NCTI MATHEMATICS MATRIX
This review of technologies available in supporting math learning for those with math difficulity will be guided by the NCTI Mathematics Matrix. The matrix identifies six purposes of technology use for supporting student mathematical learning, including (1) building computational fluency; (2) converting symbols, notations, and text; (3) building conceptual understanding; (4) making calculations and creating mathematical representations; (5) organizing ideas; and (6) building problem solving and reasoning. These six purposes support the development of students' declarative, procedural, and conceptual knowledge.
1. DEVELOPING FLUENCY IN MATH-DELAYED CHILDREN USING TECHNOLOGY
In an early study by Hasselbring, Goin, and Sherwood (1986), it was found that computerized drill and practice was ineffective in developing declarative fact knowledge in students with math difficulty. The identified problem was that typical drill-and-practice software was designed in such a way that students were practicing “procedural counting” strategies instead of developing the ability to recall facts from memory.
As a matter of fact, even studies that report reduced response latencies as a result of the use of computerized drill and practice could not demonstrate that facts were being retrieved from memory, only that procedural counting time was reduced (Christensen & Gerber, 1990; Pellegrino & Goldman, 1987).
As a result of this research, Hasselbring and Goin (2005) developed an intervention paradigm called FASTT (Fluency and Automaticity through Systematic Teaching with Technology) designed to assist students in the development of declarative fact knowledge.
The FASTT approach has been used successfully to develop mathematical fluency. It appears that the key to making the retrieval of basic math facts fluent is to first establish a mental link between the facts and their answers which must be stored in long term memory. FASTT embodies several unique design features to help develop these relationships.
2. Converting Symbols, Notations, and Text
In order to help overcome the challenge of having multiple zone of proximal development’s (ZPDs) in a classroom, computer tools have been developed to provide scaffolding to students on an individual basis. Computer tools can provide a form of scaffolding as the tools help offload some of the learner’s cognitive task to the computer
The goal of these tools is to enable the learner to eventually perform the task independently without the use of the tool (Salomon, 1993). As the students use these tools, they should begin to internalize this guidance, making the tools unnecessary.
One kind of cognitive task that can be offloaded to a computer is converting text, symbols, and mathematical notations. These tools can support students who have difficulty decoding text and symbols. By providing this individualized support, these tools are designed to take some of the burden off the teacher.
Unfortunately, there are currently only a limited number of software packages that have been developed specifically to help students with difficulties decoding as well as other learning needs and even fewer high-quality research studies identifying those that are effective.
This lack of software and supporting research can be seen as an opportunity for researchers and math educators because there is currently a large quantity of non-special education-specific software that could be used to good effect for students with math difficulty.
3. Building Conceptual Knowledge and Understanding
One approach has been the use of video technology to create scenarios of real-world math problems (Cognition and Technology Group at Vanderbilt [CTGV], 1997). This approach to math instruction is called anchored instruction and has been used successfully with regular and special education students. This approach emphasizes the importance of anchoring or situating mathematical knowledge in meaningful, real-world applications.
Source: This is a written summary of the paper entitled TECHNOLOGY-SUPPORTED MATH INSTRUCTION FOR STUDENTS WITH DISABILITIES: TWO DECADES OF RESEARCH AND DEVELOPMENT written by Ted S. Hasselbring, Alan C. Lott and Janet M. Zydney in 2006 for Center for Implementing Technology in Education.
To be continued...
So far what do you think of the first three technology used in Math instruction? Do you use any of these technologies in teaching?