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Technology Is a Tool

Moderator
Good afternoon and welcome to NCTM President Cathy Seeley's online chat. The topic today is her President's Message on "Technology is a Tool." Our first question is from

Ware Shoals, South Carolina

My high school students are fascinated by graphing calculators. All of sudden, math is not a foreign language any more. I wish our state would allow 8th graders to use a graphing calculator on our state testing. I believe 8th graders would be much more motivated to learn with this tool. I know they need the basics, but by 8th grade, the ones who don’t have the basics are probably never going to truly get them. We must move on! What do you think?

Cathy Seeley:
I would like to see state tests that have two parts—one with a calculator and one without. There are important things to assess both ways.

I believe that some students can learn their basics after 8th grade, but you’re correct that it is much more challenging to do so at that time, since many students have developed longstanding misconceptions. What I think calculators can do at that level is to allow students to deal with challenging problems that go well beyond the basics. Not only is this kind of learning essential, for some students it can also open the door for them to see the need to learn some of the skills that they have not learned thus far.

Question from
Ukiah , California

We have drill and practice in our computer lab with software programs. Our challenge is the ability to read English in order to know how to work the problem. California has many second language learners. I would like to know how other districts or schools manage their math word problems. (I have eight students emerging in English in my primary classroom.)

Cathy Seeley:
I am somewhat concerned when we use technology as a delivery system for drill and practice. There are certainly some benefits for students if this is done in an appealing way, such as in a video-game format. However, I am concerned about a couple of things. First, too much isolated drill can eventually decrease students’ interest and diminish the effectiveness of the method. Second, we should not kid ourselves that we are incorporating technology into our teaching by doing this kind of electronic worksheet. Technology has much more to offer students, and using it to approach high-level mathematics and solve complex problems tends to tap into both the power of the tool and the potential of students.

In terms of English language learners, working in small groups where students discuss the problem can be very helpful as students develop their use of appropriate vocabulary for dealing with problems. I'm not sure how effective it is to work on a computer in isolation if a student is trying to develop language; it seems more likely that students can benefit from interacting with others around the mathematics. If any chat participants have other suggestions, they may want to send them in.

Question from
Fishers, Indiana

The use of the Internet and Webquests really prepares students for how to research and acquire the mathematics they need to achieve the standards and for use throughout their lives. Does NCTM plan on creating a database and/or clearinghouse for sharing math Webquests?

Cathy Seeley:
There are no immediate plans to do this, but Council leadership, including committees, the Board and staff, continually look for ways of tapping into the potential of technology to provide resources to members. This is certainly something we can look into for the future.

Question from
Houston

Technology’s strength in the mathematical classroom lies in its interactive ability to provide opportunities for students to observe patterns and see mathematical relationships. What took tedious effort to recreate by hand now can be viewed visually and in multiple representations. What I would like to see in the classroom, and for resources to use in the classroom, would be activities where concepts are developed through the use of technology and reinforced through skill development. To develop the mathematical thinking we want our students to achieve they should be using technology to see patterns rather than to simply chunk out answers to a given problem.

Cathy Seeley:
Using technology appropriately is one of the most important ways a teacher can guide students. Certainly the goal should be developing mathematical thinking, reasoning, and problem solving that go beyond simple button pushing. Thanks for sharing your thoughts.

Question from
Brooklandville, Maryland

We have had wonderful success with the implementation of technology into the mathematics classroom in our school. There are two main reasons that this has been possible: the willingness and the ability of our mathematics teachers and the support of our administration and technology department. What can math departments do in schools where they do not have administrative support?

Cathy Seeley:
This is a challenging question. Often a lack of administrative (or community) support indicates that someone is worried about how the technology will be used. I would suggest that the first of your two factors—the willingness and ability of your math teachers—may help address the second issue. It may be helpful to show administrators an example of teaching using technology well. This can happen in a classroom in your school, or it might be helpful to have teachers and administrators visit another school. Most of the time, administrators can become quite supportive when they see effective teaching tapping into the power of technology to allow students to deal with challenging problems they couldn’t otherwise address and demonstrating good mathematical thinking in the process.

Question from
New York City

How can we make sure that the calculator is being used as a tool and not as a crutch?

Cathy Seeley:
I don’t believe that students should first know how to do something without a calculator before we let them use one. Sometimes the reverse is effective, and some tasks may simply be more appropriate for calculator use.

But I do believe that there are things students should be able to do without a calculator. Basic multiplication facts, graphing a line, and doing mental math are all examples when the teacher might simply tell students that this is not a calculator activity.

Also, the kinds of problems we give students with calculators need to be significantly different from those we might give when students don’t have calculators. Giving a long set of strictly computation problems and having students do them on a calculator is generally not effective; in that case we may be promoting rote button-pushing and not using technology to advance the level of students’ thinking and mathematical understanding. On the other hand, if we give problems where the part done on the calculator is not the focus of the problem, but rather a mechanism to use in addressing a complex situation, students can come to see the use of the technology as a tool.

Question from
San Francisco

Currently, several math help Web sites offer direct support for homework, correlated with actual textbook problems (Encarta.com, AOL Step-by-step Math, Hotmath.com, Nutshellmath.com).

According to a February 2006 ACSD Educational Leadership article, a sizeable number of students don’t do homework because they need more support to succeed with it.

Can you comment on the importance of homework for success in math learning, and the conceptual value of currently available Internet resources for this?

Part of me wants to shout out to all teachers: Get your underperforming students to these Web sites, now, before it is to late for them.

Cathy Seeley:
I think homework should be an important part of a math program, used to enhance what goes on in the classroom and used in moderation. It is a non-trivial task for a teacher to select appropriate homework that reinforces what students are learning and yet does not require someone working side-by-side with the student in order to do it. Some of these Web sites may be useful for students, although there is always the risk that the students will not find what they are looking for or might learn something other than what the teacher intended if the task is not clear. The challenge is for teachers to monitor students’ homework and provide assistance and guidance both before and after so that students are reinforcing what the teacher intends. Thanks for sharing these sites.

Question from
Columbus, Mississippi

Everything I read about today’s “Net Generation” indicates that students want to be the owners and producers of their own learning. Technology, now more than ever, offers tool software (PowerPoint, HyperStudio, Movie Maker, Producer, Garage Band, etc.) that allows students to produce and tell a story. What better way is there to relate math to a student’s real world than to have students create their own math story problems with technology and to share them with their classmates?

Cathy Seeley:
These tools have a lot of potential for students to produce and present material in any discipline and to engage students in their learning (both those presenting and those on the receiving end). I think that you are right that today’s students increasingly expect this kind of technological support. In using this kind of software, we need to help students remember to keep the focus on the mathematics and to use the technology in ways that give us more than a pencil and paper or an overhead projector might do.

Question from
St. Louis

Does use of a projector and computer as a tool for mathematics instruction impact student learning?

Cathy Seeley:
That all depends on what the computer is being used for. If it is to present a lecture, the effect may be minimal, although sometimes a computer demonstration of a geometric relationship or a probability simulation might stimulate students’ interest or set up a good problem.

I would rather see students interacting with a computer if possible, where they have to do something or approach a problem.

Question from
Hollister , California

One of the ways that I addressed the financial challenge was to apply for every local grant possible. It took 2 years, but the algebra students finally have graphing calculators. The school would not purchase them because they felt the obsolescence involved in technology would make the purchase a waste.

Cathy Seeley:
That’s a constructive approach, and I hope that folks in your school will come to see the value of this tool in advancing the level of mathematics students can do. Fear of obsolescence is a great way to ensure obsolete thinking on the part of our students.

Question from
Flensburg, Germany

My main concern—as a teacher educator—is how to show the “normal” teacher what is appropriate use of technology in math teaching. Still lots of teacher students did not learn mathematics themselves using technology. I find that many teachers use technology to avoid mathematical thinking rather than to support it.

Cathy Seeley:
It is quite likely for most of us that our students’ knowledge of technology will surpass our own. This is an area where professional development, both formal and informal, is essential. Teacher educators may face the same challenge. At every level we have to commit to learning how to best use technological tools and then helping our students learn to go even further. I absolutely agree with you that we need to use the tools to advance mathematical thinking, not to replace it.

Question from
Marshall , Texas

Financial Issue:
Upon asking for updated calculators and the like, the reply is always the same. We don’t have the money. I work in a small school district in Northeast Texas. We only have around 200 students in the entire high school. What can we do as teachers to prove to the school board/administration that if we don’t provide our students with up to date technology, like graphing calculators that are fairly recent, we are not preparing our students for college?

Cathy Seeley:
This may be an area where we need to enlist the support of our colleagues who teach in other disciplines. In Texas, for many years there were funds for schools to purchase technology (I don’t know if these TIF funds are still available). The issue was that schools were always looking for something the whole school could use. Unfortunately, this too often denied essential mathematical tools like graphing calculators or geometry software. We have to build a case that these mathematical tools are as essential to the teaching and learning of mathematics as are maps and globes to a social studies class or science lab equipment for teaching science. Students who leave school not having had experience with graphing calculators at the least, are indeed ill equipped for higher education.

Question from
Arlington , Virginia

My intern has been told to implement technology in mathematics in her lesson plans. However she has not been told how, and she is using technology in a way to say “I have included technology.” This concerns me. How can I encourage her to realize that technology should not be forced but an intricate part of teaching a concept?

Cathy Seeley:
This is something facing not only interns, but many practicing teachers as well. The term ‘technology’ is so broad that in an effort to be current, some teachers use only superficial applications of technology, such as putting an overhead presentation into PowerPoint or making a worksheet electronic. A key to successful use of technology, in my opinion, is appropriate professional development. People need to practice using the technology themselves and work together on how particular types of technology can be used for different instructional purposes. The goal must always be the mathematics first, and technology in service to the mathematics.

Question from
Belleville, Ontario

How do we get elementary schools with computer labs to develop lab timetables that are needs driven rather than rigid (i.e. allow people flexible sign up as needed rather than being scheduled like the gym)? Point of interest is that teachers (particularly 4th thru 8th grade) seem to want this, but administrators seem to want “gym-style” schedules in the interests of “equitable distribution” of the resource. Ideas being sought are ones aimed more at getting administrators to see the options.

Cathy Seeley:
This is a challenging issue, especially when a new resource of any kind becomes available in a school. Perhaps visits by administrators and teachers to schools where computer labs are being effectively integrated into mathematics instruction would be helpful. If we believe that technology is there to serve the mathematics being learned and the students learning it, then we must look at alternative strategies for scheduling access to the tools. Meanwhile, how about looking at the potential of hand-held technology, especially calculators, so that students could use another technological tool as a daily part of their math instruction?

Question from
Waukegan, Illinois

What you describe as a digital divide greater than any economic gap we have seen so far in schools is unveiling before my eyes as this is written. Our school is a large urban multicultural institution where over half our students are two years behind grade level in their mathematical proficiency. Twenty miles to the south of our school is an institution where students are required to purchase a TI-89 for their mathematics courses. The middle schools that feed into this district are going to require all students from 7th grade and up to have a graphing calculator. So the technological gap is widening every day, and as a teacher in the underprivileged urban district I see little to stop the momentum of this division. Maybe you know something I don’t?

Cathy Seeley:
This is why every school has the responsibility to provide technology to every student. It’s also a critical reason why it is unacceptable to have more resources at schools where students themselves have more resources. I don’t like the idea of requiring students or families from either of these schools to buy calculators themselves. As a community and as educators, I think we need to raise the call that these are essential instructional tools worthy of an investment, and that many students are being denied these tools and the resulting access to complex problem solving.

I wish I had a solution for urban and high-poverty schools. Some federal support programs can provide funds for these purchases, but clearly we face a paucity of resources in too many schools. This issue goes beyond your school and extends to society. We cannot remain quiet or passive as we face such inequities, and I would hope that our colleagues in the school down the road would join in the outcry.

Question from
Wyckoff, New Jersey

I am a high school mathematics teacher who is very fortunate to work in a district that understands the importance of integrating technology into the education of our students. The district provides laptop computers for all students and teachers and also provides many opportunities for professional development for teachers. Having the availability of computers allows me to create lessons that are engaging for my students by using computer software that allows them to discover or reinforce mathematical concepts. Venturing to Web sites that provide tutorials, practice, and opportunities to solve real-life problems provides my students with different opportunities to learn the concepts they are being taught. I can honestly say that I could never go back and teach the way I used to before having the availability of computers 24-7!

Cathy Seeley:
This sounds like a good example of the power of technology in the hands of a creative, committed and knowledgeable teacher! Thanks for sharing.

Question from
Charlotte , North Carolina

I teach in a small, private school. Recently I completed a 6-week research project with my fifth grade class in which I used interactive math Web sites during math instructional time. I found the results were mixed—some students definitely benefited more than others. My question is: How have other teachers tried to integrate the use of math software (in my case, delivered via free Internet Web sites) in the classroom other than simply reinforcement or enrichment? Have any actually tried to teach using math software (at least after they have introduced a new concept concretely)?

Cathy Seeley:
There are many kinds of Web sites that can support math instruction. The challenge is for the teacher to be highly selective in which sites can be used for what particular mathematical purposes. The goal should first be what mathematics is intended. We are all working in new territory here, and the landscape is rapidly changing. It will take a while to see how particular tools can help or how they may be extraneous or even dangerous in terms of supporting student learning. The key is not whether a tool is delivered on the Web, but whether it is conceptually sound both mathematically and pedagogically. The teacher continues to be the key as a decision maker about when and how to use what types of technology.

From
Swarthmore, Pennsylvania

Regarding your coming talk “Technology is a Tool,” I want to be sure you’re aware of the Math Forum site, Math Tools, http://mathforum.org/mathtools/, a community library of technology tools, lessons, activities, and support materials for teaching and learning mathematics.

The Getting Started section is helpful for perspective on this very rich site. There is a link in the left sidebar “Math Topics.” It’s a way to get an idea of the cataloging system developed to help users find resources for their specific courses and topics.

Math Tools has a browsable and searchable catalog of around 3,000 software tools, mostly free, together with reviews and discussions by teacher users. NCTM’s Illuminations resources are part of the catalog.

Chat participants might also be interested in the Technology Problem of the Week, http://mathforum.org/tpow/. These TPoWs are modeled on the Math Forum’s Problems of the Week, with the additional feature that these problems take advantage of online, interactive technology tools.

Cathy Seeley:
Thanks for sharing this important and publicly accessible resource. The Math Forum has been a long-standing teacher resource and one of the first to make use of the Internet.

Moderator:

Thank you for your participation today and for your submissions in advance. The next chat with Cathy will be at 4:00 p.m. ET on Tuesday, April 11.

Cathy Seeley:
Thanks to everyone for your participation in this chat. I’m sorry there wasn’t enough time to address everyone’s questions and comments. As usual, we had more questions submitted than we have time.

I’m looking forward to my next (and last) President’s chat next month.

Your feedback is important! Comments or concerns regarding the content of this page may be sent to nctm@nctm.org. Thank you.