2013 Conference Proceedings - University of Nevada, Las Vegas

While thinking about this problem, the teachers engaged in problem solving that expandedtheir own mathematical knowledge. Even though the CCSSM kindergarten standards state thatstudents “fluently add and subtract within 5” (CCSSI, 2010, p.11), the teachers felt that it wouldbe more robust to explore 10. During their discussion, the question ‘How many ways can wemake 10?’ was raised and as a group they engaged in figuring this out. Although severalremembered studying ‘something like this’, no one readily knew the solution, but all wanted toknow. With some guidance, they explored the patterns found with addition by exploring ‘Howmany ways can 1 be made?’ (One way: 1), ‘How many ways can 2 be made?’ (Two ways: 1+1,2), ‘How many ways can 3 be made?’ (Four ways: 1+1+1, 1+2, 2+1, 3), etc., and were pleasedwith their problem solving abilities to arrive at a solution. They also realized that the largenumber of possible ways might make the problem more accessible for their students.Phase 3 - Developing and planning a research lessonPhase 3 was designed so teachers would prepare lessons, research how the lessons workedwith children, and reflect on the experience. Teachers engaged in the typical Lesson Studyprocess involving (1) defining an instructional problem, (2) researching the problem andbrainstorming possible lessons that could speak to the issues, (3) anticipating possible studentmisconceptions that might occur, and (4) then, planning the lesson. While step (2) is oftenviewed as the most crucial, all steps should occur before the lesson is taught. This was importantbecause the research and deep thinking the teachers did before the teaching gave them ownershipof a lesson they planned and prepared to teach. In planning the research lesson, teachers used theresearch evidence they collected to prepare the lesson. When preparing the lesson they used aformat with three columns (Figure 1). In the first column they listed the planned sequence ofevents that would occur as the lesson unfolded, including key questions to ask and the rationalefor asking them. In the second column, they listed reactions and responses they anticipatedstudents would make. These responses were based on evidence they found in research as well asfrom their prior teaching experiences. Column 3 had suggestions for how the teacher couldrespond to the anticipated responses. The third column was also used to record student responsesand to think about how to use these responses when conducting whole class discussion.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 103