How to Quickly Achieve Mathematical Literacy
Our objective on this page is to provide a concise guide to the (relatively) rapid acquisition of mathematical literacy (or "numeracy") at home. Fortunately, there has never been a better time, and there have never before been better tools, for undertaking this task.
Mathematics is the study of quantities and sets, and the relationships existing among them, as well as relations of space and time. Though abstract and grounded in logic, mathematics has an empirical aspect: for example, the study of ideal constructions often yields important mathematical insights.
While many have studied mathematics for the sheer joy of discovery, and often from a love of the precision and certainty it affords, mathematics is also the gateway to scientific discovery as well as technological achievement. In its statistical dimension, it can further serve to provide valuable perspective - and, when abused, can be a tool of propagandists.
Our emphasis here is on acquiring mathematical literacy for the assistance it offers in understanding other 'STEM' disciplines (Science, Technology, and Engineering) . For a high-level overview of each of these disciplines individually go here. However, we also greatly value mathematics for its contribution to the acquisition of problem-solving skills.
Unfortunately, we believe that mathematics is often the most poorly taught subject in the school curriculum. There are a number of reasons for this: the most fundamental, perhaps, is the tendency to teach the subject in total isolation from broader concerns. However, there can also be a certain tedium to the process of undertaking calculations; and the subject is inherently abstract. Thus, learning mathematics can involve solving problems - sometimes difficult, abstract problems - when the point in doing so is sometimes omitted.
A fundamental tenet of the "maker" ethos is the belief that we learn best by doing things hands-on. To this we would also add the following tenets: we tend to learn best visually (especially mathematics), and we also tend to learn better when the relevance and importance of the subject we are learning is clear from the outset. Finally, it is often helpful to understand a subject in its historical context. This is no less true of mathematics than any other STEM discipline: mathematics hasn't sprung, full-blown, from the forehead of Zeus (so far as we know, anyway).
Perhaps the first step in developing mathematical literacy at one's own pace and/or at home is determining one's current state of knowledge. Everyone will, of course, find themselves at a different place, and we're not aware of an especially good tool for doing this sort of self-assessment. However, The Learn Math Fast System begins with arithmethic in volume 1, and proceeds through geometry by voume 7. Readers can browse the content of each volume online to review topics, and get a sense of where, if anywhere, they begin to feel lost. They may then purchase that volume and proceed, if necessary, through the rest of the course. The books are suitable for schoolchildren (though they're not especially charming), and parents may use them to teach the subject at home. They provide problems and fully worked-out solutions as well.
Youtube provides free videos of many of the topics that will be encountered here, and parents can use these books to search out relevant content in a logical order. Before beginning volume 1 of this system, number recognition and counting will have to be learned, and appealing videos for this are available there.
Khan Academy also provides good video tutorials for many of these topics though, unfortunately, there are many gaps, and overall organization can leave something to be desired. The Learn Math Fast System will help provide the parent or individual looking to brush up basic skills with a stronger sense of continuity of topics, and can serve as a guide as to which topics should be studied, and in what order.
Older readers who are more confident, and want a faster brush-up than any of these resources provide can go directly to Dorling Kindersley's Super Simple Math, produced in cooperation with the Smithsonian Institution. This book is truly superb, and unfolds with a maximum of clarity and interest through trigonometry and statistics. The flaws: there are no problems to work, and no topic is entered into in any depth. Though it's appropriate for children as young as 11, it will also strongly appeal to adults.
Folllowing Super Simple Math the reader may well want to go further with algebra, geometry, trigonometry, calculus and, perhaps, statistics, ideally in a context that makes it clear why these subjects are worth understanding and how they arose historically. Providing both sorts of context, as well as a preliminary overview of all of these topics, is Mathematics for the Million by Lancelot Hogben. Hogben's book has dated a bit in places, but it is the only one volume text we know of that features these virtues.
Having gone this far, it would be reasonable to consider oneself "numerant". However, as none of these books treat any mathematical topic in any depth, and will certainly be insufficient for the purposes of a career in science or engineering, additional understanding and preparation is highly desirable.
The best one-volume continuation from Hogben's book is probably Engineering Mathematics by K. A. Stroud. Here the reader will find greater depth of treatment of algebra and trigonometry before Stroud goes on to calculus, as well as introductions to Laplace transforms, statistics and probability. A good alternative to Stroud's book would be Maths for Science by Sally Jordan. Obviously, Stroud's book is the better choice for those looking to use math in engineering disciplines, while Jordan's is better for those pursuing the sciences.
Should the reader still be in need of a more in-depth understanding of statistics, we recommend that a study of this subject be integrated with the use of the "R" programming tool. This approach would provide a far more interactive and interesting, hands-on framework. Best for this purpose is Statistics: An Introduction Using R by Michael J. Crawley. And for a more in-depth treatment of the use of R for the biological scientist, see Getting Started With R: An Introduction for Biologists by Beckerman, Childs, and Petchey. This is also probably the single best introduction available for R.
Calculators and Computer Algebra Systems
Integral to achieving numeracy today is the use of a calculator, and perhaps also a Computer Algebra System. With a lower entry cost than software packages, and without the need to learn how to program, calculators are typically the first choice, However, there is something to be said for learning to use a Computer Algebra System with one of the CAS software packages beginning at about the middle school level, particularly for the purposes of learning math for science and engineering.
Among calculators providing a Computer Algebra System, we prefer the TI-Nspire CX II CAS calculators (also known as "handhelds"). As most are equipped with color graphic displays, they supply a nice visual-learning tool. As well, CAS calulators provide a natural bridge to the "Big 3" Computer Algebra Systems, which, again, supply essential mathematical tools for scientific and engineering purposes, as well as more robust data-handling capabilities than calculators can offer.
The "Big 3" include: Maple, Mathematica, and Matlab. Also deserving mention, however, is PTC's Mathcad Prime. The latter package is available free for a 30-day evaluation, and retains non-premium functionality beyond that period, and great resources for self-teaching, as well as templates for all four of the major engineering disciplines. Mathcad also provides integration with Excel, in addition to CAE tools.
The Editor / Everything Progressive
