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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
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
Solution: We designed stemNRICH
around the content areas needed for university STEM courses.
Problem: Students can't apply
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
- Overly Procedural thinking
Mathematics exams can often be passed by learning the content
procedurally. This means that students can answer certain
types of question by following a recipe. The problems in scientific
mathematics arise because even minor deviations from the precise
recipe cause the student to fail to know what to do.
- Lack of ability to translate mathematical meaning to
Students who are very skilled at mathematics might have trouble
seeing how to relate the mathematical process to a real-world
context; this hampers the use of common sense, so valuable in
- Lack of ability to make approximations or
Real scientific contexts are rarely simple. In order to apply
mathematics predictively, approximations or estimations will need
to be made. To make approximations or estimations requires the
student to really understand the meaning and structure of the
mathematics, along with the underlying scientific meaning.
- Lack of multi-step problem solving
Scientific mathematics problems are not usually clearly
'signposted' from a mathematical point of view. The student must
assess the physical situation, decide how to represent it
mathematically, decide what needs to be solved and then solve the
problem. Students who are not well versed in solving 'multi-step'
problems in mathematics are very likely to struggle with the
application of their mathematical knowledge.
- Lack of practice
There are two ways in which lack of practice can impact
mathematical activity in the sciences. First is a lack of skill at
basic numerical or symbolic manipulation. This leads to errors and
hold-ups regardless of whether the student understands what they
are trying to do. Second is a lack of practice at thinking
mathematically in a scientific context.
- Lack of confidence
Lack of confidence builds with uncertainty and failure, leading to
more problems. Students who freeze at the sight of numbers or
equations will most certainly underperform.
- Lack of mathematical interest
Students are hopefully strongly driven by their interest in
science. If mathematics is studied in an environment independent of
this then mathematics often never finds meaning and remains
abstract, dull and difficult.
Solution: Our stemNRICH problems
target these critical mathematical process skills.
To make the most of and enjoy a
university STEM course students need to have a solid base of
content coupled with an equivalently strong set of mathematical process skills
allowing them to apply their knowledge successfully. Insufficient
levels in either area will cause students trouble.
NRICH problems differ from many
standard textbook questions or interventions because there is
always a focus on a mathematical process; stemNRICH takes this
well-developed NRICH philosophy and applies it to scientific
It is hoped that by supplementing
standard, traditional preparations with material from stemNRICH,
students will arrive at university well equipped for a happy,
productive and successful time.