IMPACTful Thoughts - Proficiency of Mathematics for Students in Math-Related Majors

By Michael Caparula posted 10-31-2021 16:34:42


Authors: Michael Caparula and Eric Hutchinson

The IMPACT document presents a number of items that The Mathematics Intensive Committee has interest in.  However, for this month, we will be focusing on statements in the Proficiency chapter.  Our committee looks at the objectives and pedagogies of the upper-level courses such as College Algebra, Calculus I, II, III, Calculus for Business, Differential Equations, and Linear Algebra.  Proficiency is vital for all students in math courses, however, these students will be integrating mathematics (with and without technology) in their profession whether it’s in engineering, actuary science, chemistry, bio-science, or a middle school math teacher. 


The IMPACT chapter on proficiency is fully comprehensive.  We will first look at the 5 strands of proficiency as defined by the National Research Council (NRC) referenced in the chapter. 

  • Conceptual understanding: comprehension of mathematical concepts, operations, and relations. 
  • Procedural fluency: skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. 
  • Strategic competence: the ability to formulate, represent, and solve mathematical problems. 
  • Adaptive reasoning: the capacity for logical thought, reflection, explanation, and justification. 
  • Productive disposition: the habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

From a math intensive viewpoint, granted all of these are important, but we will be leaning on the 5th strand and how mathematics is productive to these students majoring in a STEM field. 

In other mathematics courses, especially the development education courses, “applying mathematics to everyday situations”  is an important pedagogical concept as it has shown to stimulate interest in the subject (Arthur, Owusu, Asiedu-Oddo, and Arhin, 2018 and Willett & Singer, 1992).  However, for mathematics at the level focused on by the Math Intensive Committee, having students do problems that are seen in everyday situations is not really applicable.  For example, finding the total flux across a surface in a magnetic field is not exactly an “everyday situation”.  The applications we do use, we hope, would be advantageous for the field the students are going into. This month we will be examining how this bullet point works with proficiency.