Principles of Best Practice in ATE Programs

A working draft of resources and reports from an NSF-sponsored project intended to strengthen the role of mathematics in Advanced Technological Education (ATE) programs. Intended as a resource for ATE faculty and members of the mathematical community. Comments are welcome by e-mail to the project directors: Susan L. Forman or Lynn A. Steen.

A vision of flexibility and strength outlining principles to practice in support of strong mathematics in Advanced Technological Education (ATE) programs. In two parts: High Quality Tasks and Effective Pedagogy

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High quality mathematical tasks are authentic, intricate, interesting, and powerful.

Authentic:

Portray common contexts and honest problems.
Employ realistic data, often incomplete or inconsistent.
Meet expectations of employers and other users of mathematics.
Use realistic input and output; avoid artificial worksheets.
Reflect the integrity of both mathematics and the domain of application.

Intricate:

Expect students to identify the right questions to ask.
Require more than substitution into formulas.
Employ multi-step procedures.
Stimulate thinking that is cognitively complex.
Confront students with incomplete (or inconsistent) information.
Demonstrate the value of teamwork.

Interesting:

Offer multiple means of approach.
Touch on areas of interest to students.
Appeal to a large number of students.
Invite many variations and extensions.
Provide horizontal linkages to diverse areas of life and work.
Reflect guidelines from NCTM, SCANS, NCRVE, and AMATYC.

Powerful:

Connect graphical, numerical, symbolic, verbal, and technological approaches.
Offer vertical integration from elementary ideas to advanced topics.
Propel students to more advanced mathematics.
Expand students' views of mathematics and its potential.
Demonstrate the value of mathematics to the modern high performance work place.

Effective teachers employ pedagogy that is active, student-centered, and contextual.

Active:

Encourage students to explore a variety of strategies.
Stimulate discussion of available data in relation to what is being asked.
Require students to seek out missing information needed to solve problems.
Make hands-on use of concrete materials.

Student-Centered:

Focus on problems that students see as relevant and interesting.
Help students learn to work with others.
Develop strong technical communication skills among students.
Provide opportunities for students to use their own knowledge and experience.

Contextual:

Ask students to engage problems first in context, then with mathematical formalities.
Suggest resources that might provide additional information.
Require that students verify the reasonableness of solutions in the context of the original problem.
Encourage students to see connections of mathematics to work and life.
Clarify relation between mathematics and its uses.

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Supported by the Advanced Technological Educaiton (ATE) program at the National Science Foundation. Opinions and information on this site are those of the authors and do not represent the views of either the ATE program or the National Science Foundation.