CHAPTER 19 - IMPLEMENTING A TECHNOLOGY PLAN
This chapter has two major sections, each focusing on a specific aspect of technology. The first, Technology: A Bridge Between Mathematics Education and Thought, opens with a brief vision of a technology infused classroom. It is followed by a discussion of the connections between mathematics education and technology. Since technology influences how and what we teach, the types of changes we might need to make concerning content, instructional practices, and assessment are also discussed.
In the second section, Incorporating Technology into an Existing Mathematics Program, a sample game plan is provided. The steps necessary to add technology to a program are explored and discussed in the order in which they should take place in a well-conceived curriculum revision. Special attention is paid to taking an inventory of current technology use, creating a vision of future use, drafting a plan for the district, providing for professional development, selecting appropriate hardware and software, and creating a budget and locating funding.
Technology: A Bridge Between Mathematics Education and Thought
The mathematics education community is in general agreement that learning is enhanced by doing mathematical assignments and projects that have meaning, by employing multisensory stimuli that improve retention, and by working in cooperative learning groups that foster group decision making and interpersonal skills. The use of technology in schools provides a vehicle through which all of these modes of learning can be realized. In order for New Jersey's Mathematics Standards to be fully implemented, technology must be infused into the daily lives of mathematics students in all New Jersey classrooms.
What might a mathematics classroom that uses technology to enhance all learning look like?
While this vignette may seem a bit futuristic, Ms. Gomez and her students use only equipment and technology that people in business and industry use in their jobs every day and which are becoming ever more present in New Jersey classrooms! Central to this vision of teachers and students using technology to learn about pi is the realization that technology can help to enhance, deepen, and extend learning. Technology is not simply a collection of faddish products that are fun to use. Technology does not lead us away from inquiry, but rather enables us to think anew about how we make sense of our world. As technology shapes our reality, we, in turn, through selective and specific use, shape it.
With the infusion of technology into the schools, the educational community will need to reevaluate the content, instructional strategies, and assessment devices that are current practices in our schools. What we teach, how we teach, and the means by which we evaluate the relative success of that teaching and learning are inextricably influenced by technology. As a result, some of what we have been teaching needs to be eliminated or revised. In addition, skills and strategies we previously didn't teach now need to be stressed.
This section addresses some curricular implications that arise from the incorporation of technology into the math classroom. While the following lists are not intended to be comprehensive, the examples provided are intended to illustrate the kinds of changes that should take place in the related areas of content, instructional practices, and assessment at both the K-8 and 9-12 levels.
Suggested K8 Curriculum Changes and Revisions
Suggested 9-12 Curriculum Changes and Revisions
Incorporating Technology into an Existing Mathematics Program
Developing a Technology Plan
Any technology plan must recognize that the velocity of change and growth in technology will make last year's innovation archaic by next year or the year after. In order to make recommendations for curricular improvement, a technological infusion plan needs to be developed. The plan for increases in technology inthe mathematics classroom needs to be clearly outlined with distinct educational goals. Additionally, the plan needs to be flexible enough to allow the professional staff to modify their expenditures in response to the available hardware and software and the changing technological environment.
In the box on the next page, a game plan is provided which describes the steps that need to be taken to assure appropriate integration of technology in the mathematics program. While the list is organized chronologically, and the steps are intended to be completed in the order listed, no real-life process will ever be as smooth and easy as this theoretical model. Given the different technologies to be integrated, the realities of merging the instructional needs of mathematics with those of other content areas, and the myriad of issues that surround funding possibilities for the infusion, many of the items on the list will most likely be addressed at more than one time and quite possibly out of the ideal sequence. The list does serve, however, to remind planners of the many issues that need to be addressed in this kind of innovation and of their interrelationships. In the box, items marked with a * are discussed further in separate sections, while the remaining items are relatively self-explanatory.
Making an Inventory
One of the first steps in ascertaining what is required to create technology-oriented mathematics classrooms is to inventory current practices concerning technology use. A sample questionnaire to aid in the conduct of such an inventory is provided in the Appendix. There are several points to remember in the survey:
Use separate survey instruments for elementary and secondary levels. The needs and objectives at the two levels are very different and a single instrument will be incapable of probing both.
Focus on instructional uses of technology only. Do not try to address administrative and school record-keeping or scheduling needs at the same time or with the same equipment.
Create questionnaires that ask probing questions and require the respondents to provide detailed answers. Some of the best ideas and suggestions will come from staff members who have been prompted to share additional ideas.
Creating a Vision
Understanding the relationships between technology and mathematics education is critical, and an important starting point is a strong statement that expresses those relationships as they will be embodied in your district. Steven Willoughby wrote, "Rapid developments in technology are changing (and ought to be changing) the way we teach mathematics both because they modify our goals for the mathematics education of people and because they provide new tools with which we can better achieve our goals" (Willoughby, 1990, p. 60). It is evident that what is stressed in instruction and assessment will be altered as a result of the use of technology. "Template exercises and mimicry mathematics - the staple diet of today's texts - will diminish under the assault of machines that specialize in mimicry. Instructors will be forced to change their approach and their assignments. It will no longer do for teachers to teach as they were taught in the paperandpencil era" (Everybody Counts, 1989, p. 63). We have the opportunity and the responsibility to use and be influenced by technology in order to help all of our students become mathematically powerful.
To that end we need to consider the role of technology in connection with how we educate our students and prepare them to be lifelong mathematical learners. Generating a mission statement, goals, and curricular objectives, and reviewing educational guidelines established by state, national, and professional organizations represents our beginning point. It is important to note, however, that we in New Jersey are not starting at ground zero. There is much work that has been done in this area on a statewide level that represents both valuable resource material and even mandates. The 1993 report Educational Technology in New Jersey: A Plan for Action, prepared by the New Jersey Department of Education, outlined a bold plan for the entire state's progress. Current documents with information about educational technology, such as the Department's Strategic Plan, are posted on the Department of Education's home page at http://www.state.nj.us/education. Districts should be aware that the New Jersey State Board of Education adopted a resolution in August, 1992 that requires that the Early Warning Test (EWT) and the High School Proficiency Test11 (HSPT11) "be constructed on the assumption that all students will be using calculators as they take those tests." Given this resolution, districts must start their technology planning by establishing student proficiency with a variety of calculators as an absolute minimum level of expectation.
Even before hardware and software purchases are made, and for a considerable period of time afterwards, professional development of mathematics teachers in the district is essential. Studies have shown that the amount of technologyrelated teacher education in a district can be a significant factor affecting student achievement.
The National Council of Teachers of Mathematics (NCTM) recommends that teachers model the use of calculators in computation, problem solving, concept development, pattern recognition, and graphing. The NCTM Position Statement on Calculators and the Education of Youth suggests that "school districts conduct staff development programs that enhance teachers' understanding of the use of appropriate state-of-the-art calculators in the classroom." (NCTM, 1991)
NCTM also calls for teachers to be "educated on the use of computers in the teaching of mathematics and in examining curricula for technology modifications ... Teachers should be able to select and use electronic courseware for a variety of activities, such as simulations, generation and analysis of data, problem solving, graphical analysis, and practice." The NCTM Position Statement on computer use goes on to state that teachers should be able to use various programming languages and spreadsheets and to keep up with advances in technology. (NCTM, 1994)
The Association of Mathematics Teachers of New Jersey, in an effort to support the professional development efforts of the state's teachers in this area, published The New Jersey Calculator Handbook in 1993. It contains numerous sample professional development plans and workshop outlines and includes many suggestions for the use of calculators with K-12 students.
Teachers' professional improvement plans may include objectives for implementing technology into the classroom. In order to assist the teacher in reaching the objectives, staff development needs to be extensive and ongoing. Districts must provide time for extensive exposure regarding the use of technology in the mathematics classroom via conferences, expert instruction, individual exploration, refinement, experimentation, observation of other teachers, review and discussion of print and electronic materials, and teamed instruction.
Attendance at professional conferences is essential for motivation, development, and maintenanceof technological awareness. Conferences such as the annual meeting of the Association of Mathematics Teachers of New Jersey and regional NCTM conferences provide a broad overview of the many technological products available for classroom use. In addition, they also provide a fertile environment for proposing and exchanging ideas.
Programs such as TRANSIT-NJ promote systemic change in mathematics education through the use of technology. In-service workshops and follow-up meetings help teachers become proficient at enhancing the instructional environment through the use of calculators and computers. Schedules of programs for teachers can be obtained by calling (201) 655-5353 or via email at firstname.lastname@example.org.
Professional development resources to facilitate the use of technology in promoting inquiry-oriented instruction in K-12 mathematics and science are available from the Center for Improved Engineering and Science Education (CIESE) at Stevens Institute of Technology. Resources include workshops, video series and related print support material, Internet-based lesson activities, administrator conferences, and turnkey training programs. Use of the Internet for collaboration, consultation with experts, and access to "real-time" data on scientific and natural phenomena, as well as instructional mathematics software are emphasized. For more information, contact CIESE at (201) 216-5375 or via email at email@example.com. Web site: http://k12science.stevens-tech.edu.
Provide professional and support staff inservice activities focusing on specific aspects of technology in the mathematics classroom. Consultants (within and outside the district), curriculum coordinators, and telecommunications networks are some of the sources who can provide services.
Provide teachers with work areas furnished with the same technology equipment and supplies found in their classrooms or laboratories. These work areas need to be available before, during, and after school.
Professional development must focus not only on instruction in the operation of particular pieces of hardware and software, but also on the instructional strategies that are most effective for the successful integration of computers, calculators, and other technologies into the curriculum.
Professional development opportunities should also include specific sessions on the advantages and on the special problems associated with the use of technology in assessment.
The Department of Education, through a competitive grant program, is establishing Educational Technology Training Centers, one per county, by the summer of 1997. Grant awards will be made to those local education agencies with demonstrated experience in providing effective professional development for the implementation of instructional technology practices. For an overview of the program, see the request for proposals (RFP) on the Department's home page at: http://www.state.nj.us/education/ (under grants) or directly through: http://www.pingsite.com/njded/grants/eetc/toc.htm/.
Types of Hardware and Software Needed in The Technology-Oriented Mathematics Classroom
Technology helps to contextualize mathematics by building bridges between theory and life. Imagine, if you will, a student who is learning about the mathematics involved with navigation. Through Virtual Reality she/he is living on Columbus' ship, learning first hand about Columbus' difficulties with navigation. Or perhaps that same student through Virtual Reality is exploring space and planning how toadjust her/his own orbital changes. Later that student might use a Verbal Computer Communications (VCC) system to report her/his learning. Through VCC, this oral text would be transcribed into written text, and if desired, the written text could be further transcribed into another language. VCC is a reality today, and will be in the classroom tomorrow. Perhaps that same student is learning about the development of the Arabic numeral systems by "visiting" the Middle East thousands of years ago and experiencing the sights, smells, sounds, and tastes of the environment, forever imprinting the experience and the information in her/his mind. Early versions of this type of multi-media instruction are currently being explored by Disney World, and will be available in the classroom in the near future. Technology can help to extend our students' learning by building bridges across disciplines, thus connecting prior knowledge with new knowledge.
But what about today? Students now can access information through global information retrieval, using either commercial enterprises or the Internet. As more locations hook up with satellite transceivers, additional twoway and multiple hookup interactions will become available throughout the world. Students will be able to statistically analyze the information received and compare their knowledge country by country, solving real problems on a real time basis. By using this technology to interact with professionals in their fields of interest, students will be entering the workforce with skills that were unheard of ten years ago. The use of technology in the mathematics classroom is exciting, challenging, thought provoking and necessary.
Whereas Virtual Reality, Verbal Computer Communications systems, and multi-media instruction will transform instruction in the classroom in the near future, the premier and universal technological tool for today's mathematics classroom is the calculator. John Kemeny, comparing how they performed the calculations used to develop the atomic bomb fifty years ago with the power of today's pocket calculators, said, "It took twenty of us working twenty hours a day for an entire year, to accomplish what one student now can do in an afternoon." Teaching students how and when to use calculators is critical.
A primary question that teachers and curriculum planners must deal with when incorporating calculators into mathematics classrooms is What functions are most useful for this grade level? How sophisticated (and costly) do these calculators have to be? The New Jersey Department of Education provides at least a floor for this discussion in their Guidelines for Acceptable Calculators for Use on the HSPT11 and EWT from 1993-1994 through 1995-1996. This document establishes these functions as the minimum set acceptable for use on the tests:
In addition, the benefits of many other functions are described in great detail in the mathematics education literature and instructional approaches incorporating them are appearing in many commercially available programs. Algebraic logic is now available in very simple, four-function calculators for young children. Extensive capabilities to change the form of and operate on fractions provide for the creation of a class of calculators which are used widely in the middle grades. Statistical functions and even graphs and plots are available in inexpensive calculators which are finding their way into all grades from four through college. However, probably the most revolutionary effect of all is being provided by two classes of calculators thatare capable of graphing functions and doing symbolic manipulations for algebra and calculus. Graphing calculators, used in conjunction with Calculator Based Laboratories (CBL), provide vivid examples of the applications of mathematics and provide excellent opportunities for collaboration between mathematics and science teachers.
In spite of the growth of calculator use in the classroom, with the many new features and the tremendous flexibility that they provide, the use of the computer is still essential. Software utility programs afford students opportunities to use spreadsheets to analyze data, to graphically represent mathematical formulas, to manipulate pictures, to make and test conjectures, to run multiple simulations, to write about mathematics, and to perform a myriad of other functions. They enable students to make connections between mathematics and the real world, to expand their own sense of reality, and to participate in generative and reflective learning.
The picture of mathematics classrooms where technology is fully integrated in intelligent, meaningful, and necessary ways is attractive. What types of hardware are needed to make this paper sketch a reality? The suggestions below may help develop a response to this question.
Introduce students to calculators at the earliest levels of schooling and progress to scientific calculators with algebraic logic, graphing, and programmable calculators as students advance through the mathematics curriculum. Overhead versions for all of the calculator models mentioned are available and should be used by the teacher for demonstration purposes.
Provide mathematics teachers with access to computers with color monitors and liquid crystal displays for demonstration purposes. These stations should be equipped with high-speed CDROM and laser disk drives.
Make a fully-equipped computer lab available to all mathematics classes. The lab should include modern computers with substantial internal memory, color displays, printer access, and appropriate software to accommodate teacher- and studentdirected activities. The stations must have hard drives, and if possible should be networked.
Choose a computer only after deciding on the software to be incorporated into the mathematics program, since programs that are well suited to specific needs may run on certain computers and not others.
Make VCR's and video disc players available to every mathematics teacher, so that they can take advantage of the increasing number of quality mathematics programs being produced in these formats.
Provide for interactive television, whether using fiber optics or ordinary telephone lines, as a practical means of visual communication between multiple sites. Mathematics courses which are otherwise too small or specialized can be offered with this tool. Specialized experiments and complex demonstrations can be conducted, and instructional resources can be accessed from remote sites, through this technology.
Equip each classroom in the school with full telephone capability to support Local Area Networks as well as on-line search capabilities through electronic networks and data bases. Fiber optic cable ispreferred for new installations. The state maintains a list of approved service providers (ISPs). The list is available online via the homepage for state contracts (http://www.state.nj.us/infobank/noa/t1572a.htm) or through a link on the NIE home page (http://k12science.ati.stevens-tech.edu/connect/connect.htm).
Equip schools to receive externally produced programming via antenna, cable, or satellite. Advanced math classes are now available through the Satellite Education Resources Consortium (SERC). In addition, a school should have the capacity to disseminate the programming to the individual classrooms.
Budget and Funding
Each district would like to provide the kinds of services and experiences that have been described in this chapter for their students. The most serious deterrent is obviously their cost. Schools have well-established funding mechanisms and sources to cover the basic day-to-day services they need to offer, but are ill-equipped to deal with necessary purchases of expensive equipment such as that needed to fully integrate technology into an instructional program. Many schools and districts have been successful, however, in accomplishing a major portion of the vision. They have used a variety of strategies including fund raising, some reliance on the local tax base, special bonding, corporate-sponsored grant and award programs, government-sponsored research and demonstration programs, and many more creative approaches. This section provides some information about activity at the state level and a sample of suggestions made by successful districts.
The State Plan
The state plan, Educational Technology in New Jersey: A Plan for Action (NJDOE, 1993), contains action plans to engage interest, guide collaboration, promote funding, and monitor policy implementation in order to ensure widespread integration of technology in all areas and at all levels across the school. Another document, Giving New Jersey's Students Power to Perform, developed by the 1993 Commissioner's Ad Hoc Council for Technology, suggests that it is imperative that key groups in the state work together to attract funding support for technology. The Commissioner's Ad Hoc Council for Technology made the following recommendations for funding the state plan activities:
Progress has been made in addressing these recommendations. The New Jersey Department of Education's Comprehensive Plan for Educational Improvement and Financing (May 1996), recommends that $50 million be included in the FY 1997/98 state budget (and for the four following years) for a distance learning network aid. Funds will be distributed on a flat, per pupil rate to all districts which amounts to $43 per student. The network for delivery of voice, video, and data offers all districts (including those that are poor and have large numbers of disadvantaged students) an opportunity to obtain quality programs for their students to effectively implement the standards. The third recommendation is addressed in part by pending funding legislation (S40 and A20). (Legislation is available on the NJ Legislative home page at http://www/njleg.state.nj.us/.) Data management is being addressed through the Department's Office of Technology, established in 1995. The fifth recommendation is addressed through the FY 95 and FY 96 grant programs for Classrooms: Connections to the Future and Educational Technology Consortia, which provided $1.3 million in funding for technology modeling incentives. For details on these and other Department of Education initiatives, see the Department's home page at http://www.state.nj.us/education/.
School districts that have already made considerable progress in educational technology recommend the following strategies.
Allocate a standard fixed percentage of the local school district budget, perhaps 1 or 2 percent, for technology equipment and maintenance.
Establish a consortium of school districts for the purpose of negotiating cost effective benefits for hardware and software through group purchase, site licensing, etc.
Develop a procedure for evaluating aging and obsolete hardware in light of local instructional needs, normal service lifetimes, and the need for systematic upgrades and replacements.
Use special state or federal funds such as Chapter I and Chapter II funds. Consistently designating these funds for technology can provide technology for special need groups and for specially identified projects and programs.
Seek funding from the National Science Foundation (NSF), the United States Department of Education, and other federal agencies. Work with colleges, state agencies, or district consortiums which have been awarded grants to promote the use of technology.
Lease purchase current technology over a two or three year period. This plan makes large district-wide implementation easier to accomplish over a shorter period of time.
Use Eisenhower funds. Each year create training models for mathematics and science teachers that target appropriate use of technology in the classroom.
Hold a budget referendum. Present the public with a technology plan that is designed to create district-wide state-of-the-art technology-oriented schools.
Establish at least one magnet school. Create a school specially focused on state-of-the-art technology and preparation for high-tech careers.
Establish a business partnership. Many large corporations have competitive grants available in varying amounts. Technology products may also be obtained through the Computer Learning Foundation's non-profit program "Technology for Education" which sponsors multiple corporate partner label collection activities; call (415) 327-3347 for information.
Technology has changed and will continue to change what and how mathematics is taught. When we think about technology and the myriad of reasons why we need to infuse technology in the mathematics classroom, we should not lose sight of the following:
We are preparing our children for a different world from the one in which their parents grew up. In order to succeed in this increasingly technological world, we must provide them with the best possible education; an education that includes the most advanced tools, techniques, and methodologies available. Our nation must have the opportunity to compete in the global economy on an even playing field. Anything less will reduce our children's prospects and weaken our nation's future.
Appendix - Sample Inventory Checklist
This checklist includes questions that address each of the categories of planning, staff preparation, curriculum, methodology, setting, availability of technology, and budget. For each question, there are three statements which are designed to help districts assess whether they are at a Minimal (M), Intermediate (I), or Advanced (A) stage of implementation.
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