The main problems with this book are its subtitle and the fact that the book is marketed as a “premier reference source.” Both of these phrases are misleading. The book consists of a series of papers one might find at a regional conference on the various uses of technology when teaching mathematics. The use of the word “emergent,” meaning “coming into being,” suggests a discussion of tools that are only now beginning to be used. However, the tools and technologies discussed in this book are all well established.
That being said, some of the chapters expound some very sound pedagogy and investigate the use of e-learning and blended learning from a theoretical perspective. Chapter 2, on blended learning, illustrates the use of a computer system to teach a technical theorem, in this case, the mean value theorem. One form of this theorem states that for a continuous function f(x) over a closed interval [a,b], there is a point c in [a,b] for which the integral of the function over [a,b] is equal to f(c)(b-a). The authors describe using WebAssign (an online instructional system) to develop a self-learning program, giving copious examples. One problem with any online system for mathematics is the creation of a large enough question bank (so that a student who repeats a problem multiple times will get different versions). Some systems provide randomization so that a simple command can generate many different examples, all of which have an appropriate level of difficulty. It is not clear whether this is done here, or whether all questions must be developed and entered individually.
There are 18 chapters in all, divided into sections of six chapters each. The sections discuss blended learning, pure online learning, and software and web resources. There is of course some overlap between topics.
Very few works discuss the use of computer algebra systems for learning mathematics, even though such systems are becoming more powerful, more suited to teaching and learning, and more accessible. There are now several excellent open-source systems, including Sage, which is mistyped SAGE in the book, and Maxima, which is not mentioned at all. Maple and its companion software Maple T.A. are also not mentioned. The use of open-source systems, or even the use of a programming language such as Python, surely counts as an “emergent technology,” yet these too are not discussed anywhere. Sage gets only a passing mention.
None of the chapters mention classroom response systems (“clickers”), which are still not widely used in mathematics education even though the technology is not new. There is also no discussion of mobile technology in mathematics teaching and learning, particularly the use of smartphones and tablets. The latter have an advantage over desktop computers and laptops in that equations can be written directly on the screen, with a stylus or even a fingertip, and then recognized by a “math recognizer” program. There is indeed a chapter with the hopeful title “Formula Editors and Handwriting in Mathematical e-Learning,” but unfortunately this chapter is more concerned with entering mathematics into a text-based dialogue, such as an online forum. There is a table of basic LaTeX expressions, which is hardly an emergent technology, but no use of palettes or visual formula templates.
Chapter 13 is the most technical in the book, focusing on investigating the use of Gröbner bases to determine if two systems of equations are the same or different. It is not hard to determine if two equations are the same (for example, (x-4)2-1, x2-8x+15, and (x-5)(x-3) all represent the same equation and may all be considered an acceptable answer to a problem), but it is harder for a system of equations, such as the examples given that relate to distances and speeds. The idea is that any system of multivariate polynomials has a corresponding Gröbner basis for which the set of linear combinations is equal to that of the original system. This is an elegant and useful approach, and it is a pity the authors did not expand on the theory in greater depth.
Another problem with this book is the publisher’s strange insistence on the use of Microsoft Word for submissions rather than LaTeX or some other TeX derivative. This means that equations are typeset in some clunky equation editor, or typeset in LaTeX and imported as images. Both methods produce results in which the text and equations are of different fonts and weights. The effect is amateurish.
There is also some sloppy editing. LaTeX is found twice in the index, both as “LaTeX” and as “LaTex.” Different authors use the terms learning management system (LMS), learning content management system (LCMS), and virtual learning environment (VLE), even though they all mean the same thing. The terms used throughout the volume should have been more consistent.
I don’t see this text as a premier resource for educators and researchers, but it does contain plenty of interesting case studies. Somebody new to e-learning and online tools for teaching and learning mathematics may well gain some useful information, but the text does not have the breadth and depth that the term “premier resource” implies.
