Helping Teachers Promote Problem Solving with Young At-Risk Children

to any formal instruction in mathematics (Carpenter & Throughout the past decade, recommendations in Fennema, 1988; Carpenter et al., 1996; Fennema, mathematics education have called for students to pose Franke, Carpenter, & Carey, 1993). The assumption is and solve problems instead of merely memorizing rules that students who really understand an idea can use it in and procedures (National Council of Teachers of Mathenumerous ways, remember it longer, and can use that matics [NCTM], 1989, 2000). Particularly in the eleknowledge to learn more mathematics (Fennema et al., mentary grades students are being asked to engage in 1993). In this way, students have a larger stake in what more complex mathematics tasks and to have a more they learn. This tenet framed our understanding and active role in their learning process. Consequently, served as the basis for developing strategies to work young children are doing mathematical problem-solving with the teachers of primary students labeled at-risk. tasks that at one time were considered quite difficult for Historically, students labeled at-risk enter school them. Additionally, instruction is aimed at helping stuwith deficits in learning. Because of their social or ecodents develop mathematical power. Such power includes nomic circumstances, they are deemed to be academi“the ability to explore, conjecture, and reason logically; cally behind their counterparts. As a result of these disto solve nonroutine problems; to communicate about and advantages, students continue to perform at a lower through mathematics; and to connect ideas within mathacademic rate than their counterparts in mathematics. ematics and between mathematics and other intellectual Although minorities (African Americans and Hispanics) activity” (NCTM, 1991, p. 1). To this end, teachers are have made great strides regarding mathematics achieveencouraged to teach mathematics in ways that may difment, national assessments reveal that they are still perfer drastically from their own experiences (NCTM, forming at levels substantially below their peers (Reese, 1991). Because recommended teaching approaches repMiller, Mazzeo, & Dossey, 1997). resent a significant departure from traditional modes of To make progress toward improving the mathematmathematics instruction, teachers need assistance to see ical achievement of at-risk students, it becomes very imthem actualized in classrooms. portant to intervene at a very early age. Challenging Several studies have influenced the current thinking these students and providing them with experiences of about what primary-age students can and should be ensuccess early on go a long way to encourage further couraged to do (Carpenter, Ansell, Franke, Fennema, & growth and development and lay a foundation for future Weisbeck 1993; Carpenter, Fennema, & Franke, 1996; mathematical learning. Therefore, opportunities to enCobb et al., 1991; Fuson, 1997; Willis & Fuson, 1988). courage problem solving cannot await later years. For example, in the primary grades, the Cognitively This article reports on the impact of a professional Guided Instruction (CGI) research has shown that studevelopment project conducted with K–2 teachers at a