Reflections on Teaching with a Standards-Based Curriculum: A Conversation Among Mathematics Educators

Abstract

Many teachers and researchers have written about the challenges inherent in adopting new teaching practices in mathematics classrooms (e.g., Chazan, 2000; Clarke, 1997; Heaton, 2000). The authors of this article, all with secondary mathematics teaching experience, are convinced by research suggesting that Standards-based mathematics curricula are beneficial for student learning.1 However, the first three authors had not used such curriculum materials in their own classrooms, and we desired experience using a Standards-based mathematics curriculum with secondary students. To this end, we taught a week-long summer course with a focus on linear functions to high school students who had previously struggled with algebra and volunteered to participate.The aim of our course was to improve students' understanding of linear functions through the use of an inquiry-based learning environment and a Standards-based curriculum. This was not a typical classroom setting since there were three instructors for less than 20 students. Nonetheless, it was useful for both teachers and students to experience participating in an inquiry-based curriculum for the first time. The purpose of this article is to stimulate thinking and conversation among teachers by sharing our own conversations about learning to teach mathematics using a Standards-based curriculum.The curriculum selected for the course was the second edition of the Connected Mathematics Project {CMP) (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2006),specifically Investigations 1 and 2 of Moving Straight Ahead which focused on linear relationships. The CMP curriculum (similar to other Standards-based curricula) uses a Launch-Explore-Summary model of instruction. During the Launch, the teacher poses a mathematical task or provides information that is intended to provide a hook to get students interested in the investigation, while making connections to their prior knowledge and experiences. During the Explore, students collaborate in small groups on a mathematical task that requires them to construct important mathematical ideas. The teacher's role during the Explore is to monitor groups' mathematical conversations and begin to plan a sequence of presentations for the Summary. Finally, the Summary provides an opportunity for students to present their work to the class and discuss the emerging mathematical ideas with one another. During the Summary, the teacher serves as a facilitator to synthesize students' ideas and draw out the key mathematical concepts and/or procedures from students' work.Upon completion of the course, the instructors agreed that Standards-based teaching requires a great deal of on-the-spot intellectual work. The pay-off, however, which we learned through teaching the course, was that students seemed to be able to make sense of the mathematics rather than following prescribed procedures. For example, in addition to calculating the slope, the students could often understand what the slope represented in each of the application problems (e.g., walking rate). Seeing students' pride - and sometimes surprise - when they realized that they were able to write an equation to model a situation or solve a challenging question without the explicit direction of a teacher, was priceless. The week ended leaving us with much to think about (e.g., how to manage mathematical discourse). Teaching using an inquiry-based model with a Launch-Explore-Summary structure highlighted many dilemmas that we were able to experience firsthand. We composed reflections based on our experiences into a series of questions. We subsequently sent them to Lisa, the fourth author, who responded to our questions using her many years of experience teaching with Standards-based curricula. Our questions fell into three overlapping categories: (1) questions about mathematical discourse, (2) questions about facilitating the Summary, and (3) questions about general pedagogy. We have posed our questions (Q) in regular font, with the answers (A) in italicized font. …