by Nancy Berkas and Cyntha Pattison (NCTM News Bulletin, October 2007)
During the 1995 NCTM Annual Conference, Frank Demana—esteemed professor from Ohio State University—held up a calculator and said, “If this tool doesn’t dramatically change the way we teach mathematics and the mathematics we teach, then we must seriously question our professional integrity.” Unfortunately, 12 years later we still haven’t harnessed the power of technology in mathematics classrooms.
The many calculators that are currently available could be used to enable every student in K–12 mathematics classrooms to learn significant mathematics. We have actually seen evidence that the use of graphing calculators in certain middle and high school projects has substantially changed the success rates of students and the pedagogy of their teachers. However, publishers still neglect to incorporate the vast capabilities of calculators into mathematics curricula. And there is evidence that calculators aren’t even being used in elementary classrooms.
With this in mind, it is not surprising that many of us also neglect to use calculators in our interventions for students who are struggling to learn mathematics. It is disappointing that this accessible, affordable, and highly motivating technology is not being used as a tool for intervention.
In our travels and our work in schools, we have noticed that more computers are being used in K–6 classrooms than calculators. (Perhaps this is a result of federally funded programs for computer-assisted instruction.) We have also noticed that computers are increasingly being used for intervention in mathematics.
Computers are powerful tools for teaching mathematics. Many programs can generate the necessary research base (who is logged on and who isn’t, how much time is spent, what is the level of achievement, etc.) to support the use of federal dollars for their purchase. The technology can make it possible to individualize activities, print out worksheets for practice, capture a picture of growth, and so on.
However, using a computer in a mathematics classroom is not a guaranteed pathway to teaching or learning significant mathematics. A curriculum isn’t always designed to have students work solely on arithmetic skills while studying significant concepts, involving operations, algebra, geometry, measurement, statistics, and probability. Nor are all computer programs designed for the exploration of the mathematics that motivates students and results in meaningful learning. Furthermore, although we know that students who have access to computers outside of school also have opportunities to learn important mathematical concepts, often the students who need intervention aren’t the ones who have access to this wonderful technology.
During our exploration of technology and intervention, we were happy to discover research organizations, such as the Center for Applied Special Technology (CAST), which are successfully combining curriculum and technology to expand learning opportunities for all individuals, especially those with disabilities. CAST works closely with schools, universities, and other partners to design and test flexible learning tools, trains teachers to individualize learning, and facilitates efforts to improve education policy. CAST aims to design curricula and resources that meet the needs of the greatest number of users from the outset. This approach makes costly, time-consuming, and after-the-fact changes to curriculum unnecessary. Wouldn’t it be great if all mathematics curricula were designed with interventions built in?
Your Classroom through the Intervention Lenses
Let’s consider the support that technology can give you and your students in the following areas:
Learning Significant Mathematics. Should the mathematics curricula be changed based on available technology and the future technology that will define our students’ lives?
Knowing the Mathematics. Are providers short-sighted when they design interventions that are not based on the ever expanding uses of technology?
Assessment and Data Gathering. Are our assessments and definitions of success limited by what we perceive as the pathways that all children must travel to learn mathematics?
Quality Planning and Delivery. Is technology flexible enough to address the needs of every student?
Alignment. Are local and state standards appropriate, considering the technology available? How are appropriate standards and goals aligned with the delivery of services to every student?
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Many thanks to Asta Svedkauskaite of Learning Point Associates and Sarah Pomerenke, a doctoral student at the University of Missouri Columbia, for adding to our understanding of these issues. We appreciate all the e-mails that we have received from NCTM members, and we will continue to craft our responses on the basis of final versions of each of the columns.