Gestures, Language, and Student Understanding

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!

AGIS - Day 2; plus, my presentation!

Day 2 of the AGIS conference was great! In the morning, I went to a lovely elementary math presentation done by Beth Winkler from Bonn International School. She is the math subject leader at her school and they do some wonderful investigative things with their kids. She was able to show us various subtraction algorithms, for example, that the kids developed together with the teacher, and to talk about how they structure always two content strands (ie. Numbers and Data/Stats) to run in parallel during any given week. Numbers strand (ie. numeracy and numerical operations) is taught and practiced more or less in isolation (facts are reinforced with games), and the second math strand (such as Data/Statistics) is incorporated into their current PYP themed unit. For example, for the PYP unit "Body Systems," they had kids measure a bunch of their body parts and to do statistical analysis on the results. They also let kids' own curiosities direct them in the direction of mathematical inquiry. Recently, they realized through one such inquiry that the girls' shoes and boys' shoes in the class have the same mean size (length), but the girls' shoes have a smaller range in size than the boys. So, the boys' claim (which was the reason for this mathematical investigation) that "Girls in our class have smaller feet!" isn't really true! How terribly cute and engaging. They also have set periods of math, to ensure that the same amount of math is covered in every grade / class, which can sometimes be a challenge for PYP schools where everything is taught in themes.

Moreover, just the way this lady talked about math was wonderful. She really wanted to focus on helping kids not to be afraid of math, and she understands how to apply concrete-to-abstract continuum in math education, not just within each lesson, but over the years. She made me really wish that our school could have such a subject specialist at the elementary level. It's something I have asked for on behalf of our department, but I don't know if there is such room in our budget to hire such a specialist. Maybe. We will have to see as the 2013-2014 budget slowly takes its shape.

Then came my own presentation! I was very nervous, to be honest. But, the presentation was very well-received by my very small audience (only about 10 people, which is a shame because there were more math people who had wanted to be there, but the session was "maxed out" on paper and so they hadn't signed up...). Everyone came up to me afterwards and said that they thought it was very interesting, even the elementary teachers and one of my own departmental colleagues. They said that they thought there were definitely ideas that they took away that they think they can adapt for their classrooms, which was wonderful because it was my first out-of-school presentation!

Here is the presentation link: http://bit.ly/AGIS2013projs It's meant to be viewed in Slideshow mode, so that you can navigate all the embedded links to slides that make this a presentation that can adjust to audience's interests in real-time. But, in the notes section of the presentation I wrote more verbose descriptions about each slide. During the presentation, I opened one external document (the directions of the 3-D project), to discuss it in details in order to let the teachers see exactly how it would be structured in my class.

Then, after my own presentation I went to a fabulous one on elementary Fun and Games. The teacher is a New Zealander, and she demonstrated various games from New Zealand Math(s) that I thought were very simple in format and easy to adapt to younger or older age groups. She wanted us in the end to brainstorm possible modifications, and I recommended that even skip-counting games like BizBuz can be modified to have students pick algebraic expressions out of a bag, show it to the class, and then say either Biz or Buz depending on whether they are divisible by either of the two expressions specified by the teacher at the start of the game. I am excited to try this game with my Grade 7s when they get to basic algebraic factorization later this year! Another game that I think is very adaptable to the MS classroom is a variation of the spelling game that she administers. Start with kids standing in a circle; one kid says a shape name, such as "Square." Then, the next ____ kids will need to state all the identifying properties of that shape. "Has 4 sides." "Opposite sides are congruent." "All angles are right angles." "All sides are congruent." "Diagonals are congruent." "Diagonals are perpendicular." When all properties have been stated, the last kid says, "Sparkles!" and does sparkly jazz hands (I'll have to see how this works out with my MSers; maybe the sparkles part is too much for them). And the next kid in the circle will get to name a different shape, and this starts over. If the "Sparkles" are prematurely called because there are properties that have been missed, then the kid who called the sparkles would sits down. If a kid says a property incorrectly, then they also sit down. Round-and-round we go to review properties of polygons....

Finally, I went to a talk on tips for school leadership, led by Paul Morris, who is an elementary principal in Stuttgart. Even though the general presentation format was not my favorite, it had some gems of advice. Specifically, these were the things that stood out to me:

• Spend more time with the people who disagree with you / dislike you than the people who like you / support you.

• If you are pushing a new initiative, you need to get a core group of supporters and then just MOVE. It's not possible to wait until everyone gets on board.
  
• Education fads come and go almost faster than shoe fashion. Get your teachers to help you decide which new trend is a fad, and which is not. Choose carefully.
  
• Consider carefully the flow of info from meeting to meeting. Design your meeting schedules in a way that pays respect to this need
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• Give parents credit for advocating for their child, even if they may appear misguided to you.
  
• Admit when you've made a mistake. This models for your teachers how to interact with children and each other.
  
• Understand that it is very difficult sometimes for international families to adjust to a new situation, and they take it out on the school because that is one thing that they feel they could have control over. Be patient.
  
• Consult as many people as possible before making a decision. But, don't be afraid to make the decision.
  
• If someone sends you a one-on-one email, do not write them back. Go find them in person to discuss it. Make opportunities to make face-to-face contact with your colleagues.
  
• Remember why you are here. Have compassion. Teachers and students are equally important.
  
  
• Work from different places. When you get out of your normal working place (ie. office), even if it's just taking your laptop and sitting somewhere else, you gain new perspectives.

OK - last day! And then, off to enjoy my Sunday evening. whew. 

TI-84Plus COLOR vs. TI-Nspire; Flexible Grouping

I saw a nifty little presentation today by a TI rep, showing off their latest gadget called TI-84PlusC. To me, it looks like a cross between the TI-83/84 series and the TI-Nspire in terms of functionality. It can import a photo behind the graph for modeling purposes, and it has colored lines and table values. It also allows you to turn on the grid inside the graph, in order to make it easier to estimate points. (These are all features on the TI-Nspire, but this calculator has the same familiar input buttons as the classic TI-83/84s.) The only drawback seems to be that it cannot work with ViewScreen, the piece of hardware that projects the student's calculator work to the wall. It has to do with TI not having enough customer demand for ViewScreen to make it worth it for them to make something that is compatible with the TI-84PlusC. Anyhow, the SmartView still works, and on the new SmartView software for TI-84PlusC, you can tab between the colored calculator view and the plain black-and-white calculator view, in order to support the kids who have different calculators in your class.

The new calculator costs a bit more (maybe 20 Euros more) than the old TI-84Plus, but is comparable in price to the TI-Nspires. I think this might be a viable option for us to order in bulk for our department, instead of TI-Nspires, because from my limited toying around, the TI-Nspires seem to generally require more keystrokes to perform the same function, which -- if true -- would put our kids at a slight disadvantage on timed external assessments like the IB. Anyhow, I am glad that there is an alternative to the TI-Nspire that is a compromise between the "old" and the "new" versions of TI calculators. They're due to be released I believe in March, and in April there will be special teachers' discounts available to bundle the teacher's software (SmartView) free with the calculator order. You can also get a free software upgrade if you already have SmartView currently installed on your computer for the plain TI-84.

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Besides that, I also heard today about a very interesting setup at Munich International School, which has to do with a fluid leveling/grouping program that they implement in the mathematics department. There they have common teaching/planning blocks in the middle school, and they agree in advance of every math unit, what the time frame of that unit will look like and what is the common assessment they will do at the end of the unit. Then, they give all the kids a pre-test and then split them up into ability groups, FOR THAT UNIT ONLY based on their pre-test scores. The kids in the lowest group are supported by an extra teacher. (There are 4 teachers for 3 ability groups, so the 4th teacher is sort of a floater who ends up helping out with the weakest group to allow more intensive attention to be given to those kids. I think this 4th teacher is also a more senior teacher who helps to facilitate with curriculum development.) In the years that they have tried this at their elementary and middle school levels, they have really experienced a lot of success for both the top and bottom kids. The last year (and they project also this year), they were able to extract 2 honors/extended classes going into high school, instead of one. They're essentially taking the best parts of streaming (allowing weaker kids to shine, allowing stronger kids to move along) and taking away the stigma that is associated with being "stuck" in an ability group. They also don't do grouping all the time, and the kids start to be advocates of their own learning, sometimes requesting to move down for a certain topic, in order to focus more on the basic skills. There are only 3 blocks a week when the students meet in these ability groups, and for the other periods they still meet in their homerooms, so they understand that the grouping does not define their identity but merely serves a very specific purpose.

It really sounds fabulous. I think there might be some challenges with implementing it at our school, but we're still excited about bringing it back as a radical idea to discuss. I wanted to pass it along in case some of you might be interested in implementing this at your schools....

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So far, the AGIS conference is going great! If only I wasn't having the allergy attack of my life, it'd be perfect.

A Presentation with Optional Paths

I have been piecewise putting together a presentation I will be doing in the early spring at a conference called AGIS (for German international schools). I'm pretty nervous since it'll be the first time that I will be doing a presentation at a conference! My only previous presentation experiences were when I did a PD to my own department back in El Salvador, on utilizing web resources, and when I quickly presented something at PCMI 2011 for what I did with GeoGebra and unit circles.  Both of those were quite informal, I think, compared to speaking at a conference... So, I've given myself plenty of head start to think carefully about the content and presentation format for the talk in the spring. As a presentation newbie, I am nervous about not knowing who my audience will be. As a teacher who tends to lecture minimally in the classroom, I am also concerned about audience engagement as a whole when I speak to them one-sidedly for a stretch of time.

This presentation that I am preparing will be on math projects as a tool for self-differentiation. One thing I decided to do for this presentation is to not assume that all teachers are very experienced with projects, OR that they're completely inexperienced. So, my presentation will start by laying the foundation for why I think math projects are beneficial for students, just to establish a common ground with everyone. And then we go into pivot points, where I'll poll the audience quickly to find out which topics they would like me to spend the most amount of time speaking about. I was inspired by the idea that within powerpoint you can have hyperlinks to other parts of the powerpoint (eg. those Jeopardy-format powerpoints), so depending on their interest, we can click through only certain math projects to discuss them in more details and to spend some more time discussing general project structures, or to click through all of the projects and discuss actual content rather than format and framework of projects.

Here is the powerpoint I've pulled together so far. Please check it out -- using actual slideshow mode -- and give me feedback! Once you see the rounded boxes, you need to click inside the boxes in order to navigate forwards and backwards... (I used the boxes in order to avoid having ugly underlined hyperlinks everywhere.) Not all of the projects are mine, and I haven't filled all the slides in with pictures yet, but I am excited about the overall idea of a presentation that self-adjusts in real-time to the responses and vibes from the audience.

Addendum: I have revised my powerpoint to make it less verbose... Now I think it's 90 or 95% finished! Check it out and keep those suggestions coming! Thanks!!