Logical Reasoning, Critical Thinking and Problem Solving Pay Big Dividends – Part 3
In Part 1 of this three part series we made the compelling case for the meta-skill set comprising logical reasoning, critical thinking and problem solving. Part 2 looks at the skill set in more detail to understand the key differences and why each is important. The final part of the series is now here and we look at practical, effective, and value-for-money steps and resources to radically improve your logical reasoning and analytical and problem solving skills.
It’s the most valuable meta-skill set… and it’s virtually free
The good news is that logical reasoning, critical thinking, and analytical and problem solving skills can be acquired at virtually no cost and the investment of less time than is needed to learn to drive a non-driverless car.
Here’s what’s involved:
First, practice. In almost every source on the topic – from the formal logic or maths end of the reasoning spectrum to the puzzles end – all authors advocate practice. Lots of practice. It’s akin to working out. No pain, no gain. Aristotle supposedly said that the roots of education are bitter but the fruits are sweet. This means putting pen to paper rather than passively highlighting important bits of text or watching videos. It means attempting lots of non-template problems or exercises of increasing difficulty.
Much like personal training, students can do this on their own or get an expert to help them out. (See the Profs’ blog article: ‘Private Tutor vs. Personal Trainer’). Like Personal Trainers, Profs Tutors are experts at getting students across the pain barriers (self-questioning, motivation etc) that arise when teaching subjects that involve analytical and problem solving skills.
Second, read and expose yourself to as much as you can on the topic. It is important to read a couple of different books, with plenty of examples, to get a feel for the various approaches taken on the topic. The books you feel most comfortable with will depend on how academic and quantitative you are, so spend some time searching online and browsing bookshops to find the best books for you. You’ll know intuitively what you should buy as it will pique your interest and resonate somehow.
I’ve found that the most rounded and useful of the books are discrete maths textbooks. They tend to cover a number of the core elements in analytical and problem solving skills: logic, proving things, how to write mathematically, combinatorics (advanced counting), probability, set theory and some even have logical puzzles.
Check out my list of favourite books at the end of the blog!
Online courses and video – Pause and Rewind!
Third, take a course. Then take another. It is essential to keep reinforcing and building on the knowledge and skills you acquire. A course can provide a structure and roadmap for your learning. There are the Massive Open Online Courses (MOOCs) in Logic and in Mathematical Thinking from Coursera in conjunction with Stanford University. Also, Coursera’s competitor, EdX (a JV between Harvard, MIT and Berkeley) offers a course in Effective Thinking Through Mathematics, and Problem Solving and Critical Thinking Skills, the latter aimed at the professional market. They are free to take or charge if you want a certificate of completion.
The great thing about MOOCs is that lectures are recorded and you can pause and rewind at any point, unlike when sitting in a physical lecture. Moreover, much like being taught online by The Profs (LINK TO ONLINE TUITION), the experience feels very proximate and real. With the Profs, of course, it is real and 100% tailored to the student.
However, one drawback of MOOC’s, unlike with one-on-one tuition, is that motivation to get through a MOOC must be self generated. Not surprisingly, drop out rates on MOOCs are high. On the other hand, usually a one-on-one good tutor will relish the challenge of motivating his/her student – success depends on it.
Apps and gaming
Apps and games are a great way to test out your new skills. Luminosity offers some 50+ effective online ‘brain training’ games ‘created by scientists and game designers’. The website Brilliant.org focuses on a wide range of maths topics and puzzles, but uses a community of users to generate content. Finally, visit the site puzzles.com to find Martin Gardner-based puzzles – to really get your brain thinking.
The journey toward improving your analytical and problem solving skills is likely to be a mixture of Odyssey, revelation and amusement. Once you cross the rubicon and master this meta-skill set, you will change; your confidence will grow, as will your grade-point average or job marketability. And you’ll never regard politicians, adverts, press articles and dinner discussion in the same light again.
Book Suggestions to Improve Your Analytical and Problem Solving Skills
Mathematical-based problem solving books:
- Discrete Mathematics by Susanna Epp.
- Schaum’s ‘Outline of Logic by Achille Varzi, Dennis Rohatyn, and John Nolt.
- Thinking Mathematically by John Mason, Kaye Stacey and Leone Burton – this is a great book on solving mathematical problems, including psychological and other tactics.
- Problem Solving Strategies for Efficient and Elegant Solutions’ – this is a good book focusing on problem solving rather than formal logic.
- How to Solve It by Polya – a long time classic on reading lists, Polya is a renowned Stanford maths professor and educator, with a hall named after him.
NOTE: Law schools and business schools entry aptitude tests are also focused on testing reasoning ability. So it’s worth checking out some LSAT and GMAT preparation guides. They are replete with examples and questions with answers. A decent guide to logical reasoning is a book designed for law school applicants: ‘LSAT Logic Games’.
Emphasis on critical thinking:
- Critical Thinking, A Beginner’s Guide by Sharon Kaye.
- Logic, A Complete Introduction by Dr Siu-Fan Lee.
Leading books on informal logic and critical thinking:
- Understanding Arguments by Walter Sinnott-Armstrong, Robert J. Fogelin.
- Good Reasoning Matters by Leo Groarke, Christopher W. Tindale.
- How to Win Every Argument by Madsen Pirie – this book covers good argument patterns, faulty reasoning and clever reasoning (To cast a shadow on someone you might ask: Are you still beating your wife? To which there is no right answer).
- Raymond Smullyan and Martin Gardiner are amongst the leaders in the area of recreational games and conundrums which rest on logical reasoning. Logical Labyrinths is a fairly unique mixture of formal logic and informal puzzles book.
- The Puzzler’s Dilemma by Niederman – this book focuses on ‘classic conundrums of logic, mathematics and life’.
- How many licks: Or, How to estimate damn near anything by Aaron Santos – read about the art of guesstimation.
- Many bookshops have ‘Smart Thinking’ shelves these days, but it’s rare to find the hardcore, rigorous texts here. Those are best found online. Google books is a good way of perusing a book before ordering online. Within the array of smart thinking books typically on offer here, ‘Algorithms To Live By: The Computer Science of Human Decisions’ stands out. Ken Watanabe’s ‘Problem Solving 101: A Simple Book For Smart People’ is a lovely, if simpler, and practical book.
This brings us to the end of the Three Part Series on Logical Reasoning, Critical Thinking, and Analytical and Problem Solving Skills. If you haven’t checked out Part 1 and Part 2, make sure you do!