Person:
Star, Jon

Profile Picture

Email Address

AA Acceptance Date

Birth Date

Research Projects

Organizational Units

Job Title

Last Name

Star

First Name

Jon

Name

Star, Jon

Filters

2007 - 200982010 - 201417

Settings

Author's Publications: search.filters.isAuthorOfPublication.f67f589b-c42d-44d9-8755-e11679b8ef92

Search Results

Now showing 1 - 10 of 25
  • Thumbnail Image
    Publication
    Model breaking points conceptualized
    (Springer Verlag, 2014) Vig, Rozy Brar; Murray, Eileen; Star, Jon
    Current curriculum initiatives (e.g. National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) advocate that models be used in the mathematics classroom. However, despite their apparent promise, there comes a point when models break, a point in the mathematical problem space where the model cannot, or arguable should not, be used. In this work, we explore the breaking point of the chip model for integer subtraction and the area model for fraction addition. Breaking is inevitable – either because no one model is robust enough to be applicable in a very large problem space and/or because the modifications required to keep the model functioning weaken or even eliminate its benefits. While models are often intended to serve as visual illustrations or embodiments of a concept, adaptions at the model breaking point can turn model use into nothing more than executing the graphical analogue to a not-well-understood procedure. The act of identifying model breaking points illuminates the affordances and constraints of the model. This provides students a unique opportunity to discriminate across mathematical models to develop a meta-level understanding of the relationship between models and the mathematics those models are intended to support.
  • Thumbnail Image
    Publication
    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.
  • Thumbnail Image
    Publication
    Evaluating Technology-Based Strategies for Enhancing Motivation in Mathematics
    (2014-10-01) Star, Jon; Chen, Jason A.; Taylor, Megan W.; Durkin, Kelley; Dede, Christopher; Chao, Theodore
    Background, context, and purpose of study: During the middle school years, students frequently show significant declines in motivation toward school in general and mathematics in particular. One way in which researchers have sought to spark students’ interests and build their sense of competence in mathematics and in STEM more generally is through the use of technology. Yet evidence regarding the motivational effectiveness of this approach is mixed. Here we evaluate the impact of three brief technology-based activities on students’ short-term motivation in math. 16,789 5th to 8th grade students and their teachers in one large school district were randomly assigned to three different technology-based activities, each representing a different framework for motivation and engagement and all designed around an exemplary lesson related to algebraic reasoning. We investigated the relationship between specific technology-based activities that embody various motivational constructs and students’ engagement in mathematics and perceived competence in pursuing STEM careers.
  • Thumbnail Image
    Publication
    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.
  • Thumbnail Image
    Publication
    Procedural and Conceptual Knowledge: Exploring the Gap Between Knowledge Type and Knowledge Quality
    (2013) Star, Jon; Stylianides, Gabriel J.
    Following Star (2005, 2007) we continue to problematize the entangling of type and quality in the use of conceptual knowledge and procedural knowledge. Although those whose work is guided by types of knowledge and those whose work is guided by qualities of knowledge seem to be referring to the same phenomena, actually they are not. This lack of mutual understanding of both the nature of the questions being asked and the results being generated causes difficulties for the continued exploration of questions of interest in mathematics teaching and learning, such as issues of teachers’ knowledge.
  • Thumbnail Image
    Publication
    Using Strategic Interruptions to Effectively Integrate Whole Class and Small Group Instruction in Mathematics
    (2013) Star, Jon; Kokka, Kari
    In this paper we explore a new way to think about the use of group work in mathematics instruction through what we refer to as strategic interruptions. Strategic interruptions involve frequent and often rapid transitions between whole class and small group instruction. Through analyses of video of Algebra I teaching, we identify patterns in the frequency, timing, rationale, and instructional practices related to the use of and switching between whole class and small group instructional formats. We postulate that use of strategic interruptions has the potential to be a powerful and easily implementable form of group work that may be especially appropriate in secondary classrooms.
  • Thumbnail Image
    Publication
    Improving Students' Proportional Thinking Using Schema-Based Instruction
    (2011) Jitendra, Asha K.; Star, Jon; Rodriguez, Michael; Lindell, Mary; Someki, Fumio
    This study investigated the effectiveness of an instructional program (schema-based instruction, SBI) designed to teach 7th graders how to comprehend and solve proportion problems involving ratios/rates, scale drawings, and percents. The SBI program emphasized the underlying mathematical structure of problems via schematic diagrams, focused on a 4-step procedure to support and monitor problem solving, and addressed the flexible use of alternative solution strategies based on the problem situation. Blocking by teacher at three middle schools, the authors randomly assigned the 21 classrooms to one of two conditions: SBI and control. Classroom teachers provided the instruction. Results of multilevel modeling used to test for treatment effects after accounting for pretests and other characteristics (gender, ethnicity) revealed the direct effects of SBI on mathematical problem solving at posttest. However, the improved problem solving skills were not maintained a month later when SBI was no longer in effect nor did the skills transfer to solving problems in new domain-level content.
  • Thumbnail Image
    Publication
    Improving Seventh Grade Students' Learning of Ratio and Proportion: The Role of Schema-Based Instruction
    (2009) Jitendra, Asha K.; Star, Jon; Starosta, Kristin; Leh, Jayne M.; Sood, Sheetal; Caskie, Grace; Hughes, Cheyenne L.; Mack, Toshi R.
    The present study evaluated the effectiveness of an instructional intervention (schema-based instruction, SBI) that was designed to meet the diverse needs of middle school students by addressing the research literatures from both special education and mathematics education. Specifically, SBI emphasizes the role of the mathematical structure of problems and also provides students with a heuristic to aid and self-monitor problem solving. Further, SBI addresses well-articulated problem solving strategies and supports flexible use of the strategies based on the problem situation. One hundred forty eight seventh-grade students and their teachers participated in a 10-day intervention on learning to solve ratio and proportion word problems, with classrooms randomly assigned to SBI or a control condition. Results suggested that students in SBI treatment classes outperformed students in control classes on a problem solving measure, both at posttest and on a delayed posttest administered 4 months later. However, the two groups' performance was comparable on a state standardized mathematics achievement test.
  • Thumbnail Image
    Publication
    An exploratory study contrasting high- and low-ability students' word problem solving: The role of schema-based instruction.
    (2012) Jitendra, Asha K.; Star, Jon
    This study evaluated whether schema-based instruction (SBI), a promising method for teaching students to represent and solve mathematical word problems, impacted the learning of percent word problems. Of particular interest was the extent that SBI improved high- and low-achieving students' learning and to a lesser degree on the indirect effect of SBI on transfer to novel problems, as compared to a business as usual control condition. Seventy 7th grade students in four classrooms (one high- and one low-achieving class in both the SBI and control conditions) participated in the study. Results indicate a significant treatment by achievement level interaction, such that SBI had a greater impact on high-achieving students' problem solving scores. However, findings did not support transfer effects of SBI for high-achieving students. Implications for improving the problem-solving performance of low achievers are discussed.
  • Thumbnail Image
    Publication
    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.