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College Algebra in Context: A Learner-centered Approach Incorporating Data-driven Activities Related to Social Issues

Michael Catalano
Dakota Wesleyan University

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In this project, we developed materials designed for use in a learner-centered, inquiry-intensive, data-driven, activity-oriented college algebra course, incorporating realistic problem situations emphasizing social and economic issues, including hunger and poverty, energy, and the environment. The project is meant to address two national needs, namely a need for U.S. citizens with a greater level of quantitative literacy, and a need for improved mathematics education for K-12 teachers. The project is also intended to support the mission of the McGovern Center for Leadership and Public Service at Dakota Wesleyan University. Pilot sections using the materials in development have been offered at Dakota Wesleyan University since the fall of 2005 with the PI as instructor. The grant period for this project (DUE-0442979), ended February 28th of 2009.

Project Goals

The primary goal was to create a text that can be used in a data-driven course incorporating a collaborative learning model at the college algebra level as described above.

Student outcomes included:
  1. Students will gain an appreciation for and understanding of how quantitative information and algebraic concepts and techniques can be used to gain insight into real-world situations including social issues, to help inform recommendations for action, and to contribute to public discourse.
  2. Students will gain facility in using technology to model and solve real-world problems.
  3. Students' attitudes towards mathematics and its applicability, and their abilities to apply mathematical concepts in a real-world context will improve.
  4. Students' confidence in their mathematical abilities will improve.
  5. Students will begin to develop into more intellectually mature, self-regulated, and intrinsically motivated life-long learners.

Project Design/Elements

Major features of the materials developed include:

  1. Incorporation of a collaborative learning model informed by the GEMS program (General Education in Mathematics and Science) at Hope College. Each chapter includes activities that are designed for students to work on in groups of two or three utilizing appropriate technology.
  2. The activities and many examples in the text are data-driven, emphasizing real-world data related to social issues like hunger and poverty, energy, the environment, literacy, resource inequality, etc. Are literate societies more democratic?
  3. Although the activities in general can be done using graphing calculators or a spreadsheet program, we have primarily been using Fathom Dynamic Data software. This software is fairly intuitive and easy to use with many unique dynamic features. Although designed more for teaching introductory statistics, it includes functionalities that are useful and appropriate in an algebra setting.
  4. Many activities involve the students in creating models based on real-world data sets. The text covers the usual set of function families, including linear, exponential, quadratic, logarithmic, and power functions.
  5. Compared to a more traditional college algebra course, there is much less algebraic manipulation and much more of a focus on real-world data and modeling. The text includes discussion of descriptive statistics, but very little with respect to operations on polynomials. Sequences and series and basic probability are included.

Evaluation and Assessment Strategies

The evaluation of the project has consisted of the following components.
  1. During the first project year, we convened focus groups of students who had completed the course in order to get more robust input for improving the course and the materials.
  2. In May of 2009, we administered a survey to all current students at Dakota Wesleyan who had taken college algebra using the College Algebra in Context materials. The survey was intended to help assess outcomes 1-4. A summary of the results of this survey are provided below.
  3. To help assess outcomes 3 and 4, many pilot sections of the class have been asked to complete the SALG (Student Assessment of Learning Gains) instrument at least once during each semester. SALG has served as a diagnostic tool to determine the perceptions of students regarding the effectiveness of the materials and pedagogical strategies being employed in the course, and to assess student attitudes regarding how well they are meeting course goals.
  4. To help assess outcome 5, students have taken the LASSI (a learning styles inventory) at the beginning and end of the course over the first two project years. This instrument was selected because it will be easy to use, and provides national norms for results.
  5. To assess outcome 3, selected items from previous college algebra final exams (before implementation of the new materials) have been included on the final in pilot sections. These items were selected for their relation to conceptual understanding and application of algebraic concepts to real-world situations. Mean scores for each pilot section on each selected item will be compared to the means for sections from previous years to see if the revised course results in improved learning. Other variables (e.g. previous math courses, ACT scores, etc.) will be taken into account.
  6. As an indirect measure of the effectiveness of the revised course in improving student motivation and confidence, the percentage of students in each section who drop, withdraw, or fail the course will be compared to sections from previous years. As confidence and motivation play a significant role in student success and retention in a course, this will be a measure of outcomes 3-5.

Summary of May 2009 Follow-up Survey (Acrobat (PDF) 59kB May21 09)

Partial results from SALG surveys (Microsoft Word 42kB May1 09)

Success rates of students in pilot sections (Microsoft Word 34kB May1 09)

Products, Key Findings, Publications

Current version of text (277 pages) (Acrobat (PDF) 2.4MB May1 09)

Related or Similar Projects

Understanding Our Quantitative World, by Janet Andersen and Todd Swanson. Written with NSF support (DUE-9652784) and published by the MAA, this book was used as one of the models for our project and is used as part of the GEMS curriculum at Hope College.