In seeking exemplary educational practices, the first natural place to look is inside classrooms during interactions between students and teachers. But classrooms do not exist in isolation. What happens in the classroom is conditioned on the systems in which the classroom is embedded, including the community and family relations of the students and the professional relations of teachers. Best practices, therefore, are not always to be witnessed in the classroom. Equally important are actions upon or within the systems surrounding the classroom. The major NSF initiatives in K-12 science and math education that were undertaken in the 1990’s---such as the rural, urban and state systemic initiatives, as well as the collaboratives for excellence in teacher preparation---were based on exactly this premise.
Social practices, we know, spread by modeling. People tend to re-create those environments, structures or conditions that they have experienced. This is just as much the case with practices of instruction in the classroom as it is with practices of management and support in professional settings, from university departments to businesses and industries. LaCEPT provided powerful positive models for the organization, development and support of teaching professionals. What I wish to describe here is an example of how that model propagated. The process outlined here culminated in an NSF-supported project in the Adaptation and Implementation Track of the program for Course, Curriculum and Laboratory Improvement in the NSF Division of Undergraduate Education. This project, which is currently underway in the Department of Mathematics at LSU, seeks to adapt LaCEPT’s approach to the support and development of high-level teaching capacity. The title of the project is: “Using the LaCEPT Model to Reform an Elementary Statistics Course.”
The LSU mathematics course entitled The Nature of Mathematics. Typically, between 5 and 10 sections of the course are taught each semester, and each section has from 20 to 35 students. Most sections are taught by full-time instructors or by graduate teaching assistants, though professors also teach it from time to time. In the five fall semesters between 1995 and 1999, the 1,564 students who took the course. Of these, 73% were female; 13% of the 1,564 were racial or ethnic minorities and 8% of the 1,564 were black. The syllabus used for the course throughout most of the 1990’s included topics in elementary set theory, logic, combinatorics, probability and statistics, with allowance for optional material at the choice of the instructor. Approximately 1/3 of the students taking the course will enter LSU’s K-8 teacher preparation program for which the course is one of 4 required mathematics courses. Thus, each year the course has direct impact on about 200 teachers-in-training. It is presently the only mathematics course in which pre-service elementary teachers at LSU are exposed to the topics of data, statistics and probability.
Instructor Phoebe Rouse and I first got involved in rethinking the course in summer 1996, when I served as mathematics liaison in a LaCEPT grant administered by the LSU Center for Science and Math Literacy, which is housed within the LSU College of Education. Under this grant, Rouse developed a set of course notes based on the existing syllabus, but including more elaborate student activities, opportunities for cooperative learning, and writing assignments intended to develop conceptual understanding. I pursued a different track, writing notes for lessons that would significantly expand or alter the existing syllabus. In the fall of 1996, we began using the new materials.
In spring of 1997 and in following years, Rouse continued to supplement, perfect and polish the materials she had developed, receiving occasional input from other instructors. I, in the meantime, continued my more exploratory approach, trying a variety of new lesson ideas and strategies for evaluation. Eventually, I found a very positive response to lessons in the style of the Dartmouth Chance Project that involved reading and responding to newspaper articles. I also found portfolio assessment to be very useful. Interestingly, a number of instructors had independently started using portfolios and student projects for assessment in their own classes. Instructor Sybille Clayton, for example, had a detailed canon for students to follow in putting together a project, accompanied by a highly developed grading rubric. Rouse also used student projects as a basis for some evaluation as did Instructor Robert Kelso.
In summer 1998, I learned that a number of university faculty members from around the state were beginning to rethink the statistics and probability content in the teacher preparation courses. I obtained support from LaCEPT for a January, 2000 workshop for Louisiana faculty that would examine current trends in teaching and evaluation in elementary statistics. I also applied to the LSU Teaching Incentive Grant program for a project intended to get more instructors at LSU involved in course reform. It is worth quoting extensively from the proposal, because the justification and rationale for that project subsequently formed a basis for the proposal to NSF:
In the last few years, probability and statistics have acquired greatly increased emphasis in the primary and secondary curricula, figuring in the National Council of Teachers of Mathematics Standards 2000 on an equal footing with four other main content areas. At the same time, a solid universal consensus among educators about how probability and statistics should be presented in an introductory college course has emerged. The new pedagogy emphasizes higher-order thinking, problem-solving and flexible skills learned in a cooperative setting, with significant technology support. There are specific content recommendations, as well. Unfortunately, many aspects of the course are inconsistent with the new standards. This poses a critical challenge. …. Strategies to address the issue must take into account several factors, particularly the fact that most sections of the course are taught by instructors. The ideal course would involve both new teaching styles and new content, but without any discipline-specific staff development programs at LSU, it extremely difficult to envision a path leading from the present situation to a satisfactory course. In designing a workable approach, we have taken into account the lessons learned from LaCEPT. Experiences with LaCEPT-sponsored course reform in several Louisiana mathematics departments have demonstrated that, with appropriate support, instructors who are in much the same position as our own have the ability to design and implement fundamental change. … The present proposal aims to implement the LaCEPT philosophy at a “micro-scale.” Rather than designing a reformed course and then training instructors to deliver it (top-down reform), the correct strategy is to entrust the instructors with the task of reform and provide them with the resources they need to do it right. This approach, by valuing the professionalism of instructors, leads to a staff that has “bought in” to the goal of improvement through self-monitored change.
This proposal was successful, and made it possible for me to meet biweekly in spring 1999 with 6 veteran instructors who had an interest in working on improving the course. At these meetings, existing conditions and recent changes in the course were reviewed. Instructors were encouraged to get their ideas for the course out into the open and to work together to develop them. The instructors identified problems and determined the kind of support they would need in order to make changes. They reached agreement on core syllabus topics and on high-level course goals, and devised a plan of action. In the end, two important things came out of this process. First, the instructors agreed upon a general design for the course based on a division into four main topics. Second they devised a strategy that would allow the course to grow and change though their contributions. On this basis, I applied to the course, Curriculum and Laboratory Improvement program in the NSF Division of Undergraduate Education for support to pursue these objectives. A $75,000 grant was awarded in January 2000 to support the project “Using the LaCEPT Model to Reform an Elementary Statistics Course,” which is currently underway.
In the rest of this essay, I want to describe the aims of this project. I shall begin by describing the four main topics for the course as described in the proposal:
1. The language of mathematics. This replaces the part of the course that previously treated a loose collection of topics, including propositional logic and elementary set theory. The new syllabus will focus on the ways in which mathematical representations are used, with particular emphasis on the basic vocabulary connected with variables, in the sense used in probability and statistics.
2. Probability. In the past, the course has featured discrete probability, with heavy emphasis on the combinatorics related to permutations and combinations. In recent years, this approach has been criticized because students’ attention is drawn to the complex counting procedures, and they fail to develop a deep understanding of the fundamental notions of randomness and probability; see the recommendations of Lajoie (1998). Students may leave a course of this kind without developing accurate intuitions about randomness, without recognizing practical situations where probabilistic thinking is useful and with no grasp of the basic concept of a probability distribution. Following recommendations of Moore (1997), the revised curriculum places more emphasis on simulation. It also emphasizes the idea of probability distributiosn, rather than simply probability calculations , following a suggestion of Lajoie (1998). Only after ideas about randomness and probability are developed is combinatorial probability treated.
3. Statistics. In the past, the course curriculum emphasized basic ideas such as mean, median, standard deviation. Exercises involved simple manipulations, i.e., given an average and a standard deviation, determine what percent of a normal population lies in such-and-such a range. Such mechanical exercises do not help students link statistical concepts to situations that are directly meaningful to them. This course will use a modification of the strategy of the Dartmouth Chance Project, where students encounter statistics in news media, and develop statistical thinking in order to interpret and evaluate news stories. Assignments asking students to collect newspaper articles illustrating specific concepts in statistics and to write commentaries on them.
4. Risk and Finance. We determined that this is a topic in which students have a natural interest. Complex assignments, such as estimating the income required in order to meet given financial obligations, predicting the eventual value of investments, or understanding and quantifying financial risks have really captured students’ imaginations. This section of the course we will have opportunities for exposing students to recent ideas that have come into powerful play in the financial markets, (e.g., pricing of securities and commodities, portfolio pricing and design). Bernstein (1996) is a useful source that emphasizes financial themes, ties many course concepts together and provides fascinating historical perspectives as well.
These four items gave us a framework for course design, but did not solve the practical problem of how to move from the present situation to the new course. We rejected the model of change in which new curriculum materials would be created all at once and then adopted. Based on LaCEPT experiences, we felt that maximum instructor involvement in the creation of materials would result in a better course, even though it might take much longer to make a complete change. We identified several mechanisms by which course instructors will monitor the course, and create, evaluate and incorporate new course structures and materials.
1. Syllabus. We picture a course that changes, grows and evolves, yet we feel strongly that at any given time there should be consistency across sections. Therefore, we agreed to maintain a syllabus that is regularly updated to reflect instructor consensus on course content and structure, but that also sets an agenda for change. For the foreseeable future, the syllabus will reflect organization around the four content areas described above.
2. Experimentation. How can we experiment with new curricula while maintaining the uniformity and quality control that we decided was important? Any instructor may in any semester choose to experiment with novel curricula or teaching strategies in any one of the four content areas. When doing this, the instructor may depart as far as desired from the official syllabus in the experimental area.
3. Group awareness. We will use the lunches at which instructors have traditionally come together as a mechanism to keep one another informed about the course. Very little additional structure needs to be imposed here in order for this to happen. We designate a particular day of the week as the “course Lunch,” and use this opportunity to communicate about the current state of course and to propose and weigh possible changes.
4. Instructor release time. All the instructors hoped to be able implement ambitious ideas, ranging widely over several designs: preparing course notes, making internet course resources, gathering materials to support lessons, and exploring new content and/or pedagogy. There was uniform agreement that in order to accomplish anything meaningful, a semester with two courses release time would be needed. (The normal teaching load for an instructor is four courses per semester.) Release time is the largest single budget item in the grant.
5. Providing information. Madden has the important role of supplying the instructors with information about content ideas and with access to relevant pedagogical research, recommendations and standards.
6. Computer equipment. Communicating with students by email and putting course materials on line is by now utterly routine in most universities. Yet our instructors still cannot do this conveniently because they lack office equipment, and can only access the Internet in the departmental computer lab. Acknowledging the importance office computers, LSU has agreed to pay two thirds of the cost of equipping the instructors.
The six structural items are not intended to produce curriculum that fits a fixed conception, but rather to produce a stable organization that has as its function the testing and assimilation of new teaching strategies and curricula and the maintenance of a course that is always moving and changing. At this stage, the project has been successful in getting a group of instructors involved in an unprecedented way in curriculum design. In this way, it is not only contributing to a large extent, this project is an on-going experiment to test whether these strategies really can lead to better instruction. As an experiment, the final results are not yet in. We have learned, certainly, that the process of change is complex and that not everything that looks good on paper really works in practice, but the main hypothesis is borne out. Good instruction is dependent upon the quality of support provided by the institution. We also see clearly that the model of support that LaCEPT has pioneered works very well in the environment where we are implementing it.
To summarize
the basic philosophy of LaCEPT, I know no better statement than that made in
1998 by Carl Franz, LaCEPT coordinator for evaluation. In Franz (1998), he characterized the
philosophy as: Bottom up reform, lateral assistance and top down support.
Bernstein, Peter L. (1998) Against the Gods: The Remarkable Story of Risk, John Wiley and Sons.
Frantz, Carl (1998). Top Ten List of Insights/Conclusions, Prepared for the Louisiana CETP PI/PD Panel Discussion, Baton Rouge, May 1, 1998.
Lajoie,Susanne P. (1998), Reflections on Statistics: Learning, Teaching and Assessment in Grades K-12, Mahwah New Jersey and London: Lawrence Erlbaum Assoc.
Moore, D. S. (1997) New pedagogy and new content: The case of statistics, International Statistical Review 65 (1997), 123--165.