when I think of patterns, but it never went to muliplication charts. Multiplication charts are most definietly patterns and in the mnay classrooms that I have been in, most have the chart taped to all the desks. I was recently in a 3rd grade classroom and again every desk had a multipliction chart and a number line. Now that I think about it a number line could probably also be considered a pattern, each number has the same spacing-3.5 is equally between 3 and 4 just as 4.5 is between 4 and 5. Just the fact that this classroom had these "patterns" on each desk I think speaks to how relevant patterns are, no matter the form.