https://orcid.org/0000-0001-8976-6202

Mathematics underpins the study of virtually any theoretical studies related to engineering. In fact, so important is mathematics to the study of engineering that your performance in mathematics is often an accurate indicator of your subsequent performance in more advanced engineering subjects as you progress through your degree programme.

For example, if you want to excel in electronics and electrical engineering, you need a thorough understanding of electrical circuit theory. This subject equips you with the analytical tools to design and troubleshoot any electronic or electrical circuit that you will come across in your practice as an engineer. And to master this very important subject, you need to have a good grasp of basic mathematics topics like matrices, complex numbers, differentiation, integration and differential equations.

If you are studying mechanical or civil engineering, then mechanics is an essential part of your studies. Mechanics deals with the forces that act on stationary bodies, and on bodies that are in motion. You therefore need a good understanding of mechanics for you to be able to design and analyse civil engineering structures like bridges and high-rise buildings. On the other hand, if you are a mechanical engineer, you need a good grasp of mechanics in order to be able to analyse and design engineering systems like automobiles, aeroplanes, and artificial limbs. And to be able to make headway in your study of mechanics, you need good mastery of mathematics topics such as vectors, differentiation, integration and differential equations.

Given the importance of mathematics to engineering, you would expect all engineering students to fully immerse themselves in studying and mastering mathematics, especially those topics that are relevant to their discipline. Sadly, this is not the case. A frighteningly huge proportion of engineering students do just enough to get by in their study of mathematics. They do just the minimum needed to progress in their mathematics modules, namely attending lectures and workshops, doing the mandatory coursework, and studying to pass the exam, and nothing more. Here at UCL Engineering, we believe that mathematics has to be a way of life, just as music is a way of life to the master musicians. Such an approach enables you to think beyond mathematics and basic engineering theory, and to reach that level of mastery where engineering innovation becomes second nature to you.

At UCL Engineering we believe that there is a lot that we can learn from music in our efforts to improve student mastery of mathematics. We are not the only ones looking to music for inspiration in the learning and teaching of mathematics. Just recently, in April 2016, the U.S. Education Department brought together musicians, educators and researchers to discuss how music can contribute to the study of mathematics, engineering and even computer science (see Washington Post, April 2016 article: Educators want to pair math and music in integrated teaching method). We believe that our students will benefit by learning mathematics in a similar manner to someone learning to play the piano.  We call this the Piano Method for learning mathematics.

The Piano Method is best described by taking you through the steps that a novice needs to go through in order to be an expert piano play. To do so I have turned to answers posted on the question-and-answer web-site, Quora, in response to the question: “How should an adult beginner start learning piano?”

The Piano Method Step by Step

1. It’s never too late to become an expert at mathematics:

There is a genuine fear of mathematics amongst  some students coming into the first year of engineering school. Some have had difficult experiences with “A” level mathematics. Some have been out of formal education for some time, and are coming back from industry. Yet more, some never did mathematics at “A” level. At UCL Engineering we believe that regardless of the route you took into engineering school, and regardless of your age, you can still become an expert at mathematics.

“It’s never too late to learn to play the piano. If you are an adult and want to learn to play the piano don’t let thinking you are too old deter you.” – Natalie White, Pianist Pro.

“You are not too old to learn piano.” – Lorri Robinson, Know organ, now I’m tackling that pesky left hand.

“Don’t worry about your age. It’s never too late to learn a new skill, older age just might make the intuitive and technical parts take longer to develop. In terms of the theoretical aspect a more mature mind actually puts you at an advantage.” – Tia, Started piano lessons at 11, self-taught since 13.

2. Be passionate about studying mathematics:

Develop a genuine love for mathematics. This will sustain you during the ups and downs that you will experience as you learn and master new concepts. A genuine love for mathematics will also enable you to spend the necessary time that you need to become an expert in mathematics.

“Great news, you already have the most important ingredient…. passion!  If you’re not passionate about music in general, and more specifically learning to play the piano, then you’ll never get good at it.” – Rich Coogan, Playing piano for 40 years via private lessons and college lessons.

“You said you’re interested, and very much so. Basically, you’re already halfway there. You’ve got motivation. Learning an instrument primarily depends on consistency, motivation and determination, ‘talent’ can only do so much to kickstart your progress …” – Tia, Started piano lessons at 11, self-taught since 13.

3. Find a good engineering mathematics textbook that you will use in your studies:

I would suggest that you use one of the textbooks recommended by your engineering mathematics lecturers. Here at UCL Engineering we recommend “Engineering Mathematics” by K.A Stroud. This textbook has a lot of practice examples that are organised progressively by order of difficulty.

“Let’s begin with the basics of your wants. A piano: There are some decent practice pianos out there, but I am personally a Yamaha person. It has the best quality, will sound like an acoustic piano if you want it to.” – Dezi Rivera

“Find an exercise book.  I recommend ‘Hanon’.  I believe there is now an easier beginners Hanon, but if you can’t find it, don’t be intimidated by the Hanon published by Shirmer Library.” – Rich Coogan, Playing piano for 40 years via private lessons and college lessons.

“I’ve become the owner of a Yamaha Key Arranger Workstation PSR710, which is fancy talk for a souped-up digital piano (or pie-nanner, if you want to annoy people). I’m using Alfred’s Adult Course for my re-learning, the Hanon book, and First Lessons in Bach.” – Lorri Robinson, Know organ, now I’m tackling that pesky left hand.

4. Practise for 20 to 30 minutes each day:

Consistent daily practice helps you to reinforce in your mind the mathematical skills and concepts that you have learned.

“Practice, practice, practice. Even 15 or 30 min here and there is better than no practice at all.” – Lorri Robinson, Know organ, now I’m tackling that pesky left hand.

“Just as you did not learn to read and write going to school once a week, it is virtually impossible to progress by practicing once a week.  Most piano teachers recommend practicing from 30 to 60 minutes per day.  Even if you can get 15 minutes of practice in on busy days, that is better than nothing.  Practicing 3.5 hours, once a week, is not the same thing as 30 minutes per day.  Concepts take time to settle in and be digested.  It is not a test your can ‘cram’ for.” – Garrick Saito, I’ve been playing for about nine years now.

5. Make it a habit to practise mathematics daily:

If the study of mathematics does not become a daily habit for you, then you are unlikely to reach the level of mastery needed to perform at the highest level in your study and practice of engineering.

“I think the best thing that you can do to prepare yourself for the journey you’re about to begin is to realize that it is, in fact, a journey.  The journey is one which requires a strong commitment on your part to learn.  Many adult students never make it past the first year of studies because they did not realize that making progress on the instrument requires daily practice.”  – Garrick Saito, I’ve been playing for about nine years now.

6. Be patient, and don’t give up:

Sometimes it may appear as if you are making no progress despite the amount of time that you are putting in. Sometimes you may get frustrated as you experience difficulties mastering certain concepts. But remember that it takes time to master a skill, and this includes mathematics.

 “The most difficult obstacle for you might be the amount of time you can spend practicing and playing.  For most players, it takes quite a while to even just get “pretty good”.  So don’t get discouraged.” – Rich Coogan, Playing piano for 40 years via private lessons and college lessons.

“Don’t let how long it might take you discourage you.” – Lorri Robinson, Know organ, now I’m tackling that pesky left hand

“Don’t get discouraged if it takes you longer than you think (and it probably will).” – Charlotte Lang, Took lessons as a kid. Thanks, Dad!

7. People have different learning rates, so set your own goals and avoid comparing yourself to others:

We all learn at different rates. Just be consistent, avoid comparing yourself to others, and learn and progress at your own rate.

“Everyone learns at different rates …” – Rich Coogan, Playing piano for 40 years via private lessons and college lessons.

“To me (I’m not a teacher, by the way), it seems distracting to have two people in the lesson.  You will both progress at different rates and your teacher’s attention to either one of you will be split into two.” – Garrick Saito, I’ve been playing for about nine years now.

8. Have fun, enjoy your studies:

“HAVE FUN!!!!” – Lorri Robinson, Know organ, now I’m tackling that pesky left hand.