Algebra

CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

The aim of this project is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Award Number: 
1743356
Funding Period: 
Mon, 03/15/2010 to Fri, 06/30/2017
Full Description: 

The aim of this CAREER project led by Amy Ellis at the University of Wisconsin is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Work of the project will produce: (a) insights into ways of unifying two previously disconnected lines of research on quantitative reasoning and proof; (b) models describing realistic ways to support development of students' proof competencies through quantitative reasoning; (c) improvement in students' understanding of algebra through engagement in proof practices based on quantitative reasoning; (d) insights into middle-school students' thinking as they negotiate the transition from elementary to more advanced mathematics; and (e) increased understanding of teachers' knowledge about proof and their classroom practices aimed at helping students progress towards understanding and skill in proof.

This project was previously funded under award #0952415.

Engaging Secondary Students and Teachers Through a Proficiency-Based Assessment and Reassessment of Learning Outcomes (PARLO) System in Mathematics

This project is researching the efficacy of a learning and assessment system that emphasizes students' attaining proficiency or better on a limited set of high value learning objectives in Algebra.

Award Number: 
0918474
Funding Period: 
Thu, 03/01/2012 to Thu, 02/28/2013
Project Evaluator: 
Research for Better Schools
Full Description: 

Using a clustered randomized control trial of 44 secondary schools in the greater Philadelphia area, the project is researching the efficacy of a learning and assessment system that emphasizes students' attaining proficiency or better on a limited set of high value learning objectives in Algebra and Geometry. The study allows for and expects students to resubmit assignments and be reassessed until they achieve proficiency or greater. In this new classroom dynamic, students assume more responsibility for and be active agents in their own learning. For their part, teachers will adopt instructional strategies and techniques that support their students' ongoing and continuous learning, including defining learning outcomes, providing frequent and individualized feedback, and participating in professional development.

The research questions are: 1) Does the use of proficiency-based assessment and reassessment of learning outcomes (PARLO) in Algebra lead to increases in secondary students' achievement and engagement in mathematics? 2) Does PARLO lead to increased student interest in pursuing more complex mathematics or science courses? Two cohorts of ninth grade students are being followed.

Mapping Developmental Trajectories of Students' Conceptions of Integers

This project is using data from interviews with 160 K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0918780
Funding Period: 
Sat, 08/15/2009 to Sun, 07/31/2011
Project Evaluator: 
West Ed (Juan Carlos Bojorquez)
Full Description: 

The project Mapping Developmental Trajectories of Students' Conceptions of Integers, led by faculty from San Diego State University, is using data from 160 interviews with K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.

Two questions frame and guide the proposed research:

* What are students' conceptions of integers and operations on integers?

* What are possible developmental trajectories of students' understandings?

The investigators are seeking answers to those questions through structured interviews with students in elementary grades prior to instruction about negative numbers (Grades 2 and 4), students in middle grades whose formal learning experiences have already included explicit instruction about integers (Grade 7), high school students who are expected to use prior knowledge about integers in more advanced mathematics (Grade 11 PreCalculus and Calculus students), and adults who use integers in their work.

In addition to providing an empirically-based picture of ways that students reason about negative numbers, the project is producing useful interview protocols and a reliable and valid assessment instrument for describing the understanding and skill of students at various stages on such a progression.

Both the characterization of common learning progressions and the assessment instruments will be broadly useful to curriculum and test developers and teachers in K-12 mathematics classrooms.

Introducing Dynamic Number as a Transformative Technology for Number and Early Algebra

This project operationalizes research in number, operation, and early algebra. It builds on the paradigm of Dynamic Geometry (the interactive and continuous manipulation of geometric shapes and constructions) with a new technological paradigm, Dynamic Number, centered on the direct manipulation of numerical representations and constructions. Using The Geometer’s Sketchpad as a starting point, KCP Technologies is developing new software tools to deepen students’ conceptions of number and early algebra in grades 2–8.

Project Email: 
Lead Organization(s): 
Award Number: 
0918733
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
John Olive

Mathematics Discourse in Secondary Classrooms (M-DISC): A Case-Based Professional Development Curriculum

This project is developing, designing, and testing materials for professional development leaders (e.g., teacher educators, district mathematics specialists, secondary mathematic department chairs) to use in their work with secondary mathematics teachers. The aim is to help those teachers analyze the discourse patterns of their own classrooms and improve their skills in creating discourse patterns that emphasize high-level mathematical explanation, justification, and argumentation.

Award Number: 
0918117
Funding Period: 
Sat, 08/01/2009 to Thu, 07/31/2014
Project Evaluator: 
Horizon

Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-modeling Environment (NMRSD-CCME)

The purpose of this project is to create a research-based model of how students with learning disabilities (LDs) develop multiplicative reasoning via reform-oriented pedagogy; convert the model into a computer system that dynamically models every students’ evolving conceptions and recommends tasks to promote their advancement to higher level, standard-based multiplicative structures and operations; and study how this tool impacts student outcomes.

Project Email: 
Lead Organization(s): 
Award Number: 
0822296
Funding Period: 
Fri, 08/01/2008 to Wed, 07/31/2013
Project Evaluator: 
Dr. C. Brown
Full Description: 

PUM (PhysicsUnionMathematics) Exploration

The PuM project develops and conducts research on a learning continuum for seamless instruction in middle school physical science and high school physics. The ultimate goal is to use physics as the context to develop mathematics literacy, particularly with students from underrepresented populations and special needs students. The research component analyzes the effects of the curriculum on students' learning while simultaneously investigating teachers' pedagogical content knowledge in a variety of forms.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0733140
Funding Period: 
Sat, 09/01/2007 to Tue, 08/31/2010

Foundations of Algebra in the Elementary and Middle Grades: Supporting Students to Make, Represent and Justify General Claims about Operations

This project develops images, extended examples, and principles that illustrate how the articulation, representation and justification of general claims about operations evolve in the elementary grades and how this work supports the transition from arithmetic to algebra in the middle grades. An online course uses the Sourcebook as a text to engage teachers in considering the underlying pedagogical and mathematical aspects of the work and implementing these ideas in their instruction.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0550176
Funding Period: 
Sat, 07/01/2006 to Thu, 06/30/2011
Project Evaluator: 
Megan Franke

CAREER: Collaborative Learning with Classroom Networks: Integrating Technological and Pedagogical Innovations

This project studies teaching practices in a year-long high school algebra course that integrates hand-held and other electronic devices. Of particular interest is how these technologies can support learners' capacity to efficiently and effectively draw on the distributed intelligences that technical and social networks make available. The investigation focuses on collaborative learning tasks centered on collective mathematical objects, such as functions, expressions, and coordinates that participants in a group must jointly manipulate through networked computers.

Award Number: 
0747536
Funding Period: 
Tue, 07/01/2008 to Sun, 06/30/2013

A Longitudinal Comparison of the Effects of the Connected Mathematics Program and Other Curricula on Middle School Students' Learning of Algebra

This project compares the effects on algebraic learning when using the Connected Math Program to the effects of using other (non-NSF supported) middle school mathematics curriculum materials at the middle school level. The algebra focus skills/concepts to be assessed are: conceptual understanding and problem solving; algebraic manipulative skills; solution strategies, representations and mathematical justifications.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0454739
Funding Period: 
Tue, 03/01/2005 to Mon, 02/28/2011

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