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Lynch, Kathleen

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Lynch

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Lynch, Kathleen

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Author's Publications: search.filters.isAuthorOfPublication.41ef9c33-3b0b-4569-97b6-52dfadae6732

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Now showing 1 - 8 of 8
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    Learning from Comparison in Algebra
    (2014-04-28) Star, Jon; Pollack, Courtney Morgan; Durkin, Kelley; Rittle-Johnson, Bethany; Lynch, Kathleen; Newton, Kristie; Gogolen, Claire
    Mastery of algebra is an important yet difficult milestone for students, suggesting the need for more effective teaching strategies in the algebra classroom. Learning by comparing worked-out examples of algebra problems may be one such strategy. Comparison is a powerful learning tool from cognitive science that has shown promising results in prior small-scale studies in mathematics classrooms. This study reports on a yearlong randomized controlled trial testing the effect of an Algebra I supplemental comparison curriculum on students’ mathematical knowledge. 141 Algebra I teachers were randomly assigned to either implement the comparison curriculum as a supplement to their regular curriculum or to be a ‘business as usual’ control. Use of the supplemental curriculum was much less frequent than requested for many teachers, and there was no main effect of condition on student achievement. However, greater use of the supplemental curriculum was associated with greater procedural student knowledge. These findings suggest a role for comparison in the algebra classroom but also the challenges of supporting teacher integration of new materials into the curriculum.
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    Exploring Teachers’ Implementation of Comparison in Algebra I
    (2014) Lynch, Kathleen; Star, Jon
    Discussions where teachers engage students in the comparison of multiple solution strategies to a single problem have been recommended in curriculum policy documents, yet integrating these discussions into teachers' normative routines is not widespread. In this paper, we begin to explore variations in teachers' implementation of Algebra I curriculum materials specifically focused on comparison. We explore (via case studies) implementation of the curriculum materials by two teachers with similar teaching backgrounds. The case studies suggest that these two teachers’ implementation of the comparison materials differed markedly, raising questions about possible factors which may have contributed to implementation differences.
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    Teachers' views about multiple strategies in middle and high school mathematics: Perceived advantages, disadvantages, and reported instructional practices
    (Taylor & Francis, 2013-08-30) Lynch, Kathleen; Star, Jon
    Despite extensive scholarship about the importance of teaching mathematics with multiple strategies in the elementary grades, there has been relatively little discussion of this practice in the middle and high school levels or in the context of introductory algebra. This paper begins our exploration of this practice by addressing the following questions: (1) What do middle and high school Algebra I teachers describe as the advantages of instruction that includes a focus on multiple strategies?; and (2) What disadvantages to this practice do these teachers describe?. Our analysis, based on the data from interviews (N=13) and surveys (N=79) conducted with experienced middle and secondary mathematics teachers, indicates that middle and secondary math teachers’ reported views surrounding multiple strategies appear to differ in important ways from those typically associated with teaching with multiple strategies in the elementary grades.
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    Views of struggling students on instruction incorporating multiple strategies in Algebra I: An exploratory study
    (2013-08-30) Lynch, Kathleen; Star, Jon
    Although policy documents promote teaching students multiple strategies for solving mathematics problems, some practitioners and researchers argue that struggling learners will be confused and overwhelmed by this instructional practice. In the current exploratory study, we explore how six struggling students viewed the practice of learning multiple strategies at the end of a yearlong algebra course that emphasized this practice. Interviews with these students indicated that they preferred instruction with multiple strategies to their regular instruction, often noting that it reduced their confusion. We discuss directions for future research that emerged from this work.
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    Understanding the development of flexibility in struggling algebra students
    (2011) Newton, Kristie; Star, Jon; Lynch, Kathleen
    The ability to flexibly solve problems is considered an important outcome for school mathematics and is the focus of this paper. The paper describes the impact of a three-week summer course for students who struggle with algebra. During the course, students regularly compared and contrasted worked examples of algebra problems in order to promote flexible use of solution strategies. Assessments were designed to capture both knowledge and use of multiple strategies. The students were interviewed in order to understand their rationales for choosing particular strategies, as well as their attitudes toward instruction that emphasized multiple strategies. Findings suggest that students gained both knowledge of and appreciation for multiple strategies, but they did not always use alternate strategies. Familiarity, understandability, efficiency, and form of the problem were all considerations for strategy choice. Practical and theoretical implications are discussed.
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    The Role of Prior Knowledge in the Development of Strategy Flexibility: The Case of Computational Estimation
    (2009) Star, Jon; Rittle-Johnson, Bethany; Lynch, Kathleen; Perova, Natasha
    The ability to estimate is a fundamental real-world skill; it allows students to check the reasonableness of answers found through other means, and it can help students develop a better understanding of place value, mathematical operations, and general number sense. Flexibility in the use of strategies is particularly critical in computational estimation. The ability to perform complex calculations mentally is cognitively challenging for many students; thus it is important to have a broad repertoire of estimation strategies and to select the most appropriate strategy for a given problem. In this paper, we consider the role of students' prior knowledge of estimation strategies in the effectiveness of interventions designed to promote strategy flexibility across two recent studies. In the first, 65 fifth graders began the study as fluent users of one strategy for computing mental estimates to multi-digit multiplication problems such as 17 x 41. In the second, 157 fifth and sixth graders began the study with moderate to low prior knowledge of strategies for computing mental estimates. Results indicated that students' fluency with estimation strategies had an impact on which strategies they adopted. Students who exhibited high fluency at pretest were more likely to increase use of estimation strategies that led to more accurate estimates, while students with less fluency adopted strategies that were easiest to implement. Our results suggest that both the ease and accuracy of strategies as well as students’ fluency with strategies are all important factors in the development of strategy flexibility.
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    Learning Lessons From Instruction: Descriptive Results From an Observational Study of Urban Elementary Classrooms
    (Teachers College Record, 2018) Hill, Heather; Litke, Erica; Lynch, Kathleen
    Background: For nearly three decades, policy makers and researchers in the United States have promoted more intellectually rigorous standards for mathematics teaching and learning. Yet, to date, we have limited descriptive evidence on the extent to which reform-oriented instruction has been enacted at scale. 
Purpose: The purpose of the study is to examine the prevalence of reform-aligned mathematics instructional practices in five U.S. school districts. We also seek to describe the range of instruction students experience by presenting case studies of teachers at high, medium, and low levels of reform alignment. Participants: We draw on 1,735 video-recorded lessons from 329 elementary teachers in these five U.S. urban districts.
 Research Design: We present descriptive analyses of lesson scores on a mathematics-focused classroom observation instrument. We also draw on interviews with district personnel, rater-written lesson summaries, and lesson video to develop case studies of instructional practice. Findings: We find that teachers in our sample do use reform-aligned instructional practices, but they do so within the confines of traditional lesson formats. We also find that the implementation of these instructional practices varies in quality. Furthermore, the prevalence and strength of these practices corresponds to the coherence of district efforts at instructional reform. Conclusions: Our findings suggest that, unlike other studies in which reform-oriented instruction rarely occurred, reform practices do appear to some degree in study classrooms. In addition, our analyses suggest that implementation of these reform practices corresponds to the strength and coherence of district efforts to change instruction.