Selecting a Mathematics Curriculum (Essay Sample)

Johnston, K. M. (2014). Rethinking mathematics curriculum in a K-5 rural setting: Comparing inquiry-based to traditional approaches (Doctoral dissertation, UNIVERSITY OF SOUTH DAKOTA).
Selecting a mathematics curriculum that aids students in developing a solid mathematical foundation anchored in the principles of instruction is critical in elementary schools. The purpose of this study was to determine the effectiveness of a math curriculum by examining achievement outcomes on value-added measures. The study also compared the instructional practices of inquiry-based approaches in elementary mathematics classrooms to more traditional mathematics instruction.
The population for the study consisted of 24 classrooms of students producing a total population of 467 students. Six classrooms made up the experimental (inquiry-based) group and eighteen classrooms made up the control (traditional) group. Of the 467 students, 113 (24%) received math instruction in classrooms using the Pearson's Investigations curriculum (inquiry-based, experimental group), while 354 (76%) received math instruction in classrooms using MacMillan McGraw-Hill's Math Connects curriculum (traditional, control group). The students were not randomly selected and assigned to the experimental and control groups.
This study analyzed data from both a math achievement test and a word-problem assessment and compared those using the experimental curriculum and those using the traditional curriculum. Students' responses and strategies to the math word problem assessment were scored by a team of teachers using a rubric. Students were scored on receiving the correct answer and solving the question using more than one problem-solving strategy. The students' gains in the math achievement test and word-problem assessment were compared for the experimental and control groups.
The study found that there was not a statistically significant difference in the gains in the math achievement scores between students who were instructed with the inquiry-based curriculum compared to the more traditional curriculum. However, students instructed with the inquiry-based curriculum did show statistically significant gains over the students instructed with the traditional mathematics curriculum on the math word-problem assessment (p<.05).
Stein, M. K., Kaufman, J., & Kisa, M. T. (2014). Mathematics teacher development in the context of district managed curriculum. In Mathematics Curriculum in School Education (pp. 351-376). Springer Netherlands.
The purpose of this study was to develop and test the viability of a conceptual framework for analyzing mathematics instruction and mathematics teacher development within the context of policies regarding district-wide adoption of curriculum. The framework takes three dimensions of curriculum-based instruction into account independently: use, congruence (the extent to which instruction aligns with district and curricular guidelines), and quality (the extent to which instruction maintains the cognitive demand of appropriately challenging tasks, takes account of and builds on student thinking, and situates intellectual authority in mathematical reasoning). Based on analyses of multiple observations of 36 teachers across two districts, teachers were classified into one of four implementation profiles (flounderer, mechanical, canonical, maverick) that were created by crossing the three dimensions; in addition, their trajectory through those profiles was traced over a two-year period. Results suggest teachers were more likely to use the district-adopted curricula as the source of their lessons than to align their practice with curricular and district guidelines. Teachers' demonstration of high-quality lessons was less frequent. Differences across the two districts in the percentages of teachers falling into each of the implementation profiles suggests that district actions may have shaped teachers' uptake of the curriculum. Finally, results suggest a more uneven pathway toward high-quality instruction than had been initially conjectured
Reys, B. J. (2014). Mathematics curriculum policies and practices in the US: the common core state standards initiative. In Mathematics Curriculum in School Education (pp. 35-48). Springer Netherlands.
In the U.S. three curriculum strategies are being used to improve school mathematics programs and student learning outcomes: (a) the movement to common standards; (b) advances in technology-based instructional resources; and (c) the pressure of accountability measured by end-of-year assessments. Together, these strategies are creating a "perfect storm" for significant changes in mathematics curriculum. Elements of the reform strategy are reviewed and discussed. In addition, an argument is made for systematic monitoring of the initiative in order to learn about its impact and inform future policy decisions.
Cheung, A. C., & Slavin, R. E. (2013). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88-113.
The present review examines research on the effects of educational technology applications on mathematics achievement in K-12 classrooms. Unlike previous reviews, this review applies consistent inclusion standards to focus on studies that met high methodological standards. In addition, methodological and substantive features of the studies are investigated to examine the relationship between educational technology applications and study features. A total of 74 qualified studies were included in our final analysis with a total sample size of 56,886 K-12 students: 45 elementary studies (N = 31,555) and 29 secondary studies (N = 25,331). Consistent with the more recent reviews, the findings suggest that educational technology applications generally produced a positive, though modest, effect (ES = +0.15) in comparison to traditional methods. However, the effects may vary by educational technology type. Among the three types of educational technology applications, supplemental CAI had the largest effect with an effect size of +0.18. The other two interventions, computer-management learning and comprehensive programs, had a much smaller effect size, +0.08 and +0.07, respectively. Differential impacts by various study and methodological features are also discussed.
Wu, H. H. (2014). Potential impact of the common core mathematics standards on the American curriculum. In Mathematics Curriculum in School Education(pp. 119-142). Springer Netherlands.
In June of 2010, the Common Core State Standards in Mathematics (CCSSM) were introduced in the U.S. Long before the advent of the CCSSM, American schools had a de facto national mathematics curriculum, namely, the curriculum dictated by school mathematics textbooks. While there are some formal differences among these books, the underlying mathematics is quite similar throughout. The resulting curriculum distorts mathematics in the sense that it often withholds precise definitions and logical reasoning, fails to point out interconnections between major topics such as whole numbers and fractions, and employs ambiguous language that ultimately leads to widespread non-learning. The CCSSM make a conscientious attempt to address many of these problems and, in the process, raise the demand on teachers' content knowledge for a successful implementation of these standards. This article examines, strictly from an American perspective, some of the mathematical issues (primarily in grades 4–12) that arise during the transition from thede facto curriculum to the curriculum envisioned by the CCSSM. Although the CCSSM would seem to be strictly an American concern, these mathematical issues transcend national boundaries because there are very few deviations in the K-12 curriculum across nations (for the K-8 curriculum, see p. 3-31 to p. 3-33 of National Mathematics Advisory Panel 2008).
Brodie, K., Shalem, Y., Sapire, I., & Manson, L. (2013). Conversations with the mathematics curriculum: Testing and teacher development.
This paper addresses the question: how do mathematics teachers make meaning from curriculum statements in relation to their teaching practices. We report on a teacher development activity in which teachers mapped test items from an international test against the national curriculum statement in mathematics. About 50 mathematics teachers across Grades 3-9 worked in small groups with a graduate student or staff member as a group leader. Drawing on focus group interviews with the teachers and the group leaders we show that the activity focused the teachers on the relationships between the intended curriculum and their teaching, i.e. the enacted curriculum, in four areas: content coverage; cognitive challenge; developing meaning for the assessment standards; and sequence and progression. We argue that the activity illuminates ways in which international tests can provide a medium for teacher growth rather than teacher denigration and alienation.
Stein, M. K., Kaufman, J., & Kisa, M. T. (2014). ...