Teachers of mathematics are constantly challenged with finding the most effective methods of reaching students. Primary school and high school students today are part of a group with a lot of technological tools at their disposal. They play games, listen to music, and watch more movies than students ever have. While these types of technology may seem more entertaining than tool, teachers today are finding ways to work with various forms of visual media to help gain and keep students’ attention.
The mathematics community nationwide has also seen potential value in the variety of technology now available. In 2000, the National Council of Teachers of Mathematics found technology to be of such importance and hence included a Technology Principle in their six Principles and Standards for School Mathematics. Specifically, the principle states that “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.” Technology supports students to investigate in every area of mathematics such as geometry, statistics, algebra, measurement, and number (National Council of Teachers of Mathematics [NCTM], 2000). NCTM’s “Technology Principle” challenges mathematics teachers to rethink the mathematics they teach, investigate technological tools for learning mathematics, and consider how they can support students in learning mathematics with technology as a tool.
To better reach the current generation of students, some instructors have implemented new technologies in the classroom, including various forms of computer software for teaching and learning mathematics. Some of these types of softwares allow the students to interact with, and manipulate data they create and to analyze those data. Students therefore interact with the software rather than simply viewing static pictures. The basis is that this interaction will help students gain a deeper understanding of the topics they are studying by helping them become participants in their learning, rather than being passive spectators. In an attempt to reach more students through this constructivist style of teaching, many teachers have eagerly implemented the use of these programs as a new way of teaching mathematics.
The use of technology has a long history in mathematics education. Many societies, for example, introduce arithmetic with an abacus, for two reasons. First, the abacus supports computation. Second, the abacus presents a tangible image of mathematics, which helps students understand difficult concepts.
Computation and representation go hand-in-hand, both historically and in the present. For example, in primary school classrooms, many teachers use concrete manipulatives, such as Geoboards (allowing children to make geometric figures by stretching rubber bands over a grid of nails) or multi-base blocks (providing children with a physical model of the place-value system). In secondary school, researchers have found that more advanced tools are necessary. These advanced tools help students learn by supporting computation and by giving abstract ideas a more concrete form. Researchers have found that whereas physical manipulatives are the right tangible form for elementary school, ICT-based tools are the right tangible form for secondary school (Kaput, 1992; Kaput 2007).
Researchers have found that ICT can support learning when appropriately integrated with teaching techniques, curriculum, and assessments (Means & Haertel, 2004). Through the use of calculators, computers, and dynamic software, middle and high school students can study complex algebraic relationships, self-discover fundamental geometric theorems, and analyze large sets of data (Kaput, 1992; Hershkowitz, et al, 2002; Mariotti, 2002)
Computers provide extensive opportunities for supporting the learning of mathematics in schools. There are many types of computer applications in mathematics education. Web based interactive learning objects, spreadsheets and graphing programs are some of these tools.
Spreadsheets, out of these softwares, have a number of very significant benefits. First, they facilitate a variety of learning styles which can be characterised by the terms: open-ended, problem-oriented, constructivist, investigative, discovery oriented, active and student-centred. It can be seen that spreadsheet is a key component of the constructivist teaching repertoire. In addition, they offer the following additional benefits: they are interactive; they give immediate feedback to changing data or formulae; they enable data, formulae and graphical output to be available on the screen at once; they give students a large measure of control and ownership over their learning; and they can solve complex problems and handle large amounts of data without any need for programming (Beare, 1993). Herrington and Standen consider that many multimedia educational packages tend to present material in an instructivist manner, thus placing the learner in a passive role. They would prefer to see learning posed in an authentic setting to provide a constructivist learning environment, and it is the spreadsheet that provides just such an environment.
With the instructivist approach to teaching, students are not able to apply their knowledge to unknown problem solving situations (Honebein, Duffy, & Fishman, 1993). This is unfortunately still an issue that needs addressing today with teachers using technology.
Among the many different technologies endorsed by the NCTM (2000), the electronic spreadsheet (e.g., Excel) is utilized throughout its proposed grades 3-12 mathematics curriculum. Spreadsheet lessons and tasks (e.g., NCTM Illuminations) include using pictures, number lines, and ready-made templates to convey mathematical ideas to younger students. Older students use the spreadsheets to organize and explore data, generalize formulas, and view multiple representations of mathematical concepts. Using spreadsheets can also promote and develop higher order thinking and problem solving skills by allowing students to posit “what if…” type questions (Abramovich & Nabors, 1998).
These questions can be explored quickly by allowing students to use spreadsheets to interactively update values and engage in a generative role in learning (Clements, 1989; Masalski, 1990). Students are able to control the values they are inputting in the spreadsheet; they are able to use values of their own choosing, thus controlling the displays and different representations of the mathematical concept. This exploration allows students to take ownership of their own learning. In addition, spreadsheet displays and representations generated by a student can be explored and discussed with other students, allowing each student to benefit not only from his or her own experience with the content, but also from sharing and discussing this experience with other students.
Hesse and Scerno (2009) assert that the use of spreadsheets in mathematics instruction also gives students the opportunity to study their results to verify that the answers make sense. “Not since the days of slide rules have we been emphasizing what the answer should look like; this allowed students to sharpen their intuition and common sense”. Battista and Borrow (1998) add that spreadsheet-based tasks relieve students of the demands of computations and encourage them to progress through different levels of sophistication in their thinking about the procedures they are using. Tasks of this nature allow students to formulate “abstractions and related mental operations that are a necessary part of meaningful algebraic thinking”.