September 8, 2008
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Math + Media = Constructive Learning
By Joann Flick, AIT’s Broadcast/Training Professional
An analysis of the TIMSS (Trends in International Mathematics and Science Study, 3rd edition) and the NAEP (National Assessment of Educational Progress 2005) reports indicates that at the end of 8th grade, students in the United States perform below their peers in Belgium, Hungary, Korea, Japan, and the Netherlands. The National Council for Teachers of Mathematics (NCTM) recently issued a report calling for the use of “Curriculum Focal Points” in addition to standards-based instruction in order to be certain that learners are not exiting school without a contextual framework for understanding and applying math in everyday life (NCTM, 2006). These reports illustrate concern about the performance of U.S. students in mathematics. At the same time, a review of high school graduation requirements reveals that students are expected to be able to apply and solve algebraic equations, including linear equations, and to understand how algebra relates to geometry (High School Graduation Requirements: Mathematics, 2005).
The economic benefits of a strong math education are evident. The 2004 American Diploma Project report, “Ready or Not,” noted that more than 80 percent of those who complete Algebra II in high school earn more and are three times more likely to complete a bachelor's degree. The Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education From Functions to Equations: Introduction of Algebraic Thinking to 13 Year-Old Students (2004) provides a well-researched theoretical framework for the instruction of solving and applying algebraic equations. This report advocates a functional approach to permit learners to develop various heuristics to attack an algebraic problem. The report finds the demonstration-practice model for teaching how to solve equations as inappropriate to both the cognitive level of the learner and the nature of the skill being taught.
Vygotsky's Zone of Proximal Development theory holds that the greatest advances of learning occur when a learner is pushed a bit beyond his or her current understanding and is faced with the opportunity to construct meaningful understanding as s/he wrestles with a challenging task (1978). Bruner (1966) identified a process of cognitive conflict that needs to occur to effect learning. The theoretical work of Bruner, Vygotsky's theory, and others have come to represent a body of instructional theory generally called “constructivism.” This theory relates the need to provide supportive and diverse learning experiences. Learners and their peers have significant responsibility for choice in the process. There is greater emphasis on metacognition in a constructivist curriculum. Bruner noted that for constructivist practices to be successful, the teacher had to assure that essential prior knowledge was evident and that appropriate guided practice was also provided.
Educators use the term “scaffolding” to refer to the appropriate assistance in the form of instruction and resources. The use of video segments designated as scaffolds is appropriate (Wiley et. al., 2005). Video has also been shown to be processed by the parts of the brain most associated with affective learning (emotion), leading to suggestions that motion media could be more effective in changing the opinions of learners or in motivating them to learn more (Bergsma, 2002). Gardner's Multiple Intelligences Theory (1983) also supports the use of motion media from the standpoint that different learners may need different types of presentations of information to promote the best possible learning outcome.
The literature validates the use of media to provide direct instruction, to augment teacher-directed instruction, and to support learners as a scaffolding device in constructivist learning environments. There is documentation indicating that the level of performance of high school math students remains a concern. Yet, providers of media services report that math teachers don't use media very often. Why is this? Do math teachers hold perceptions that impede their use of media technologies? Read last month's Featured Article to find out about a recent study that sought to answer this question.
Jo Flick was part of a group of media consultants that conducted a study about math teachers and their utilization of media in 2006 and reported on it this spring. Other members of the Math Media Study Group are: Laura Hunter, Utah Education Network; Marta Bechtol and Kristin Leglar, Wisconsin Educational Communications Board; Sandra Pelham and Alvita Howard, Florida Knowledge Network; and Danny Henley, KERA-TV in Dallas.