Grounded Theory

Fostering Pedagogical Argumentation: Pedagogical Reasoning with and About Student Science Ideas

This project will use an iterative approach to design activities and supports that foster pedagogical argumentation for use in undergraduate teacher education courses. This project will examine: 1) whether and how PSTs engage in pedagogical argumentation and 2) whether and how this engagement impacts how they listen and respond to student ideas.

Award Number: 
1316232
Funding Period: 
Tue, 10/01/2013 to Sun, 09/30/2018
Full Description: 

Effective and ambitious teaching in science requires that teachers listen and respond to student ideas. But research shows that doing so in the classroom can be logistically, socially, and intellectually challenging for both expert and novice teachers. Listening to student ideas requires teachers to anticipate and interpret multiple lines of thinking that may be expressed ambiguously and simultaneously. Responding to student thinking, both in-the-moment and in future instruction, presents further challenges because teachers must balance their choices with other instructional priorities. Unfortunately, little work has been done to date in supporting these challenging practices in those who are learning to teach, pre-service teachers (PSTs). In order to address this gap, researchers in this Exploratory project will introduce a new approach to teacher education: pedagogical argumentation. Pedagogical argumentation creates a supportive environment in which the PSTs learn and refine these practices of listening and responding by using student ideas as evidence to construct and defend potential pedagogical decisions.

Over three years researchers from the University of Wisconsin-Madison will use an iterative approach to design activities and supports that foster pedagogical argumentation for use in undergraduate teacher education courses. This project will examine: 1) whether and how PSTs engage in pedagogical argumentation and 2) whether and how this engagement impacts how they listen and respond to student ideas. Working with both elementary and secondary PSTs, researchers will probe and explore their changing listening and responding practices by: collecting records of pedagogical argumentation (both video and written) as it occurs in the science teaching methods courses; conducting interviews about PSTs understanding of student ideas; and documenting PSTs teaching experiences in their school placements.

The science teacher education community writ large is in need of systematic approaches to teacher education that better support PSTs in learning ambitious teaching practices such as listening and responding to student ideas. The proposed study addresses this need and, in doing so, will support both immediate PSTs in engaging in this work as well as the broader teacher education community as it struggles with these same challenges. Moreover, the novel practice of pedagogical argumentation advances the fields theoretical understanding of the problem space for supporting these challenges by combining insight from two extensive programs of research in teaching and learning: 1) teacher reasoning about student ideas, and 2) argumentation about science content. As such, the practice of pedagogical argumentation has the potential to transform how teacher educators approach pre-service education.

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.

Lead Organization(s): 
Award Number: 
1252575
Funding Period: 
Thu, 08/01/2013 to Fri, 07/31/2020
Full Description: 

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.


Project Videos

2019 STEM for All Video Showcase

Title: Differentiating Mathematics Instruction for Middle School

Presenter(s): Amy Hackenberg, Rebecca Borowski, Mihyun Jeon, Robin Jones, & Rob Matyska


INK-12: Teaching and Learning Using Interactive Ink Inscriptions in K-12 (Collaborative Research: Koile)

This is a continuing research project that supports (1) creation of what are termed "ink inscriptions"--handwritten sketches, graphs, maps, notes, etc. made on a computer using a pen-based interface, and (2) in-class communication of ink inscriptions via a set of connected wireless tablet computers. The primary products are substantiated research findings on the use of tablet computers and inscriptions in 4th and 5th grade math and science, as well as models for teacher education and use.
Award Number: 
1020152
Funding Period: 
Wed, 09/01/2010 to Sun, 08/31/2014
Project Evaluator: 
David Reider, Education Design Inc.
Full Description: 

The research project continues a collaboration between MIT's Center for Educational Computing Initiatives and TERC focusing on the enhancement of K-12 STEM math and science education by means of technology that supports (1) creation of what are termed "ink inscriptions"--handwritten sketches, graphs, maps, notes, etc. made on a computer using a pen-based interface, and (2) in-class communication of ink inscriptions via a set of connected wireless tablet computers. The project builds on the PIs' prior work, which demonstrated that both teachers and students benefit from such technology because they can easily draw and write on a tablet screens, thus using representations not possible with only a typical keyboard and mouse; and they can easily send such ink inscriptions to one another via wireless connectivity. This communication provides teachers the opportunity to view all the students' work and make decisions about which to share anonymously on a public classroom screen or on every student's screen in order to support discussion in a "conversation-based" classroom. Artificial intelligence methods are used to analyze ink inscriptions in order to facilitate selection and discussion of student work.

The project is a series of design experiments beginning with the software that emerged from earlier exploratory work. The PIs conduct two cycles of experiments to examine how tablets affect students learning in 4th and 5th grade mathematics and science. The project research questions and methods focus on systematic monitoring of teachers' and students' responses to the innovation in order to inform the development process. The PIs collect data on teachers' and students' use of the technology and on student learning outcomes and use those data as empirical evidence about the promise of the technology for improving STEM education in K-12 schools. An external evaluator uses parallel data collection, conducting many of the same research activities as the core team and independently providing analysis to be correlated with other data. His involvement is continuous and provides formative evaluation reports to the project through conferences, site visits, and conference calls.

The primary products are substantiated research findings on the use of tablet computers, inscriptions, and networks in 4th and 5 grade classrooms. In addition the PIs develop models for teacher education and use, and demonstrate the utility of artificial intelligence techniques in facilitating use of the technology. With the addition of Malden Public Schools to the list of participating districts, which includes Cambridge Public Schools and Waltham Public Schools from earlier work, the project expands the field test sites to up 20 schools' classrooms.

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