Concept Goals for Mathematical Science Students

Cognitive Goals – 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences
Every mathematical sciences major should be designed to help students acquire “mathematical habits of mind .” Students should develop the ability and inclination to use precise language, reason carefully, solve problems effectively, and use mathematics to advance arguments and increase understanding . These cognitive goals are not achieved in a single assignment or course; they must be approached within the context of each student’s mathematical maturation throughout his or her undergraduate years . A well-constructed curriculum supports students in learning concepts, acquiring skills, and achieving cognitive goals . In the following paragraphs we describe several cognitive goals in more detail .
Cognitive Recommendation 1:  Students should develop effective thinking and communication skills.
  • Major programs should include activities designed to promote students’ progress in learning to
  • state problems carefully, articulate assumptions, understand the importance of precise definition, and reason logically to conclusions;
  • identify and model essential features of a complex situation, modify models as necessary for tractability, and draw useful conclusions;
  • deduce general principles from particular instances;
  • use and compare analytical, visual, and numerical perspectives in exploring mathematics;
  • assess the correctness of solutions, create and explore examples, carry out mathematical experiments, and devise and test conjectures;
  • recognize and make mathematically rigorous arguments;
  • read mathematics with understanding;
  • communicate mathematical ideas clearly and coherently both verbally and in writing to audiences of varying mathematical sophistication;
  • approach mathematical problems with curiosity and creativity and persist in the face of difficulties;
  • work creatively and self-sufficiently with mathematics.

Cognitive Recommendation 2:  Students should learn to link applications and theory.

Mathematics students should encounter a range of contemporary applications that motivate and illustrate the ideas they are studying, become aware of connections to other areas (both in and out of the mathematical sciences), and learn to apply mathematical ideas to problems in those areas . Students should come to see mathematical theory as useful and enlightening in both pure and applied contexts .

Cognitive Recommendation 3:  Students should learn to use technological tools.

Mathematical sciences major programs should teach students to use technology effectively, both as a tool for solving problems and as an aid to exploring mathematical ideas . Use of technology should occur with increasing sophistication throughout a major curriculum .

Cognitive Recommendation 4:  Students should develop mathematical independence and experience open-ended inquiry.

A mathematical sciences major should be structured to move students beyond the carefully choreographed mathematical experiences of the classroom . A major curriculum should gradually prepare students to pursue open-ended questions and to speak and write about mathematics with increasing depth and sophistication .