Copyright ©Tatar 2006
Handhelds have the potential to be important devices for changing math learning; they are cheap, flexible and teachers love them. Math teachers are less likely than any other teacher to take advantage of computing in the course of teaching. Yet math is arguably one of the most important venues for computing. First, at the low end, math is often the course which limits students' ability to progress in academia, because of a lack of minimum demonstrated competence. Second, at the high end, even when students understand how to solve a routine problems, they often fail to understand the sources of their success. Vanishingly few students in America can use math creatively as a tool. One way of addressing both of these problems is by providing students with active, rich representations of the relationship and processes that underlie the formalisms.
In the NetCalc project, we have developed a one month long intervention involving several kinds of activities that has been used with high performing 8th graders. At the end of the month, not only had the students improved dramatically on the problems that we gave created, but 18/25 students, at the beginning of their Algebra learning sequence, were able to do the four qualitative Advanced Placement Calculus problems that we gave them.
Below on this page is a discussion of the activities developed in the project. Other related issues include the visualization tool for monitoring what is happening in the connected classroom, the Look meta-tool for teacher formative assessment, and Scaling Up SimCalc, our large study in Texas of the related desktop version of SimCalc used to teach the math of change and variation. Also, see my publications page and, if you are really interested, a little discursion on Logo and how I got my start in educational computing.
In the course of this month, students used four kinds of activities:
Match-My-Graph is one of a class of information hiding activities. Information hiding activities take advantage of the differences between screens to create learning opportunities.
Sack Race is an expressive activity, in which students write a story to explain the activity of the function they created.
Slot Machine is a matching game that focuses on matching different representations of the same data.
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A Slot Machine Problem: Do we have "three lemons"? That is, do all the representations show compatible behavior? |
A Slot Machine Solution: The user guesses that the animation and position graph are the same, but the velocity graph is different. |
A Slot Machine Correction: The user's partner checks whether a different problem has been solved correctly. |
We also have aggregating activities, in which data are aggregated across machines to produce a pattern.
We have five papers on this topic:
Vahey, P., Tatar, D. and Roschelle, J. (2006) Using Handheld Technology to Move Between the Private and Public in the Classroom. In van't Hooft, M. A. and Swan, K. (Eds.) Ubiquitous computing: Invisible technology, visible impact. Mahwah, NJ: Erlbaum. This is about the relationship between technology, usage, and learning.
Tatar, D. , Roschelle, J., Vahey, P. and Penuel, W. (2003) Handhelds Go to School. IEEE Computer , 36(9), 30-37. Acceptance rate: 5/87. This short paper summarizes several math and science studies.
Vahey, P., Tatar, D., and Roschelle, J. (2004) Leveraging Handhelds to Increase Student Learning: Engaging Middle School Students with the Mathematics of Change. Proceedings of the Sixth International Conference of the Learning Sciences. Los Angeles, CA, June 22-26, 2004. This is the central paper reporting the project.
Roschelle, J., Vahey, P., Tatar, D. , Kaput, J., & Hegedus, S. J. (2003). Five key considerations for networking in a handheld-based mathematics classroom. In N. A. Pateman & B. J. Dougherty & J. T. Zilliox (Eds.), Proceedings of the 2003 joint meeting of PME and PMENA (Vol. 4, pp. 71-78). Honolulu, Hawaii: University of Hawaii. This paper reports some of our early thoughts and goals.
Tatar, D. (under review) The Design Tensions Framework. Journal of Human-Computer Interaction. This paper discusses a method for grasping complex inter-relationships of values and choices in designing socio-technical systems.
To find out more about this project, see my Publications page, go to the SRI or U Mass Dartmouth SimCalc sites.