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Special Issue Article: A Look at Technology's Role in Professional Development of Mathematics Teachers at the Middle School Level by Ihor Charischak Web version of article that appeared in School Science and Mathematics (November, 2000)

IIn last month's issue of School Science and Mathematics, Glenda Lappan wrote about the dilemma of supporting teachers in continuing to grow professionally by learning more mathematics content, improving their pedagogical and assessment skills, and adapting the curriculum to the needs of their students. Though it is clear that this kind of learning is best done in the context of what is going on in the classroom, teacher's schedules and other problems make it difficult to implement a coherent classroom based professional development program. In this article, the author adds two more knowledge domains to this mix: the ability to use and teach with technology. Since learning and teaching is a dynamic process, he envisions the classroom as a laboratory where teachers get to practice and improve in these six areas and get feedback from an audience of their peers. His reflections are based on a current project he is working on in Paterson, NJ where he helps middle school teachers use computer software to improve mathematics teaching and learning.

The technology wizards, pundits, and even ordinary people love to reflect on and predict what the future will hold as a result of new and emerging technologies. The designers of the 1939 World's Fair were no exception when they predicted that by 1969 we would have smart cars that would keep a safe distance from other cars by radio control (PBS, 1997). That goal was not reached (though cars were somewhat safer in '69), but the U.S. did manage to land a man on the moon. So that begs the question: Why were scientists not able to do something as straight forward as designing cars that can manage to avoid each other if they were able to do something as complex as a moon landing? Predicting all the political and social minefields that can delay or derail a project is almost impossible.

Behind the 1939 vision was a belief that technology could eventually solve most if not all our problems. In the early '80s, the National Educational Computer Conferences were gathering places for educators touting technology's promise for education. Education, of course, is not immune to similar social and political issues that automakers had in producing safe cars. 

As a high school student I was thrilled to be chosen as one of the few students who got to take algebra in the eighth grade. At the time, my teachers and administrators did not look ahead to what we might do as seniors after we finished the usual 12th grade program in the 11th year. Fortunately for them, serendipity stepped in and a new technological innovation called "programmed learning" appeared which with much fan-fare I helped pioneer. It was a lot quieter the following December when our teachers realized that though we got all the programmed questions right (you could not turn the page if you did not answer correctly) we could not pass the tests and did not have a clue as to what we were learning. 

Despite the fact that the historical educational technology landscape is littered with expensive by-products of best intentions, the new millennium begins with schools investing heavily in technology, getting wired for and connected to the Internet, etc. as if the ghost of programmed learning was not lingering in the background waiting for its next victim. But today's technologies are fundamentally different in that they are more highly integrated into the culture and fabric of society. That does not automatically mean that schools will fully take advantage of it for teaching and learning. A course needs to be charted that will refocus school's attention on the ultimate prize, which is student's authentic learning. The ideas in this paper have to do with the kind of professional staff development that would use technology as a catalyst for helping teachers learn mathematics in an interesting, engaging way and employ effective strategies in the classroom that promote student learning.

I joined the computer educational technology bandwagon when I discovered firsthand in the late '70s that microcomputers in the hands of students can make a difference in their approach to learning. The computer created a context in which some of my students actually wanted to learn the mathematics, because it was now "cool" to learn it! I knew that I had stumbled onto something fundamentally different and potentially more rewarding than any resource I had ever used before.

Though I had seen the light and I acted on it during my teaching days, the light blinded me from seeing the difficulties other teachers would encounter using this technology effectively. As I gained computer experience, I began to share it with my colleagues. A few took to it, but most them ignored it. It was frustrating. I started gaining some perspective on this problem after I learned of some pioneer research that examined why so many innovations were not making an impact on schools. David Dockterman, an educational software developer at Tom Snyder Productions, told me about a Rand Study (Berman & McLaughlin, 1978) examining a host of various technologies in the schools and reporting on the problems these innovations had in taking root in the classroom. 

Newman's view echoes the new Principals and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000) technology principle, in which technology's role is said to amplify and enhance mathematics curriculum and instruction and not be the answer (as some of the vendors would like for us to believe) for all our "math woes." 

With this new understanding, I approached my staff development duties by first asking teachers how I could help them achieve their goals, rather than do something I decided was good for them. The challenge was to see how I could incorporate my vision of technology in education in ways that the teachers could buy into and support. 

The Paterson Experience
Two years ago Paterson, an urban school district in New Jersey, and Stevens Institute of Technology 's Center for Improved Engineering & Science Education (better known as CIESE) joined in a partnership for a 3 year period in an initiative called "Integrating Mathematics and Technology Teacher Training" (IMATTT). The goal was to help 39 teachers in six different buildings integrate computer software into the teaching of sixth, seventh, and eighth grade mathematics. In addition to the math teachers involved, a computer teacher was included as a part of the school teams. Two of my colleagues (retired former math teachers) and I embarked on a course of workshops (summer and after school) and academic year classroom visitations, with the objective being to help the teachers teach computer-related lessons. During my visits and observations, I noticed that I can view the lesson from different perspectives or levels (Charischak, 1994). At first glance I was aware of how the teacher handled classroom management. I watched to see what the teacher was doing to achieve his or her goals. I looked to the students to give me clues. Did they appear to be acting responsibly? Were they listening? Were they doing their assignments? Looking a bit closer and deeper, I gauged the student's level of engagement. Were the students really interested in what the teacher had proposed? Was it consistent with the goals? Were they engaged with other students in doing things that support (aid and abet) the teacher's agenda? Then I looked even deeper --- at the third level --- the level of learning. What were the students actually learning as they did the activity? Did their conversations yield clues as they worked toward a solution to a problem? Were they listening intently and asking questions to clarify the ideas presented? Did they leave at the end of the class still talking about the activity? This third level was not easy to gauge because students can be good at looking like they are learning. (I know, because I was one of those students.) Asking the students some questions about the activity revealed good clues. What I discover is that many students were just going through the motions, motivated only by extrinsic rewards such as grades and completing required assignments. This lack of engagement at the learning level could be one of the more significant problems (Steinberg, 1996). Students seem to have made some covert agreements (or compromises) with their teacher as to how they shall define achievement in the class. The agreement might be that if the student can answer correctly on average 70% of the questions on the tests, then the teacher and the student will agree that the student knows the material well enough to pass the course. Howard Gardner called this the "correct-answer compromise," which takes the teacher and the student off the hook for really making sure that learning happens (Gardner, 1991.) If educators are to make inroads at this third, "rubber meets the road" level then student engagement must be more than just passing tests and following teacher's prescriptions. The classroom needs to be place where both teachers and students play hard at learning together. 

In the October 2000 issue of SSM, Glenda Lappan stated, 

These six domains will be reviewed in the context of the mission of my project at Paterson, which is to help teachers integrate computer software into the teaching of mathematics. Teachers' knowledge in each of these domains guides me in best helping them in my visits and workshops. 

Ability to use and access resources such as computers, software, calculators, hand-held devices, and the Internet. 
This is the part that teachers like the best, not only because it offers them a knowledge base of what they can do with students, but it also enhances their personal and professional understanding of important aspects of our modern world. Becoming e-mail proficient offers opportunities for gaining confidence in using the technology, while the World Wide Web offers unlimited possibilities for classroom resources.

Creating Technology- oriented Learning Environments. 
Teachers need to plan ahead to adapt their classroom environment to accommodate new resources and teaching strategies. Some strategic approaches that teachers need to become familiar with include:

• Using a projection device and a one computer station to lead a whole class discussion or activity involving multi-teams.
• Organizing a small number of computers in the classroom for individual or group activities or projects.
• How to take advantage of a computer lab (if available) where there is a one-to-one (or one-to-two) ratio of computers to students.

Mathematical Background and Attitude Toward Learning Mathematics.
In the IMATTT workshops, teachers learn to use various software programs. They also work on developing a deeper understanding of the topics they are teaching. For example, a spreadsheet program is an excellent vehicle for getting teachers to work on a question in which coming up with a conjecture depends on collected data, analyzed with a graphical display. But what kind of graph should be used and why? The spreadsheet offers an array of choices, not answers. I have seen some school hallways adorned with colorful graphs that are not clear as to what story is being told. One of the IMATTT workshops this past year was devoted to a discussion of graphs that were dealing with the United States Census that were hanging in the hallway. The teachers planned to improve that lesson this coming year. A more detailed discussion of this activity and others can be found at the IMATTT website (http://www.ciese.org/imattt). 

Pedagogical Strategies and Discourse. 
The new Principles and Standards stated that students should work on problems that are embedded in a context that they understand and that the solutions yield insights into the details of mathematics, how it works and the power of abstraction. (See, for example, the Jinx problem.) I had hopes that after I modeled the lesson others would try it (with my help.) Not many did. I assumed they could go make the transition. Since the teachers were still not completely comfortable with using technology, having someone (no matter how friendly and supportive) makes them uneasy. Also, I realized they needed lots of practice in doing group activities, as well as adopting a new style of teaching.

Personalizing the Curriculum. 
Since the textbook usually defines the curriculum most teachers look to the teacher's guide for ideas to help them teach a particular lesson more effectively. Unfortunately, the guides are not very helpful when it comes to technology. The activities tend to be generic and need modifications in order for them to be useful. The IMATTT curriculum provides more interesting technology and standards-based activities. By integrating these activities into their curriculum, teachers are taking a more active role in modifying, learning about and personalizing the mathematics lessons they teach.

Assessment Strategies.
There was a teacher I worked with who passed away a few years ago, and I attended her wake. The place was full of students mourning the loss of this teacher. Of the six domains identified in this article, her strongest was assessment. She made it a point to make sure she touched every student in her class in some way every day. At the beginning of class she would stand at the door and make sure that every student was ready to participate in the lesson of the day. She made sure students had a pencil, book or whatever was needed. (She had an endless supply of pencils.) After the activity and the assignment, she would take three or four students aside and talk them about the lesson just completed. Those students left knowing that the assessment and pep talk that they just received would be repeated over and over again throughout the year. A key to successful assessment is being personal, caring and consistent.

Putting the Six Domains of Knowledge Together: "A Scene from a Dynamic Classroom"
The first three areas - resources, teacherís knowledge and interest in math, and the way the room is set up for classroom activities - is the "background" for the classroom event that will take place. The school offers a script - either very specific or in broad strokes - that suggests to the teacher what is important to teach. The curriculum may offer suggestions as to the kind of discourse that students have with their teachers and each other. It may include guidelines for assessment to determine whether the mission of the school is being carried out. The resources, teacherís math knowledge, and the learning environment set the stage, while the dynamics of the curriculum (context), the discourse (engagement in the activity), and assessment (reflection) determine the success of the lesson or activity.

But how do I as a staff development educator help teachers to grow in these six areas so that they can put together what I call a dynamic classroom? The traditional method of college courses in these areas does not seem to be working very well. Stein, Smith, & Silver (1999) suggest that what is needed is a new way of looking and addressing the teaching of teachers for the 21st century. In The Development of Professional Developers: Learning To Assist Teachers In New Settings In New Ways, the authors "describe the challenges that practicing teacher educators and professional developers would encounter as they design and implement new programs to help teachers learn new paradigms of teaching and learning amidst current educational reforms." (Stein, Smith, & Silver 1999). The model they suggest is very similar to what I am trying to accomplish in Paterson, but the reality is that the vision is elusive. According to the authors the new paradigm has these features: (The features are theirs; the commentary is mine.)

Teacher assistance embedded in or directly related to the work of teaching.
Most teachers like to be helped in the classroom, be assisted in planning more effective lessons and help with carrying out the lessons especially when the lesson involves the use of technology. This is at the heart of what it means to work towards getting schools to support the kinds of classroom activity that meaningfully goes after success at the learning level. The challenge for staff developers is how best to do this given that each school has similar, but unique set of circumstances and obstacles that prevent them from operating more fully at this higher level of pedagogy.

Teacher assistance grounded in the content of Teaching & Learning 
This feature suggests that the teachers need to learn mathematics content in the context of the curriculum they are teaching. Many of the textbooks assume that the teacher has a good background in mathematics and do little with helping the teacher understand the underlying mathematics and only superficially how to effectively teach it. This can be a problem even with the very best of curriculums. So staff development needs to focus on personalizing the curriculum for each teacher giving them a sense of ownership of the curriculum by engaging them in activities that allows them to contribute and learn from each other while being guided by the staff developer. 

Development of Teacher Communities of Professional Practice.
In Paterson we have after school workshops open to any IMATTT teacher interested in the topic of the workshop. Other workshops are scheduled individually at each school for the teachers that teach at that school to work on specific activities. Also, we encourage teachers to contribute to the on-going development of the curriculum that improves from year to year. Unfortunately, there are so many other competing important and urgent matters that need to be handled that focusing on professional practice does not get the attention it deserves. 

Collaboration with Experts Outside the Teaching Community. 
As someone connected to the professional world of teacher education, I keep in touch with developing ideas and share these ideas with the teachers in workshops, newsletters, and through the IMATTT website. The teachers are invited to participate in local conferences. For example, one of the IMATTT sixth grade teachers, Saundra Generals and I led a workshop session at this year's annual NCTM meeting in Chicago. This fall she will lead a similar workshop at a state level mathematics teacher's conference in New Jersey. This kind of activity empowers teachers to grow and become leaders in their school communities. This can also be a problem for an individual school when a teacher becomes so skilled (in this case, technology) that she transfers to another school within the district to become a technology teacher.

Consideration of Organizational Content. 
There is agreement that teachers need regular on going staff development in order to improve the quality of their teaching and learning through a variety of workshops, courses and trainings. However, if these activities though worthwhile and stimulating for the teacher are not well coordinated, they will not necessarily make any significant difference in the teacher's classroom habits. For that reason Susan Loucks-Horsley, Peter Hewson, Nancy Lowe, and Katherine Stiles (1998) believe that teacher assistance should be a design process "not about importing models or following formulas, but rather about thoughtful, conscious decisionmaking." (Stein, Smith, & Silver 1999). This translates into many classroom visits and adjustments of the game plan in order to be responsive in a constantly changing environment, while at the same time not losing perspective on the real goal which is student's learning. 

As I look back at my previous and on going efforts in Paterson and reflect on the future what comes to mind is what Seymour Papert wrote in his seminal book Mindstorms (Papert, 1980 p. 101) about "bugs" and "debugging",

References.
Berman, P., & McLaughlin, M. W. (1978). Federal programs supporting educational change. Vol. VIII: Implementing and sustaining innovations. Santa Monica, CA: Rand Corporation.

Charischak, I. (1994) Levels of looking at pedagogy: reflections on learning and teaching with technology. Paper presented at the Spring Association of Mathematics Teachers of New Jersey Regional Conference, Rowan College, Rowan, NJ.

Dockterman, D. (1997). Great teaching in the one computer classroom. (Tom Snyder Productions: Watertown, MA.)

Gardner, H. (1991). The Unschooled Mind: How Children Think and How Schools Should Teach. New York, NY. Basic Books. 

Lappan, G. (2000). A Vision of Learning to Teach for the 21st Century. School Science and Mathematics. 100(6) 

Loucks-Horsley, S., Hewson, P., Love, N. & Stiles, K. E. (1998). Designing professional development for teachers of science and mathematics. Thousand Oaks, CA: Corwin Press.

National Council of Teachers of Mathematics, (2000) Principals and Standards for School Mathematics. Reston, VA. National Council of Teachers of Mathematics, Inc.

Newman, J.M. (2000) Following the yellow brick road. Phi Delta Kappan, 81(10), 774

PBS Online Newshour. (1997, August 8). Automating automobiles. Transcript [Online] Available: (http://www.pbs.org/newshour/bb/transportation/august97/smartcars_8-8.html)

Papert, S. (1980) Mindstorms: Children, Computers, and Powerful Ideas. New York, NY. Basic Books.

Snyder, T. (1994) Blinded by science. The Executive Educator, 16(3), 36-40

Stein, M. K. Smith, M. S. Silver, E. A. (1999) The development of professional developers: learning to assist teachers in new settings in new ways. Harvard Educational Review, 69, (3), 237-269.

Steinberg, L. (1996). Beyond the classroom:Why school reform has failed and what parents need to do. New York: Simon & Schuster.

Ihor Charischak
Stevens Institute of Technology
Center for Improved Engineering & Science Education
Castle Point on the Hudson
Hoboken, New Jersey 07030
201-216-5076
icharisc@stevens-tech.edu