World Wide Web sites for learning and teaching math
Mark VanHooser
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The World Wide Web has given mankind the opportunity to access a great amount of information at his fingertips. Educators can now use the web as a tool for students to learn mathematics, to help educators prepare for lessons, or as a method of professional development. Teachers need many tools to help them facilitate students’ learning of mathematics. The web is another one of those tools. Online activities and teacher resources are some of the resources that the Internet provides (Branzburg, 2005). The availability of interactive and engaging activities is one of the attractive elements of the internet. By using the web students can manipulate more representations of mathematical problems than are feasible by paper and pencil, which will extend the range of problems accessible to the students (National Council of Teachers of Mathematics, 2000). There once was a time where the only way students could practice mathematics was with paper and pencil. Today students of all ages enjoy using the computer, and there are many different interactive websites that can help reinforce and strengthen math skills (McCourt, 2006). Learning through using a computer is more than an individual working on a computer.
Students learn better when they interact with each other about the subject they are learning. When students are in a computer lab, students tend to interact more with each other than with their teacher (Sinclair, 2005). This alternate approach of teaching using the web is not only more enjoyable to students, but also more conductive to their learning (Bliwise, 2005). By using online activities students have the ability to gain more control of their learning and become more independent learners (Bliwise, 2005).
Part of the students’ enjoyment of using the web is that the question of why students are learning mathematics is answered for them by helping the students understand the link between the skills they learn in mathematics and the real world (Nelson, 2004). “Teachers can use simulations to give students experience with problem situations that are difficult to create with out technology, or they can use data and resources from the Internet and the World Wide Web to design student tasks.” (National Council of Teachers of Mathematics, 2000, p. 26). Students can use real time data that can be acquired by using the Internet for the assignments given to them in the classroom. Students are betters learners of mathematics if the math being learned is made real and relevant to the students.
Teachers have been using manipulatives for years. Manipulatives can become costly, and pieces can become lost or broken over the years. It takes time to incorporate them and a lack of adequate time to incorporate them has plagued their usage. Using virtual manipulatives provided on the Internet helps solve many of these barriers (Lindroth, 2005). It is suggested in the readings that teachers who plan to use online manipulatives give students a short time to explore the site and “play” with the tools, because the students are going to play anyway and will give them some comfort in using the site. Then they should be encouraged to explore each tool with definite activities in which the students will complete (Lindroth, 2005).
The web-based tasks assigned in the classroom can also be accessed on any computer, and now that computers are a common place in the home, students can continue assignments at home. Cubic Science Incorporated developed the web site GoMath.com; their stated mission is to give students access to the methods of learning math via their home computers (Armstrong, 2006). The online activities that are done at home should reinforce mathematical concepts that are taught in the classroom (Lindroth, 2005). When activities are sent home, the parents should get involved in their child’s learning of mathematics. Parents should understand that activities that are assigned on the web are valuable homework practice and not just game play (Lindroth, 2005). Students that are struggling in the classroom can use web-based interactive tutorials at home or in the classroom. These tutorials can offer an effective supplement for students learning (Bliwise, 2005).
Teachers can use the web for resources to supplement their classroom instruction. Electronic slides can be downloaded from the web and can be reused providing considerable work savings in the long term because the material can be reused (Stefansson, 2004). Activities from the Internet can also be used as demonstrations or whole class activities. There are added benefits to student learning when teachers used web-based demonstrations and tutorials as supplements to course lectures (Bliwise, 2005). The web can bring up-to-date information to the teacher’s notes. The web also contains lesson plans for teachers, which are very useful for beginning teachers.
Because of the vast amount of information on the Internet, finding valid and useful information can be difficult and time-consuming. Problems finding information on the Internet is not unique to teachers and is not only an issue of training but also an issue of time (Kauwell, 2002). When looking for websites, most people go to the big search engines such as Google or Yahoo. Each search engine has its unique query language that increases the amount of time for the user to learn and implement. Boolean operators are universal for search engines. However less than 5% of all searches use Boolean operators, and it is estimated that 50% of them are not used correctly (Kauwell, 2002). Fortunately most search engines make learning the Boolean operators obsolete by having an advanced search option. The advanced search option uses clearer language in drop-down menus to achieve the same results as Boolean operators. Plus there are other options that will help narrow the search and make the results more relevant. To overcome problems searching the Internet, many advocate teaching better search skills that rely on the searchers’ cognitive abilities to formulate a query, filter information, assess validity, organize results, and make sense of the information that is found (Kauwell, 2002). Having better search skills may reduce the amount of time it takes to gather more reliable results but teachers may find more time is needed than they are willing to put into finding what they are looking for. Professional journals and periodicals contain reviews of websites that are useful for teachers. Most of these journals and periodicals have online sources that can be searched for relevant websites. It is found that online resources created by professional organizations have better instructional design than those created by individuals (Handal, Handal, & Herrington, 2006). This paper contains reviews of websites from various sources.
Once a website is found, it needs to be evaluated for suitability for instructional needs. The content can focus on validity or functionality issues, but if a site is being used by students it needs to be evaluated for motivational quality as well (Small & Arnone, 1999). There is an evaluation instrument that is theoretically based, user-centered, and uses a research approach called WebMAC (Small & Arnone, 1999). It can be found at http://digital-literacy.syr.edu/resources/webmac.shtml. This evaluation form is adapted for several age groups: junior (grades 1-4), middle (grades 5-8), senior (grades 9-12), and professional (for teachers) (Small & Arnone, 1999). WebMac is very thorough but also time consuming.
For those who wish for a self evaluation of the website, the following are some important features to evaluate: introduction, displays, motivation, navigational aids, questions, self evaluation, directions, methodologies, and format of feedback. (Handal et al., 2006). The introduction should have complete, accurate, and clear directions with ample information about the task that is written at the students’ level (Handal et al., 2006). The displays should be uncluttered and is maintain attention to relevant information (Handal et al., 2006). A webpage should motivate and challenge the user across different displays and maintain the users’ interest (Handal et al., 2006). Navigational aides should be checked for activity, because users may get confused if it is perceived that a tool should be active when it is not (Handal et al., 2006). Questions should be presented in a variety of formats and be relevant (Handal et al., 2006). There should be clear choices for questions and possibly more than one try (Handal et al., 2006). The types of questions that are asked, such as multiple-choice, open-ended, open-middle, and close-ended, are important for the type of instruction that the website is planned for. Self evaluation can be achieved through visual cues that indicate progress, self tests, self quizzes, or results from in a simulation activity (Handal et al., 2006). Directions for a webpage should start with providing the user with an overview of the topics to be covered and how to access them though hyperlinks in maps or menus (Handal et al., 2006). A webpage’s methodology whose interaction is more proactive rather than reactive emphasizes learner construction (Handal et al., 2006). The format in which the students receive feedback should consider the awareness of the learner’s progress in the learning activity (Handal et al., 2006). The amount of information should be organized in such a way as not to overwhelm the user (Handal et al., 2006). It also should be clear to the user how to complete the steps necessary to progress (Handal et al., 2006). An important element that was not listed that is of importance to teachers is if the website includes the standards for the lesson. Other elements can be evaluated that are specific to individual needs.