Lessons Learned Concerning a Student-Centered Teaching Style by University Mathematics Professors from Secondary School Educators
Introduction
Student-centered learning has been a catch phrase in teaching methodologies in education for at least the last decade. Some of the more prominent aspects of this style include group work, student projects, real data analysis, written and oral presentations, and open-ended queries. One very popular aspect of student centered teaching is teaching by group.
This group instruction approach is widely used by many university professors, especially in colleges of business, and it has been well documented (Gailey & Carroll, 1993; Harmon & Harumi, 1996; Kahl & Newman, 2003; Yobaccio, Kennedy, & Schumacher, 2006).
As noted by Johnson, Johnson, and Smith, group learning has roots at the university level as early as the 1940s. They also state that in the early 1970s, K-12 educators joined the effort of investigating and researching the use of cooperative learning, and it was at this level that cooperative learning really took hold and grew (Johnson, Johnson, & Smith, 1998). In the 1990s the interest in cooperative learning at the university level was rekindled. Dilip Datta describes the early application of these teaching methods for university mathematics classes in his book, “Math Education At Its Best:
The Potsdam Model” (Datta, 1993). Furthermore, cooperative learning as part of the reform movement in university statistics is discussed in detail by Joan Garfield (Garfield, 1993). There are some mathematics professors who have adopted a group teaching style, but the lecture approach still seems to be the favored way to teach university level mathematics. Johnson, et al. emphasize that university professors have been slow to adapt.
They point out that many mathematics professors still ignore the power of students learning cooperatively. They observe, “the whole instructional system aims to pluck out and nurture solitary individual genius” (Johnson et al., 1998). It is important to note that group instruction in itself is not student centered teaching.
Another aspect of this teaching approach is that it be experiential. This involves the use of hands on material and projects and problems with real data sets. The use of real data enhances the integration of topics from multiple disciplines.
Again, many business, mathematics and statistics classes at the university level have taken the lead in this type of application based teaching (Kolb, 1984; Li & Baille, 1993; Yobaccio et al., 2006).
However, for true student centered teaching methodology, the changing secondary education in this country may hold the key for university professors. The thesis of this paper is to highlight how mathematics university professors can learn from their secondary colleagues.
We will provide an example of a mathematics professor’s attempt to teach a freshman mathematics class by group methodology and an evaluation of that attempt with ideas of improvement that have been learned from some secondary school mathematics teachers.
The Changing Secondary Curriculum Today, the No Child Left Behind Act has begun to influence sweeping changes in secondary education and these changes directly impact university curriculum changes as well (Government Statistics, 2004).
Nationally for over a decade, K-12 mathematics curriculums have been undergoing drastic changes based on national standards which were first proposed in the Curriculum and Evaluation Standards for School Mathematics in 1989 by the National Council of Teachers of Mathematics (NCTM). Since that time, standards based teaching has resulted in curriculum changes regarding most disciplines in elementary and secondary schools throughout the country.
States have published their own standards, and many of these are tied to state testing. There is also an effort to align these standards across the states (Mcrel.org, 2006). In this effort of reconciliation, Rhode Island, New Hampshire and Vermont have developed the New England Common Assessment Program (NECAP) which produced a set of mathematical Grade Level Expectations (GLEs) that identify the concepts and skills which will be used as the basis of state assessment of mathematics in grades 3-8, and they established a corresponding set of Grade Span Expectations (GSEs) for grades 9-10 and suggested GSEs for grades 11 and 12.
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