2013 Conference Proceedings - University of Nevada, Las Vegas

found multiple correct solutions. This is a tribute to the depth of thinking the teachers did indeciding on the task to investigate, and in knowing the significance of the mathematics involved.2. The effort teachers made to fine tune the task paid off. The task was challenging butaccessible. While the CCSSM only focuses on knowing numbers 1 – 5, each child was able towork successfully on this task. Even those students who basically could only approach theproblem by putting tickets one at a time were able to engage meaningfully with the task.3. The teachers were able to use discourse and communication in a meaningful way. Becauseof the specific structure incorporated into the lesson, with anticipated responses and suggestionsfor handling the responses, communication options occurred they never considered before.Students who struggled to find a solution still were comfortable sharing what they made and whythey thought they made 10. Similarly, when a student had an incorrect solution, he or she couldcount and determine that it was not 10. When either of these things happened, teachers askedother students, “How can we help _____ make 10?” Interestingly, students were able to providemultiple answers to this question. This shows the benefits of effective planning for studentresponses and actions the teacher should be prepared to take.4. The task proved well suited for the English Language Learners students in the class. Theycould do the mathematics expected of them while being coached through the words needed toexplain their work. The decision the teachers made to have students record the value of eachlength of scrip used when making their collections provided a representation that helped preparethe students for the explanations they were to give. As a result of their research, teachers becamemore aware that a focus on communication in mathematics supports other parts of thecurriculum.5. Interesting discussions were forthcoming when the teachers asked, “How are these thesame, and how are they different?” While children realized they were all showing 10, thediscussion of same and different led to excellent comparisons. Some children said a 2, 3, 3, 2 anda 2, 2, 3, 3 were the same because they each used two 2s and two 3s, while others said they weredifferent because the order was different. Some saw that 1, 2, 3, 2, 2 and 2, 2, 3, 2, 1 were‘reversed’. The language used in the discussions exceeded teachers’ expectations, suggesting thatthe preliminary discussions the teachers had about these same questions filtered into their lessonsand instruction.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 107