"If you could have secondary teachers understand one thing about elementary school math learning, what would that be?" - David Sabol (@Dave_Sabol) As an elementary school teacher and instructional coach, I am so appreciative of this question. And especially that so many teachers from #TMC18 are asking about what we do in elementary school mathematics. I think these conversations are essential in helping us all learn together and provide a more cohesive experience for all of our students. Using and connecting representations is a huge part of our work in elementary school - along with providing many opportunities for conversation to make sense of mathematical ideas. In conversations with teachers, I often refer to the image below from Lesh and his colleagues to show how these representations are connected in making sense of mathematical ideas. Through these multiple representations, students deepen their understanding of the mathematical content. In Ohio, our standards are written so that students move from concrete to iconic/pictorial to abstract/symbolic representations. Some of these ideas build across years - which gives learners the time and space to develop these ideas in a deeper and more connected way. They have the opportunity to build, then draw, and then use symbolic notation to represent their mathematical ideas. Throughout this process, there would be many conversations and writing about their ideas as they connect these different representations. (Let me be clear - this is something we are still working on and I am not claiming that we have it all figured out at the elementary school level! We are improving at making these connections and deepening our conversations about mathematical content.) In the photos below, you can see 1st grade students using blocks, pictures, equations, and apps such as Number Line to represent their ideas about Graham Fletcher's Bright Idea 3-Act Task. Students worked in groups to refine their ideas and then shared during a whole class conversation. In the next example below, 3rd grade students worked in groups to write a story about creating bouquets of flowers. The groups were then asked to draw a picture and write an equation that would match the story. During the class conversation, students were looking to see whether the story, equation, and picture were a match. This video provided a chance to see students working to make sense of what these different representations mean and how they might be connected to the mathematics and context of the problem. In the following example, 5th grade students debate whether the answer to a problem is 4/5 or 4/7. I was fascinated by how what students knew about addition and multiplication of fractions interfered with their ability to make sense of this problem: In a bag, 3/5 of the marbles are blue and the rest are red. If the number of red marbles is doubled and the number of blue marbles stays the same, what fraction of the marbles will be red? I thought this would be a quick warm-up exercise - instead it turned into a debate that lasted 30 minutes and continued to the next day. (Which made for fantastic discussion!) I see these classroom conversations as essential to empowering students to think mathematically. Robert Berry describes this eloquently in his post Positioning Students as Mathematically Competent. What types of conversations are happening in secondary mathematics classrooms? How does what we do in elementary school influence what comes later? What can we do as elementary school teachers to build stronger coherence for our students? I would love for there to be further conversation between elementary and secondary mathematics teachers. We have so much to learn from one another!
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AuthorSharing what I'm learning from others. Collaborative experiences and communication are essential in building a shared understanding of mathematics! Archives
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