Technology and Algebra in Secondary Mathematics Teacher Preparation Programs

Session Presented at the Research in Undergraduate Mathematics Education annual conference in February, 2014, in Denver, CO.

Abstract: Most recently, the Conference Board of the Mathematical Sciences has advocated for incorporating technology in secondary mathematics classrooms. Colleges and universities across the United States are incorporating technology to varying degrees into their mathematics teacher preparation programs. This study examines preservice secondary mathematics teachers’ opportunities to expand their knowledge of algebra through the use of technology and to learn how to incorporate technology when teaching algebra in mathematics classrooms. We explore the research question: What opportunities do secondary mathematics teacher preparation programs provide for PSTs to encounter technologies in learning algebra and learning to teach algebra? We examine data collected from a pilot study of three Midwestern teacher education programs conducted by the Preparing to Teach Algebra (PTA) project investigating algebra. Our data suggest that not all secondary mathematics teacher preparation programs integrate experiences with technology across mathematics courses, and that mathematics courses may provide few experiences with technology to PSTs beyond strictly computational.

In this session, we presented results from an analysis of opportunities to use technology to support algebra teaching and learning in secondary teacher preparation programs. The data was collected during the PIlot phase of the Preparing to Teach Algebra project.

Presentation of Findings

We found that instructors responded in interesting ways regarding their use or non-use of technology in support of algebra teaching and learning:

  • Practical Concerns:
    • Not useful in certain courses:
      • …It just doesn’t strike me as really helpful… [University A, Structure of Algebra]
      • It’s abstract for a reason. [University C, Abstract Algebra]
    • Issues of access:
      • …we don’t have money in our department to buy them. So, we don’t have those and our students… need to know those things. [University A, Secondary Math Methods]
    • Not enough time or support:
      • I do not have time to work all the [PowerPoint] slides… [University B, Linear Algebra]
      • …I think …we should have a nice computer-simulated programs that make you see the difference [between convergence and uniform convergence of functions]. … For me, I see it in my head….But I can’t see how. I really can’t see how. [University B, Analysis]
  • Impeding Learning:
    • Blocks Students from Developing Memory
      • … because of the calculator and all these technologies [people] don’t … develop their memory.  But then you are asking them to develop their memory on something that is harder than adding or subtracting, you know? [University B, Analysis]
    • Computational Use Blocks Concept Development
      • But I also want them to know the concepts involved so sometimes … I make a point to tell them that they shouldn’t use technology… [University A, Linear Algebra]
      • [A]t a college level we’re now quite concerned because … we have students who can’t multiply…because they have always had a calculator, you know.  There are students who can’t tell you what the graph of y = x looks like.  …[T]o be able to think about what y = x and y = x2 looks like — they can’t do without a machine.  …So, we are actually moving to not using technology. [University A, Secondary Math Methods]
  • Enhancing Learning:
    • Making the Abstract More Tangible
      • [Technological tools] can bring some of these more abstract things to make them more tangible for students. [University C, Middle School Math Methods]
    • Allowing Different Perspectives
      • I think it …gives them a way to see the problem from a different perspective…understand it from a learner’s perspective and …to think about how to instruct students in multiple ways… [University B, Secondary Math Methods 1 and 2]
    • Conceptualizing Mathematics
      • All of these tools represent ways to represent and conceptualize mathematical ideas that go beyond the symbolic. They’re important tools to really develop a conceptual understanding of mathematics. Moreover, it’s critical that our students are prepared to use these same tools … to foster the same sorts of understandings. [University B, Secondary Math Methods 3 and 4]
  • Whether or not to use technology is complicated:
    • Which courses could use technology?
      • In this course none. …In other courses that I teach I do use technology… I know that that is kind of counter-intuitive because textbooks always have technology stuff in there and some textbooks are even focused on technology. To me that is not what this [course] is about and the more technology you have in a course like this the less that there is for algebra. [University C, Differential Equations]
    • What are instructional consequences of technology use?
      • … there are times where instructionally it may be not the best thing to always use technology and so making that kind of judicious choice is something we talk about as well. [University A, Secondary Math Methods]

We also found some examples of activities to support preservice teachers in decided whether, when, and how to use technology:

  • Affordances of technology, e.g.:
    • engagement
    • enhances some concept development
  • Constraints of technology, e.g.:
    • instructor’s/instructional time
    • impedes some concept development
  • … you don’t just use a tool or technology just because it’s going to be fun; but you really have to think about – What does this particular tool or technology afford me in terms of students’ understanding the content? …sometimes when we’ve used technology it didn’t really offer us any more than if we had just drawn [on] a piece of paper…. [University B, Secondary Math Methods 1 and 2]

We shared two examples of use of technology to support algebra teaching and learning, one from a mathematics course and the other from a mathematics methods course:

RUME-01RUME-02

Acknowledgements:

This study comes from the Preparing to Teach Algebra project, a collaborative project between groups at Michigan State (PI: Sharon Senk) and Purdue (co-PIs: Yukiko Maeda and Jill Newton) Universities. This research is supported by the National Science Foundation grant DRL-1109256.

Stehr, E.M. & Guzman, L. (2014, February). Technology and algebra in secondary mathematics teacher preparation programs. Paper presented at the Seventeenth Annual Conference on Research in Undergraduate Mathematics Education (RUME). Denver, CO.

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