Papers by Jonathan Brendefur
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Changing teacher practices to improve student learning is a challenge. For teachers' practices to... more Changing teacher practices to improve student learning is a challenge. For teachers' practices to change, faculties within schools must build communities of practice. However, supporting teachers' collaborative learning within a Professional Learning Team can be an elusive challenge. We found through the Instructional Learning Team (ILT) model of professional development that teachers have a focused model to make effective changes to their practice. ILTs promote school improvement by providing a process through which teachers collaboratively focus on sustained reflection about student learning tasks, instruction, and student work using the Japanese Lesson Study and critiquing their work using Newmann's (1996) Intellectual Quality framework. We followed two teams of teachers over a semester and qualitatively examined changes in four elements of professional learning: shared ideas and values, focus on student learning, reflective dialogue, and deprivatization of practice. Through the ILT process all four elements of professional learning communities increased. This process of changing practice through examining instructional tasks, practices and student work has a direct impact on helping teachers move toward implementing the Common Core State Standards (CCSS). 1. Literature Review Changing teacher practices to improve student learning is a challenge in United States public schooling. According to DuFour and Eaker (1998) and Smith (2003), for teachers' practices as a whole to change, faculties within schools must build communities of practice (Wenger, 1998). Improved practices can be achieved through a collaborative environment focusing on the instruction, curricular materials and student work (Newmann & Associates, 1996). A professional development model: Instructional Learning Teams (ILTs) promote school improvement by providing a process through which teachers collaborate with other professionals using rubrics to guide reflective discourse regarding tasks, instruction, and student work while engaging in short cycles of informal action research (Newmann, Secada, & Wehlage, 1995; Stewart & Brendefur, 2005b). For over a century, U.S. teachers have been disenfranchised as passive receivers of university-based research. We aim to contribute to Stenhouse's argument that teacher " research [is] the route to teacher emancipation " (cited in Cochran-Smith & Lytle, 1993, p. 8). In order for teachers to examine their work in ways to increase student understanding, we combined the Japanese Lesson Study, intellectual quality and professional learning communities. The purpose of this paper is to describe how these elements of research are put together to form Instructional Learning Teams (ILTs) and to describe the results of two case studies implementing ILTs. The ILT model allows teachers a meaningful way to examine their practices. It provides them with a framework for new discourse, acculturating them into a learning community committed to working on improved practice and improved student learning and performance. This type of team and individual study is a " rigorous examination of one's own practice as a basis for professional development, the idea is that each school, and indeed each classroom, is a laboratory in which the curriculum and problems experienced as problems by teachers are subjected to empirical examination by practitioners " (Henson, 1996, p. 53). Learning to teach well, even for veteran teachers, is a complex, uncertain, and difficult task. However, quality teaching is an essential ingredient to increasing student achievement and promoting student understanding (Haycock,
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Much research has been conducted on how elementary students develop mathematical understanding an... more Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with her colleagues how other algebra students have mathematically modeled a bacteria growth problem with no prior formal instruction. Analysis revealed that the teacher was able to use students' algebraic thinking to structure her class and begin promoting mathematical understanding. The implications for building on students' conceptions of algebra are explored throughout the paper.
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In the present research, we evaluated the effectiveness of a multi-year professional development ... more In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and statistics. We also examined the relation between mathematical knowledge and teaching practices. Across the three domains neither pretest nor posttest mathematical knowledge were related to classroom teaching practices. However, change in knowledge was positively related to six different dimensions of teaching practice for number and operations, and for measurement and geometry; and was positively related to four or six dimensions for probability and statistics. That is, those teachers with greater changes in knowledge demonstrated more effective instruction.
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In this article we examine how secondary school students think about functional relationships. Mo... more In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so. Instead, these students tend to represent the physical characteristics of the situation. In addition, we discovered that middle-school students had sophisticated ideas of dependency and covariance. All the students were able to use their models of the situation to generalize and make predictions. These findings suggest that secondary students have the ability to describe covariant and dependent relations and that their models of functions tend to be more intuitive than mathematical – even for the students in algebra II and calculus. Our work suggests a possible framework that begins describing a way of analyzing students' understanding of functions.
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(2015). Developing a comprehensive mathematical assessment tool to improve mathematics interventi... more (2015). Developing a comprehensive mathematical assessment tool to improve mathematics intervention for at-risk students. Abstract Students who complete kindergarten with an inadequate knowledge of basic mathematics concepts and skills will continue to experience difficulties with mathematics throughout their elementary and secondary years and may be at increased risk for math disabilities. There is a critical need to identify students experiencing difficulties in mathematics in the early elementary grades and to provide immediate and targeted instruction to remediate these deficits. Most early math screening tools focus on only a single skill, resulting in an incomplete picture of student performance and limited predictive validity. To address this need, we are developing a multiple-gating system of math assessment, the Primary Math Assessment (PMA), that both screens and provides diagnostic information in six domains. In this study, we present the results of the development and validation of items across the domains that will comprise
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This paper describes the effects of a professional development (PD) program – Developing Mathemat... more This paper describes the effects of a professional development (PD) program – Developing Mathematical Thinking – on student achievement. Six Title I elementary schools with similar demographics, within one school district, were chosen to participate as either a treatment or comparison school. Three schools were chosen to participate in professional development that incorporates effective PD recommendations. All the teachers had to participate in all aspects of the PD, thereby eliminating potential self-selection bias. Using the state standardized achievement test as the before and after measure, results suggest improved student performance after professional development was implemented over a two year period.
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This study examines the relationship between mathematics teachers' beliefs and instructional prac... more This study examines the relationship between mathematics teachers' beliefs and instructional practices related to learning, pedagogy, and mathematics in regards to components of intellectual quality for eight high-school mathematics teachers. Research has demonstrated that the higher the degree of intellectual quality for instruction is rated the higher student achievement is on standardized assessments. The findings in this study demonstrate a consistent pattern between teachers espoused beliefs and their instructional practices. Even though teachers' practices changed as they wrote curricular units to be more in line with intellectual quality characteristics, their beliefs stayed consistent over an 18 month period and were correlated to their instructional practices at the beginning and end of the project.
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Place value is a concept in which students in elementary school struggle and instruction and curr... more Place value is a concept in which students in elementary school struggle and instruction and curricular materials continue to introduce and teach place value in a disconnected fashion. This study introduced place value through a modeling perspective, focusing specifically on using the bar model to represent units and quantity. The investigation piloted a place value module highlighting the use of the bar model in four first grade classrooms with high percentages of diverse learners, many from low-income families and with limited English language proficiency. The results indicated students successfully described the differences between units of 1 and 10 and could build and describe numbers in their teens and twenties. Students' vocabulary and understanding of place value improved over a three-week period, suggesting visual models can be used as an effective model to promote place value understanding.
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Journal of Vocational Education Research, 2003
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As mathematics teacher educators, it is imperative that we have high-quality tools that conceptua... more As mathematics teacher educators, it is imperative that we have high-quality tools that conceptualize and operationalize mathematics instruction for large-scale examination. We first describe existing instructional practice survey scales, including their conceptualization of practice and related validity evidence. We then present the framework and initial validity evidence for our mathematics instructional practice survey. Survey participants were in-service teachers in a statewide mandated mathematics professional development course. Statistical analyses indicate the items measure two constructs: social-constructivist and transmission-based instructional practice. Of particular interest is the result that these two constructs were negligibly correlated. This is in contrast to the generally accepted notion that social-constructivist and transmission-based instructional practices are the two polar ends of a single construct for describing instructional practice.
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Advances in Social Sciences Research Journal, 2015
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Papers by Jonathan Brendefur