Algebra

Linear Algebra and Geometry

Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.

Author/Presenter:
Al Cuoco
Kevin Waterman
Bowen Kerins
Elena Kaczorowski
Michelle Manes
Year:
2019
Short Description:

Linear Algebra and Geometry is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. The materials are organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.

Thinking scientifically in a changing world

Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.

Lombardi, D. (2019). Thinking scientifically in a changing world. Science Brief: Psychological Science Agenda, 33(1). Retrieved from https://www.apa.org/science/about/psa/2019/01/changing-world.aspx

Author/Presenter:
Doug Lombardi
Year:
2019
Short Description:

Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.

A first-year algebra student’s curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics.
Author/Presenter:
E. Paul Goldenberg
Cynthia J. Carter
Year:
2017
Short Description:

A first-year algebra student’s curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics.

Resource(s):

Constructing and Role-Playing Student Avatars in a Simulation of Teaching Algebra for Diverse Learners

From the perspectives of Graduate Research Assistants (GRAs), this study examines the design and implementation of a simulated teaching environment in Second Life (SL) for prospective teachers to teach algebra for diverse learners. Drawing upon the Learning-for-Use framework, the analyses provide evidence on the development of student avatars in construction and role-playing activities. The study reveals challenges, procedures, and suggestions for future simulations. This study also calls for research efforts toward preparing mathematics teachers for cultural diversity.

Author/Presenter:
Tingting Ma
Irving A. Brown
Gerald Kulm
Trina J. Davis
Chance W. Lewis
G. Donald Allen
Year:
2014
Short Description:

This study examines the design and implementation of a simulated teaching environment in Second Life for prospective teachers.

Illuminating Coordinate Geometry with Algebraic Symmetry

A symmetric polynomial is a polynomial in one or more variables in which swapping any pair of variables leaves the polynomial unchanged. For example, f(x, y, z) = xy +xz + yz is a symmetric polynomial.

Author/Presenter:
Ryota Matsuura
Sarah Sword
Year:
2015
Short Description:

A symmetric polynomial is a polynomial in one or more variables in which swapping any pair of variables leaves the polynomial unchanged. For example, f(x, y, z) = xy +xz + yz is a symmetric polynomial. If we interchange the variables x and y, we obtain yx + yz + xz, which is the same as f(x, y, z); likewise, swapping x and z (or y and z) returns the original polynomial. These polynomials arise in many areas of mathematics, including Galois theory and combinatorics, but they are rarely taught in a high school curriculum. In this article, we describe an application of symmetric polynomials to a familiar problem in coordinate geometry, thus introducing this powerful tool in a context that is accessible to high school students.

SmartGraphs: Algebra

The Concord Consortium has developed 19 activities for teaching and learning algebra that are available online or as an app for iPad or Android tablet computers. These activities—which cover a variety of algebra topics, from linear equations to transformations of functions—help students develop skills creating and using algebraic functions and graphs to solve problems.

Author/Presenter:
The Concord Consortium
Year:
2014
Short Description:

The Concord Consortium has developed 19 activities for teaching and learning algebra that are available online or as an app for iPad or Android tablet computers. These activities—which cover a variety of algebra topics, from linear equations to transformations of functions—help students develop skills creating and using algebraic functions and graphs to solve problems. Hints and scaffolds support learners who need help.