I'm out sick with stomach stuff again, today. Quite irritating. Illnesses can really put a damper on the energy and enthusiasm for an experience like this. I was sick a lot when I taught elementary school. It wasn't very pleasant then, either.
For my math planning, I was given a math workbook, in Spanish, that mirrors the Guatemalan curriculum. I am supposed to cover what is in the book, but have some freedom with how I approach it. This is quite fortunate because this book is like most math workbooks: they demonstrate one way of solving a problem (algorithm), then provide a list of number problems, and expect the students to solve them in that manner.
The section of the workbook that I am supposed to cover is currently on factores and divisores. From looking at their math work on Monday, I was able to assess that many of the student had algorithmic knowledge of math, but perhaps do not have a solid foundation in the concepts behind these algorithms. I philosophically believe that its crucial for students to have conceptual understanding of math before they can truly be proficient in it.
On Wednesday, I was able to teach a conceptual lesson on the factors of the numbers between 1-20. My goal was for them to visually see and explore the rich relationships between factors and divisores. The lesson is really simple. All of the students have small, blank, centimeter grid-lined math journals. I had them use the grids to draw representations of the factors of each number. For example, the number "6" can include 1x6, 6x1, 2x3, or 3x2. The picture above shows how one of my students represented "6" (you can also see 8 and 9 to the right).
For my first class, this lesson went really well. They were up to the challenge. After I introduced the concept, I constantly floated around the room as they showed me their work. They like to either show me their progress or ask me if they're doing it right. I usually either say, "Excellent! Keep going!" (but in, Spanish, of course) or direct them to something they might be missing.
I found myself giving these kids a lot more clues than I would normally do to kids in the States (certainly more than I do my college students). In fact, I have a reputation amongst the elementary education majors in my college of never giving the answer. I believe that it's important for students to learn how to problem solve on their own and to develop these skills in such a way that they become confident on how their brain works. In the real world, we are confronted with many "problems." Should I buy this car? Why or why not? What is the interest rate? How much do I need to make to support it? In these instances, you don't normally have a math teacher nearby to ask, "Teacher, is this right?"
So, my dispersal of clues and hints in math instruction is much higher down here. I currently attribute this to 2 reasons: 1) My Spanish is intermediate and I do not have the command of the language to provide nuanced responses to students who may be struggling with a concept, 2) I am still learning about their culture and experiences and how I can best teach them. They seem to be very used to a teacher-centered model of classroom instruction (i.e. the teacher is all-knowing). I don't advocate for this model, but I must accept that it is what the students know and that in my three weeks here, I cannot undo years of teaching practices that run counter to my inclination. Since these kids are used to teachers supplying clues or answers, I feel it is my job to stretch them where they are. I feel I would overwhelm them if I expected the same amount of independent exploration as I would my students back home.
I took about 40 minutes of video of this lesson and have been looking at it. I mainly wanted to provide an indication of what it looks like and sounds like in the classroom. I took more than 1,000 pictures last time, but I'm even more excited about the possibility of video.
The video below is of me giving feedback, and a bit of coaching, to a student. I am giving feedback on a students representation of the products of 16. As you can see, she successfully found 16x1, 1x16, and 4x4. For those of you that need some translation, I basically said, "Very good, I see you have 16x1, 1x16, and 4x4. Are there more?" (Hay mas?).
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