Maria Droujkova, from Natural Math, read and commented on my recently published article about the development and use of Jump Patterns in the classroom. Here are some excerpts from an interesting exchange we had today on the Natural Math forum based on her questions after reading the article:
Maria: Great article, Malke - thanks for sharing! I loved the photos, and especially the cool graphic organizers and visuals you use. Do kids like to use the charts? Does it depend on the person?
Malke: What plays out again and again in this program is that teachers are really surprised when they see how enthusiastic their students are when it comes to writing about their experiences in Math in Your Feet. Recording their patterns using the one best word to describe each category of each beat *is* challenging, but they are motivated toward accuracy because it is *their* pattern. Also, it usually plays out that within each team of two, one person is more comfortable in the 2D realm of the page than the other, and one is more comfortable moving than the other -- it's a team effort, which makes it more comfortable for everyone. Once the kids do the tough work to record their pattern using the descriptive words, it's actually quite easy for them to plot their feet on the simple grid. I still think there is a better, maybe more mathematically accurate way to do this, I just don't know what it is yet!
There are, however, whole groups of kids who still just need the physical portion of the program (more and more, sadly). These are kids who never had a chance to develop spatial reasoning in preschool, for instance. They don't have enough math, even in 4th or 5th grade, to use the program to take them further -- I find that they begin to understand the math concepts as if it's the *first* time they've ever seen or heard about them. In these cases, I require just the minimum in their workbooks, and I purposefully stay in the physical realm. It may be the only time they will ever have to just 'play' with math.
Maria: Mathematics is "embodied" in that its grounding, basic metaphors come from bodily experiences and observations. You can't skip over that and go into formal math. Even working with adults, I find that you need to go through folding, building, mirroring, measuring and other physical activities and/or stories if math does not make sense to them.
Malke: This is great to hear, and I believe it wholeheartedly based on what I see kids do in my program and in my personal math (re)learning...I just gave a very well attended 90 minute hands-on presentation at the NCTM [National Council of Teachers of Mathematics] annual meeting and it was surprising how many of these adults were really quite challenged. It has nothing to do with being 'good' at dancing and everything to do with not having enough experience working with and within a physical realm. I attended a session on the van Hiele Levels [for developing geometric thought] and realized that this probably applies to adults as well -- experience is key to understanding.
What is interesting to me is that my 'hunch' eight years ago, that there might be math in what I did as a percussive dancer, is now more true than I initially imagined. At that point in my life I believed, as most of us probably do, that math is primarily symbolic. I realize now that the math I bring to children in the form of rhythm and dance is some of the experiential math they may not have ever had, and that they need this kind of experience to move forward. I've heard that only 10% of us will understand the symbolic realm of mathematics without needing to first have, as Maria says, "...bodily experiences and observations". Just this fact alone makes DOING hands-on, experiential math that much more of an imperative.
Here's the link to our full conversation on the Natural Math forum.
Maria: Great article, Malke - thanks for sharing! I loved the photos, and especially the cool graphic organizers and visuals you use. Do kids like to use the charts? Does it depend on the person?
Malke: What plays out again and again in this program is that teachers are really surprised when they see how enthusiastic their students are when it comes to writing about their experiences in Math in Your Feet. Recording their patterns using the one best word to describe each category of each beat *is* challenging, but they are motivated toward accuracy because it is *their* pattern. Also, it usually plays out that within each team of two, one person is more comfortable in the 2D realm of the page than the other, and one is more comfortable moving than the other -- it's a team effort, which makes it more comfortable for everyone. Once the kids do the tough work to record their pattern using the descriptive words, it's actually quite easy for them to plot their feet on the simple grid. I still think there is a better, maybe more mathematically accurate way to do this, I just don't know what it is yet!
There are, however, whole groups of kids who still just need the physical portion of the program (more and more, sadly). These are kids who never had a chance to develop spatial reasoning in preschool, for instance. They don't have enough math, even in 4th or 5th grade, to use the program to take them further -- I find that they begin to understand the math concepts as if it's the *first* time they've ever seen or heard about them. In these cases, I require just the minimum in their workbooks, and I purposefully stay in the physical realm. It may be the only time they will ever have to just 'play' with math.
Maria: Mathematics is "embodied" in that its grounding, basic metaphors come from bodily experiences and observations. You can't skip over that and go into formal math. Even working with adults, I find that you need to go through folding, building, mirroring, measuring and other physical activities and/or stories if math does not make sense to them.
Malke: This is great to hear, and I believe it wholeheartedly based on what I see kids do in my program and in my personal math (re)learning...I just gave a very well attended 90 minute hands-on presentation at the NCTM [National Council of Teachers of Mathematics] annual meeting and it was surprising how many of these adults were really quite challenged. It has nothing to do with being 'good' at dancing and everything to do with not having enough experience working with and within a physical realm. I attended a session on the van Hiele Levels [for developing geometric thought] and realized that this probably applies to adults as well -- experience is key to understanding.
What is interesting to me is that my 'hunch' eight years ago, that there might be math in what I did as a percussive dancer, is now more true than I initially imagined. At that point in my life I believed, as most of us probably do, that math is primarily symbolic. I realize now that the math I bring to children in the form of rhythm and dance is some of the experiential math they may not have ever had, and that they need this kind of experience to move forward. I've heard that only 10% of us will understand the symbolic realm of mathematics without needing to first have, as Maria says, "...bodily experiences and observations". Just this fact alone makes DOING hands-on, experiential math that much more of an imperative.
Here's the link to our full conversation on the Natural Math forum.
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