Understanding Classroom Interactions Among Diverse, Connected Classroom Technologies

Principal Investigator: 
Project Overview
Background & Purpose: 

We implemented the combination of two new technological ingredients for 3-6 weeks in several Algebra 1 classrooms at the high school level. These were: 1) SimCalc MathWorlds® - a dynamic, interactive and representationally-rich piece of software designed at UMass Dartmouth and 2) wireless connectivity in the form of Texas Instrument’s Navigator product. Such development was coupled with the design of mathematically-meaningful curriculum to enhance the teaching and learning of core Algebra ideas, such as linear functions, simultaneity, co-variation and slope-as-rate.

The purpose of the study was to determine the root sources of Classroom Connectivity’s (CC) potential to improve teaching and learning, and to measure their impact in reliable ways on classroom participation and engagement so that the promise of CC can be realized through appropriate technology, curriculum, and teacher professional development. We defined three Opportunity Spaces generated by CC and posed central questions associated with each: (1) learning and activity structures, (2) teaching and pedagogy, and (3) assessment, classroom management and information flow.

Setting: 

University of Massachusetts Dartmouth -- START Program (a class for College Freshman with disadvantaged backgrounds in mathematics) and pre-service, in-service and senior mathematics courses on technology (taught by the PI). Two schools districts in Southeastern Massachusetts (Fairhaven High School & Dartmouth High School).

Research Design: 

The research design for this project is comparative, and is designed to generate evidence that is descriptive [case-study, observation] and associative/correlational [quasi-experimental]. The project includes an intervention, SimCalc MathWorlds® for Calculators (software and curriculum), along with the TI-Navigator Learning system. Our curriculum materials covered approximately 40% of a standard Algebra 1 curriculum. The comparison condition is business as usual: other Algebra 1 classrooms in the same schools.

This project collects original data using diaries/journals/records kept by study subjects, assessments of learning/achievement tests, observation [personal observation, videography], survey research [paper and pencil self-completion questionnaire, and face-to-face semi-structured/informal interviews.

We collected a range of data including pre-post test data on content items related to core algebraic ideas and questions involving applied problem-solving techniques, an attitude survey (administered pre- and post- intervention), student work, student interview and teacher interviews, and digital video data of the student and teachers (using 2 camera angles). The pre-/post-tests and rubric were created with teacher input, to attend to concepts meeting the Massachusetts frameworks. The attitude surveys were created based upon prior work, and input from our external advisory board and was tested for validity purposes and revised during the course of the project (see attached documents). We also developed student interview questions, which were reviewed and revised in house and used as a protocol for interviewing 25 selected students who participated in the intervention. Rationales for each interview were given and approved internally.

Data analysis was completed via various quantitative and qualitative techniques. We analyzed pre- and post-test data, as well as pre- and post-attitude survey data using SPSS. Methods included Exploratory and Confirmatory Factor Analyses, standard inferential statistical methods (e.g. t-tests), odds ratios and logistic regression.

We created case studies of particular students who were statistically significant in certain ways (using pre- and post-test data, pre- and post-attitude survey data, video data, observation notes and student interviews). Various methods of discourse analysis from linguistic anthropology were used including the analysis of turn-taking, particularly student-student interactions vs. teacher-student interactions in our intervention classrooms, participation frameworks, and use of deictic markers. In addition, we are completing a full categorization of our video data of classroom participation. We have complete 60 vignettes analyzing classroom episodes under each of the following: (1) Identification, (2) Gesture, (3) Linguistic expression, (4) Flow of discussion/discourse, and (5) Aesthetics.

Findings: 

Our main effect was statistically significant and showed that students in the SimCalc group had a higher gain on items related to linear functions, slope as rate, proportion, linear variation, seeing across representations, and graphical interpretation. Across gender, from pre-to-post, female students in the SimCalc group had a statistically higher gain than male students in the same group. Female students in the Comparison group had a higher gain than male students in the same group, however male students in the SimCalc group had a slightly higher gain than the female students in the Comparison group. Finally, the majority of teachers who used the SimCalc intervention had the most significant gains. A teacher used SimCalc in one of his classroom and not in another classroom. The class in which he used SimCalc, showed the highest gains out of all the classes involved. And, the gain for his SimCalc class was statistically higher than that for his Comparison classroom.

Along with pre- and post-content tests, an attitude survey was administered. The survey was broken down into three categories: (1) positivity toward mathematics/school, (2) preferring to work along, and (3) comfort with technology for mathematics. The analysis of the results revealed that pre-to-post, the SimCalc group tended to move from feeling more comfortable with technology for mathematics towards a neutral feeling of technology for mathematics, while the Comparison group felt more comfortable with technology for mathematics pre-to-post. This seems almost counter-intuitive since the SimCalc group were using technology in their mathematics classroom daily. But, the SimCalc software and curriculum was challenging, increasing student knowledge and transforming their experiences. Data regarding the technology used in the Comparison class was not collected, however upon asking several Comparison teachers what technology they used in their classes, they either did not use technology or they used graphing calculators in a very superficial way (i.e., using “y=” vs. using the use of an application). So while students in the SimCalc group felt less comfortable using technology, they became more realistic regarding the technology used; rather than using a calculator for computation, they were creating functions, seeing across representations, and making generalizations about variation.

A technical report on our overall findings was published by the James J Kaput Center for Research and Innovation and is available at: http://www.kaputcenter.umassd.edu/products/technical_reports/

Publications & Presentations: 

Journal Publications:

Hegedus, S. (to be submitted). Discourse and pedagogy in new networked classrooms. Journal for the Learning Sciences.

Hegedus, S. (to be submitted). New forms of participation and engagements in representationally-rich networked classrooms. To submit to Journal of Learning Sciences (Summer 2009).

Hegedus, S. (in preparation). Reflective aesthetics. To submit to Journal of Mathematical Behavior (Spring 2009).

Hegedus, S. (in preparation). Mathematics of Change and Variation in Middle School. For Mathematics Teaching in the Middle School. NCTM. (January 2009)

Hegedus, S., Dalton, S., Brookstein, A., Tapper, J. (in preparation). Impact of new activity structures on algebra learning in connected classrooms. To submit to International Journal of Mathematical Thinking and Learning. (January 2009).

Hegedus, S. & Moreno-Armella, L. (in preparation). Evolution of a Reference Field through digital media. For Educational Studies in Mathematics? (Spring 2009)

Hegedus, S. & Tapper, J. (in preparation). Measuring affect and attitude of high school students using social and representationally-rich technology. Unknown journal. (Spring 2009).

Hegedus, S., Penuel, B., Brookstein, A., & Dalton, S. (in preparation). Flow of argumentation using social technology in mathematics classrooms. Unknown journal. (Summer 2009)

Hegedus, S. & Sinclair, N. (in preparation). Role of aesthetics in technology-enhanced classrooms to motivate expressivity and mediate social discourse. For International Journal of Computers for Mathematical Learning.

Hegedus, S., Moreno, L. , Radford, L., & Sabena, C. (in preparation). Semiotic mediation through gesture. For Educational Studies in Mathematics. (Summer 2009)

Hegedus, S. & Moreno-Armella, L. (in preparation). The future of social technology in a digital world of signs. For Nature. (Summer 2009)

Hegedus, S., & Kaput, J. (under revision). Improving algebraic thinking through a connected SimCalc MathWorlds classroom. Journal for Research in Mathematics Education.

Hegedus, S., & Moreno-Armella, L. (in press). Intersecting representation and communication infrastructures. For ZDM: The International Journal on Mathematics Education.

Hegedus, S. & Moreno-Armella, L. (in press). Dynamic representations: A new perspective on instrumental genesis. For the Learning of Mathematics.

Hegedus, S., Moreno-Armella, L., & Dalton, S. (under review). Technology that mediates and participates in mathematical cognition. For International Journal of Computers for Mathematical Learning.

Moreno-Armella, L., & Hegedus, S. (under revision). Co-action with digital technologies. For ZDM: The International Journal on Mathematics Education.

Roschelle, J., Shechtman, N., Tatar, D., Hegedus, S., Hopkins, B., Knudsen, J. (under revision). Scaling up SimCalc: Results from Random-Assignment Field Trials in Seventh and Eighth Grade Mathematics. Submitted to American Educational Research Journal.

Moreno-Armella, L., Hegedus, S., & Kaput, J. (2008). Static to dynamic mathematics: Historical and representational perspectives. Special issue of Educational Studies in Mathematics: Democratizing Access to Mathematics Through Technology Issues of Design and Implementation. Vol. 68(2), 99-111.

Hegedus, S., & Penuel, B. (2008). Studying new forms of participation and classroom identity in mathematics classrooms with integrated communication and representational infrastructures. Special issue of Educational Studies in Mathematics: Democratizing Access to Mathematics Through Technology Issues of Design and Implementation. Vol. 68(2), 171-184.

Hegedus, S. (2007). Classroom connectivity. Educational Technology, XLVII(3), 21-25.(special issue on Mobile Computing).

Hegedus, S. (2006). Jim Kaput — 1942-2005: A mentor, a colleague, a friend. For the Learning of Mathematics 26(1), 26–28

Roschelle, J., Penuel, W. R., & Abrahamson, L. A. (2004). The networked classroom. Educational Leadership, 61(5), 50-54.

Stroup, W. (2005). Learning the basics with calculus. Journal for Computers in Mathematics and Science Teaching 24(2), 179-196

Books & Non-Periodical Publications:

Hegedus, S. (in preparation). Representation and communication. Proposal submitted to Springer, January 2009.

Hegedus, S. (in press). Enforcing scientificity in qualitative research. In B. Sriraman & L. English (Eds). (2009) Advances in mathematics education. Theories of mathematics education: Seeking new frontiers. New York: Springer. (January 2009).

Hegedus, S., & Moreno-Armella, L. (2008). Analyzing the impact of dynamic representations and classroom connectivity on participation, speech and learning. In L. Radford, G. Schubring & F. Seeger (Eds.), Semiotics education: Epistemology, history and culture (pp. 175-194). Rotterdam, The Netherlands: Sense Publishers.

Hegedus, S., Kaput, J., J., Dalton, S., Moniz, R., & Roschelle, J. (2007). SimCalc classroom connectivity project 2: Understanding classroom interactions among diverse, connected classrooms technology—Overview of the present finding of a 4-year study (2004-2008). Technical Report. Dartmouth, MA: University of Massachusetts Dartmouth, James J. Kaput Center for Research and Innovation in Mathematics Education.

Hegedus, S. (2005, September). Dynamic representations: A new perspective on instrumental genesis. In Proceedings for the Fourth Congress of the European Society for Research in Mathematics Education.

Hegedus, S. & Beaton, D. (2006, May). Constructing an architecture for an interactive educational research database—Issues of design and implementation. Proceedings of the IADIS Virtual Multi Conference on Computer Science and Information Systems.

Hegedus, S., Dalton, S., Cambridge, L., & Davis, G. (2006). Patterns of participation in networked classrooms. J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings of the 30th International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 257-264). Prague: Program Committee.

Hegedus, S. & Kaput, J. (2004). An introduction to the profound potential of connected algebra activities: issues of representation, engagement and pedagogy. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 129-136). Bergen, Norway: Program Committee.

Hegedus, S. & Moreno-Armella, L. (in preparation). Evolution of a reference field through digital media. Submitted to Psychology of Mathematics Education – North American Chapter – Atlanta. (January 30th 2009).

Hegedus, S., Moreno, L., & Dalton, S. (2007). Technology that mediates and participation in mathematical cognition. In Proceedigns of the 5th Congress of the European Society for Research in Mathematics Education (CERME) Conference. Larnaca, Cyprus.

Hegedus, S., Moreno-Armella, L., Dalton, S., Brookstein, A. (2009). Establishing a longitudinal efficacy study using SimCalc MathWorlds®. Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (CERME) Conference, Lyon, France, January 2009.

Hegedus, S., & Rodriguez, S. (2006). Role of gesture as a form of participation in networked classrooms. In S. Alatorre, J. L. Cortina, M. Sáiz & A. Méndez (Eds.), Proceedings of the 28th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 168). Mérida, Yucatán, Mexico: Program Committee.

Kaput, J. Hegedus, S., & Lesh, R. (2007). Technology becoming infrastructural in mathematics education. In R. Lesh, J. Kaput, & E. Hamilton (Eds.), Foundations for the future: The need for new mathematical understandings and abilities in the 21st century (pp. 172-192). Mahwah, NJ: Lawrence Erlbaum Associates.

Roschelle, J., Knudsen, J., & Hegedus, S. (in press). From new technological infrastructures to curricular activity systems: Advanced designs for teaching and learning. To appear in I. Jacobsen (Ed.), Advanced designs for technologies of learning: International learning sciences perspectives on innovative pedagogical environments.

Roschelle, J., Tatar, D., & Kaput, J. (in press). Getting to scale with innovations that deeply restructure how students come to know mathematics. In A. Kelly, R. Lesh, & J. Baek (Eds.), Handbook of design research methods in mathematics, science and technology education. Mahwah, NJ: Lawrence Erlbaum.

Vahey, P., Tatar, D., & Roschelle, J. (2004). Leveraging handhelds to increase student learning: Engaging middle school students with the mathematics of change. In Proceedings of the 6th International Conference of the Learning Sciences (pp. 553-560). Mahwah, NJ: Lawrence Erlbaum Associates.

Other Products: 

Curriculum & software packages – SimCalc MathWorlds® software and associated materials are a commercial product.

Curriculum, video tutorials and analyses of classroom participation are being packaged as a summer Pedagogical Institute for teacher professional development in Educational Technology