Table 1:
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Table 2:
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We are about to begin the second "pentium" of the decade of implementation of the NCTM Standards. As we continue to wait for more enlightened curricular materials via NSF-funded projects, secondary mathematics educators are being assaulted from all sides. On one side there is the NCTM calling for the implementation of a "Core Curriculum" for grades 9-12 through which all students pursue significant and connected mathematics. On another side, there are pressures to restructure; we are asked to restructure our school day (intensive scheduling, etc.), to reorganize our course sequences, to rethink our goals for our students at graduation, to incorporate new assessment strategies, etc. The list seems endless and intimidating. The issue that these calls for restructuring address is the perception that high schools do not produce graduates who are well prepared for the post-secondary challenges that face them. Numerous sources have provided glimpses of the competencies that workers of the 21st Century must possess. Business, industry, and governmental agencies have shared their perceptions of our graduates and without malice.
For example, recently a meeting between the Engineering Department of Armstrong World Industries, Inc.. and a group of mathematics and science teachers from IU#13 was held in Lancaster. Among the issues that were discussed, the following insights were shared:
What Armstrong is seeks in a prospective employee:
* people who truly care about the job.
* people who want to get the job done and done right.
* people who want to take ownership of their work.
* people who can think.
* people who have intellectual curiosity.
* college degree or 2 year technical school (no place for the unskilled in the future!)
What Armstrong would like schools to do:
* include group projects (some small, some in depth).
* encourage development of verbal skills through individual and group presentations in math and science.
* develop computer skills.
* keep standards high for grades.
* be a good model in the way we approach our own job of teaching.
* allow students to develop self esteem through personal achievement rather than through external methods of trying to make them feel good!
* communicate our needs to businesses‹keep the lines of communication open.
One of the restructuring strategies is the development of pathways through the high school years. These pathways represent sequences of courses that prepare students for their eventual post-secondary situations: the world of work, vocational training schools or two or four year institutions of higher learning. Students are to select a pathway as early as 8th or 9th grade and be directed to a sequence of courses that address the needs of that pathway and its eventual target. This system necessitates the early and continual exposure of students to career education beginning in Middle School.
Concerns have been raised in two major areas: 1. Flexibility: Given the developmental level of most 8th and 9th graders, pathways must be sufficiently flexible to allow students to revise and refine the direction of their education as they grow and mature. 2. General vs. Specific: Much of the traditional approach to secondary mathematics has been founded on the principle of imparting general and in many cases, abstract, theoretical truths. Students would learn these truths in isolation and later learn to apply them as they selected their paths in life. Even the NCTM Standards call strongly for a Core Curriculum so that all students in 9-12 pursue essentially the same content, leveled by instructional strategy. This appears to be a conflict between the goal of developing a core curriculum for all students and the goal of developing courses that support pathways to specific occupational arenas.
Our district is pursuing the pathways approach which hopefully will resolve these concerns and will provide a framework for the connections of our mathematics curriculum to a variety of contexts. Table 1 details our view of possible pathways.
This scheme allows us to pursue the goal of a Core Curriculum in that all strands deliver significant mathematics consistent with the Pennsylvania Mathematics Curriculum Framework and the NCTM Standards. The design pursues the goal of providing meaningful experiences for all students in the content areas of Algebra, Geometry, Probability and Statistics, Functions and Relations, and Trigonometry in settings that will promote problem solving, reasoning, communication and connections. Our goal in this design is that all students experience all of the same topics and that the courses are leveled by instructional methodology as opposed to selection of topics. In addition, a substantial number of our students accelerate either by taking Algebra I in 8th grade, taking two math courses, or by summer school. This acceleration provides substantial enrollments in both the AB and BC Calculus courses and beginning next September, AP Statistics.
The issue of flexibility within the clusters of each of the pathways is resolved by designing a scheme of connections within each year's courses (see Table 2). Via this scheme, students will experience a wide variety of applications and will be better able to choose their individualized direction.
We are presently in the process of reorganizing the applications included in the CORD Applied Mathematics program and other sources to create a resource guide for the traditionally academic courses so that their content can also enjoy a wealth of diverse connections and applications.
We believe that the process of restructuring the 9-12 curriculum into pathways can provide us the opportunity of pursing the goals of a Core Curriculum and of a truly connected mathematics program. While the task is not a simple one, restructuring does have the support of many administrators and consequently may be a vehicle that will allow us to continue our pursuit of the vision of the NCTM Standards with greater support and authority.
Comments, questions and suggestions are most welcome. You may contact the author at Manheim Township School District, Box 5134, School Road, Lancaster, Pennsylvania 17601.