ection 3.2Course Outline Example
ection 3.2
Course Outline Example
Course Catalog Description:
This course gives students an opportunity to apply two-year college mathematics to an authentic situation, use research methods and tools, and create elucidative products. The starting points are real-world technology problems that can be addressed with two-year college mathematics. Each problem is explored, analyzed, and illuminated using bibliotechnology research, mathematics tools, a model portfolio, and a thesis defense.
Contact Hours per Week: |
Credit Hours: |
Prerequisite(s):
Consent of the faculty member -- The mathematics foundation required is determined by the specific laboratory(ies) that the faculty member selects for the course. The prerequisite mathematics topics for a Mathematical Journeys lab are described in the particular lab.
A. Scope: The objective of (insert title selected for course) is to enable the student to: deepen and extend his/her understanding of two-year college mathematics as well as its relation to real-world technology problems, engage in scientific inquiry through explicit application of the scientific method (problem, question, hypothesis, test, decision), decide the appropriate use of a learning technology – calculator, computer, data collection device such as a CBL™, become acquainted with print and electronic resources, conduct bibliotechnology research, create products that clarify and communicate the technology problem and its solution, and defend a thesis. Acceptable products might include: videos, Power Point documents, printed materials, computer and calculator programs, outputs from data collection devices, physical models, mathematical models, etc.
B. Required Work: Determined by faculty member as described in the course syllabus.
C. Attendance and Participation: Students are expected to attend each class, arrive on time, complete all assignments and learning assessments in accord with the syllabus schedule, and participate in the in-class learning process. (Specific policies of the faculty member are included in the course syllabus.)
D. Methods of Instruction: The methods of instruction are determined by each faculty member and may include, but are not limited to: lecture, lecture/discussion, small group collaborative learning, experiment/exploration, student presentations, and use of audio-visual materials, computers, and graphing calculators.
E. Objective, Outcomes, Assessment: The following objectives and outcomes represent the department's core requirements for student achievement.
| LEARNING OBJECTIVES | LEARNING OUTCOMES | ASSESSMENT METHODS |
| To demonstrate an understanding of: | Student will: | As measured by: |
| Problem solving/ Reasoning | a) Prepare research-based descriptions of the technology problem. b) Define pertinent terms/processes relating to the technology problem. c) Describe the environment of the technology problem. d) Develop thesis. e) Identify mathematics topics. f) Construct a model(s) that elucidates the technology problem. g) Develop a solution of the technology problem. |
Homework assignments; Written and oral communication of work in-class; A portfolio; Presentation of the portfolio to an audience |
| Bibliotechnology research | a) Identify categories of pertinent print resources. b) Access print material in each category. c) Identify categories of pertinent electronic resources. d) Access electronic material from each electronic resource category. e) Identify other resources such as technology-based industries. | |
| Mathematics topics | a) Identify pertinent mathematics topics. b) Identify variables of interest. c) Link mathematics topics to the technology problem. d) Perform all requisite mathematics operations. | |
| Scientific inquiry | Apply the five-step scientific method to the technology problem. | |
| Connecting mathematics with other disciplines | a) Develop working understanding of technology-problem terminology. b) Interrelate pertinent mathematics and technology-problem elements. | |
| Communication | a) Work collaboratively with other members of team. b) Communicate technology in writing and speech. c) Compile the work in a model portfolio. d) Prepare a written defense of the thesis, and deliver the defense orally to an audience. | |
| Technologies for learning/knowing | Use graphing calculators, computer programs, the Internet, audio-visual tools, etc. |
Note 1: The foregoing table of learning outcomes should not be considered exhaustive; other learning outcomes may also support the objectives. The list is not intended to limit the learning outcomes that can be used to support the objectives.
Note 2: The order in which the learning outcomes are addressed and the relative emphasis given to each will vary from one faculty member to the next.
Note 3: The particular list of assessment methods is not exhaustive. Other methods that measure the learning outcomes may be used.
F. Texts and Materials: Mathematical Journeys I Partially supported by the National Science Foundation, © Capital Community College, 950 Main St., Hartford, CT., 06103.
G. Information Technology: Use of a graphing calculator and the web is required. Also, computer application software such as a word processor, an algebra system, spreadsheet, presentation software, etc. may be helpful. A CBLÅ will be useful for some labs.
This is an interdisciplinary, collaborative learning team course in which each team must work to fulfill the requirements of a selected lab. In turn, this requires that each team create a model portfolio and deliver a defense of its embedded thesis according to the schedule provided by the syllabus. This example of an outline is based on a 15-week course composed of 45 classes. The course has been subdivided into three phases: Course and Lab Introduction, Solution Development, Thesis Defense. The outline is written for a course that uses only one lab; if the course uses more than one, the outline would need to be adjusted accordingly.
Phase I is developed to a high level of detail. On the other hand, Phases II and III can only be addressed in more general terms because of the open-ended character of the labs.
Class 1Provide an overview of the course and introduce the concept of a Technology Problem.
Assignment: Each student will prepare one typewritten page that addresses the following two questions: "When working with others toward a team goal, what do you see as the major difficulties and major benefits? What special strengths/abilities/talents do you see yourself bringing to cooperative teamwork?" The paper should include a title, the student's name and an opening and closing paragraph. The paper should be a reflection of thoughtful introspection, well organized, and grammatically correct. In addition to the paper on cooperative teamwork, each student should read the assigned lab or the laboratory abstracts (Chapter 1, Section 1.1), depending on the option used to select a lab.
Class 2 and Class 3Explain that Bibliotechnology Research refers to the process of identifying, locating, and using either print or electronic sources to address the problem under consideration. It is important to emphasize the need and format for referencing sources.
Assignment: Each team will develop and write down at least two questions concerning the lab and at least one thing about the technology problem that the team would like to uncover. Also, each team will assemble an initial list of at least five correctly referenced resources pertinent to the technology problem. This resource list, augmented as the course continues, will provide a bibliography for the model portfolio. This assignment could be completed in less than one typewritten page, including the heading.
Class 4Provide an overview of Mathematics Tools.
Assignment: Each team will assemble an initial list of mathematics tools that would appear to help represent and solve the technology problem. As the course proceeds, students are expected to find that they need to add further mathematics tools to the initial list. The resulting mathematics tool-set will provide the mathematical foundation for the model portfolio and thesis defense. As the second part of this assignment, each team will add to the resource list and question set that it started in the previous class. This assignment should occupy no more than two typewritten pages.
Class 5 Describe the Model Portfolio.
Assignment: Each team will prepare a one-page outline of its model portfolio.
Class 6 Explain the concept of a thesis and a Thesis Defense.
A thesis is a significant claim that one makes about a situation. In this context, a thesis is a significant claim about the technology problem. It may be possible to develop more than one thesis about the technology problem. A thesis defense is a logically structured assemblage of facts, explanations, representations and arguments that, taken collectively, support acceptance of the thesis. It should be noted that acceptance of a scientific thesis is not absolute; such acceptance remains open to review on the basis of new information. A thesis that was accepted at some point in time may later be rejected or revised as new discoveries are made. The thesis and thesis defense form the backbone of the model portfolio. "Delivery of the thesis", which is often referred to more simply as "thesis defense", means orally communicating the model portfolio to an audience.
Assignment: Each team will make some pertinent statement (a thesis) about the technology problem and write a defense of the statement. The students should demonstrate an introductory understanding of what is meant by "defense of a position or claim". The students should clearly identify the reasons used to support their thesis or claim including facts, sources, and logical arguments. This assignment should not exceed 2 typewritten pages.
3rd – 13th Week: Model Portfolio Creation (Classes 7–39)During this phase, your role will move in the direction of facilitator, guide, co-learner, and progress evaluator. The specific content, approach and schedule of activities for the course will become more student directed. As such, you should expect the teams to regularly communicate their research findings to you so that you can learn from them and respond to them. As a participant-learner, you will be in a better position to suggest pathways for continued research; provide background explanations of pertinent mathematics, technology, or scientific topics; and offer new sources of pertinent information.
You should emphasize to the students that effective teamwork means that they will need to develop collaborative learning skills. While students will contribute in different ways to their team's efforts, each one is fully responsible for the quality of the team's output.
You should inform the teams that it is necessary to keep an accurate record of their work. This paper trail should be sufficiently complete to allow a third party to repeat the team's work step-by-step and test its thesis. Also, a record will be indispensable for supporting the thesis, preparing the model portfolio, or writing an article for publication.
Research on the technology problem will introduce terminology that is specific to the technology under consideration. Such terminology may involve words or expressions that are unfamiliar to the student, or the student may know the usual meanings of words that have different meanings in a specific technology. Thus, it is advisable for students to create a glossary of key terms and add them to ones provided in the lab.
It is important to keep in mind that the model portfolio is the embodiment of the research process and application of the scientific method. The model portfolio must reflect in structure and content the research process – understanding/describing/representing the problem, searching for and using bibliotechnological sources, giving meaning to source data, transforming data into information with the aid of mathematics tools and technology as appropriate, organizing information into a coherent work with the aid of technology as appropriate, and observing accepted academic protocols and standards for research papers. The model portfolio must also reflect scientific inquiry, that is, application of the scientific method. Each team should be expected to form some thesis about the technology problem and collect data, or cite data obtained from bibliotechnology research, to make a decision about the thesis.
While the research process and scientific inquiry are infused in all labs, the mathematical, technological, and model-building content of the solution phase is driven by the particular lab selected. A major role of the professor during the solution development phase is to help students select and cull acquired material. An important part of research involves identifying and selecting whatever advances the development of a solution and discarding materials that lead to dead ends. Nonetheless, as in a maze, paths not leading to the goal often help us reach it. To take advantage of such apparently useless information, it is important for students to record both their obviously productive steps as well as their apparent missteps. We learn from our mistakes.
The professor will need to make decisions about treating mathematics topics in depth or breadth. Shortage of time or complexity of a mathematics topic may not permit the students to address it in depth. On the other hand, embedding mathematics topics in larger mathematical contexts unifies instruction and learning, provides a structure for establishing logical relationships, and yields results of sufficient generality to be of value in other times and places. For example, if logarithms are needed, it may be well to discuss them in the context of functions, exponential functions, and inverse functions. The professor also must decide how much to help students use a learning technology.
In summary, during the solution development phase, the professor will use the classes to respond to questions, teach mathematics, provide additional resources, and regularly review the status of the teams' in-progress model portfolios.
Assignments: At the beginning of each week, the teams will hand in a report of the work they accomplished during the preceding week. Teams will use the weekly reports as a basis for preparing their model portfolios. Thus, the weekly reports should be well organized, accurate, and complete. The teams should retain print and electronic copies of their reports. Between the 7th and 8th week, the teams should submit an in-progress model portfolio in accord with established criteria.
Note: The Faculty Notes are located in Section 1.2 of Chapter 1.
14th – 15th Week: Delivery of the Thesis Defense (Classes 40–45)The thesis defense phase involves communication by the teams of the thesis developed in their model portfolios. Each team will present the model portfolio and defend its underlying thesis to a selected audience. About 45 minutes should be allocated to each team's thesis defense. Students in the class could do a criteria-guided peer assessment of each thesis defense, the results of which would be directly communicated to the team presenters. (See Section 3.3 – Phase III for an assessment form, criteria, and rubric.) The number of classes allocated to thesis defenses depends on the number of teams, and therefore will vary somewhat from one course to the next. The very last class should be reserved by the professor to sum up the work done, remind students of the lab's unifying themes, invite students to share their views of the course, speak about probable future directions for Mathematical Journeys courses, etc.
Options for delivering the Thesis Defenses
Option 1: The audience is the class. In the interest of using the presentation time to best advantage, each team could be asked to make its model portfolio available for review by all class members a few days prior to delivering the thesis defense. The thesis defenses could also be videotaped for presentation to the public. However, any public distribution requires that permission/release forms be signed by all individuals who contributed to the videotape. Typically, the forms can be obtained from a college administrator. In any case, check with your college administration to determine the policies and procedures regarding public distribution of any materials.
Option 2: The thesis defenses could be delivered to audiences such as a science club, college administration (President, Deans, Department Chairs, etc.), mathematics club, or a meeting of a professional organization such as AMATYC, an AMATYC Affiliate, a science or technology association, or a technology-based industry or governmental organization. The thesis defenses could also be videotaped for presentation to the public. As noted above, any public distribution requires that permission/release forms, be signed by all individuals who contributed to the videotape. Typically, the forms can be obtained from a college administrator. In any case, check with your college administration to determine the policies and procedures regarding public distribution of any materials.