Browsing by Subject "Math education"
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Item Internationally benchmarked : comparing the common core state standards to the Singapore mathematics framework(2013-05) Garner, Brette Ashley; Marshall, Jill AnnThe Common Core State Standards for mathematics and English language arts were released in June of 2010 and have been adopted by a majority of U.S. states. The authors of these standards have claimed that they are internationally benchmarked -- that is, that they are as rigorous, focused, and coherent as the standards and expectations used in high-performing countries -- but have not provided evidence to back up these claims. Singapore, whose students have scored at the top of recent international assessments, is frequently touted as a leader in mathematics education. To test the claims of international benchmarking for the Common Core, this paper uses the methodology of the Surveys of Enacted Curriculum to compare the Common Core State Standards for Mathematics to the Singapore Mathematics Framework in terms of rigor, focus, and coherence. The Common Core State Standards and the Singapore Mathematics Framework do call for similar levels of conceptual understanding, mathematical reasoning, and problem-solving. However, the content expectations outlined by the Common Core are somewhat more rigorous than those outlined by the Singapore Mathematics Framework.Item Math identities information : Latin@ students tell their math stories(2015-05) Adams, Melissa; Empson, Susan B.Bilingual fourth graders’ math stories were collected to explore their math identities. Students expressed identities of powerfulness and powerlessness and identified the key resources they need in order to feel like successful mathematicians. These resources included collaboration, manipulatives, their native language, and the support of family. Implications and suggestions for educators are discussed.Item Municipality characteristics and math achievement : a multilevel analysis of Mexican secondary schools(2011-05) Hubert Lopez, Celia; Potter, Joseph E.; Marteleto, Leticia J.This study examines the impact of the municipality level characteristics on the average Math achievement of students in third year of lower secondary schools in Mexico. Using data from different Mexican and international sources and multi-level regression models the present work shows that municipality characteristics provide additional explanation of the unexplained variability in educational achievement controlling for school-level factors and even without accounting for student characteristics. Although school factors are highly correlated with municipality’s characteristics, the present study finds that unobservable characteristics of the municipality are playing an important role in Mexican students’ achievement which goes beyond the possible impact that school factors have on achievement.Item 'Playing the game' of story problems : situated cognition in algebra problem solving(2010-12) Walkington, Candace Ann; Petrosino, Anthony J. (Anthony Joseph), 1961-; Carmona-Dominguez, Guadalupe; Marshall, Jill; Walker, Mary; Greeno, JimThe importance of mathematics instruction including "real life" contexts relevant to students’ lives and experiences is widely acknowledged (Common Core State Standards Initiative, 2010; National Council of Teachers of Mathematics, 2000; 2006; 2009), however questions about why contextualized mathematics is beneficial and how different types of contextualization impact problem solving have yet to be fully addressed by research. Common justifications for contextualized mathematics include the idea that relevant contexts may help students to apply what they learn in school to out-of-school situations, and that relevant contexts may scaffold learning by providing a bridge between what students understand and the content they are trying to learn. The present study investigates these justifications, as well as students' beliefs and problem-solving methods, using story problems on linear functions. A situated cognition theoretical framework (Greeno, 2006) is used to interpret student behavior in the complex, social system of "school mathematics." In a series of interviews, students from a low-performing urban school were presented with algebra problems. Some problems were personalized to the ways in which they described using mathematics in their everyday lives, while others were normal story problems, story problems with equations, or abstract symbolic equations. Results showed that students rarely explicitly used situational knowledge when solving story problems, had consistent issues with verbal interpretation of stories, and engaged in non-coordinative reasoning where they bypassed the intermediate step of understanding the given situation before trying to solve the problem. After completing most of Algebra I, students still had considerable difficulty with symbolic representations, and struggled to coordinate formal and informal mathematical reasoning. Problems with the same mathematical structure with different amounts of verbal and symbolic support elicited different strategies from students, with personalized problems having high response rates and high use of informal strategies. This suggests that students can use sophisticated, situation-based reasoning on contextualized problems, and that different problem framings may scaffold learning. However, results also demonstrated that the culture of schooling, and story problems as an artifact of this culture, undermines many of the justifications for contextualizing mathematics, and that students need more authentic ways to develop their mathematical reasoning.