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Special Issue Article:
A Look at Technology's Role in
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
Glenda Lappan wrote about the dilemma of supporting teachers in
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
is best done in the context of what is going on in the classroom,
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
he envisions the classroom as a laboratory where teachers get to
and improve in these six areas and get feedback from an audience of
peers. His reflections are based on a current project he is working on
in Paterson, NJ where he helps middle school teachers use computer
to improve mathematics teaching and learning.
The technology wizards, pundits, and even
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
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
but the U.S. did manage to land a man on the moon. So that begs the
Why were scientists not able to do something as straight forward as
cars that can manage to avoid each other if they were able to do
as complex as a moon landing? Predicting all the political and social
that can delay or derail a project is almost impossible.
Behind the 1939 vision was a belief that
eventually solve most if not all our problems. In the early '80s, the
Educational Computer Conferences were gathering places for educators
technology's promise for education. Education, of course, is not immune
to similar social and political issues that automakers had in producing
As a high school student I was thrilled to be
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
11th year. Fortunately for them, serendipity stepped in and a new
innovation called "programmed learning" appeared which with much
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
Despite the fact that the historical
landscape is littered with expensive by-products of best intentions,
new millennium begins with schools investing heavily in technology,
wired for and connected to the Internet, etc. as if the ghost of
learning was not lingering in the background waiting for its next
But today's technologies are fundamentally different in that they are
highly integrated into the culture and fabric of society. That does not
automatically mean that schools will fully take advantage of it for
and learning. A course needs to be charted that will refocus school's
on the ultimate prize, which is student's authentic learning. The ideas
in this paper have to do with the kind of professional staff
that would use technology as a catalyst for helping teachers learn
in an interesting, engaging way and employ effective strategies in the
classroom that promote student learning.
I joined the computer educational technology
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
to learn the mathematics, because it was now "cool" to learn it! I knew
that I had stumbled onto something fundamentally different and
more rewarding than any resource I had ever used before.
Though I had seen the light and I acted on it
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
that examined why so many innovations were not making an impact on
David Dockterman, an educational software developer at Tom Snyder
told me about a Rand Study (Berman & McLaughlin, 1978) examining a
host of various technologies in the schools and reporting on the
these innovations had in taking root in the classroom.
[The Rand Study said] that any time you
inject an innovation
into a school without taking into account the complex social nature and
workings of the institution, that innovation will failÖ.
(also) fail unless that technology directly benefits one or more adults
who are central to the institution. It is not enough to improve people
or make them more efficient. They have got to like the new technology
than what they had before; itís got to feel better to them in
way. (Snyder, 1994)
I began to realize that technology in schools is
by the latest and greatest gizmo, no matter how good it was, but rather
what fits best into the school's current structure. Judith Newman put
this way: "We choose tools based on what we believe about learning in
first placeÖ all the important questions are really about
and instruction" (Newman, 2000).
Newman's view echoes the new Principals and
for School Mathematics (National Council of Teachers of Mathematics,
technology principle, in which technology's role is said to amplify and
enhance mathematics curriculum and instruction and not be the answer
some of the vendors would like for us to believe) for all our "math
With this new understanding, I approached my
duties by first asking teachers how I could help them achieve their
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
Jersey, and Stevens Institute of Technology 's Center for Improved
& Science Education (better known as CIESE) joined in a partnership
for a 3 year period in an initiative called "Integrating Mathematics
Technology Teacher Training" (IMATTT). The goal was to help 39 teachers
in six different buildings integrate computer software into the
of sixth, seventh, and eighth grade mathematics. In addition to the
teachers involved, a computer teacher was included as a part of the
teams. Two of my colleagues (retired former math teachers) and I
on a course of workshops (summer and after school) and academic year
visitations, with the objective being to help the teachers teach
lessons. During my visits and observations, I noticed that I can view
lesson from different perspectives or levels (Charischak, 1994). At
glance I was aware of how the teacher handled classroom management. I
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
Were they listening? Were they doing their assignments? Looking a bit
and deeper, I gauged the student's level of engagement. Were the
really interested in what the teacher had proposed? Was it consistent
the goals? Were they engaged with other students in doing things that
(aid and abet) the teacher's agenda? Then I looked even deeper --- at
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
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,
only by extrinsic rewards such as grades and completing required
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
define achievement in the class. The agreement might be that if the
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
well enough to pass the course. Howard Gardner called this the
compromise," which takes the teacher and the student off the hook for
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
If it takes the view that teaching of
science) that our [as teachers] is to support learning by aiding and
students through an animated conversation on the subject we have to ask
ourselves what does the teacher need to know to in order to do this
Lappan identified four domains of knowledge as
areas to know about in the teaching of mathematics: content for
pedagogy, learning, and evaluation. Two more domains may be added that
help in successfully implementing technology in the classroom: (1)
of technological resources and how to use them and (2) knowledge of how
to create and use technology-based learning environments.
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
Ability to use and access resources such as computers,
calculators, hand-held devices, and the Internet.
This is the part that teachers like the best, not
because it offers them a knowledge base of what they can do with
but it also enhances their personal and professional understanding of
aspects of our modern world. Becoming e-mail proficient offers
for gaining confidence in using the technology, while the World Wide
offers unlimited possibilities for classroom resources.
Creating Technology- oriented Learning Environments.
Teachers need to plan ahead to adapt their
environment to accommodate new resources and teaching strategies. Some
strategic approaches that teachers need to become familiar with include:
There is a strong need for the teachers to use
a repertoire of effective activities for teaching in these kinds of
Appropriate lessons are needed. In the Paterson IMATTT project, we have
put together a curriculum guidebook (a work in progress), which
such examples. With the convergence of handheld and desktop
these computer model distinctions are slowly fading, because applying
models depends on what device the students can have in front of them.
example, a classroom set of graphing calculators can turn a standard
into a computer lab. Software programs that were once only available on
stand-alone desktop computers can now be run on calculators and PDAs
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
individual or group activities or projects.
How to take advantage of a computer lab (if
there is a one-to-one (or one-to-two) ratio of computers to students.
Mathematical Background and Attitude Toward Learning
In the IMATTT workshops, teachers learn to use
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
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
offers an array of choices, not answers. I have seen some school
adorned with colorful graphs that are not clear as to what story is
told. One of the IMATTT workshops this past year was devoted to a
of graphs that were dealing with the United States Census that were
in the hallway. The teachers planned to improve that lesson this coming
year. A more detailed discussion of this activity and others can be
at the IMATTT website (http://www.ciese.org/imattt).
Pedagogical Strategies and Discourse.
The new Principles and Standards stated that
should work on problems that are embedded in a context that they
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
Since the teachers were still not completely comfortable with using
having someone (no matter how friendly and supportive) makes them
Also, I realized they needed lots of practice in doing group
as well as adopting a new style of teaching.
Personalizing the Curriculum.
Since the textbook usually defines the curriculum
teachers look to the teacher's guide for ideas to help them teach a
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
more interesting technology and standards-based activities. By
these activities into their curriculum, teachers are taking a more
role in modifying, learning about and personalizing the mathematics
There was a teacher I worked with who passed away
years ago, and I attended her wake. The place was full of students
the loss of this teacher. Of the six domains identified in this
her strongest was assessment. She made it a point to make sure she
every student in her class in some way every day. At the beginning of
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
book or whatever was needed. (She had an endless supply of pencils.)
the activity and the assignment, she would take three or four students
aside and talk them about the lesson just completed. Those students
knowing that the assessment and pep talk that they just received would
be repeated over and over again throughout the year. A key to
assessment is being personal, caring and consistent.
Putting the Six Domains of Knowledge Together: "A Scene
from a Dynamic
The first three areas - resources,
and interest in math, and the way the room is set up for classroom
- is the "background" for the classroom event that will take place. The
school offers a script - either very specific or in broad strokes -
suggests to the teacher what is important to teach. The curriculum may
offer suggestions as to the kind of discourse that students have with
teachers and each other. It may include guidelines for assessment to
whether the mission of the school is being carried out. The resources,
teacherís math knowledge, and the learning environment set the
while the dynamics of the curriculum (context), the discourse
in the activity), and assessment (reflection) determine the success of
the lesson or activity.
But how do I as a staff development educator
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
does not seem to be working very well. Stein, Smith, & Silver
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
Developers: Learning To Assist Teachers In New Settings In New Ways,
authors "describe the challenges that practicing teacher educators and
professional developers would encounter as they design and implement
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
in Paterson, but the reality is that the vision is elusive. According
the authors the new paradigm has these features: (The features are
the commentary is mine.)
Teacher assistance embedded in or directly related to the
Most teachers like to be helped in the classroom,
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
support the kinds of classroom activity that meaningfully goes after
at the learning level. The challenge for staff developers is how best
do this given that each school has similar, but unique set of
and obstacles that prevent them from operating more fully at this
level of pedagogy.
Teacher assistance grounded in the content of Teaching
This feature suggests that the teachers need to
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
mathematics and only superficially how to effectively teach it. This
be a problem even with the very best of curriculums. So staff
needs to focus on personalizing the curriculum for each teacher giving
them a sense of ownership of the curriculum by engaging them in
that allows them to contribute and learn from each other while being
by the staff developer.
Development of Teacher Communities of Professional Practice.
In Paterson we have after school workshops open
IMATTT teacher interested in the topic of the workshop. Other workshops
are scheduled individually at each school for the teachers that teach
that school to work on specific activities. Also, we encourage teachers
to contribute to the on-going development of the curriculum that
from year to year. Unfortunately, there are so many other competing
and urgent matters that need to be handled that focusing on
practice does not get the attention it deserves.
Collaboration with Experts Outside the Teaching
As someone connected to the professional world of
education, I keep in touch with developing ideas and share these ideas
with the teachers in workshops, newsletters, and through the IMATTT
The teachers are invited to participate in local conferences. For
one of the IMATTT sixth grade teachers, Saundra Generals and I led a
session at this year's annual NCTM meeting in Chicago. This fall she
lead a similar workshop at a state level mathematics teacher's
in New Jersey. This kind of activity empowers teachers to grow and
leaders in their school communities. This can also be a problem for an
individual school when a teacher becomes so skilled (in this case,
that she transfers to another school within the district to become a
Consideration of Organizational Content.
There is agreement that teachers need regular on
staff development in order to improve the quality of their teaching and
learning through a variety of workshops, courses and trainings.
if these activities though worthwhile and stimulating for the teacher
not well coordinated, they will not necessarily make any significant
in the teacher's classroom habits. For that reason Susan
Peter Hewson, Nancy Lowe, and Katherine Stiles (1998) believe that
assistance should be a design process "not about importing models or
formulas, but rather about thoughtful, conscious decisionmaking."
Smith, & Silver 1999). This translates into many classroom visits
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
Paterson and reflect on the future what comes to mind is what Seymour
wrote in his seminal book Mindstorms (Papert, 1980 p. 101) about "bugs"
One does not expect anything to work at the
One does not judge by standards like "right-you get a good grade" and
get a bad grade." Rather one asks the question: "How can I fix it?" and
to fix it one has first to understand what happened on its own terms.
then can we make it happen on our terms.
All I can say is that we are not there yet, but
we are working
on it. The vision keeps us going.
Berman, P., & McLaughlin, M. W. (1978).
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Charischak, I. (1994) Levels of looking at
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Association of Mathematics Teachers of New Jersey Regional Conference,
Rowan College, Rowan, NJ.
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Gardner, H. (1991). The Unschooled Mind: How
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Center for Improved Engineering & Science
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