When this class began, and high level thinking and open-ended math tasks were introduced and highly encouraged, I had mixed feelings about how I would be able to implement this into my placement. I thought it sounded like a great and ideal way of teaching mathematics, but I also wondered if it was really applicable with Kindergarteners. Some students in my placement are still working on counting using 1-1 correspondence. This made me wonder whether or not they would be able to engage in high level math tasks. While it is easier to provide students who have already mastered basic math skills (such as counting) with high level tasks, it can be done for all students. For example, I worked with one particular student who was working on counting. She put one bear in a line each time she said a number as she counted from 1-8. After discussing how each time she put one down and said a number there were that many bears in the line. This showed the student that numbers actually represent a certain value, and you can count these values.
I still think that students need these foundational skills before asking them to complete a high level task from the CGI book; however, I have realized there are high level and meaningful ways for students to master these basic math skills. I feel I have grown a lot so far in becoming more comfortable and confident in teaching meaningful mathematics. I don't think I will feel fully confident in this until I have taught it to a number of different students, over many years.
Remember that your lessons and everyday teaching need not be "super-high-level-task-teaching" with super-advanced activities. Rather, what I think is most important is the disposition of analyzing student work, anticipating student thinking, and asking students meaningful questions that lead them towards mathematical thinking. This can be applied every day, no matter what the lesson or context. So even as you are exposing students to the "basics" and the "fundamentals" remember that what's most important is helping them to engage in the mathematical thinking, asking good questions to help them connect ideas, and creating tasks that give them the opportunity to actually think and solve problems mathematically.
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