Some math workshop sessions have gone really well while others have been less than stellar, and that is also how reading and writing workshop goes from time to time. Since I've been doing workshop teaching in language arts for over 20 years, I have become accustomed to the ups and downs of this kind of approach and how to address particular issues. I've developed faith in the children's ability to work out their reading and writing problems and to come to love reading and writing if they're given time, choice, appropriate materials, and mini lessons to guide them in their learning. I am working towards that learning curve with math.
In math workshop the children design a question with math content (choice), carry out their investigation (time), and then reflect on their learning (my opportunity for teaching). The following are snippets of some of the investigations that my students were engaged in during a recent math workshop.
--K. was measuring the width of the classroom. First, she used unifix cubes and then the length of her foot as measuring tools. Since she didn't have enough unifix cubes to carry out her investigation I suggested she measure the width and then the length of the carpet and compare the two measurements; there were enough unifix cubes to carry out this investigation. Her question became: how many unifix cubes long and wide is the carpet? And, will these measurements be the same? She discovered that the length and the width of our carpet are not the same. "What does it tell you about the shape of the carpet?" I asked her, thinking that while this was a great math question it would prove too difficult for a grade two to extend her thinking in this way. "It's not a square," she said. "What shape is the carpet, then?" I asked. "It's a rectangle," she responded. "How do you know?" I countered. "All sides are not equal," she said.
--M. was working on a structure using centimeter cubes. This was the second math workshop that he had been working on this question. He was trying to break his previous record by making this week's structure taller. M. knew that each cube equalled one centimeter even though we had never labeled them as such. He built a structure that was 4x4x8 but only considered the length and the width and not the depth of his structure. He was not thinking in terms of three dimensions even though he had a tangible object in front of him. When asked how many cubes he used this time, he answered that he used 80 centimeter cubes for his structure. Yet, when we counted the cubes there were 128. We counted by making groups of tens and then adding on the extra cubes. "How can we account for this discrepancy?" I asked him. Although he couldn't tell me and since our math workshop time was over for that day, this became the subject of a focus lesson on a subsequent day. Although the thinking involved in trying to figure out why M. miscalculated the number of cubes used was too advanced for many of the children in the class it was an opportunity for the children to experience puzzling ideas in math and to consider designing their own investigation to try to figure out what happened.
--R. explained that to add 30 + 26 she first added 30 + 20 (not 3 + 2), which equals 50. Then she added 0 + 6 = 6. Finally, she added 50 + 6 = 56. She is starting to understand the concept of adding two-digit numbers and how to put these numbers together so that they make sense. By not using the algorithm for addition, R. was forced to think about place value and the relationships between and among numbers.