“New students expect to encounter technology in the classroom. They haven’t necessarily seen the computer algebra systems or the statistics programs, but they have enough familiarity using graphing utilities to be dazzled by TI-Nspire technology.”
Interview with
Dr. Rose Zbiek
Professor of Education, Mathematics Education
Penn State University
New graduates of Penn State University’s pre-service mathematics teacher education program are in-demand. What’s the attraction? These future educators are prepared, ready and willing to incorporate technology into their classrooms. Just what tech-minded mathematics supervisors and coordinators are looking for as they continue to develop curriculum around the use of tools like interactive geometry software, interactive whiteboards and TI-Nspire™ handhelds and computer software.
“One of our students was hired in suburban Pittsburgh because they wanted somebody who was going to be able to use technology,” Dr. Rose Zbiek, Professor of Mathematics Education at Penn State, said. “They actually expected her to become a leader in technology for them, which created a nice little exchange of ‘you help me continue developing skills in terms of pedagogy and classroom organization and I’ll help you with the technology.’ We’ve even had students who have been recruited by one of the technology magnet schools in Maryland.”
Open lines of communication
Frequent discussions between Penn State education professors and district mathematics coordinators and supervisors – those who have the most input and influence regarding curriculum and technology decisions – have led to the university obtaining a more accurate gauge on how technology is being implemented in high schools and middle schools. What the professors hear and see, they share back with the university and this helps them ascertain whether recent technology developments should also be reflected in the education program.
“We have not only the actual knowledge of which technology the schools are using, we have an idea of what they are doing with it and where they’d like to go with it,” Zbiek said. “Our goal is to recreate what the schools use and want in their classes to create that sense of realism and adequate preparation for our students. For instance, what better way to justify installing interactive whiteboards in our college classrooms and having prospective teachers use them regularly than to point out that about 45 percent of area schools already have them and another 20 percent expect to next year.”
Interactive whiteboards combined with TI-Nspire technology appear most prevalent among the range of instructional tools incorporated in high schools across the state, according to Zbiek.
“One of our school districts implemented two classroom sets of TI-Nspire handhelds last year,” Zbiek said. “I just talked to the math coordinator and she’s ordering three more class sets next year. It seems like a natural step. Many of our schools have received Classrooms for the Future grant money. As a result, what they tend to come up with is invariably interactive whiteboards and TI graphing products.”
Old perceptions, new realities
Such an acceptance of classroom technology, and the eagerness to add more from year to year, exemplifies the steady shift in perception by math coordinators. Compared to what they knew and felt about technology in the mid-1990s and even into 2000, according to Zbiek, the attitude toward technology as a viable teaching tool has advanced significantly.
“They don’t ask ‘should we use the technology,’ rather they ask ‘which technology,” Zbiek said. “The math coordinators are tech savvy.”
So are the students – secondary education majors and math education majors – who are applying to enter the Penn State education program. Chances are they used a graphing calculator in high school, such as the TI-84 Plus family models.
“There has been a drastic change in the last 5-10 years,” Zbiek said. “New students expect to encounter technology in the classroom. They haven’t necessarily seen the computer algebra systems or the statistics programs, but they have enough familiarity using graphing utilities to be dazzled by TI-Nspire technology.”
Math always comes first
However, it’s not these “dazzling” features of the technology that are an area of focus in the program. A concentration on knowing the math content inside-and-out sets the stage for future teaching methodology.
“We work from the perspective that we do want students to know how to use technology, yet the math education courses are not meant to specifically teach the technology,” Zbiek said. “Once our students see the mathematics they can do with technology, they learn more about the specifics of a piece of technology needed for particular lessons.”
For example, a Penn State professor may start a course or class by introducing a mathematical topic or problem and, from that, determine a specific goal or outcome that requires particular technology skills – skills that are expected of students by the end of the semester, according to Zbiek.
“This new generation of students is not hesitant to do new things, although some may at first say they dislike technology,” Zbiek said. “We tell them that if by the end of their education experience, should they still dislike it that’s okay as long as they can give a good reason. It has to be based on evidence and principles. Interestingly enough, very few of them end up not embracing it.”
Technology’s indirect impact
Recent research efforts led by Zbiek have further reinforced the impact of technology in the classroom – at least indirectly.
“During my current sabbatical, I have visited classrooms of about 10 of our first-year teachers and student teachers to see how they deal with the mathematical processes of generalizing, justifying, designing and representing – not so much their use of technology,” Zbiek said.
Zbiek is in the process of submitting the research papers to professional journals and other venues. The manuscripts are under review for publication and should be available soon.
“Preliminary analysis suggests that good mathematics and good technology use occur when generalizing and justifying are key parts of the classroom learning process,” Zbiek said. “Students don’t want to just take someone else’s results or explanations. They want to create results that often go beyond what the curriculum expects and justify those in terms of referring to different representations and not-yet-formal arguments that lead to connecting ideas and reasons that offer explanations.
“The technology, when it is used well, is part of the bigger picture. What the teacher knows about the math allows him or her to do some amazing things with the technology.”
With this pedagogical theory approach in mind, the Penn State education program matches well with what future teachers can expect to see and use in their new classrooms, according to Zbiek. The math department’s geometry course features the Geometer’s SketchPad mathematics visualization software, which is a highly regarded skill set favored by hiring schools.
Simple can be amazing
Yet, Zbiek emphasizes that doing “simple” mathematics extremely well with TI-Nspire or SketchPad or interactive whiteboard technology is important to the success and effectiveness of first-year teachers. Doing “amazing things” may not be as practical at first.
“It’s not a matter of what they can do with the technology but what they can teach effectively with it,” Zbiek said. “It’s easy in a college classroom to have students do interesting things in which they may need to use differential calculus or linear algebra. They can develop really interesting problems. Then they are faced with teaching their own students in their first year of algebra or pre-algebra. These students are not yet experienced or sophisticated enough in the math or the technology. You can still use technology to develop some fundamental ideas that follow the curriculum and gets the kids excited.”
For example, a student teacher in a middle school algebra class created a PowerPoint presentation with a cash register simulation to help emphasize how solving a linear equation involved using properties to rewrite expression in equivalent forms. An applet model followed to introduce the details of the symbolic manipulation.
“These simple things brought home to his students the purpose of solving equations and blended conceptual and procedural aspects of equation solving. The part we discussed afterward, but I never saw him use, was a graphical piece that could lead students from graphing equations in the form of y=mx+b to the solution of a linear equation as it relates to the point of intersection of two lines, and how the typical procedure leads to different pairs of lines with each pair intersecting at (s, y) where “s” is a solution of the equation, if one does exist – and to use this idea to make sense of why some equations don't have real solutions.”
Zbiek added: “One of the things that is true, regarding what got us here in looking at what teachers know about mathematics and how it effects what they do in the classroom, is because of our (Penn State’s) use of technology that allows for multiple representations, exploration and extending mathematical ideas. In fact, we hope to learn more as to why some teachers embrace technology and run with it. What is it about what they understand mathematically that is so powerful for embracing the technology?”
It is that thinking at Penn State that helps tomorrow’s educators experience technology-enhanced student gains in classrooms through a continued focus on maintaining a strong technology-enhanced pre-service teacher program.
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