Published 2011 Revised 2019
Mathematics is critical to the study of any STEM subject; indeed, historically the development of science, technology, engineering and mathematics has often gone hand in hand.
The scientist or engineer needs to embrace mathematics in order to get the most from their studies. Unfortunately, students often struggle with the mathematical aspects of their scientific degree courses. In this article we explore some of the main mathematical problems arising. Far from simply a lack of content knowledge, we believe that the main area of concern is in mathematical process skills.
Problem: Students don't know enough maths!
Whilst preparing stemNRICH it was clear that sometimes certain content knowledge was lacking: those teaching biology, chemistry, physics and engineering courses often claimed that students didn't know enough about various topics in mathematics. Sometimes this lack of content knowledge was obvious: students in engineering need to know about complex numbers; other times it was graded or more subtle: biologists needed to know more about graphs and equations. Whilst these various topics obviously varied across universities and courses, interestingly, there was a surprising large overlap between the mathematical needs.
The following core topics seemed to emerge across many disciplines:
|Topic||Easier application||Harder application|
|Estimation||Real world contexts||Problems with missing data|
|Powers||Orders of magnitude||Half lives|
|Equations and graphs||Growth curves||Scientific curves|
|Areas and Volumes||Approximating natural shapes||Packing structures|
|Proportional reasoning||Working out a dilution||Gas laws|
|Logarithms||Working out a pH||Buffers|
|Geometry||Packing problems||Spherical triangles|
|Fractions and decimals||Genetics||Error bounds|
|Data and statistics||Pattern spotting||Confidence intervals|
|Probability||Combinatorics in chemistry||Scale invariance|
|Calculus||Finding maxima and minima||Rates of change|
|Matrices||Transformations||Crystal symmetry structure|
|Complex numbers||Electric circuits|
|Differential equations||Simple mathematical models||Models of the atom|
|Technology||Fitting curves to data|
Problem: Students can't apply their knowledge!
Beneath any issues which might arise in knowledge of content, many students with good grades in mathematics seem to find it difficult to apply the mathematical knowledge that they might have. Why would this be the case?
It seems that there are several main reasons, common to all disciplines: