Dynamic Geometry: The Geometer's SketchpadTM is the only math-specific piece of software that teachers nationwide identified in the Becker survey. It is the top software currently used in classrooms according to the Math Forum survey (25% of teachers found it useful). Dynamic geometry, in general, was important in every other data source, too (Show Me center survey: 734 total uses). Dynamic geometry on the web is reasonably well supported by Java Sketchpad and other Java-based tools, but clearly math teachers would appreciate if JOMA authors would extend the collection of great uses of dynamic geometry.
Cartesian Graphing: Cartesian graphing of algebraic functions and data sets came up in nearly all the sources we considered as well (Math Forum: 23% of teachers in the survey found it useful; Show Me center survey: 193 current uses/143 potential). It was also one of the most common tools available on the EOE site. The popularity of graphing calculators points to the importance of this capability. In our experience with the EOE site, for example, many online graphing calculators offer only partial features relative to popular Texas Instruments devices. As we argued above, JOMA could serve an important role by pushing for integration of powerful graphing features into a common graphing tool that many lesson authors could use.
Calculators: It was not surprising to find that both teachers and students regarded graphing calculators as the most useful classroom tool (Math Forum survey, 25% of teachers; 13% of students). Similarly, four-function and scientific calculators were the tools most often directly called for in the four curricula that the Show Me center evaluated, and many simple calculators are available on line through the EOE site and others. Our experience tells us, however, that students and teachers find the numbers of buttons on physical calculators confusing for teachers and students, so an interesting JOMA contribution could focus on a calculator with a more refined interface, which is more easily tuned to the computations a student is likely to do in a particular chapter or course.
Probability Simulators and Stats Plots: Probability tools were also one of the top tool requests made by teachers in our Math Forum survey. Both the Show Me curricular analysis and development of ESCOT components helped to specify important features: the ability to generate large numbers of random experimental trials appears to be an important function. Moreover, the survey suggested that a rather small collection of simulated devices could cover most needs: a collection of spinners, cards, dice, coins, dominos, and marbles in a bag would cover a lot of ground. Of course, to go with these simulators, math teachers need a collection of statistics plots, such as histograms, box & whiskers plots, scatter plots, etc. This area is fertile for component-based designs that allow mixing and matching random generators and plot types (as in the topnotch commercial offering, Fathom, from KCP Technologies). While probability applets were found on the EOE site, many of them were gambling-related and therefore not necessarily appropriate for middle-school students.
Spreadsheets, Tables and Lists: These tools emerged across our surveys as representations and tools teachers frequently use, and that fill many curricular needs in middle school. For example, 75% of all ESCOT PoW's incorporated some form of a data table or spreadsheet. Yet most noncommercial web-based mathlets we have seen have fairly primitive and ad hoc data organizers. Commercial spreadsheets, on the other hand, appear to be overly complicated for most K-12 students to master. This category strikes us as fertile ground for JOMA authors to investigate and innovate in.
Computer Algebra Processing: A subset of graphing tools, computer algebra processing tools also have widespread uses on their own. The Show Me center data found 50% more potential uses for this type of technology than currently are called for in reform mathematics textbooks. Although many educational applications could benefit from including computer algebra processing, computer algebra processing code is hard to write and is commonly available only in proprietary systems. This makes computer algebra a great candidate for a reusable library that many mathlets could draw upon. Perhaps JOMA authors would step up to the challenging of an open source computer algebra system for education.
This list is by no means complete, but it covers the kinds of tools that came up most frequently across the data sources we considered. Other needs that came up less frequently include number lines, charting tools, visualizations of fractions, visualizations of fractals, turtle graphics, pattern explorations (e.g. tessellations), number sense manipulatives, and Venn diagrams.
The results of this study hold several implications for the development, collection and distribution of technology tools for math learning for middle school classrooms and beyond. Most important from the perspective of the electronic marketplace, there appears to be some consensus among the various stakeholders in mathematics education regarding the "product line" of mathlets that should be made available for classroom use. In addition, because this list is targeted and primed for reuse, development efforts are estimable and can be focused. Finally, we hope that the "product line" presented here will become a catalyst for grounded discussions of design features, reuse issues, and engineering approaches among the JOMA community.
JOMA will be successful only if it becomes more that a catalogue of the best of "what's out there" in mathlets. Like any good journal, it should encourage authors to contribute to cumulative, reusable, increasingly integrated outcomes. In this case, those outcomes should be a product line of mathlets that meets teachers' needs. In this column, we articulated some of these needs, as well as the minimal form a contribution ought to take, a reusable design. In future columns, we'll talk more specifically about how authors can structure their contributions to build on others' work and allow others to build on their work.
Poulin, J.S. (1999). Reuse: Been There. Done That. Communications of the ACM, 42, pp. 98-100.
Becker, H. and Reil, M. (1999). Teacher and teacher-directed students' use of computers and software. Center for Research on Information Technology and Organizations. University of California, Irvine, CA, 3.