I went to a fabulous AGIS session this morning on sign language in the elementary classroom. It was led by Armin Martin and Johnnie Wilson from the Munich International School. They showed videos of kids who use their hands to touch different parts of their heads (front, back, left, right, top, bottom), in order to figure out how many "faces" a cube has. The kids are able to link the mathematical word "face" to layman's definition of "face", in order to bridge the gap between the concepts.
A very interesting point that was made during this presentation was that signs can be used as an intermediary between normal language and academic language, or between home language and school-instruction language. Intentional incorporation of appropriate signs can be a strategy that works not just with our ESL / EAL population but even with our normal kids, and it ties nicely into math because when you gesture in space, you are quickly illustrating and bringing in extra dimensions that are hard to do/experience on paper. The presenters presented research that said that even when you later take away the gestures, the kids still retain the primitive, physical understanding that they had achieved through gesturing. So fascinating, because this discussion/session got me thinking about a lot of different things that previously I had thought to be disconnected:
1. Recently my 7th-graders have been working on percent word problems such as "64 is 40% of what number?" Sure, some kids can easily navigate the proportional reasoning --> 10% of that number must be 16, so 100% of that number must be 160. But, for many kids they need a different strategy, and so we have been practicing setting this up as a proportion. Even then, for kids to read a problem like this and then to consistently set it up correctly, is not trivial. They need to be able to:
a.) Parse the verbal description.
b.) Correctly associate the value given (in this case, 64) with either the fractional percent (in this case, 40%) or the whole (100%).
c.) Set up proportion accordingly.
d.) Solve algebraically.
Of this, part B is the most difficult for 7th-graders. I found this year that when I went around to conference with kids about this process and to help them get started on the assignment, I can just point at the value within the problem (64), and then gesture to them using distance between my hands to ask, "Is this the part or the whole?" This has helped them tremendously, because they can associate the rather multi-stepped numerical operations to a simple visualization, and then they only need to focus on part A (re-reading the question to themselves) in order to make that determination and to carry out the rest of the steps by themselves. This simple gesturing was able to shrink my conference time with each kid to under 1 minute; they immediately would say, "Oh, I get it now," and then proceed with the other questions which were not always phrased in the same way or giving the same information. ("42 is what percent of 70?" "What is 20% of 95?" etc.)
2. When I taught 8th-grade back in New York, I taught one particular 8th-grader who was very economical with his words. I would always put explanation questions on the test, and he was so concise with his explanations that he could always write down the correct answer in about half of the word that I would need to use. This is an incredible skill, because in order to do this, the kid needed to:
a.) Know/master the concept and relevant vocabulary.
b.) Prioritize information in his head.
c.) Formulate his understanding in as few words as possible using the prioritized list.
3. I have read somewhere that babies can already understand physical rules in the world. If you play an optical illusion on them that is against their normal experience, they will keep staring at the place where the ball disappeared after dropping. At this stage, their understanding is far beyond their ability to verbalize it. So, I think it is definitely true that we understand a lot more than our words are able to describe, especially at a young age or as a language-learner.
So, in short, I think gestures are a fabulous way to help kids understand concepts when their language is not yet developed enough to explain or describe a concept (old or new) fully. But, this intentional incorporation of gestures should lead in mathematics to a formalization of those concepts, and attachment of specific language. Because in doing so, we are teaching the value of specificity and prioritization, which are very important skills for the older students to have/develop in the long run.
Hope this little reflection was helpful to you in jogging your brain about how to bridge abstract concepts quickly to visual/kinesthetic understanding for kids. Please share with me if you have had similar success in other examples of utilizing intentional gestures to build intuitive understanding!
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