This project will develop and study a professional development framework that is designed to help high school geometry teachers attend more carefully to student prior knowledge, interpret the learning implications of student prior knowledge, and adjust teaching practices accordingly. Participating teachers will participate in study groups that analyze animations of productive teaching practices; they will collaborate in planning, implementing, and analyzing geometry lessons; and they will critique videos of their own classroom instruction.
Advocates of problem-based instruction argue that the approach can help students develop a deeper understanding of mathematics, acquire more positive attitudes toward mathematics, and gain experience with more authentic applications of mathematics. Engaging students in problem-based instruction, however, increases challenges to teachers who must attend to the influence of student prior knowledge and adjust instruction accordingly. The proposed project will develop and study a professional development framework that is designed to help high school geometry teachers attend more carefully to student prior knowledge, interpret the learning implications of student prior knowledge, and adjust teaching practices accordingly. Participating teachers will learn to perform these complex tasks by participating in study groups to analyze animations of productive teaching practices; to collaborate in planning, implementing, and analyzing geometry lessons; and to critique videos of their own classroom instruction. Prior research has shown that collective examination of videos can help teachers increase attention on student thinking, a key to noticing and accommodating student prior knowledge.
A key, innovative feature of the professional development framework for this study is the use of animated vignettes of classroom instruction to prepare teachers to examine videos of their own practice. The advantage of using cartoon-based animations of classroom practices is that they can be designed to depict specific teaching actions while excluding the usual distractions in videos, such as physical features, clothing, or individual mannerisms. Also, teachers can develop a critical eye for relevant interactions without feeling the need to be overly polite when discussing fictional scenarios portrayed by cartoon characters. This preliminary practice will also enable teachers to develop a common language about noticing and responding to student prior knowledge before critiquing videos of their own classroom practices.
This project advances knowledge of professional development experiences that help teachers notice and take into account the prior knowledge that students bring to the classroom. Results from studying the effects of coupling analysis of animated vignettes of classroom practices with critiquing videos on one's own classroom practices have the potential to significantly enhance professional development practices among mathematics teachers, as well as teachers in general. Results from the project will be broadly disseminated via conference presentations, articles in diverse media outlets, and a project website that will make project products available, be a location for information about the project for the press and the public, and be a tool to foster teacher-to-teacher communication. The results of this study, as well as the protocols and instruments developed during the research project, will inform and support the researcher's own efforts to better understand and improve teacher learning. The education plan of the researcher focuses on translating the outcomes of this study to the practices of preservice teacher education by connecting instructional decision-making more explicitly to research on student learning, thereby promoting learning trajectory based instruction.
CAREER: Investigating Differentiated Instruction and Relationships Between Rational Number Knowledge and Algebraic Reasoning in Middle School
The proposed project initiates new research and an integrated education plan to address specific problems in middle school mathematics classrooms by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students' algebraic reasoning and rational number knowledge in mutually supportive ways.
Middle school mathematics classrooms are marked by increasing cognitive diversity and students' persistent difficulties in learning algebra. Currently middle school mathematics instruction in a single classroom is often not differentiated for different thinkers, which can bore some students or overly challenge others. One way schools often deal with different thinkers at the same grade level is by tracking, which has also been shown to have deleterious effects on students, both cognitively and affectively. In addition, students continue to struggle to learn algebra, and increasing numbers of middle school students are receiving algebra instruction. The proposed project initiates new research and an integrated education plan to address these problems by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students' algebraic reasoning and rational number knowledge in mutually supportive ways. Educational goals of the project are to enhance the abilities of prospective and practicing teachers to teach cognitively diverse students, to improve doctoral students' understanding of relationships between students' learning and teachers' practice, and to form a community of mathematics teachers committed to on-going professional learning about how to differentiate instruction.
Three research-based products are being developed: two learning trajectories, materials for differentiating instruction developed collaboratively with teachers, and a written assessment to evaluate students' levels of reasoning. The first trajectory, elaborated for students at each of three levels of reasoning, focuses on developing algebraic expressions and solving basic equations that involve rational numbers; the second learning trajectory, also elaborated for students at each of three levels of reasoning, focuses on co-variational reasoning in linear contexts. In addition, the project investigates how students' classroom experience is influenced by differentiated instruction, which will allow for comparisons with research findings on student experiences in tracked classrooms. Above all, the project enhances middle school mathematics teachers' abilities to serve cognitively diverse students. This aspect of the project has the potential to decrease opportunity gaps. Finally, the project generates an understanding of the kinds of support needed to help prospective and practicing teachers learn to differentiate instruction.
The project advances discovery and understanding while promoting teaching, training, and learning by (a) integrating research into the teaching of middle school mathematics, (b) fostering the learning of all students by tailoring instruction to their cognitive needs, (c) partnering with practicing teachers to learn how to implement this kind of instruction, (d) improving the training of prospective mathematics teachers and graduate students in mathematics education, and (e) generating a community of mathematics teachers who engage in on-going learning to differentiate instruction. The project broadens participation by including students from underrepresented groups, particularly those with learning disabilities. Results from the project will be broadly disseminated via conference presentations; articles in diverse media outlets; and a project website that will make project products available, be a location for information about the project for the press and the public, and be a tool to foster teacher-to-teacher communication.
Science Journalism Experiences from a Youth Perspective: Who or What Transforms? In T. Sato, Learners in Action
Science Journalism as a Preparation for Everyday Scientific Literacy. In L. Bricker, Reading, writing and communication science.
Interact with noted authors, science educators, and NSTA program managers as they share strategies for integrating science and literacy using high-quality science trade books.
Enhancing science literacy through science journalism has been the goal of this NSF-funded project.