Theoretical Roots of Contextual Teaching and Learning in Mathematics

[Contextual teaching and learning represents a concept that involves connecting the content that students are learning with the context in which that content could be used. Connecting content with context is an important part of bringing meaning to the learning process.

For that connection to take place, a variety of teaching approaches may be used. Over the years, a body of literature has emerged based on research and development on how people learn. The following teaching approaches include context as a critical component and are found in the literature on teaching and learning:

"Contextual teaching and learning emphasizes higher-level thinking, knowledge transfer, collecting, analyzing, and synthesizing information and data from multiple sources and viewpoints" (Howey, 1998). Of critical importance is that the above approaches be used at the student's developmentally-appropriate level of learning, that the environment be established to support self-regulated learning, that culturally-relevant pedagogy be applied, that knowledge about multiple intelligences be considered, and that appropriate authentic assessment be included.]*

*: This definition/explanation of Contextual Teaching and Learning is taken from CTL website at Bowling Green State University by Berns, R. .G. & Erickson, P. M. (2000).



Problem-Based Learning

Problem-based learning is an instructional approach that uses real-world problems as a context for students to learn critical thinking and problem-solving skills, and to acquire knowledge of the essential concepts of a course.

  • PBL in Mathematics: What a Concept!
    How do we ensure that our students have the necessary skills to succeed in the workplace of the 21st century? We can't predict the future, but we will always have problems to solve. This session shares an innovative approach to teaching and evaluating problem solving and critical thinking skills in an arithmetic class.
  • Problem Based Learning
    The NEW Applied Math Curriculum: A Change in Pedagogy.
  • Center for Problem-Based Learning
    The Center for Problem-Based Learning (CPBL) was established by the Illinois Mathematics and Science Academy to engage in PBL research, information exchange, teacher training, and curriculum development in K-16 educational settings.
  • Paper
    Title: Examining How Middle School Students Use Problem-Based Learning Software.
  • Paper
    Problem-based, inquiry learning is a model of instruction that promotes critical thinking by presenting students with interesting and puzzling problems to solve. The problem solving process involves observing developing and testing predictions, collecting and organizing data and formulating concepts and explanations. The model works best when the problem presented promotes genuine inquiry and the materials used provides valuable instruction. It is important for students to experience the discovery of new knowledge, therefore the problem presented should be based on discoverable ideas.
  • Ford Middle School
    This site links to other sites that provide information about using technology and problem-based Learning in the classroom. This list should be a starting place for information about problem-based learning. Also, this site includes examples of how teachers at Ford Middle School have integrated the use of technology and problem-based learning into the curriculum.
  • Problem-Based Learning Design
    This site describes steps involved in designing problem-based Learning for the classroom.

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Collaborative/Cooperative Learning

Collaborative/Cooperative learning is an instructional approach that uses small groups so that students work together to maximize their own and each other's learning.

  • Cooperative Learning In The Classroom: The Importance of a Collaborative Environment for Computer-Based Education
    Cooperative behavior of students playing an educational computer game was investigated. The combination of gender and whether one or two computers were present significantly affected the level of achievement as measured by the number of puzzles completed in the game. Female/Female pairs playing on two computers, on average, completed less puzzles than any other pairs in any other condition. Differences were also observed for gender pairs sharing control of the mouse while playing on a single computer. Male/Male pairs had a higher number and percentage of refusals to give up control of the mouse.
  • Research on Cooperative Learning and Achievement: What We Know, What We Need to Know
    This research offers Four Major Theoretical Perspectives on Cooperative Learning and Achievement: Motivational Perspectives, Social Cohesion Perspectives, Cognitive Perspectives, Developmental Perspectives and Cognitive Elaboration Perspectives.

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Project-Based Learning

Project-based learning is a comprehensive approach to classroom learning designed to engage student investigation of authentic problems, including an in-depth study of a topic worth learning.

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Service Learning

Service learning is an instructional method that combines community service with a structured school-based opportunity for reflection about that service, emphasizing the connections between service experiences and academic learning.

  • Community Based Learning
    CBL works with businesses and social service organizations to provide students with internships in the community as a part of their academic experience. CBL provides the opportunity for faculty interested in K-12 education to participate in school reform and curriculum development discussions.
  • Community-Based Learning: A Foundation for Meaningful Educational Reform
    This topical synthesis summarizes what we have learned over the past 20 years about various community-based learning programs and describes how community-based learning can serve as an important contribution to educational reform in the future.

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Work-Based Learning

Work-based learning is an instructional approach in which students use the context of the workplace to learn content of school-based courses and how that content is used in the workplace.

  • Work-Based Learning
    A report on educators in the workplace. This page consists of feedback on summer educator externships. The externships provided teachers an opportunity to see what is really happening in business/industry so they could then adjust their curriculum as necessary. In turn, this will help students to become more excited about career opportunities thus spurring more interest in job shadowing and then specific training to qualify for particular occupations of interest.


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The Department of Mathematics Education
University of Georgia