CAREER: Reciprocal Noticing: Latino/a Students and Teachers Constructing Common Resources in Mathematics
The goal of this project is to extend the theoretical and methodological construct of noticing to develop the concept of reciprocal noticing, a process by which teacher and student noticing are shared. The researcher argues that through reciprocal noticing the classroom can become the space for more equitable mathematics learning, particularly for language learners.
The goal of this project is to extend the theoretical and methodological construct of noticing to develop the concept of reciprocal noticing, a process by which teacher and student noticing are shared. The researcher argues that through reciprocal noticing the classroom can become the space for more equitable mathematics learning, particularly for language learners. Thus, the focus of the project is on developing the concept of reciprocal noticing as a way to support better interactions between teachers and Latino/a students in elementary mathematics classrooms.
The project uses a transformative teaching experiment methodology and is guided by the initial conjectures that to make mathematics classrooms intellectually attractive places, Latino/a students and teachers need to learn to develop common resources for teaching and learning mathematics, and that reciprocal noticing as a process supports teachers and students in developing these common resources for teaching and learning mathematics. The project design centers around two research questions:How do teachers and Latino/a students tune to each other's mathematical ideas and explicitly indicate to one another how their ideas are important for discourse that promotes mathematical reasoning in classrooms characterized by reciprocal noticing? What patterns emerge across four classrooms when teachers and Latino/a students engage in reciprocal noticing?
The concept of reciprocal noticing can significantly enhance emerging research in mathematics education about the importance of teacher noticing. Further, this revised concept of noticing can transform mathematics classroom to better support English Language Learners.
The PI will incorporate project findings and videos into methods courses for preservice elementary teachers.
CAREER: Community-Based Engineering as a Learning and Teaching Strategy for Pre-service Urban Elementary Teachers
This is a Faculty Early Career Development project aimed at developing, implementing, and assessing a model that introduces novice elementary school teachers (grades 1-6) to community-based engineering design as a strategy for teaching and learning in urban schools. Reflective of the new Framework for K-12 Science Education (NRC, 2012), the model addresses key crosscutting concepts, disciplinary core ideas, and scientific and engineering practices.
This is a Faculty Early Career Development project aimed at developing, implementing, and assessing a model that introduces novice elementary school teachers (grades 1-6) to community-based engineering design as a strategy for teaching and learning in urban schools. Reflective of the new Framework for K-12 Science Education (NRC, 2012), the model addresses key crosscutting concepts (e.g., cause and effect: mechanism and explanation), disciplinary core ideas (e.g., engineering design, and links among engineering and society), and scientific and engineering practices (e.g., identifying a problem, and designing solutions for technology-related problems in local school or community environments). It builds on theoretical perspectives and empirical foundations, including situated learning, engineering design cognition,and children's resources and funds of knowledge, including cultural and linguistic diversity. The study integrates research and education plans that investigate the short-term impact of the model on 90 novice teachers' learning through their pre-service coursework and practice teaching, and its longer-term impact on a subset of 48 of those teachers as they begin their first year of in-service teaching.
The study employs a design-based research that addresses three phases: (a) a development phase to create a community-based engineering module and assessment instruments; (b) an iterative implementation phase that includes three cycles of community-based engineering experiences with three cohorts of novice teachers; and (c) a synthesis phase focused on generating cumulative findings and recommendations. Its hypothesis is that incorporating community-based engineering into elementary teacher education will enhance novice urban elementary teachers' engineering design competency, understanding of engineering and scientific practices, and ability to identify and respond to student ideas and practices in science and engineering. This hypothesis guides four research questions: (1) How do novice urban elementary teachers' engineering design abilities evolve during community-based engineering experiences?; (2) How do the teachers' understandings of engineering and scientific practices evolve during community-based engineering experiences?; (3) How do the teachers' engineering abilities and understandings of engineering and scientific practices impact how they identify and respond to students' science and engineering ideas and practices?; and (4) Does participating in extended professional development on community-based engineering impact the teachers' (a) understandings of engineering and scientific practices, (b) abilities to identify and respond to student thinking, or (c) incorporation of science/engineering lessons into their first two years of teaching? The research plan articulates a descriptive thread and an experimental thread. The descriptive research thread addresses the first three research questions, inclusive of three constructs: (a) novice urban elementary teachers' engineering design abilities, (b) their understandings of practices of science and engineering, and (c) their abilities to identify and respond to students' ideas and practices. The experimental research thread addresses the fourth research question, which assesses the impact of community-based engineering professional development on two of the constructs (b and c mentioned above), as well as on the frequency and characteristics of the science-engineering lessons that new teachers will implement with their students in their first two years of teaching. Data gathering strategies include the use of valid and reliable instruments, such as the Creative Engineering Design Assessment, a curriculum critique and revision task, and a video-case-based assessment. Data analysis include both quantitative and qualitative methods.
Expected outcomes are: (1) a research-informed and field-tested strategy to incorporate community-based engineering into elementary teacher education and elementary grades science classrooms, (2) samples of modules demonstrating this strategy, and (3) a digital guide on incorporating community-based engineering experiences into elementary science teacher education programs, particulalrly in underserved urban areas.
CAREER: Fraction Activities and Assessments for Conceptual Teaching (FAACT) for Students with Learning Disabilities
The goal of this project is to study and support the development of conceptual understanding of fractions by students with learning disabilities (LD). The researcher proposes that rather than focusing on whether LD students can or cannot develop conceptual understanding of fractions, research should attempt to uncover the understanding LD students have and examine how growth of conceptual knowledge occurs in these students.
The goal of this project is to study and support the development of conceptual understanding of fractions by students with learning disabilities (LD). The researcher proposes that rather than focusing on whether LD students can or cannot develop conceptual understanding of fractions, research should attempt to uncover the understanding LD students have and examine how growth of conceptual knowledge occurs in these students. This approach suggests a reconceptualization of research and instructional practice in mathematics that focus on the conceptual knowledge students with LD can in fact develop.
Through a series of teaching experiments that involve cycles of theorizing, design, implementation, and refinement, the project develops instructional trajectories for LD students in the area of fractions. The research question addressed are: What initial and developing key developmental understandings of fractions do students with learning disabilities evidence through employed strategies, language, and representations? How do students with learning disabilities progress in developing and solidifying conceptual understandings of fractions through their mathematical activity? And, to what extent does an intervention reflective of a research based instructional trajectory facilitate strategic development and increased fraction conceptual knowledge in students with learning disabilities?
The main outcomes of the project include (a) a research-based instructional trajectory for students with LD specific to conceptual understandings of fractions as numeric quantities, (b) a set of 90 fraction tasks to be used for instruction and/or formative assessment in fraction concepts, (c) scoring/coding frameworks and checklists for use with key tasks as formative assessments, (d) decision-making frameworks, task sequencing guides, and suggestions to aid teachers in designing individualized, student-centered instruction, all available via the Internet. Most important, the project has the potential to offer a transformative approach to mathematics instruction for students with LD, bringing together expertise on learning disabilities and mathematics education to address a area in which there is very little research.
The PI will incorporate finding from the study into methods courses for both mathematics education and special education students. She will also develop a graduate course entitled Diagnosis and Remediation.
Formerly under Award # 1253254.
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.