Algebra

The Development of Student Cohorts for the Enhancement of Mathematical Literacy in Under Served Populations

This project is developing and conducting research on the Cohort Model for addressing the mathematics education of students that perform in the bottom quartile on state and district tests. The predicted outcome is that most students will remain in the cohort for all four years and that almost all of those who do will perform well enough on college entrance exams to be admitted and will test out of remedial mathematics courses.

Lead Organization(s): 
Award Number: 
0822175
Funding Period: 
Mon, 09/01/2008 to Wed, 08/31/2011
Project Evaluator: 
Inverness Research, Inc.
Full Description: 

Project Summary

This is a Full Research and Development proposal which addresses the Contextual Challenge: How can the learning of significant STEM content be achieved to ensure public literacy and workforce readiness?  Our nation is failing to prepare millions of youth for meaningful and productive participation in an information-based society. The target population are those students performing in the bottom quartile on state and national tests, many of these are children of color living in under resourced communities, and most of these young people do not finish high school and end up diverted into an underground economy, gangs, and prisons.   

This project addresses this failure by further developing and testing an approach that the Algebra Project is developing for high school mathematics, in which students form a cohort that stays together for all four years of high school, study mathematics every day using project-designed curricular materials with teachers who participate in project professional development, and are supported by local community groups. 

The Algebra Project seeks to stimulate a demand for math literacy in those most affected by its absence -- the young people themselves.  It stresses the importance of peer culture, using lessons learned from experiences in the 1960s Civil Rights Movement, as well as in the emergence of project graduates into a group with their own perspectives and initiatives. 

In the 60s, project founders learned how to use the meeting place as a tool to engage and empower the people that the meeting was intended to serve.  In the proposed project, there are two meeting places: the students’ high school mathematics classroom and supplementary education activities; and the network of sites around the country that are communicating and learning how to develop and implement cohorts. Young peoples’ roles in each of these settings are key to creating the motivation and commitment needed for student success as well as developing local interest.  The combination of classroom and professional development work, innovative curriculum materials, and community involvement creates an intervention that can significantly transform the peer culture, even in the face of negative forces.

The Algebra Project has developed a cohort model that we predict will stimulate and enable students to pass the state and district mandated tests in mathematics, to pass the mathematics portions of any graduation test, and to score well enough on the SAT or ACT to enter college, and to place into mathematics courses for college credit (not remedial courses).  Building on previous awards, the project will continue to research and develop the cohort model, and will create a small network of cohorts to establish that our model can be widely successful.

Intellectual merit:  This project will demonstrate how students entering high school performing in the bottom quartile nationally and state-wide can be prepared for college-level mathematics, using lessons learned from many years of past experience working in such communities and in their middle schools, and more recently in their high schools and in collaboration with university mathematicians.  The research results are critical to the nation’s learning how to improve mathematics achievement for all children – to gaining a sense of what such a program “looks and feels like”, and what resources and commitments are required, from which institutions. 

Broader impact:  The results of this discovery research project will advance understanding of how to improve mathematics learning and achievement in low performing districts, so students are prepared to take college mathematics without repeating high school mathematics in early college.  It will also demonstrate the resources and commitments needed to reach this result.

Connecting Content and Pedagogical Education of Pre-service Teachers (CONCEPT)

The primary goal of the project is to enhance secondary mathematics teacher education for pre-service teachers by developing, implementing and disseminating resources from a four-course curriculum that brings together the study of mathematics content and pedagogy. Three of the courses are problem-based technology enhanced (PBTE) courses in Algebra and Calculus, Geometry, and Probability and Statistics. A fourth course is a capstone course in Teaching and Learning Secondary School Mathematics.

Lead Organization(s): 
Award Number: 
0455797
Funding Period: 
Wed, 06/01/2005 to Sun, 05/31/2009

Examining Different Curricular Approaches and Their Impact on High School Students' Understanding of Algebra: Phase 1 -- Studying the Intended Curriculum

We are analyzing the intended algebra curriculum as represented in a variety of high-school mathematics textbooks – Core Plus Mathematics Project (CPMP), Discovering Mathematics (Key Curriculum Press), EDC's Center for Mathematics Education, Glencoe, Interactive Mathematics Program (IMP), and University of Chicago School Mathematics Project (UCSMP). The textbook analysis is based on two dimensions frequently used for curriculum analysis: a content dimension and a cognitive dimension.

Lead Organization(s): 
Award Number: 
0901311
Funding Period: 
Wed, 09/03/2008 to Thu, 01/31/2013

Project Delta: Digital Environments for the Learning and Teaching of Algebra

The purpose of Project Delta is two-fold: (1) to extend an existing library of 17 interacting CD-ROM digital learning environments on numbers and operations by adding an algebra strand, and (2) to evaluate the impact of the new algebra materials on teacher development. Each of the digital environments features classroom sessions that allow for exploration of a mathematics topic, children learning over time, and teachers? instructional techniques.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0822034
Funding Period: 
Fri, 08/15/2008 to Sat, 07/31/2010

Transition to Algebra: A Habits of Mind Approach

This research and development project provides resources for ninth-grade mathematics students and teachers by developing, piloting, and field-testing intervention modules designed as supplementary materials for Algebra 1 classes (e.g., double-period algebra). Rather than developing isolated skills and reviewing particular topics, these materials aim to foster the development of mathematical habits of mind—in particular, the algebraic habit of abstracting from calculations, a key unifying idea in the transition from arithmetic to algebra.

Project Email: 
Award Number: 
0917958
Funding Period: 
Tue, 09/01/2009 to Sat, 08/31/2013
Project Evaluator: 
Jim Hammerman, TERC
Full Description: 

Transition to Algebra, A Habits of Mind Approach, is aimed at very quickly giving students the mathematical knowledge, skill, and confidence to succeed in algebra, and showing them that they can be good at things they believed they couldn't do. The students were all smart and intrepid when they were six. Even now, they are better and more persevering than we are about figuring out their smartphones and video games. Transition to Algebra aims to tap that smart, intrepid, persevering spirit of puzzling things out and making sense of them by presenting mathematics based in common sense, not arbitrary rules.

This project is developing a collection of modules introducing key ideas of algebra in ways that complement the core curriculum when a school is offering double period algebra. The key habit of mind being developed is abstracting from calculation. Modules deal with the transition from arithmetic to algebra, rational numbers, expressions/equations/word problems, graphs and equations, geometry of algebra, and proportional reasoning. The target population is students in urban high poverty schools with a significant ELL sector.

Our hypothesis is that instructional materials focused on developing conceptual understanding and mathematical habits of mind can complement traditional skill-focused algebra instruction in ways that are engaging to students. Furthermore, they argue that using materials with such meta-cognitive aims will actually strengthen the learning of core algebraic concepts and skills.

The supplementary algebra modules are being developed by a form of design research. Concurrent with development and field test of the student and teacher materials, the investigators are addressing four research questions. The first two questions are focused on the effects of the intervention in developing student habits of mind and in improving their competence and confidence in algebra. The other two address the feasibility of implementing the new approach to double-period algebra in a variety of school settings. A small-scale quasi-experimental field test is being used to give preliminary estimates of the effectiveness of the instructional materials and the implementation guidelines. The core purpose of these research activities is to inform development and refinement of the student and teacher instructional materials.

Products of this development effort will be a valuable resource to schools as they devise strategies for helping all students master the essentials of elementary algebra.

Linear Algebra and Geometry: Advanced Mathematics for More Students

EDC is developing a high school capstone course in linear algebra. Student resources contain a core semester that develops two- and three-dimensional geometry using vectors and that treats matrix algebra and its applications to geometry; a semester of material that completes a typical undergraduate course (exploring bases, determinants and eigentheory); and 5 stand-alone modules that develop applications of this core to mathematics, engineering, science, and other STEM fields.

Project Email: 
Award Number: 
0733015
Funding Period: 
Mon, 10/01/2007 to Mon, 09/30/2013
Project Evaluator: 
University of New Hampshire

Simulation and Modeling in Technology Education (SMTE)

This project develops and researches the academic potential of a hybrid instructional model that infuses computer simulations, modeling, and educational gaming into middle school technology education programs. These prototypical materials use 3-D simulations and educational gaming to support students’ learning of STEM content and skills through developing solutions to design challenges.

Project Email: 
Lead Organization(s): 
Award Number: 
0821965
Funding Period: 
Fri, 08/01/2008 to Sun, 07/31/2011
Project Evaluator: 
Dr. Deborah Hecht

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