Curriculum Development Annotated Plan Excerpts

Excerpt 1 [University of Tennessee, Chattanooga]

Project Features:
Describes project philosophy/rationale

The philosophy which underlies this project and the OZ text includes the following critical beliefs:

• The fundamental concepts of the subject are kept clearly in focus at all times.
• The "holy trinity" of graphical, numeric, and symbolic approaches is imperative.
• The text provides many avenues for visualization and discovery of mathematics.
• Computers and graphic calculators can be effectively used to illuminate mathematics.
• The OZ approach to "reform" is relatively conservative, and neither we nor our department are interested in a radical restructuring of the course.
• The text can be used effectively in the wide variety of settings represented by our consortium.
• The text is well and thoughtfully written, and so serves as a fine example for our students of good expository writing in mathematics. Requiring students to explain themselves is an important part of the "reform" process.
• The text has a variety of interesting exercises and there are much more novel and thought-provoking than is typical.
• We want to avoid a problem of a student saying that what he liked about the old book is that you can do the problems without knowing what you are doing.
• Many exercises are well suited to small group/cooperative work and serve as catalysts for meaningful mathematical discussions.
• The wider variety of approaches in the text appeal to a wider audience and offer more diverse learning styles, including females and minority groups.

Excerpt 2 [University of Michigan]

Project Features:
Describes project philosophy

We believe that motivational factors interact with cognitive factors in determining development, especially for women and minority students, who often fail to elect further courses even when their performance is at a satisfactory level. Rather than using introductory courses to screen out students who are not already highly motivated and skilled, introductory courses need to do a better job of helping students develop a meaningful understanding and appreciation of their field.

Excerpt 3 [New Mexico State University]

Project Features:
Describes project goals

One of the main goals of the program is to design and study the design of appropriate projects to assign in the calculus. Projects' mathematical content should be deeper than that expected on a test or homework, the wording of the project should allow the student to begin working on his own, the reading level should be at an appropriate level so that we can be sure that a students' inability to solve a project is not caused solely by the inability to read the problem. Most calculus texts have variations on a rather small number of project ideas. We will use scientists, engineers, and economists to help design projects which demonstrate the mathematical underpinnings of solutions to applied problems.

Excerpt 4 [University of Michigan]

Project Features:
Lists project goals

The major goals of the program are:

1. a concept driven course,
2. students are better prepared for, and more likely to take further mathematical and science courses,
3. a more enjoyable experience for students.

Excerpt 5 [University of Illinois, Urbana-Champaign]

Project Features:
Lists project goals and strategies

1. To create and implement an electronic interactive courseware in which students learn all levels of calculus and elementary differential equations through active learning via student experimentation and computer visualization.
2. To revise calculus and differential equations courses so that both are approached from a modern viewpoint. This included dropping some inert topics, emphasizing the interplay between calculus and initial value problems, emphasizing use of the computer and de-emphasizing rote algorithms better done by computer than by pencil and paper through memorization.

Excerpt 6 [University of Hartford]

Project Features:
Describes project goals

The goals can be divided into four groups: goals for the students, faculty, institutions, and the State of Connecticut. At the student level, we want to get students excited about mathematics and to deepen their understanding of how mathematics is actually used. We want students to learn the appropriate role of technology in problem solving and be able to use the technology. We want to give students increased ability to reason geometrically and to see problems from different perspectives (geometric vs. algebraic). We want students to come away with a better understanding of some of the "big ideas" of calculus.

For faculty, we hope to provide a framework and means for achieving student goals, rekindle their interest in teaching, and deepen their understanding of calculus.

At the institutional level, our goal is to get as many faculty as possible involved. We want each institution to implement some kind of lab/technology approach in all their calculus classes.

At the state level, the goal is to get all the two and four year colleges and universities involved in calculus and as many of the high schools as possible.

Excerpt 7 [University of Michigan]

Project Features

The University of Michigan plans to completely revise its first year calculus program over a three year period adopting the materials developed in the Harvard consortium project. The main features of the new program are:

1. an intensive and ongoing instructor training program for all faculty and teaching assistants,
2. a classroom environment that incorporates cooperative learning and experimentation by students,
3. major syllabus revision which emphasize problem solving, geometric visualization, and quantitative reasoning,
4. integration of the graphing calculator into the curriculum.

Excerpt 8 [University of Illinois, Urbana-Champaign]

Project Features:
Describes new curriculum resources and how students use them

Calculus and Mathematica is probably the most technology intensive of all the calculus reform projects. The course is based on an entirely interactive text in which the student has access to as many examples as desired. Through the use of technology, students see calculus as a course in scientific measurement, calculation and modeling. The course consists of four main sections. Students are expected to attend 3 one-hour laboratory sessions every week. Section instructors make assignments and prepare examinations, conduct weekly discussion hours, and help students in the lab. Students learn the course content through lessons called "notebooks" installed on the computer progressing from "basic" problems that introduced key concepts, followed by "tutorial" problems in techniques and applications. The notebook closes with "give it a try" section that includes problems to be solved. Students solve the problems using standard word processor and calculating software with graphic capabilities. These solutions become a key component of each student's notebook which is electronicallly submitted to the instructor for comments and grading.

Excerpt 9 [University of Hartford]

Project Context

Project Participants, Audiences & Other Stakeholders:
Describes different ways stakeholders are involved in the project

A group of 18 institutions is working together. The laboratory materials developed at the Univeristy of Hartford and the text materials being developed by the Core Calculus Consortium (led by Harvard University) are being integrated into the new course. The Connecticut schools that have agreed to participate in the project are: [names about 20]. This represents a wide variety of different types of schools; large, small, public and private, four year schools, two year schools, and high schools. Two of the schools are women only.

Excerpt 10 [Iowa State University]

Our proposal is to create an integrated set of worksheet "tutorial" materials, which eventually will be synthesized into a full-scale workbook. This workbook will then be ready for use in several different courses both in physics and chemistry. As a practical matter — due to differences in notation commonly used in chemistry and physics, etc. — it will probably be necessary to create two separate "tracks." That is, the final workbook might have a "Physics" track and a "Chemistry" track, or it might actually be necessary to create two separate (though closely related) workbooks.

Project Context:
References prior research

Based on published research regarding learning of concepts in thermodynamics, and our own extensive teaching experience, we will begin to draft sequences of questions and exercises focused on our targeted topics. The material will consist of a tightly linked set of (1) brief textual expositions in highly "interactive" format, (2) multiple-choice, concept-oriented questions for use with classroom communication systems in large classes, (3) structured series of questions that lead students to elicit and then resolve conceptual difficulties, and finally (4) exercises to strengthen understanding. The emphasis throughout will be on qualitative reasoning and mastery of fundamental concepts. A great deal of pictorial, diagrammatic, and graphical material will be incorporated. Detailed descriptions of each of these types of materials are given in Appendix A; included in the descriptions are references to lengthy samples of each type, which are provided in Apendices D, E, F, G, and H.

Project Participants, Audiences & Other Stakeholders

The development of these initial drafts will be assisted by Graduate Student Research Assistants, one a member of the Physics Education Research Group, and the other a member of the Chemistry Education Research Group. Draft worksheets will be class-tested in recitation sections, labs, and during lecture presentations. Feedback obtained through the class testing will be immediately utilized for revision and redesign. We have already obtained agreement in principle with some of the instructors in the targeted courses to cooperate with the testing of these materials. A detailed description of the actual process we have carried out to create some of the sample materials included in this proposal is contained in Appendix B. This provides a model that will guide our future activities as this project evolves.

The Graduate Student R.A.'s participate in all aspects of this work. They assist in formulating initial drafts, help to test them out in recitation sections, and give input for revisions and rewrites. They help carry out extended "interview" questioning to probe student understanding in depth. They also contribute to the creation of high-quality graphic materials (diagrams, drawings, etc.) that form an integral part of the worksheets. (This is one of the more labor-intensive aspects of this type of curriculum development.)

In addition to graduate student involvement in this work, we will be drawing in selected advanced undergraduate students to participate in the process of testing and assessing the curricular materials. We will focus in particular on students who plan to become high-school physics and chemistry teachers. These students can benefit tremendously by participating in the instructional activities in the tutorial sessions (whether these occur during recitations, labs, or "lectures"). As they walk around the room, listening to students' comments as they work through the materials and providing guidance by asking leading questions, these future teachers will gain first-hand experience with common learning difficulties and strategies for confronting them. As a result, they will be able to make valuable contributions to the curriculum development work by providing insight into student learning difficulties. They will also help in directly monitoring student responses to the new materials. In work at Southeastern Louisiana University (as well as at the University of Washington), this type of participation by undergraduate students has been extremely beneficial to all concerned (as well as being very cost effective).

Project Features:
Lists planned curriculum topics

The thermodynamics topics to be covered will include all those normally discussed in introductory general physics and general chemistry courses, as well as a core of advanced topics typically covered in junior-level thermodynamics and physical chemistry courses. This is our core list of planned topics (more may be added later):

1. Kinetic theory of gases, ideal gas equation of state, equipartition of energy
2. First law of thermodynamics: heat, work, internal energy and enthalpy
3. Heat Engines, Carnot cycle
4. Entropy and the Second Law of Thermodynamics
5. Free energy, Maxwell's relations; third law of thermodynamics
6. Non-mechanical work: voltaic cells, magnetism
7. Phase transitions, Clausius-Clapeyron equation, Van der Waals theory
8. Chemical potential, phase equilibria, phase rule
9. Gibbs-Duhem equation, colligative properties

With the exception of an introductory section on kinetic theory of ideal gases, our approach will be almost entirely macroscopic. We feel that this is a more accessible approach for most introductory students, and we will not at this time be focusing on the statistical approach to thermodynamics concepts.