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Carla Tayeh's INTIME Journal

Preparing Pre-Service Teachers to Integrate Technology 

into the Elementary Mathematics Classroom 

Introduction

Few people would argue today that information technologies are having and will continue to have major impacts on how we in education view schooling, teaching, and learning. Some see technology as the driving force for all that will be good about education in the future, and more specifically, about how pre-service teachers are prepared to integrate technology into mathematics instruction. Others see information technology as a force that will destroy education as we now know it and drive us toward all of the negative aspects of consumerism.

Like most complicated technological developments and their associated social changes, the truth is somewhere between these two extreme positions. However, those who fear the consequences of information technology developments may do so because of the possibilities these technologies present for a fundamental shift in how we think about schooling, teaching, and learning. Unfortunately, people who advocate this shift and support technology have failed to show how technology can actually promote the core values of American education.

If technology is indeed a facilitator of quality education in mathematics and all content areas, how will it be used? How can developments in information technology facilitate an education appropriate for the 21st century while enhancing student achievement in core areas deemed important to our democratic society? How can pre-service teachers be prepared to integrate this technology into mathematics instruction to optimize learning for all students? 

One model that addresses these issues and provides answers to these questions is currently being developed at the University of Northern Iowa through a U.S. Department of Education grant, Preparing Tomorrow’s Teachers to Use Technology (PT3). Called Technology as Facilitator of Quality Education (TFQE), the model is established under the I
NTIME project (Integrating New Technologies into the Methods of Education, www.INTIME.uni.edu). This three-year project addresses deficiencies in teacher education programs in preparing pre-service teachers to use technology effectively in the PreK-12 classroom. The purpose of INTIME is to provide the necessary resources for methods faculty to revise their courses, model technology integration, and require pre-service teachers to integrate technology and components of quality education in their lessons and units. A consortium of five participating Renaissance Group universities is working together in this project to create new learning resources and implement new standards for technology integration in pre-service teacher preparation. 

This project is intended to produce change in teacher education programs in three ways. First, it has generated new learning resources on the web to support new teaching and learning processes in education methods courses. New learning resources include video scenarios of PreK-12 teachers effectively integrating technology, along with components of quality education, in a variety of grade levels and content areas. These videos are accessible online nation-wide. Second, methods faculty in mathematics and other content areas are revising their courses to model technology integration using the video scenarios and online discussion forum, requiring students to apply technology, and implementing the Pre-service Teacher Technology Competencies as exit criteria for their courses. Finally, methods faculty will share strategies for integrating technology and course revisions with other faculty involved in the grant through a variety of activities.

The Technology as Facilitator of Quality Education (TFQE) model includes seven major dimensions organized in a circular fashion to show their interconnections:

  1. Students at the center of their own learning; 

  2. Principles of good learning; 

  3. Aspects of information processing; 

  4. Standards from content disciplines, and 

  5. Tenets of effective citizenship in a democratic society.

  6. Teacher knowledge and behavior

  7. Technology 

Figure One

INTIME model

These seven dimensions of the TFQE model provide a way for educators to view the integration of technology related tools into a robust educational environment. The model identifies key points at which technology should be implemented and evaluated to determine its impact. It simultaneously allows for the integration of new research findings into the appropriate segments of the model while maintaining the structure to evaluate the impact of technology tools on these new findings as part of an ongoing evaluation process. In so doing, it allows a variety of users (pre-service teachers, teachers, administrators, and others) to see the complex process that is education and how technology is affecting that process.

Review of the Literature

A review of the literature used to develop the essential elements of quality education for the TFQE model answers questions regarding a support for the shift in our educational activities toward technology and how the model can prepare pre-service teachers to integrate technology effectively into mathematics instruction.

Students at the Center of Their Own Learning

The TFQE model revolves around the central element of "student-centered learning (SCL), [which] places the student (learner) in the center of the learning process. In student-centered learning students are active participants in their learning rather than passive recipients; students learn at their own pace and use their own strategies..." (Learner-Centered Classrooms, Problem Based Learning and the Construction of Understanding and Meaning, 1999). 

Student-centered learning is distinguished from teacher-centered learning or instruction that is characterized by the transmission of information from a knowledge expert (teacher) to a relatively passive recipient (student/learner) or consumer (McCombs & Whisler, 1997). By putting students at the center of their own learning, we blend these various components into a unique learning system, a system that allows us to view the complicated process that is learning and its individual parts.

According to Stiggins (1997), "The most valuable lesson we have learned in recent years from those studying cognitive processes is that rote memorization does not ensure understanding, and thus is not a powerful way to promote learning" (p. 257). 

The construction of knowledge means that the learner links new information with existing and future-oriented knowledge in unique and meaningful ways (McCombs, 1997, p.5). Although knowledge acquisition processes are needed to form the base, that knowledge is useful to the degree it can be applied or used to create new knowledge (Marzano et al., 1988, p.33). Learning and self-esteem are heightened when individuals are in respectful and caring relationships with others who see their potential, genuinely appreciate their unique talents, and accept them as individuals (McCombs & Whisler, 1997). 

For student-centered learning to occur, high quality classroom management is needed. Woolfolk (2001) cited three reasons for the importance of such a management system: to allocate more time for learning, to give more access to learning, and to help students develop their self-management. 

Principles of Learning

This second essential element in the Technology as a Facilitator of Quality Education model includes aspects of what we now know about learning. Current research in cognitive science has suggested that big differences exist between knowledge based on recall and deeper forms of understanding. Ewell (1997) described seven insights about learning: 

Active Involvement – The learner is not a "receptacle" of knowledge, but rather creates his or her learning actively and uniquely.

Patterns & Connections – Learning is about each individual learner making meaning by establishing and reworking patterns, relationships, and connections.

Informal Learning – Every student learns all the time both in “formal” education and in informal learning situations out of direct interactions with complex environments and a range of “cues” from peers and mentors.

Direct Experience – Direct experience decisively shapes individual understanding that certainly lends credence to educators’ efforts to create active student engagement in any teaching situation. 

Compelling Situation – Maximum learning tends to occur when people are confronted with specific, identifiable problems that they want to solve and that are within their power to solve.

Reflection – Building lasting cognitive connections requires sizeable periods of reflective activity, meaning that effective learning situations need to include thinking time.

Enjoyable Setting – Effective learning, which is social and interactive, occurs best in a cultural context that provides enjoyable interactions and substantial personal support. 

Aspects of Information Processing 

Developing the dispositions and skills necessary for informed information processing has become a necessary component of education in an information age. Switzer, Callahan, and Quinn (1999) suggested using The Pathways to Knowledge model (Pappas &Tepe, 1997) that allows users to see how contemporary technology influences the individual parts of their model and to view the parts as a coherent element of the TFQE model.

The component parts of the process include: 

Appreciation – of literature, arts, nature, and information through varied multiple formats (stories, film, paintings, natural settings, music, books, periodicals, the Web, video, etc.)

Pre-search – Making connections between a topic, question, or information need and the searcher’s prior knowledge.

Search – Identifying appropriate information providers, resources and tools; planning and implementing a search strategy.

Interpretation – Assessing the usefulness and quality of their information gathered and reflecting to develop personal meaning.

Communication – Organizing, applying, and presenting new knowledge relevant to the searcher’s research. Choosing a format that reflects the new knowledge; plan and create the product.

Evaluation – Evaluating by both self and peers at each stage of this nonlinear information process model (Pappas & Tepe, 1997).

Standards from Content Disciplines

In recent years, content standards have been developed for almost all of the discipline areas, including mathematics, either by teams from the disciplines themselves or by agencies in various states (Switzer, Callahan, & Quinn, 1999). These content standards serve as a third dimension of effective learning and integration of technology using the TFQE model. Content standards in the model are explained for the arts, foreign language/ESL, health/pe, language arts, math, social studies, science, vocational education, and other areas.

Tenets of Effective Citizenship in a Democratic Society 

Research on the tenets of democracy in a robust learning environment show great similarity between what we know about good classrooms and what we know about democracy. At the heart of our education system is the preparation of students to lead productive lives consistent with the basic tenets of a democratic society. Unfortunately, most schools and classrooms are not organized to consciously promote democratic disposition and skills. The basic tenets of democratic schools and classrooms include the following which serve as the fourth component of the TFQE model:

Tolerance - the capacity for or the practice of recognizing and respecting the beliefs or practices of others (The American Heritage Dictionary, 1982).

Critical Thinking and Decision Making – People who think critically proceed on the basis of careful evaluation of the premises and evidence and come to conclusions as objectively as possible by considering all pertinent factors and using valid logical procedures (Good, 1973). To think critically, citizens must gather necessary information using inquiry skills (observe, describe, compare, identify, etc.) and avoiding common problems in logic (for instance, getting personal, making false comparisons, saying things everyone will like, arguing in circles etc.) (Callahan, 1998). Then citizens must decide on the reliability of the information that they use as evidence to support their positions on complex social problems. 

Decision-making in democracies is a process of reaching agreement in group situations through dialogue, discussion, debate, and analysis (Callahan, 1998) 

Thinking Together and Making Meaning – Citizens must decide how to deal with complex social problems: how to define the problem, what values should be pursued, what public policies should be supported, what candidates should be elected to office, what actions should be taken with respect to social concerns (Engle & Ochoa, 1988, p. 61). Steiner (as cited in Lipset, 1995) argued that in a democratic society as many people as possible should be involved in making decisions to help sharpen the issues and check the soundness of the arguments. The discipline of team learning starts with dialogue and the capacity of team members to suspend assumptions and enter into genuine "thinking together" (Senge, 1990). 

Power Sharing and Empowerment – Empowerment is "the opportunity and means to effectively participate and share authority" (Bastian, Fruchter, Gittell, Greer, & Haskins, as cited in Simon, 1987, p. 374). Empowerment can lead to rapid intellectual growth (Hill, 2000, p. 61) and the ability to deal with complexity, uncertainty, and ambiguity. 

Individual Responsibility and Civil Involvement with Others – These traits will grow with the opportunities in a democracy to share the mutual tasks for the orderliness and welfare of the group and for personal independence (Good, 1973). Hollingshead (1941) noted that democracy is not solely a political organization, but rather a social relationship, a conscious striving on the part of each member for the advancement of the common welfare; a shared responsibility with individual accountability (pp. 17-18). 

Teacher Knowledge and Behavior

This essential element of the TFQE model describes the following components of an effective teacher in any subject area: knowledge of student characteristics, teachers’ in-depth content knowledge, classroom management, and pedagogy. 

Teacher Knowledge: Student Characteristics – Research has revealed the importance of adjusting learning activities to the learner. The closer the match between students’ learning styles and their teachers’ teaching styles, the higher the grade point average (Dunn, R., Griggs, Olson, Gorman, & Beasley, 1995). A Learning Style Model (R. Dunn & Griggs, 1995) revealed that students are affected by five main factors: their immediate environment, their own emotionality, their sociological preferences, their physiological characteristics, and their processing inclination. Accommodating instruction to these styles is much easier with the rich resources available thru various technologies. 

Practitioners throughout the United States have reported statistically higher test scores or grade point averages for students who changed from traditional teaching to learning-style teaching at all levels – elementary, secondary, and college (Brunner & Majewski, as cited in Shaughnessy, 1998; Alberg, Cook, Fiore, Friend, & Sano, 1992).

Teacher Knowledge: Teachers In-Depth Content Knowledge – To teach all students according to today’s standards, teachers need to understand subject matter deeply and flexibly so they can help students create useful cognitive maps, relate one idea to another, and address misconceptions. Teachers need to see how ideas connect across fields and to everyday life and then assist their students in seeing these connections. This kind of understanding provides a foundation for pedagogical content knowledge that enables teachers to make ideas accessible to others (Shulman, 1987, 1986). "If beginning teachers are to be successful, they must wrestle simultaneously with issues of pedagogical content (or knowledge) as well as general pedagogy (or generic teaching principles)" (Grossman, as cited in Ornstein, Thomas, & Lasley, 2000, p. 508). 

Teacher Behavior: Classroom Management – School and classroom management aims to encourage and establish student self-control by promoting positive student achievement and behavior. Thus academic achievement, teacher efficacy, and teacher and student behavior are directly linked with the concept of school and classroom management (Froyen & Iverson, 1999). Classroom management focuses on content management, conduct management, and covenant management. 

Teacher Behavior: Pedagogy – The professional teaching standards represent the teaching profession’s consensus on the critical aspects of the art and science of teaching (pedagogy) that characterize accomplished teachers in various fields, including social studies. Effective teachers display skills at creating curriculum designed to build on students' present knowledge and understanding and move them to more sophisticated and in-depth abilities, knowledge, concepts, and performances. Teachers in social studies employ a range of instructional strategies and resources to match the variety of student skills. They observe and assess students in the context of ongoing classroom life. They understand and respect diversity in students’ cultures, values, languages, and family backgrounds (National Board of Professional Teaching Standards, 1998).

Technology Components

Technology is the set of the powerful tools that the teacher and learner can use to facilitate his/her own learning process. Technology resources can be used to provide opportunities for learning and create the "conditions that optimize learning" (Switzer, Callahan, & Quinn, 1999). 

To ensure that technology is used to facilitate quality education, the key elements of the TFQE model need to be matched with a set of standards for the appropriate uses of technology. The I
NTIME project is using the Pre-service Teacher Technology Competencies, performance-based competencies modeled on several national standards documents, developed by the UNI Teacher Education faculty. 

These technology competencies include: Basic Technology Equipment Operations and Concepts, Technology Resources and Tools for Information Literacy, and Technology Resources and Tools for Content Areas. 

Design and Instrumentation

To document how the Technology as a Facilitator of Quality Education model prepares pre-service teachers to integrate technology into mathematics instruction, the researcher used the UNI Pre-service Teacher Technology Competencies (www.INTIME,uni.edu/model/technology/comps1.html).

These technology competencies listed below identify the areas of proficiency required by pre-service teachers to effectively use technology resources to provide learning opportunities and create the conditions that optimize learning. Using the various competency levels, teachers find out their strengths and weaknesses so they may then address the weakness areas.

Each competency is written in a rubric format for student assessment with five defined levels of proficiency: 1) Pre-Novice (no experience), 2) Novice/Awareness (minimal experience), 3) Apprentice/Professional Skill (experience doing something on a personal level) , 4) Practitioner/Curricular Integration (experience using these resources to create learning opportunities), and 5) Expert (reflection upon the use of these resources to create learning opportunities).

Teachers’ in-depth knowledge of technology resources will greatly enhance their ability to provide instruction that is relevant for today and tomorrow’s classrooms. (Switzer, Callahan, & Quinn, 1999). 

In keeping with the goals of the I
NTIME grant, the researcher revised the mathematics methods courses based on the TFQE model. Using new learning resources on the INTIME web site (video scenarios demonstrating effective integration of technology with components of quality education), the researcher incorporated these and the pre-service teacher technology standards into the revised methods courses. 

Evaluation

Pre-service mathematics teachers will evaluate the revised methods course to determine how the TFQE model using Pre-service Teacher Technology Competencies has helped them become better able to integrate technology to optimize learning. Students will evaluate the course at the beginning of the semester and at the end of the semester using the Pre-service Teacher Technology Competencies to evaluate their own skill acquired to use technology effectively in their mathematics lessons and units. 

Recommendations and Conclusions

The methods class in this study was revised to focus on how technology could more effectively be used in the elementary mathematics classroom, specifically, to investigate how technology can be used to more effectively teach statistics in grades K-6 using online resources and data analysis software including spreadsheets. What follows is a series of activities to introduce pre-service teachers to software tools that focus on the teaching of statistics in the elementary school mathematics classroom. The activities were sequenced such that pre-service teachers would experience the potential of using technology in the mathematics classroom prior to viewing one of the INTIME project videos and then could more critically reflect upon the lesson in the video. The INTIME videos highlight a variety of classrooms using technology in different ways. The video used in this study focused on an interdisciplinary lesson in grades 1 and 2 that resulted in students compiling data in a spreadsheet. Using a Web CT bulletin board for their discussion, the pre-service teachers reflected upon the lesson in the video using the TFQE model to frame the discussion.

Activity 1. Identify state and national benchmarks on the teaching of data analysis in the elementary classroom. Benchmarks can be found online.

Activity 2. Become familiar with software available for the elementary mathematics classroom. For example, the Ice Cream Truck software (Sunburst Publications) simulates an ice cream business in a small town. Students make decisions about the quantity of ice cream to buy, the best route through town for the ice cream truck, and the best price to sell the ice cream. Costs and revenue are automatically compiled in a spreadsheet. 

Activity 3. Become familiar with spreadsheet and graphing software appropriate for the elementary classroom, for example, Data Explorer (Sunburst) or Graph Club (Tom Snyder Productions) and how it might be used to collect and analyze data in a variety of contexts including collecting survey data.

Activity 4. Investigate the potential of spreadsheets as a tool to solve problems in mathematics.

Activity 5. Create a statistics activity appropriate for students in grades 3-5 using developmentally appropriate data that students can find online. Show how to use graphing software to graph and interpret the data from the activity. Identify the state or national benchmarks met by the activity.

Activity 6. View the INTIME video, “Give 'Em the Business”. In this video a class of first and second grade students run their own business. For example, one group makes and sells sandwiches. The children video tape commercials, create print advertisements on the computer using a drawing program, and use a spreadsheet program to compile data about their business and graph the profits.

Activity 7. Reflect on the lesson in the video, “Give 'Em the Business”. Discuss the lesson with others on the Web CT bulletin board. Use the TFQE model to guide the discussion.

Pre-service teachers completed a Teacher Technology Competencies pre- and post-test. Technology competencies were rated on a scale from 0 to 4 (0 = pre-novice, 1 = novice, 2 = apprentice, 3 = practitioner, 4 = expert). A wide variety of competencies were assessed including but not limited to a) operate basic and discipline-specific equipment (e.g. laser disc players, VCRs, graphing calculators in math, or video cameras) and use it to support instruction and inquiry specific to the content area; b) demonstrate knowledge of equity, ethics, legal and human issues concerning use of computers and technology; c) use multimedia software to create multimedia reports or presentations; d) use WWW authoring software or HTML code to create an educational Web site; e) use spreadsheets to calculate and display information and produce meaningful reports to aid in problem solving; and f) demonstrate awareness of resources for adaptive devices for students with special needs.

Whereas, 29% (5/17) of the students showed positive change in technology competency, the other 71% (12/17) showed no change. The technology competencies addressed in this mathematics methods course focused on those competencies that were subject specific rather than the broad range of technology competencies identified for pre-service teachers on the Teacher Technology Competencies pre- and post-test. Further, students may have increased their awareness about a particular technology, however, still rate their competence level as novice. The pre- and post-tests of teacher technology competencies serve to highlight the challenges for teacher educators as they prepare future teachers to more effectively use technology in the classroom.

The Web CT bulletin board discussion provided another window into student learning about effective uses of technology in the elementary mathematics classroom, especially with respect to the TFQE model. Whereas the TFQE model includes seven inter-woven dimensions, two portions of the TFQE model were given more emphasis throughout the semester in classroom discussions: a) students at the center of their own learning, and b) principles of learning. After viewing the I
NTIMEvideo, "Give ‘Em the Business", students raised a number of issues related to these specific elements of the TFQE model. For example, in addressing how well the lesson in the video addressed the “principles of learning” in the TFQE model, a number of students focused on the relevance of the activity to the children's lives. Several students commented that the lesson itself presented children of this age with a situation they would genuinely want to explore. 

A student wrote, 
“The fundamental ideas behind the unit were focused on real life events and were meaningful to the student.”

Another student added,
“The technology used in this lesson just made the lesson more exciting for the students. They were able to watch themselves on video, see their picture on the computer, hear their voice on tape."

A student responded,
“Without the ability to easily document the statistics or create fun, entertaining commercials, I think the students would be less interested in the unit.”

Other students agreed that technology plays a role in motivating students, even at such a young age.

Concerns were raised, however, related to the “students as the center of their own learning” element of the TFQE model. Key to student-centered learning is that students are active participants in their learning – constructing knowledge by linking new information with existing knowledge in meaningful ways. 

One student wrote,
Do students in grades 1 and 2 have the prior background knowledge to understand the reasoning behind a spreadsheet and graph to show profit? Did the teacher explain the idea of a spreadsheet to students in some concrete way before students started producing their products and determining the price for their products?

Another student responded,
“It would be better if the kids were given more opportunity to explore independently.”

A student followed this by writing,
“The children needed lots of assistance [from the teacher] .”

The Web CT discussion showed that the students were keenly aware of how the children were making sense of the mathematics underlying the lesson. Issues of whether the technology was pushing the curriculum in ways that were not developmentally appropriate were raised.

In sum, the mathematics methods course can play a significant role in increasing pre-service teacher competence with technology however, without the integration of technology throughout a teacher preparation program, pre-service teachers may not move beyond feeling like novices with technology in the classroom.

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