Working Group 3:

 

Continuing professional development

Edward Laughbaum

Galena, USA

 

Gregory D. Foley

Mathematics teacher development that works

Rosalyn Hyde

Creating a professional development network

Mark L. Klespis

An on-going program of professional development in hand-held technology for instructors of prospective teachers

Judy O'Neal

Technology as a vehicle for updating middle grades content and pedagogy

 

1. The need

2. Professional development in isolation or with the support of a group

3. Brief summaries and discussions at CPD sessions

4. Issues brought forth by participants

5. Conclusion

 

1       The need

Continued technological developments of hand held and desktop computing devices have dramatically given rise for the need of on-going professional development for in-service mathematics teachers. Computers that have been adapted for educational uses and graphing calculators originally designed for mathematics education are still changing the way many of us teach. Yet the pedagogical advantages of these technologies remain untapped by many in the profession. In addition, general population growth on one hand and a diminishing number of qualified mathematics teachers on the other has promoted an increase in the practice of using non-math trained teachers in the mathematics classroom. Further, the professionalism of teaching demands all teachers participate in continued professional development, and nothing in the literature suggests that the continued professional development effort meets this demand nor did any presenter suggest such a state of fulfillment exists.

With the need for professional development in both content and methods, technology is the desired tool for connecting the two needs. For example, consider the teacher who may be able to teach his/her students how to factor trinomials by traditional pencil and paper algorithms, but at the same time does not remember, or even consider that there is a connection between the zeros of a trinomial function and the linear factors of the related trinomial that can also be used to factor. The zero-factor connection may not be considered because the teacher and students do not have access to a graphing calculator that makes this algorithm possible. Yet this method is steeped in mathematical richness. Here, technology plays the facilitator to connect the method to the mathematics. How is the teacher to learn about such methods with­out continued professional development? Or as another example consider the algorithm for dividing a polynomial by a first-degree binomial x + a. The pencil and paper algorithm can be very calculation intensive. Because of this, students have the opportunity to make numerous arithmetic errors. But using the list features of the graphing calculator, it is a simple process and the arithmetic can all be done on the edit line of the list editor. In this case, technology has solved a problem plaguing the pencil and paper algorithm, while at the same time en­hancing the traditional algorithm. How are teachers to learn of such techniques if not through professional development?

Another teaching method that has become increasingly popular is the use of manipulatives and the related teaching/learning activities that accompany the manipulative. Judy O’Neal, in her presentation, demonstrated an activity for middle school children where the graphing cal­culator facilitates the mathematics. In this case it was analysis of the data obtained from color counts of M & M candy given to each student. The calculator was used to display re­sults. Whether it is in the form of a pie graph, statistical calculations, or answering “what if” questions, the graphing calculator was germane to the activity and the mathematics taught. Other mathematical content can be extracted from the same manipulative. For example, when introducing the exponential function in an algebra class, an entire bag of candy can be emp­tied on a table and a total count taken. Then remove all those candies with the M facing down and re-count. Re-bag those left and again dump them on the table. Remove all those candies with the M facing down and re-count. Continue this pattern. All the while the activity is pro­gressing, the data is being entered in lists on the graphing calculator. The graph can be dis­played to determine its behaviors and leading questions can be asked to help the class de­termine a model for the data. It is activities like these that may well be new to many teachers. If they are new, then how are teachers to learn what they are, how to use them, and the bene­fits of using manipulatives and graphing calculators?

2       Professional development in isolation or with the support of a group

An issue that surfaced during the ICTMT 5 conference was the expectation that in-service teachers should learn new teaching methods or learn about the implementation of technology in the classroom on their own. While this has been a common practice in the UK and Europe, it is growing in popularity in the United States because of the Internet. That is, the teacher is presented with a set of materials, either in hard copy form or in electronic form, and is ex­pected to learn from them. While this may be acceptable, the question becomes whether it is sufficient. As we all know from attending a conference, new ideas within the participant are quite often generated by what the presenter might say, or a question asked by another parti­cipant, or something overheard at lunch, etc. So the issue becomes whether learning in iso­lation is optimized? At some point, the learner must confirm whether their ideas generated by the situation are valid. The immediacy of confirmation of new ideas from a group can be per­sonally satisfying and a boost to the learner’s self esteem.

Another aspect, perhaps even an advantage, of learning within a group setting is the net­working with people who have been through the same experience. Communication via email after the professional development has been delivered is commonplace. In addition, follow-up face-to-face sessions can be good both from a networking perspective, and can be produc­tive for new learning due to the fact that reflection on the original content has taken place after the initial meeting.

What if teaching/learning activities (such as the M & M activity) are described on paper or verbalized on streaming audio on the Internet? How would this be beneficial when a large part of learning using manipulatives and the related activities comes from the group members participating in the activity? The general consensus of participants at CPD presentations seemed to be that face-to-face professional development is desired.

3       Brief summaries and discussions at CPD sessions

Judy O'Neal from North Georgia College and State University presented the paper, "Tech­nology as a vehicle for updating middle grades content and pedagogy". She believes that no one course can single-handedly produce excellent mathematics teachers, but technology brings exciting possibilities. She reported on her own highly technology intensive courses for middle grade mathematics teachers, and offered a sample activity used during her profes­sional development offering.

Greg Foley from Appalachian State University gave a paper entitled "Mathematics teacher development that works". He described five CPD projects in which he has been involved (C2PC, T3, CalcNet, MELT and the NCTM Academy), with full details appearing in his pa­per. He then extracted what he identified as common characteristics of success. A program must have a clearly focused purpose, based in mathematical content and relevant to the par­ticipants. The presenters must be expert and stimulating, and themselves, present an example of good practice, but also, the program must also include plenty of active involvement of participants. The best programs should provide a vehicle that allows participants to develop and implement their own action plans, with ongoing support and follow-through from the organizer. Important in all this is the provision of opportunity and mechanisms for par­ticipants to reflect on what they are learning, both during the course sessions and afterwards.

Mark Klespis of Sam Houston State University presented "An ongoing project of professional development in hand-held technology for instructors of prospective teachers". MTE, the Mathematics Teacher Educator program, is an ongoing professional development program and is part of the T3 college short course program. It is designed to help US college faculty integrate technology into their mathematics content courses for prospective elementary teachers. The paper discusses the collaboration of this with an NSF project COMPET (Coa­lition for the mathematical preparation of elementary teachers). More details appear in the paper.

During discussion, issues of fostering technology confidence in teachers, facilitating teacher reflections, program evaluation, and providing a balance among content, pedagogy, metho­dology, and technology were discussed.

Finally Ros Hyde of the Mathematics Association in the UK talked about T3 Europe, with its mission of creating teacher support and a community of technology users, lobbying for change, developing materials and “training”, although the preferred language here was pro­fessional development. She discussed her networks and European structures. She noted that there were many non-specialist teaching mathematics, so some subject content was necessary alongside the technical and pedagogical ideas, so it is not just about which buttons to press but about using the excitement about the mathematics to inspire people to find buttons for themselves. The aim is to change classroom practice, help teachers to face the threats (of changing balance of power when technology is used), and to develop appropriate ways of using technology to enhance mathematics learning. She outlined a communication network for involved people, pointing out that many teachers prefer to be emailed at home, as even if their school is online, there are too many distractions there!

 

 


 

 

Fig. 1

 

4       Issues brought forth by participants

5       Conclusion

To Teachers: More teachers must recognize and accept their responsibility to maintain a pro­fessional standing by seeking out the opportunities of professional development.

To Facilitators: The mathematics-technology connection is a natural bridge that must be capitalized on to present professional development. Mathematics teaching and learning with­out the fully integrated and appropriate use of technology is unacceptable.

 

 

 

 


Mathematics teacher development that works

Gregory D. Foley

Boone, USA

 

1. Calculator and computer precalculus

2. T3 • Teachers Teaching with Technology

3. CalcNet: Calculus reform network

4. MELT: Mathematics education leadership training

5. The NCTM academy for professional development

6. Summary and conclusions

 

Selected U.S. examples are used to illustrate several key features that can contribute to an effective technology-intensive professional development program for secondary school mathematics teachers. To be effective, the program needs a clearly focused purpose that is relevant to the participants. It must have expert and stimulating presenters with participant involvement and reflection. The initial program should be residential with at least a week of instruction. Participants should create and implement an action plan, with ongoing support and follow-through activities. Good facilities and organization are important.

Since the summer of 1988, the author has been involved in professional development institutes for teachers of mathematics that have been technology intensive—mostly involving hand-held technology, especially graphing calculators. This paper focuses on several of these institutes that have been designed for high school teachers, that is, teachers of students generally, from 14 through 18 years old. It looks back over these 14 summers to reflect on the aspects of these institutes that have combined to make them successful both in the eyes of the participating teachers and in terms of the positive effects they have had on the careers of these teachers.

Five examples of professional development programs are described below. Four of the five are ongoing. All have involved follow-through activities. The initial institutes have varied in length from 1 to 4 weeks. The most effective ones have been residential, allowing participants to focus on the institute without distractions. Other key factors leading to successful programs have been—

       a clear purpose for the institute based in mathematics content,

       the relevance of the purpose to the participants,

       the quality of the presenters,

       active involvement of the participants,

       opportunities and mechanisms for participant reflection.

 

In the best programs participants have developed and implemented action plans, and have been given ongoing support including specific follow-through activities and workshops. In order to have a successful technology institute, adequate facilities with good local arrangements and organization are needed.

1       Calculator and computer precalculus

This professional development program began as part of the Ohio State University Calculator and Computer Pre-Calculus (C2PC) project (see Waits & Demana, 1993), which received support from the National Science Foundation, Standard Oil of Ohio, and the Ohio Board of Regents. This weeklong institute program was first offered in 1988 and was directed by Franklin Demana and Bert K. Waits. The instructors were Waits, Demana, Gregory D. Foley, Alan Osborne, and Charles Vonder Embse—all university professors. In 1992 C2PC became a part of the Teachers Teaching with Technology (T3) program, an ongoing collaboration among Texas Instruments Incorporated, university faculty, and school teachers. Since that time, the C2PC institutes have been taught by selected high school teachers who had attended earlier institutes. In 2000, the institute’s name was changed to T3 Precalculus. The institute's curriculum has undergone three major revisions. The latest version of the institute materials is being pilot tested during Summer 2001 at seven sites around the United States.

The distinctive features of the current T3 Precalculus institute curriculum include—

       realistic applications and genuine data;

       the linking of verbal, algebraic, numerical, and graphical representations;

       the use graphing calculators and associated technology;

       a systematic approach to problem solving; and

       the development of the conceptual underpinnings of calculus.

 

Use of the TI-83 Plus graphing calculator is integrated throughout to visualize and solve problems and develop graph viewing skills. The calculator’s built-in graphing, table-building, matrix, and statistical applications are used as well as selected Flash applications. Texas Instruments data collection devices (CBR or CBL-2) are used at least daily during the weeklong institute. The mathematical emphases embraced are viewing windows and scale, local behavior of functions, end behavior of functions, graphical-numerical solutions, geometric transformations, and multiple linked representations.

In the first half of 1987 and during the entire 1987-1988 school year, Demana, Waits, and Foley each paired with a high school mathematics teacher in Columbus, Ohio to pilot the C2PC textbook materials that were being written by Demana and Waits. Through this process, they developed curricular materials for a yearlong course for advanced secondary school students to strengthen their problem-solving skills and improve their understanding of functions, graphs, and analytic geometry. An important feature of the resulting course was that teachers and students made regular, daily use of graphing calculators, microcomputer graphing software, or both. The first regular edition of the textbook was Demana and Waits (1990), and it is now in its fifth edition (Demana, Waits, Foley, & Kennedy, 2001). To date, more than 300,000 copies of Precalculus have been sold in the United States. Over 200 C2PC institutes have been held for some 5,000 teachers.

Numerous research studies have been conducted related to the C2PC project. Some examples are Browning (1989), Dunham and Osborne (1991), and Quesada and Maxwell (1994). Several other related investigations are summarized in Dunham and Dick (1994).

Purpose and relevance

The 1988 institutes were developed to prepare teachers who wished to field-test this new curriculum during the 1988-1989 school year. They came to learn how cutting-edge graphing technology could be used to help their students acquire the knowledge and skills necessary for the successful study of calculus and science. For the first 5 years, the Precalculus summer institutes were designed to prepare teachers to use the Precalculus textbooks. To this day, copies of Precalculus are still given to participants though many of the participants now teach using other textbooks. Most of the precalculus textbooks used in U.S. high schools today incorporate the use of graphing technology and contain content similar to Demana, Waits, Foley, and Kennedy (2001). So teachers still come to learn how to use graphing technology to help their students prepare for success in calculus and science.

Presenters

From 1988 through 1991 the presenters were Professors Demana, Waits, Foley, Osborne, and Vonder Embse. Since 1992 when C2PC became part of the T3 program, high school teachers have been the instructors for the institute. Initially these teachers were selected by Demana and Waits. Now they are chosen by the T3 office in consultation with T3 Precalculus Academic Coordinator Foley. To ensure quality instruction, the selection criteria for the high school presenters have always included strong knowledge of the mathematical content, facility with the technology, and experience as workshop presenters. The institute presenters have consistently received extremely favorable evaluations by the participants.

Participant involvement and reflection

Participants actively engage in explorations and discovery activities that are modeled and launched by the presenters. Discussions and homework give participants a chance to practice new skills and to reflect on what they are learning.

Action plans and ongoing support

In the early years, participants were selected in large part on the basis of the implementation plans they submitted with their applications, and they were expected to attend a two-day follow-up meeting in December to report on the progress of their classroom implementation. Now selection is often on a first come, first served basis. Nonetheless, many participants still develop and carry out less formal action plans. The implementation of these action plans is supported by the T3 web site, the Texas Instruments Explorations publications, and the annual T3 International Conference if summer participants elect to attend.

Facilities and organization

Initially, the institutes were held at Ohio State University in Columbus, USA and organized by Demana, Waits, Osborne, and Foley. Though the living quarters were plain, the classroom and computer facilities were more than adequate, and the operation ran smoothly. The participants had ample opportunity to work together on homework outside of class time, which reinforced the group’s camaraderie.

For 10 years, the institutes have been offered at numerous locations throughout the United States with various individuals serving as local organizers. The T3 office in Dallas, Texas screens and supports the organizers and provides extensive advice with its How to Host a T3 Institute manual (T3 • Teachers Teaching with Technology, 2000).

2       T3 • Teachers Teaching with Technology

This program is an outgrowth of the C2PC project. “The mission of T3 is teachers teaching teachers to create and deliver the highest quality professional development to enable teachers to use powerful tools to enhance their teaching leading to higher levels of student learning” (http://www.t3ww.org/t3/). For the summer of 2001, the T3 program is offering a menu 19 different institutes for secondary school mathematics teachers at various locations throughout the United States. The program has spread in various forms to 25 other countries. See the T3 web site for further details (http://www.t3ww.org/t3/).

The popularity and success of the U.S. T3 program rests largely on several of the factors identified above: content-based institutes with a clear purpose that is relevant to the participants, top-notch presenters, and active participant involvement. The support from the T3 office in Dallas is critical. They provide instructor training and assignment, Texas Instruments equipment loans, reduced prices on equipment purchases, a limited number of small grants, a How to Host a T3 Institute manual (T3 • Teachers Teaching with Technology, 2000), and the annual T3 International Conference. The conference can be used as a significant follow-through activity for institute participants. The T3 office monitors and evaluates the institutes, the instructors, and its own manuals. It supports a network of Academic Coordinators who oversee the various institutes. T3 offers customized institutes to meet local and regional needs.

3       CalcNet: Calculus reform network

This teacher-enhancement project was directed by Foley and sponsored by Sam Houston State University with the support of the United States Department of Education through Ohio State University. The CalcNet institutes were offered during the summers of 1991, 1992, and 1993. This project synthesized the mathematical and pedagogical approaches of successful calculus reform efforts at U.S. colleges and universities, adapted these approaches to the needs of high school students, and then disseminated the adapted methods to high school calculus teachers throughout the United States. Fundamental to the project was the creation of a network of high school teachers who implemented the project’s approach in their calculus classes and disseminated it to colleagues in their local areas. The network grew from intensive two-week summer institutes and was fostered through annual follow-up conferences each December. In all, the project taught 85 teachers whose implementation and dissemination efforts were monitored and evaluated.

The instructors were Thomas P. Dick, Demana, Waits, Foley, Vonder Embse, Charlene Beckmann, and David Ruch. The curriculum of each institute included both mathematical content and instructional methodology. Such concepts as numerical derivatives, slope fields, and error analysis in numerical integration, which were unfamiliar to most calculus teachers in the United States, were stressed along with standard mathematical content that can be enhanced through the use of graphical and numerical representations. The institutes gave a great deal of attention to the use of graphing calculator technology to enhance the teaching and learning of calculus. The use of cooperative groups and mathematical writing as means to enhance student learning was included.

The project teachers implemented technology-enhanced calculus curricula in their classrooms. They have made hundreds of presentations to other teachers. At least six CalcNet teachers or teams have led their own summer institutes to train other calculus teachers. Well over 1,000 calculus teachers have been reached through the workshops and institutes offered by CalcNet participants.

4       MELT: Mathematics education leadership training

Begun in the summer of 2000, the goal of the MELT Scholars Program is to develop high school mathematics teachers as leaders through their groundbreaking work in the classroom and as in-service workshop instructors. Through the program, each MELT scholar becomes a resource to his or her students and to other mathematics teachers. The MELT project is supported by the Cain Foundation, the Shodor Education Foundation, the Teachers Teaching with Technology program, and the Appalachian State University Mathematics and Science Education Center and Department of Mathematical Sciences.

All 2001–2002 MELT scholars attended three weeklong MELT Technology Institutes plus a weeklong Implementation and Dissemination Planning Conference during Summer 2001, and will attend a series of follow-through workshops during the 2001–2002 school year. MELT scholars selected three of the six Technology Institutes offered during the first 4 weeks of the program.

Week 1: 10–15 June 2001.

       Either T3 Algebra (Instructor: Tommy Eads, Carmen Wilson, and Anita Kitchens)

       Or T3 Middle School Mathematics (Instructor: Ruth Casey)

Week 2: 17–22 June 2001.

       Either T3 Geometry (Instructor: Milton Norman)

       Or Middle Grades Mathematics on the Web and in Print (Instructors: Holly Hirst and Deanna Wasman)

Week 3: 24–29 June 2001.

       T3 Advanced Placement Statistics (Instructors: Jeff Witmer and Landy Godbold)

Week 4: 8–13 July 2001.

       T3 Connecting Algebra and Geometry (Instructor: Charles Vonder Embse)

Week 5: 15–20 July 2001.

       Implementation & Dissemination Planning (Instructors: Gregory D. Foley, Ellen Hook, and Anita Kitchens)

The six MELT Technology Institutes offered during Weeks 1–4 were open to all mathematics teachers. Each institute features nationally known instructors and the latest technology. MELT scholar benefits include a total package worth some $3,000 per MELT scholar—

       complimentary institute registration,

       tuition and fees for summer, fall, and spring course work,

       $50/day summer stipend, room and board, parking, travel, mileage, plus

       assorted hand-held technology, computer software, and print materials.

 

Each scholar writes weekly reflective statements during the summer institutes, and develops and carries out an implementation plan and a dissemination plan.

5       The NCTM academy for professional development

Begun in 2000 to support the implementation of the Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics (NCTM, 2000), this is a program directed by NCTM’s Academy Services Committee and organized by NCTM’s professional staff. Institutes are conducted at four grade band levels: preK–2, 3–5, 6–8, and 9–12. So far, the institutes for secondary school teachers (Grades 9–12) have involved substantial use of hand-held technology, especially graphing calculators and data collection devices. During 2000–2001, the institutes focused on the six NCTM principles for school mathematics: equity, curriculum, teaching, learning, assessment, and technology. During 2001–2002, the institutes are focusing on the algebra content standard. In future years, each institute will focus on one of the five content standards: number and operations, algebra, geometry, measurement, or data analysis and probability.

Though still in their infancy, early indications are that the NCTM Academies focusing on a content standard will be highly successful because they possess the key components for success: a focused, relevant purpose, top-flight instructors, and active participation and reflection by the participants. The ongoing web support through TeacherLine offers great promise. (See http://www.nctm.org/meetings/academy/ for further details.)

6       Summary and conclusions

This paper is not based on formal research, but rather it is based on informal yet careful observation during 14 years of experience organizing, conducting, and teaching summer institutes and follow-through activities. The findings are consistent with the literature on the professional development of mathematics teachers (Aichele & Coxford, 1994, especially, Clarke, 1994) and provide an additional perspective. This article is intended to offer components to be carefully considered when designing professional development programs secondary school mathematics involving a focus on hand-held technology, but the components of success identified apply to other professional development for teachers of mathematics.

Summer technology institutes for secondary school mathematics teachers can serve as catalysts to begin the long-term process of change in teacher beliefs and behaviors that in turn bring about changes in curriculum, instruction, and student assessment in their classroom. Not only have the teachers who participated in the institutes sited above incorporated technology into their classroom instruction, many of them have led their own summer institutes to help other mathematics teachers. For some, these institutes have changed the participant’s self-perception from one of blue-collar laborer to professional educator. Several of the teachers have described the summer institute experience as “life changing.”

 

References

Aichele, D. B. and Coxford, A. F. (eds.) (1994) Professional development for teachers of mathe­matics: 1994 yearbook. National Council of Teachers of Mathematics, Reston, VA.

Browning, C. A. (1989) Characterizing levels of understanding of functions and their graphs (Doctoral dissertation, The Ohio State University, 1988). Dissertation Abstracts International, 49, 2957A.

Clarke, D. (1994) Ten principles from research for the professional development of mathematics teachers. Aichele, D. B. and Coxford, A. F. (eds.) (1994) Professional development for teachers of mathe­matics: 1994 yearbook. National Council of Teachers of Mathematics, Reston, VA., 37-48.

Demana, F., Waits, B. K., Foley, G. D., and Kennedy, D. (2001) Precalculus: Graphical, numerical, algebraic (5th ed.). Addison Wesley Longman, Reading, MA.

Demana, F., Waits, B. K., Foley, G. D., & Kennedy, D. (2001) Precalculus: Graphical, numerical, algebraic (5th ed.). Addison Wesley Longman, Reading, MA.

Dunham, P. H., and Dick, T. P. (1994) Research on graphing calculators. Mathematics Teacher, 87, 440-445.

Dunham, P. H., and Osborne, A. (1991) Learning how to see: Students graphing difficulties. Focus on Learning Problems in Mathematics, 13(4), 35-49.

Foley, G. D. (1993) CalcNet: Disseminating calculus reform to high school teachers. In P. Jaworski (Ed.), Proceedings of the Conference on Technology in Mathematics Teaching. University of Birmingham, Birmingham, England, UK, 523.

National Council of Teachers of Mathematics. (2000) Principles and standards for school mathe­matics. Author, Reston, VA.

Quesada, A. R., and Maxwell, M. E. (1994) The effects of using graphing calculators to enhance college students' performance in precalculus. Educational Studies in Mathematics, 27, 205-215.

T3 • Teachers Teaching with Technology. (2000) How to host a T3 institute [revised for 2001]. Texas Instruments, Dallas, TX.

Waits, B. K.and Demana, F. (1993) Using graphing calculators to enhance the teaching and learning of university mathematics: The United States experience. P. Jaworski (ed.), Proceedings of the Conference on Technology in Mathematics Teaching. University of Birmingham, Birming­ham, UK, 73-80.

 

 

 

 

 


Creating a professional development network

Rosalyn Hyde

Southampton, UK

 

1. Background

2. The T3 mission

3. T3 England, Wales and Northern Ireland

4. Teachers Training Teachers

5. Trainers’ meetings

6. Internet

7. TI-TIME

8. Lobbying for change

9. Material development

10. Summary

 

Recent developments in T3 (Teachers Teaching with Technology) in England will be used as a case study to explore the setting up of formal and informal networks for professional development in the context of an increased emphasis from government on continuing professional development for teachers. The intention is to explore the creation of networks that are enabling and empowering for teachers and that provide teachers with the support and resources they need to take responsibility for their own professional development.

1       Background

Teaching is a profession undergoing constant change world-wide. An English perspective shows an education system dealing with examination and curriculum changes, changing expectations from society, teacher shortages and the challenges presented by new technology, amongst others.

In recent years in England we have seen huge investment in computers and computer equipment in schools and in teachers’ Information Technology (IT) skills through the New Opportunities Fund training. Despite these, there remain issues in terms of suitability of, access to, and availability of suitable materials for using technology for the teaching and learning mathematics in secondary schools. There are more suites of networked computers in schools than before, but more students are studying Information and Communications Technology as a subject in its own right. All subjects in the curriculum want access to the limited IT resources in schools (see Wright, 2001). Handheld technology (graphics calculators and dataloggers) offers teachers access to affordable, flexible and portable technology designed for teaching and learning in schools. It is also technology that has the capability to link to other similar units, to a computer, and, by using suitable software, to access data from other sources. The new guidance for the curriculum for mathematics for 11-14 year olds in England (DfEE, 2001a) contains the expectation that students will use both computers and graphics calculators in their mathematics lessons:

The main uses of ICT in mathematics in Key Stage 3 stem from:

       the use of calculators for calculating purposes;

       small programs, such as number games or investigations in a particular context;

       programming languages, such as Logo or Basic, and the programming capabilities of graphical calculator;

       general purpose software, particularly spreadsheets, but also databases;

       content-free mathematics software, such as graph plotters, dynamic geometry software and data-handling packages;

       ILS (Independent learning Systems), which provide and manage practice in mathematical techniques tailored to the needs of individual pupils;

       graphical calculators and data-loggers;

       CD-ROMs and the Internet. (p.25)

 

In another initiative, our government announced a new Continuing Professional Development (CPD) Strategy for teachers in England in March of 2001 (DfEE, 2001b). This includes elements relating to professional development in the early years of teaching, research scholarships for teachers, leadership development, bursaries for teachers for CPD and a limited programme of sabbatical opportunities. The intention is that the teaching profession in England will further develop into one with an increased ethos of continuing professional development and into one where teachers take more responsibility for their own professional development.

2       The T3 mission

T3 Europe has delivered over half a million hours of training to a total of over 30 000 course participants since it started in 1996. It has a four-fold mission statement focusing on increasing the implementation of graphing technology in the classroom through:

       teacher support/community

       lobbying for change

       material development

       training

 

Our annual T3 co-ordinators’ meetings show many common issues amongst the T3 communities in Europe, despite our diverse situations. Many of us face the common need to work towards a stronger positioning of handheld technology under the wider heading of IT. We are also concerned with reaching those teachers who are not enthusiastic about using technology in their teaching. We have shared ideas for evaluating T3 courses and created a common format for T3 literature across Europe. As a group of co-ordinators we are also sharing and debating approaches to assessment and matters relating to assessing students’ mathematics given the availability of graphics calculators and Computer Algebra Systems. As national T3 co-ordinators we act as a support network for one another as well as helping each other with practical requests from time to time. As a joint project for the last year we have produced a CD-ROM containing articles demonstrating good practice with handheld technology from across Europe.

3       T3 England, Wales and Northern Ireland

T3 was first set up in the U.K. in 1996 and was facilitated for its first three years from the University of Plymouth. Since April 2000 T3 England, Wales and Northern Ireland has been co-ordinated through The Mathematical Association by myself as the Professional Development Officer for the Association. We face key challenges currently in terms of wanting to see more use of handheld technology in classrooms and in supporting teachers with developing the use of this technology.

4       Teachers Training Teachers

A key part of the T3 philosophy is that of having teachers training teachers. This fits in well with the current emphasis from the English Department for Education and Employment whose new CPD strategy uses ‘Learning from each other….learning from what works’ as its key phrase, and with the English General Teaching Council’s recommendations in this area.

The professional development strategy document (DfEE, 2001b) states that teachers need to select development activities that help them to learn from each other (p.5) and that the regional strategy launch conferences are “designed to bring people together from across the profession who are strongly committed to professional development – to build networks, share ideas and experience….” (p.5) as well as saying that networks and partnerships should be used to enhance the quality of development (p.19).

In practice, in England this has led to the development of partnerships with Local Education Authorities where T3 has trained teachers identified locally by the Authority’s staff. These teachers have then been supported by T3 in training other teachers within the authority. This has the advantage of having T3 trainers who have skills locally with the technology and, in particular, credibility as being excellent classroom practitioners. For those teachers acting as trainers, this opportunity adds to their skills and to their career profiles. This also leads to the development of local networks of teachers supporting one another and sharing ideas with one another and to local expertise in using handheld technology to enhance the teaching and learning of mathematics and science.

5       Trainers’ meetings

Any person offering training needs support, but if we are using teachers as trainers we need particularly need to ensure that we support them in their role. Many countries in Europe have meetings for those who offer T3 training. These are an opportunity to meet others, share ideas, update skills, learn about developments in the field of handheld technology, review and develop materials and to look at all of these from an appropriate pedagogical viewpoint. In England our recent trainers’ meeting included experienced trainers, potential new trainers as well as those who lobby and support T3 in other ways. Each participant is asked to bring a student activity with them to the meeting to share with the other participants. This is an opportunity for teachers to add to the bank of activities we are developing that closely matches our new curriculum in England. It is also an opportunity to learn more about the skills each trainer has, in using the technology, presenting, and in understanding and communicating the related pedagogy. These meetings also offer opportunities for informal discussion, problem-solving and for the discussion of practical matters relating to the smooth running of T3 in England.

 


 

 

Fig. 1

 

 

6       Internet

With the increase in the number of computers in schools, increased access to the Internet and more training opportunities as well as limited opportunities for teachers to purchase a personal computer at a reduced cost, more and more teachers now have easy access to email. This allows us to promote T3 courses through our web site, through email lists and through email newsletters. It also allows informal communications between interested parties, which has proved valuable for the sharing of ideas, for support and for getting help with problems. Many teachers feel isolated in their schools and classrooms and being able to put them in contact with a like-minded teacher from another school can be a real support and encouragement for them.



 

 

Fig. 2

 

 

A new and exciting area for development for T3 is T3 online. Sample materials are available on the web site. Using the Internet to deliver CPD is a rapidly developing area and one that many organisations in England are interested in seeing utilised more effectively in providing professional development for teachers.

These opportunities need to be thought through carefully so that the opportunities of being able to offer courses online are maximised (such as anytime access, flexibility of length of session, being able to access materials flexibly) and the disadvantages are minimised (such as the isolation of studying alone, access and connection speed). It should also be borne in mind that Internet access is not generally free in the U.K. and is paid for through such systems as flat monthly fees or by call charges or a combination of both.

We have not yet explored the opportunities offered by online discussion groups or chat rooms.

7       TI-TIME

TI-TIME is a magazine produced by Texas Instruments and mailed to teachers. It features articles and information of interest to teachers about using handheld technology. It provides another opportunity for the sharing of ideas and for support round another network of teachers in the U.K.

8       Lobbying for change

The T3 community uses another set of different, but overlapping, networks in order to lobby for change. The steering team for T3 England consists of representatives from the subject associations for mathematics teachers teaching students at school and college level, the subject association for science teachers, the association that represents Local Education mathematics advisors and a representative from university mathematics education. We use conferences and journals to inform and influence both teachers, teacher-trainers and the research community about the potential of handheld technology. We are also able to use meetings with a wide range of people involved with education and other networks of mathematics educators for the same purposes.

9       Material development

A key part of the philosophy of T3 is that training is delivered by teachers and that materials are developed by teachers. Not all teachers make good trainers and not all teachers make good writers. However, for those that do, there is a great sense of satisfaction gained from the final product. The materials produced by T3 England are closely matched to our curriculum, include materials focused in the classroom and have a strong pedagogical emphasis. These key aspects are also emphasised in our courses.

10  Summary

As the ENC publication ‘Ideas that Work: Mathematics Professional Development’ says: “Networks also build the capacity of their members to identify and solve their own problems. Teachers develop a sense of confidence in their individual and collective ability to make improvements” (p.29).

The Department for Education and Employment’s strategy for professional development suggests research evidence shows that professional development is most likely to lead to successful changes in teachers’ practice where “teachers are supported, by their headteachers or heads of department, and by participation in wider teacher networks” (DfEE, 2001b, p.11).

Remarks such as these show that a networking approach to professional development, as in T3, is a profitable route to follow. T3 is about more that offering training for teachers in using graphics calculators to teach mathematics to teach mathematics and science. It is about developing a culture of appropriate use of handheld technology in teaching and about creating a climate where that is possible by providing networks of support, providing materials and lobbying for change.

 

References

Eisenhower National Clearing for Mathematics and Science Education. Ideas That Work: Mathematics Professional Development. www.enc.org

Department for Education and Employment (2001a) Key Stage Three National Strategy Framework for Teaching Mathematics: Years 7, 8 and 9. DfEE, London.

Department for Education and Employment (2001b) Learning and Teaching: A Strategy for Profes­sional Development. DfEE, London.

Wright, D. (2001) Handheld Technology and Mathematics. Micromath Summer 17/2, 36-38.

 

Web-pages

Dep. of Education and Skills, England:

https://www.gov.uk/government/organisations/department-for-education-and-skills

General Teaching Council for England:

http://www.gtce.org.uk/

T3 web site:

http://www.t3ww.org/

T3 online:

http://www.t3.com

TI-TIME UK web site:

http://www.ti.com/calc/uk/newsletter.htm

 

 

 

 


An on-going program of professional development
in hand-held technology
for instructors of prospective teachers

Mark L. Klespis

Huntsville, USA

 

1. Introduction

2. The Ohio state university technology college short course program

3. The need for professional development in Texas

4. Creation of CoMPET

5. Findings

6. Summary

 

The Mathematics Teacher Educator (MTE) program is an on-going professional development program of the U. S. Teachers Teaching with Technology (T3) and is designed to assist college faculty to inte­grate technology into their mathematics content courses for prospective elementary and secondary teachers. The paper focuses on a collaboration of the MTE program with a parallel NSF-funded pro­ject directed by the author.

1       Introduction

Calculators and other forms of technology have been in mathematics classrooms for a long time. Recent advances in software and hardware have created a generation of technology that is more advanced and cheaper than ever before. While there are still serious equity issues related to which students have access to this technology, it is quite evident that these tools are part of the educational landscape and thus mathematics teachers at all levels must be know­ledgeable about their use and impact on learning mathematics.

The leading mathematics and mathematics education societies in the United States have un­derstood the significance of this impact. In the United States, appropriate incorporation of technology has been recommended by the Mathematical Association of America (Call for Change 1991), the National Council of Teachers of Mathematics (Curriculum and Evaluation Standards 1989 and the Principles and Standards of School Mathematics 2000), the Ameri­can Mathematical Association of Two-Year Colleges (Crossroads in Mathematics, 1995), the National Research Council (Everybody Counts, 1989), and the Mathematical Sciences Edu­cation Board (Counting on You: Actions Supporting Mathematics Teaching Standards, 1991).

However, professionals in the field of teacher preparation have made far too little progress toward preparing elementary and secondary school teachers to meet the recommendations of these various organizations. Many mathematics instructors who teach mathematics to pro­spective elementary and secondary teachers are ill informed about impact and implementation of technology and hence, ill-equipped to teach or to prepare their students to use technology appropriately.

Little change in the precollege curriculum can take effect unless those who deliver the cur­riculum have the necessary background in mathematical content and pedagogy. In 1991, the NCTM published the Professional Standards for Teaching Mathematics, a companion to the Curriculum and Evaluation Standards. This document addressed the requisite professional standards for teaching mathematics, for the evaluation of teaching mathematics, and for the development of teachers of mathematics.

Faculty in higher education needed to shoulder the burden of moving teachers forward. In­deed, the Professional Standards indicated that [College] Instructors need to experiment with new tasks, tools and . . . models of instructional strategies. This necessitates collegial inter­action and support, as well as participation in professional development activities (128).

2       The Ohio state university technology college short course program

The College T3 Program had its origins in workshops given by Dr. Bert Waits and Dr. Frank Demana at The Ohio State University in the 1980's. Early workshops used computer graphing software and (when they became available) graphing calculators to enhance the teaching and learning of mathematics.

The purpose of the Demana/Waits College T3 Program was to provide a stimulating learning environment for college and university faculty to learn how to use hand-held CAS and graphing calculator technology to enhance the teaching and learning of collegiate mathe­matics. One important outcome of the College T3 Program was to help professors provide a vibrant and dynamic technology-enhanced classroom environment, one in which students can better understand and apply mathematics and where students can find value in mathematics.

In the summers of 1997 and 1998, the College Short Course program convened a group of mathematicians and mathematics educators to develop technology based materials geared specifically for college mathematics courses that are typically taught to elementary or secon­dary teacher. The author was a member of the elementary and middle school writing teams and is now an editor of the MTE materials as well. The following is an abridged description of the elementary MTE Short course.

The Mathematics Teacher Educator - Elementary (MTE-E) course is designed for mathe­matics teacher educators involved in the both content and methods courses for pre-service elementary teachers. The MTE-E course is developed around a series of modules. A current list of modules: Number Relations, Geometry, Algebra, Probability/Statistics/Data Analysis, Beyond Algebra, and Calculator Apps. Each of these modules addresses the content and pedagogical tools needed by the mathematics teacher educator in implementing technology enhanced lessons as well as providing future lesson ideas for the pre-service elementary school teacher. Hosts and instructors select appropriate modules based on the interests and needs of the participants at each particular site. The elementary modules will use the TI-15, TI-34II, TI-73, TI-83 Plus, TI-92 Plus, CBL 2™, CBR™.

Detailed information about the MTE Short Courses and the College Short Course program can be found at: <http://www.math.ohio-state.edu/shortcourse/>.

3       The need for professional development in Texas

The Texas Statewide Systemic Initiative (TSSI) was created to improve mathematics and science instruction in Texas. One area identified as needing help was the mathematical prepa­ration of elementary teachers. In 1995 a survey of higher education institutions in Texas con­ducted by the TSSI found that 60% of the community college districts and 22% of the mathematics departments at universities responding did not offer a specific mathematics course for preservice elementary teachers. Furthermore, 14% of the universities responding to the survey indicated that they did not have a faculty member whose specialization was mathematics education. Thus, a significant number of students were not being exposed to the type of mathematics instruction that would prepare them to teach mathematics to young chil­dren – particularly in the area of technology.

As a result, the TSSI published the Guidelines for the Mathematical Preparation of Prospec­tive Elementary Teachers in 1996. The TSSI then made funds available for two rounds of grant programs to help institutions revitalize (or, in some cases, create) mathematics courses for elementary school teachers.

The author along with faculty from area two-year colleges created a coalition that would im­pact prospective elementary teachers at all three institutions by using the Guidelines to pro­vide students with a set of consistent mathematical experiences through the creation of a common syllabus and student projects.

4       Creation of CoMPET

The cohort that developed the materials from the TSSI funding realized the need to dissemi­nate this information to a wider audience. Thus, funding was sought from the National Science Foundation (NSF) to create CoMPET: Coalition for the Mathematical Preparation of Elementary Teachers.

This 18-month project expanded the existing coalition to a network of 16 two-year colleges and 11 four-year colleges and universities seeking to revitalize their mathematics courses for elementary teachers. The extended coalition grew from an intensive five-day institute in June 1998 and was fostered by mentoring, e-mail, and follow-through workshops in October 1998 and May 1999.

CoMPET staff used the student projects and instructor's guide from the original coalition project. The problem was that only three of the 25 projects were technology based. Thus, the MTE materials from the Ohio State University Technology College Short Course Program for mathematics teacher educators were well suited for inclusion in the project.

5       Findings

Participants were surveyed one year after the project activities had ended. Of the original 39 participants, 17 responses were received. The CoMPET staff was particularly interested in finding out what modifications (if any) had occurred in the areas of

       instructional philosophy,

       use of technology,

       mathematical content of preservice elementary mathematics courses,

       instructional approach, and

       methods of assessment.

A summary of responses to each area follows.

Instructional philosophy

Of the 17 responses, only one participant indicated a significant shift in instructional philoso­phy. He wrote, “I am now less concerned about the students’ understanding of formal mathematics and more concerned about the students’ ability to think through and answer questions independently.” Another person mentioned that she had come to the project with an instructional philosophy similar to CoMPET’s, so she had used her experience to find tune her thinking. The majority of the participants found that they now spent less time on formal lec­ture in their classes. Instead, they have opted for a more student-centered instructional at­mosphere. They felt that they are now asking more students to take responsibility for their learning.

Use of technology

It is interesting that the responses in this category rarely referred to a specific type of techno­logy (an exception will be noted shortly). Rather, six people responded that they benefited from seeing how technology could be used to enhance mathematics learning for prospective elementary teachers. Most linked the use of technology to mathematical content – that is, they saw technology as a means of enhancing understanding. Thus, the use of technology was transparent – the mathematical content was of primary importance and technology is a means to achieve the desired end of having a better understanding of mathematics. The one type of technology mentioned specifically by participants was dynamic geometry software. This pro­gram was relatively new to most people in the project and it certainly made a strong impres­sion on them. Finally, it is worthwhile to note that one person responded that while many of the project ideas were worthwhile, she had not made any changes in her use of technology because, “I have no budget and can’t afford technology.”

Mathematical content

Nearly all respondents indicated that they have a college or state mandated content that must be taught. Thus, the topics of the courses had not changed, but the methods of teaching the same content did. Two people mentioned that they had been able to institute a math lab on their campus to help extend ideas mentioned during the class time.

Instructional approaches

Survey responses indicated that there was less use of lecture and more on group work and use of manipulatives. This led to more student/teacher and student/student interactions. Ten of the 17 people responding indicated that moving from lecture to a more student center instruc­tional environment was a significant change. All responses indicated some shift away from the traditional lecture as the primary vehicle of instruction.

Methods of assessment

Traditional mathematics tests are still used, but all respondents indicated an increased use of student projects and lab activities as additional means of assessing student understanding. Other types of assessment mentioned included assignments requiring more written explana­tion of mathematical ideas and the use of peer evaluations. No one specifically mentioned any changes in assessment due to the increased use of technology. This was somewhat dis­appointing because the topic was addressed in the initial institute and both follow through workshops.

6       Summary

Based on the surveys returned it appears that CoMPET was able to achieve its goal of helping college mathematics instructors make the transition to modeling instructional approaches re­commended by NCTM, AMATYC, etc. al. This, in turn, provides prospective elementary teachers an alternative vision of how mathematics can be taught and understood, and where technology is much more likely to be incorporated.

 

References

Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus (1995) American Mathematical Association of Two Year Colleges, Memphis, TN.

Mathematical Sciences Education Board (1991) Moving Beyond Myths: Revitalizing Undergraduate Mathematics. National Academy Press, Washington, DC.

National Council of Teachers of Mathematics (1989) Curriculum and Evaluation Standards. Reston, VA.

National Council of Teachers of Mathematics (1991) Professional Standards for Teaching Mathe­matics. Reston, VA.

National Council of Teachers of Mathematics (2000) Principles and Standards in School Mathe­matics. Reston, VA.

National Research Council (1989) Everybody Counts: A Report to the Nation on the Future of Mathe­matics Education. National Academy Press, Washington, DC.

The Mathematical Association of America (1991) Call for Change: Recommendations for the Mathe­matical Preparation of Teachers of Mathematics. Washington DC.

The Texas Statewide Systemic Initiative (1996) Guidelines for the Mathematical Preparation of Pro­spective Elementary Teachers. The Charles A. Dana Center for Mathematics Education, Austin, TX.

 

 

 

 


Technology as a vehicle for
updating middle grades content and pedagogy

Judy O’Neal

Dahlonega, USA

 

1. Guiding principles

2. Planning and development

3. Initial implementation and evaluation efforts

4. Conclusion

 

Technology has become an essential tool for teaching and learning mathematics. As with chalk or dry erase markers, technology’s usefulness and effectiveness in the mathematics classroom is dependent upon the teacher and how it is used to promote and enhance student learning. The primary focus areas for most technology-based professional development activities are ensuring that practicing teachers are aware of currently available hand-held and computer-based technology, are knowledgeable of the ways technology can be used for concept exploration, problem solving, thorough investigations, and representation, and are confident in their ability to use technology in their teaching. The professional development program described in this paper approaches technology training from a slightly different perspective. It utilizes technology as a vehicle for updating the content and pedagogical skills of middle grades mathematics teachers in northeast Georgia who have taken fewer than four upper-level college mathematics courses. This program responds to a statewide initiative to end out-of-field teaching at the middle grades level through the upgrading of teachers’ mathematics content in the areas of number theory, algebra, geometry, probability, and statistics. A description of this model’s guiding principles, planning and development phase, and initial implementation and evaluation efforts are presented.

1       Guiding principles

The role that professional development plays in improving the teaching of mathematics at all levels has received considerable attention during the past decade. Leading the way with its Professional Standards for Teaching Mathematics (NCTM, 1991), the National Council of Teachers of Mathematics (NCTM) has presented six standards specifically addressing the professional development of teachers of mathematics:

(1)   experiencing good mathematics teaching,

(2)   knowing mathematics and school mathematics,

(3)   knowing students as learners of mathematics,

(4)   knowing mathematical pedagogy,

(5)   developing as a teacher of mathematics, and

(6)   the teacher’s role in professional development.

 

These standards are based on the assumptions that the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) forms the foundation upon which professional development must be built, teachers’ practices are influenced by the teaching they see and experience, learning to teach is a process of integrating theory and practice, the process of educating teachers is on-going, and level-specific needs exist and must be addressed.

A common vision of effective professional development is shared by organizations such as the NCTM, National Research Council, and National Staff Development Council. Components of this vision include a well-defined image of effective classroom learning and teaching that reflects a belief in the ability of all children to learn mathematics; opportunities for teachers to develop content knowledge, teaching skills, and an understanding of how children learn; use of instructional methods that mirror those to be used with students; construction and strengthening of a learning community of mathematics teachers; preparation and support for teachers desiring to serve in leadership roles; encouragement of linkages to other components of the educational  system; and continual assessment of the program (Loucks-Horsley, Stiles, and Hewson, 1996).

2       Planning and development

Designing professional development for teachers is a dynamic and fluid process. Planning, implementing, reflecting, revising, and evaluating are key elements in this process. In the planning phase, goals and activities, knowledge base of participants, and context in which the professional development is to occur are important considerations. Of equal importance is anticipating that the initial design should and will change over time in response to changes in teachers’ learning goals (Loucks-Horsley, Hewson, Love, and Stiles, 1998).

The primary goal of this professional development program is the production of solidly competent teachers of middle grades mathematics. For the purposes of this program, competent teachers refers to those who possess an in-depth understanding of the mathematics they will teach; pedagogical skills for mathematics teaching excellence; the ability to facilitate appropriate use of multiple forms of technology, manipulatives, and activities that acknowledge multiple intelligences and learning styles; and the ability to nurture collaboration, critical thinking, hands-on exploration, and problem-based inquiry among students from diverse backgrounds. Teachers accomplish this goal by:

a)      engaging in technology-rich and manipulative-based experiences to learn the content of algebra, number theory, geometry, probability, and statistics courses;

b)      experiencing varied instructional delivery strategies such as cooperative and collaborative learning groups, and student presentations;

c)      gaining confidence in their ability to do mathematics;

d)      demonstrating proficiency in using instructional technology in their classroom teaching;

e)      adapting instructional activities to meet middle grades students’ academic levels, learning styles, and diverse perspectives;

f)        utilizing varied informal and formal assessment techniques and scoring rubrics for evaluating students’ mathematical understanding;

g)      reflecting critically on their teaching performance and the selection of instructional strategies and materials; and

h)      participating in a support network for middle grades mathematics teachers by utilizing e-mail and WebCT’s chat room capabilities.

 

Teachers’ knowledge of mathematics affects what and how they teach mathematics, as well as the types of discourse displayed in their classrooms. Understanding specific mathematical concepts and procedures and the connections among them is essential if teachers are to develop a meaningful picture of school mathematics across the elementary, middle, and high school levels. In this model the incorporation of technology as a tool for learning and doing mathematics is the vehicle by which teachers build this comprehensive mathematical knowledge base. Technology is particularly effective for constructing a mathematical foundation that supports how both children and adults learn and do mathematics (Dunham and Dick, 1994; Rojano, 1996; Sheets, 1993). Hart and Stewart (1998) encourage teachers to first think about students’ learning in terms of active engagement in investigating and making sense of mathematics. Through technology real problems are accessible and an investigative approach is made viable. It is the development of mathematical thinking, rather than mere computational facility that technology fosters.

Solomon and Solomon (1995) suggest that teachers’ use of technology in their classroom can be increased by: (1) giving teachers technology to use at home; (2) providing training, on-site technical support, and online resources; (3) increasing access time; and (4) supporting collaboration with colleagues. The inclusion of technology as one of the six principles in NCTM’s Principles and Standards for School Mathematics (NCTM, 2000) reflects the value placed on technology by the mathematics community. Meaningful professional development assists mathematics teachers in realizing that technology is not a replacement for them, but rather an efficient tool for graphing, visualizing, computing, investigating, and problem solving.

The context for this professional development program is either university based or local school system based. The university-based model consists of a series of four 50-hour courses that are taught during summers at the university site and are available to area teachers. Two of the four courses are taught each summer and are offered on a two-year rotation cycle. The school system-based model is customized to meet the needs of specific local school systems and includes both a 50-hour course taught during the summer in the local system and an additional 10-hour academic year sustained contact phase.

Although the mathematics content of the professional development program is prescribed by the state teacher certification agency, the delivery and implementation modes are flexible. Funding for the delivery of the 50-hour courses is provided through a Title II grant from the US Department of Education to the Georgia Professional Standards Commission. Teachers receive a $300 stipend for each completed course plus materials selected by the instructor such as an overhead TI-73 or TI-83 Plus, CBR, and technology-based activity books. The system-based course and academic year sustained contact is funded through an Eisenhower Higher Education grant and local school system professional development funds. Teachers receive a $750 stipend for each course plus technology-based equipment and materials for their classroom.

3       Initial implementation and evaluation efforts

It is during the implementation phase that professional developers encounter the on-going dilemma of maintaining a focus on changing the philosophy of teaching and learning while being responsive to teachers’ more immediate needs for assistance with implementation issues (Mundry and Loucks-Horsley, 1999). While achieving a balance between philosophical and pragmatic approaches is certainly desirable, there are no formulas or time allocation percentages that work consistently with different groups of teachers. It is imperative that pedagogically sound instructional and assessment models are utilized as we in turn model the teaching behaviors that we seek to develop or refine in practicing teachers. Experiencing good mathematics teaching is one of the most influential factors in shaping the instructional delivery practices employed in a mathematics teacher’s classroom (Rahal and Melvin, 1998; Raymond, 1997; Stanford, 1998). In essence teachers teach as they are taught. Consequently, it is important for professional developers to orchestrate exemplary experiences which ensure that worthwhile mathematical tasks are posed; teachers are engaged in mathematical discourse; a variety of tools such as manipulatives, calculators, computers, and pictorial models are utilized; learning environments that support and encourage mathematical reasoning are created; and intellectual risks in doing mathematics independently and collaboratively are expected and encouraged.

Throughout the model’s summer sessions, emphasis is placed on modeling effective instructional and assessment practices. The TI-73 and TI-83 Plus are used to develop basic concepts of number theory, fractions, percent, decimals, data representation and analysis, probability, rates of change, and functions. Used in conjunction with data-collection devices such as the Calculator-Based Ranger (CBR) or Calculator-Based Laboratory (CBL) and its sensors, both the TI-73 and TI-83 Plus provide media through which problem solving and connections between mathematics and other disciplines, as recommended in the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), are solidified. Cooperative and collaborative learning activities utilizing the TI-73, TI-83 Plus, CBR, or CBL provide a structured basis for group projects and student-led technology presentations. Dynamic geometry programs are used to enhance students’ experience with two- and three-dimensional geometry (Healey, 1993). Middle grades teachers complete activities that incorporate interactive geometry software such as Geometer’s Sketchpad (GSP) or the TI-92’s Cabri in a dynamic investigation of geometric concepts, making and validating conjectures, and writing paragraph proofs or justifications. Fathom, TI-InterActive, the TI-83 Plus, and the CBR and CBL are used to develop statistical concepts. On-line data sites supplying real-world data that can be represented, analyzed, and interpreted engage teachers in explaining and predicting real-world phenomena. In addition, participating teachers examine how the incorporation of hands-on and technology-based activities affects teacher planning, instructional strategies, and student evaluation. 

The format of the sustained contact sessions includes teacher dialogue, teacher presentations, hands-on activities, and reflection on practice. The dialogue portion provides participants an opportunity to discuss implementation issues, their perspective on classroom successes, and ideas for improvement based upon actual classroom experiences. The presentation portion is conducted by teacher-participants and focuses on the demonstration of instructional activities and assessments that have proven to be particularly effective in the presenter’s mathematics classroom. The hands-on activities portion includes additional instruction in the areas of content, manipulative and technology utilization, and the assessment of student learning. The reflection on practice portion includes self-assessments, reflective logs, and video analyses that are designed to engage teachers in a critical analysis of their teaching performance and the selection of instructional strategies, materials, and assessment alternatives. The instructor is available upon request to provide follow-up instructional support in teachers’ classrooms.

Throughout the implementation phase, the processes of reflection and revision are ongoing. Reflecting and revising function most effectively in tandem since neither is meaningful in the absence of the other. Therefore, teachers are asked periodically to provide written evidence of how the course and/or sustained contact phase is proceeding and to offer suggestions for modifying the experience to better support teachers’ needs. During the follow-up sessions, participants share classroom successes or dilemmas and offer suggestions for improvement so that their experiences can serve to inform others.

The evaluation phase is often the component that receives the least attention, possibly because of the inherent difficulty in judging the long-term effectiveness of the professional development experience. Evaluation of this professional development program focuses on four main areas: (a) the teacher’s ability to comprehend, apply, and retain course content knowledge, (b) the teacher’s ability to blend mathematical knowledge with effective instructional and assessment practices while simultaneously addressing the diverse backgrounds of students, (c) the teacher’s ability to lead students of diverse groups to understand middle grades mathematics content, and (d) the teacher’s attitude toward learning, doing, and delivering mathematics. The inclusion of multiple formative and summative assessment techniques such as teacher interviews, participants’ reflective logs, observations during class meetings and sustained contact sessions, written analysis of classroom performance videos, content proficiency demonstrations, peer and self-assessment, portfolios, and analyses of teachers’ and their students’ mathematics classroom performance feedback provides a comprehensive view of both the teacher’s development and the professional development program’s effectiveness.

4       Conclusion

Developing excellent mathematics teachers is a complex process. Just as there is no one tool or course that can single-handedly accomplish this task, there is no one model for effective professional development that can be transported from one place to another. However, it is clear that technology has certain unique capabilities that support the learning, doing, teaching, and assessing of mathematics. Accepting that these capabilities are ever changing as new tools are developed, the design of innovative and effective professional development programs for motivating and inspiring the current and next generation of mathematics teachers promises to be a rewarding and stimulating endeavor.

 

References

Dunham, P. H., and Dick, T. P. (1994) Connecting research to teaching: Research on graphing calculators. Mathematics Teacher, 87(6), 440-445.

Hart, E. W., and Stewart, J. (1998) Reflections on high school reforms and implications for middle school. In L. Leutzinger (Ed.), Mathematics in the middle. National Council of Teachers of Mathematics, Reston, VA.

Loucks-Horsley, S., Stiles, K., and Hewson, P. (1996) Principles of effective professional development for mathematics and science education: A synthesis of standards. NISE Brief, 1(1).

Loucks-Horsley, S., Hewson, P. W., Love, N., and Stiles K. (1998) Designing professional development for teachers of science and mathematics. Corwin, Thousand Oakes, CA.

Mundry, S. and Loucks-Horsley, S. (1999) Designing professional development for science and mathematics teachers: Decision points and dilemmas. NISE Brief, 3(1).

National Council of Teachers of Mathematics. (1989) Curriculum and evaluation standards for school mathematics. Author, Reston, VA.

National Council of Teachers of Mathematics. (1991) Professional standards for teaching mathematics. Author, Reston, VA.

National Council of Teachers of Mathematics. (2000) Principles and standards for school mathematics. Author, Reston, VA.

Rahal, B. F., and Melvin, M. J. (1998) The effects of modeling mathematics discourse on the instructional strategies of preservice teachers. Action in Teacher Education, 19(4), 102-118.

Raymond, A. M. (1997) Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-576.

Rojano, T. (1996) Developing algebraic aspects of problem solving within a spreadsheet environment. In N. Bednarz, C. Kieran, and L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching. Kluwer, Dordrecth, Netherlands.

Sheets, C. (1993) Effects of computer learning and problem-solving tools on the development of secondary school students’ understanding of mathematical functions (Doctoral dissertation, University of Maryland College Park, 1993)

Solomon, G., and Solomon, S. (1995) Technology and professional development—10 tips to make it better. Learning and Leading with Technology, 23(3), 38-39, 71.

Stanford, G. C. (1998) African-american teachers’ knowledge of teaching: Understanding the influence of their remembered teachers. Urban Review, 30(3), 229-43.