Teaching Fractions With Technology: What Type of Support Do Students Need as They Learn to Build and Interpret Visual Models of Fractions Ordering Problems?

This study examined 78 students as they began learning how to use a computer system to create visual models of fractions ordering problems and then use the visual models to reason about the correct answers to the problems. We used quantitative data collected by the computer system during a 2-day intervention to identify groups of students with similar performance characteristics. After the intervention, we conducted individual interviews with 10 students for the purpose of investigating qualitative differences between the groups. Our results indicated that most of the 78 students learned to use the computer system to create accurate models in a relatively short period, but not all students learned how to use the models to reason about the correct answers to the problems by the end of the intervention. We hypothesize that we can improve future versions of the system by creating differentiated scaffolds for students with different performance characteristics. In addition, we may be able to improve the learning outcomes associated with implementing this type of technology in classrooms by providing teachers with more detailed data about their students’ performance and the correct and incorrect strategies their students use to solve problems.

[1]  Thomas R. Post,et al.  Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum. , 2002 .

[2]  Douglas H. Clements,et al.  Rethinking "Concrete" Manipulatives , 1996 .

[3]  Karen S. Karp,et al.  Elementary and Middle School Mathematics: Teaching Developmentally. , 2012 .

[4]  N. Hoffart Basics of Qualitative Research: Techniques and Procedures for Developing Grounded Theory , 2000 .

[5]  Nancy Earnheart Nute The impact of engagement activity and manipulatives presentation on intermediate mathematics achievement, time-on-task, learning efficiency, and attitude , 1997 .

[6]  Lara M. Triona,et al.  Point and Click or Grab and Heft: Comparing the Influence of Physical and Virtual Instructional Materials on Elementary School Students' Ability to Design Experiments , 2003 .

[7]  Maria Mendiburo,et al.  Virtual manipulatives and physical manipulatives: technology's impact on fraction learning , 2010 .

[8]  A. Strauss,et al.  The discovery of grounded theory: strategies for qualitative research aldine de gruyter , 1968 .

[9]  David W. Brooks,et al.  The Impact of Virtual Manipulatives on First Grade Geometry Instruction and Learning , 2006 .

[10]  Jennifer Suh Third graders' mathematics achievement and representation preference using virtual and physical manipulatives for adding fractions and balancing equations , 2005 .

[11]  Kathleen A. Cramer,et al.  Teaching about fractions: What, when, and how? , 1989 .

[12]  Richard Lesh,et al.  ORDER AND EQUIVALENCE OF RATIONAL NUMBERS: A CLINICAL TEACHING EXPERIMENT , 1984 .

[13]  Lara M. Triona,et al.  Hands on What? The Relative Effectiveness of Physical versus Virtual Materials in an Engineering Design Project by Middle School Children , 2007 .

[14]  Jennifer Suh,et al.  Developing Students’ Representational Fluency Using Virtual and Physical Algebra Balances , 2007 .

[15]  Hosin Shirvani National Library of Virtual Manipulatives , 2008, J. Educ. Technol. Soc..

[16]  Patricia S. Moyer,et al.  Third Graders Learn about Fractions Using Virtual Manipulatives: A Classroom study , 2005 .

[17]  Lawrence Joseph Pleet The effects of computer graphics and mira on aquisition of transformation geometry concepts and development of mental rotation skills in grade eight , 1990 .