The relationship between enactment of reform math (namely Common Core State Standards – Mathematics [CCSSM]), student misconceptions, and teacher variables was investigated. After providing professional development on enactment for the Standards of Mathematical Practice (SMP) of the CCSSM, observations were conducted to determine the degree of enactment of SMP in 22 classrooms of nine teachers in an urban charter school network consisting of three high schools. Students were all boys, 98% African American, and predominantly of low socio-economic status. Data included curricular documents, observation notes, quarterly assessments, and a teacher survey. Results indicated experienced teachers with high efficacy who expected students to reason and discuss their work were related to higher levels of SMP enactment and fewer misconceptions. Implications for teacher education and teacher practice are discussed.
TopIntroduction
Based on the Third International Mathematics and Science Study (TIMSS) of 1995 (now called Trends in International Mathematics and Science Study) findings that examined what is taught in 37 countries, Schmidt et al. (2002) characterized mathematics content as seen in standards and textbooks in the United States as unfocused, highly repetitive, undemanding, and incoherent, compared to the curricula of higher-performing countries. In response, the Common Core State Standards - Mathematics (CCSSM) were created as narrower, yet deeper in focus than previous standards. The CCSSM were released in 2010, and include the Standards for Mathematical Practice (SMP), which have eight standards that teachers are expected to develop in their students in order to build deeper understanding rather than a reliance on procedures. These are: SMP1: Make sense of problems and persevere in solving them, SMP2: Reason abstractly and quantitatively, SMP3: Construct viable arguments and critique the reasoning of others, SMP4: Model with mathematics, SMP5: Use appropriate tools strategically, SMP6: Attend to precision, SMP7: Look for and make use of structure, and SMP8: Look for and express regularity in repeated reasoning (National Governors Association Center for Best Practices, & Council of Chief State School Officers, 2010).
The narrower, deeper focus of the CCSSM content standards and the research-based SMP provide a response to student errors and misunderstandings created by what has been described as a national mathematics curriculum that is varied in content yet shallow in conceptual understanding. Specific causes of student errors have been found to be within the curriculum (Monaghan, 2000; Schmidt et al., 2002), and teaching methods that stress procedural knowledge over conceptual understanding of the material (Hiebert & Grouws, 2007; Kieran, 2007).
This study responds to the need to examine the relationship between classroom enactment of CCSSM (i.e., reform) and student achievement (Heck et al., 2011). Teachers received professional development (PD) on enacting CCSSM, specifically the SMP. Then, the current study examined enacted curricular documents, teaching practice, a teacher survey, and quarterly assessments to determine the correlation among enactment of SMP, alleviation of student errors, and teacher variables. Specifically, the following questions were asked: