Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four mathematics classrooms. The Elementary School Journal, 102(1), 59-80.
With NCTM’s and research on reform’s emphasis on the importance of concept-based teaching, the authors sought to better understand how a teacher’s “press for learning” may effect student’s conceptual thinking experiences (p. 60). The authors’ describe “high-press exchanges” as those in which students were pushed to provide more than simply procedural descriptions, but rather were expected to provide both explanations and justification using mathematical vocabulary, evaluation of others’ strategies and work collaboratively with other students to come to consensus, (p. 64). The authors’ describe “low-press exchanges,” as those in which teachers did expect conversations about mathematics, but they focused more on procedures, celebrating correct solutions, while paying little attention to incorrect or inefficient ones, and while students may have been asked to work in partners or groups, true collaboration was not expected (p.68). The authors stress that teachers that foster an environment with “high-press exchanges” helps use conceptual mathematics as the backbone for student interactions.
Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22(3), 215-243. doi:10.1007/s10648-010-9125-8 The authors performed extensive meta-analysis in order to determine if mathematics learning is greater when computer technology (CT ) is implemented, in which situations is the effects of CT moderated, and what are the “optimal conditions” for mathematics learning with CT (p.220). Through this review and analysis of literature on the subject, the authors found that context is especially important when implementing CT for mathematics education. For example, when a CT intervention is used in a constructivist classroom versus a behaviorist classroom, the constructivist class was, “significantly and consistently higher” than the behaviorist classroom (p. 220). The authors found that in general, students learning mathematics with CT had higher achievement than those that learned mathematics without CT. However, it is not simply the use of CT that increases achievement, but the way it is used. It was found to be more effective with elementary school students and students with special needs. Also, the duration of the intervention, played a role; shorter interventions (6 months or less) were more effective than longer term intervention.
Smith, M.S., Bill, V., & Hughes, E.K. (2008). Thinking through a lesson: A key for successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14(3), 132-138.
This article describes and supports the use of TTLP (Thinking Through a Lesson Plan). This lesson planning protocol requires teachers to articulate a mathematical goal, anticipate student responses (see Inoue, 2009), and create a plan for discussion that allows for assessment of student thinking. This protocol is designed to allow cognitively difficult mathematics challenges to take place in the classroom while mitigating concerns over a teachers lack of control over the many pathways to possible solution
In this study, an intervention to preservice teachers that focused on building greater conceptual understanding and using this conceptual understanding to frame their pedagogy yielded teachers that had a better understanding of themselves as mathematical learners. By experiencing a community of learners in which teachers had the opportunity to be mathematical learners, teachers strengthened their self-confidence about mathematics. However, the translation of participating in a community of learners as a teacher to creating a community of learners within the classroom proved to be a greater challenge, with many of these preservice/novice teachers reverting to the more traditonal methodology that they see in their school site. The authors contend that it is necessary to examine how teachers can reap the benefit of their own experiences within community of learners to then establish these types of communities within their classroom.