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. 

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

Lead Organization(s): 
Year: 
2019
Short Description: 
Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.

A Student Asks About (-5)!

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.
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): 

Problematizing and Assessing Secondary Mathematics Teachers’ Ways of Thinking

STEM Categorization: 
Day: 
Thu

Engage with presenters as they discuss assessment and rubrics designed to measure secondary teachers’ mathematical habits of mind.

Date/Time: 
9:30 am to 11:00 am
Session Materials: 

Work in secondary mathematics education takes many approaches to content, pedagogy, professional development and assessment. This session aims to illuminate the richness of hte content of secondary mathematics and the field of secondary mathematics education by sharing two such approaches and reflecting on the differences and commonalities between the two.   

Session Types: 

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.

Lead Organization(s): 
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.

SmartGraphs: Algebra

The Concord Consortium has developed 19 Smartgraphs: Algebra coveractivities 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.

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.

Teaching Viable Argumentation and Measuring the Effects

Day: 
Tues

How do we encourage referent-based mathematical argumentation without encouraging students to request that examples accompany otherwise viable arguments? Assessment concerns are explored and discussed.

Date/Time: 
1:45 pm to 3:45 pm
2014 Session Types: 
Feedback Session (Work in Development)
Presenters: 

The LAMP project has developed a sequence of lessons in a hypothetical learning trajectory that targets students’ ability to write viable arguments in algebraic contexts. Most of the lessons encourage students to produce a referent (e.g., variable expression or equation, generic example, diagram) as the foundation of their argument. Students come to the lessons with a predisposition for example production in support of their claims and to augment arguments.

Student Materials, Professional Development, and Assessment Organized Around Habits of Mind in the CCSSM

Day: 
Tues

Learn about three projects centered on algebraic habits of mind: a puzzle-centric curriculum for middle school and at-risk algebra students, professional development on the Standards for Mathematical Practice, and an assessment for teachers.

 

Date/Time: 
1:45 pm to 3:45 pm
2014 Session Types: 
Collaborative Panel Session
Session Materials: 

Algebraic habits of mind, at the core of five of the Standards for Mathematical Practice, become both a potent and appealing intervention for at-risk algebra students and a solid prevention-model middle-school course either to accelerate algebra or to ensure success in a later algebra course. The session focuses on the habits of mind in that context, in related professional development work that addresses the Standards for Mathematical Practices, and on assessment of algebraic habits of mind in teachers.

Pages

Subscribe to Algebra