Beth Bos

Virtual math objects with pedagogical, mathematical, and cognitive fidelity

The examination of mathematical and cognitive fidelity for math related websites has been studied by Web designers; yet teachers, and especially pre-service teachers, as users of technology in the classroom, also need to be familiar with pedagogical, mathematical, and cognitive fidelity. What is pedagogical, mathematical, and cognitive fidelity; and, what makes a math website high in pedagogical, mathematical, and cognitive fidelity are discussed in this article. Evidence is shown that technology high in pedagogical, mathematical, and cognitive fidelity, when used in the classroom, improves student academic achievement.

Technology with Cognitive and Mathematical Fidelity: What it Means for the Math Classroom

Technology according to the National Council of Mathematics plays a special role in teaching and learning mathematics. Technology when used effectively can deepen mathematical understanding and lead to greater abstraction. But, not all uses of technology lead to this desired result. Defining cognitive and mathematical fidelity and using it to determine which Web-based formats lead to greater generalizing and abstraction will help in understanding why interactive math objects empower teachers to build a better, deeper understanding of math concepts.

Strategies to Prepare Middle School and High School Students for College and Career Readiness

Abstract Trends among adolescents continue to be discouraging in terms of career and college readiness based on National Assessment of Educational Progress (NAEP) achievement reports and high school graduation rate data. In response, this article presents five goals and eight strategies we have engaged in during a seven-year research study focused on building college and career readiness among adolescents. During our final year of helping students build college and career readiness, we found associated improvements in their academic-related perceptions, beliefs, and strategies; positive personal achievement and goal orientation; rising perceptions of college; improving trends in academic performance; and stronger perseverance in high school when compared to a control group. Because the students in this study have not completed their high school senior year, we do not have data that predict their college acceptance or career readiness.

The Effect of the Texas Instrument Interactive Instructional Environment on the Mathematical Achievement of Eleventh Grade Low Achieving Students

Teaching and learning mathematics with technology poses a unique dilemma. If technology is to enhance mathematical achievement (NCTM, 2000), why do documented studies indicate that this may not be the case (Waxman, Connell, & Gray, 2002)? This study looks at the learning environment used when teaching with technology. What in the instructional environment actually maximizes technologys ability to increase mathematical achievement? The instructional environment used with Texas Instrument InterActive software is examined to determine its affect on the mathematical achievement of eleventh grade at-risk students when studying quadratic functions. The Texas Instrument instructional environment uses technology to manipulate mathematical objects to observe patterns, make generalizations, and test conjectures. Technology is used as a tool to perform action on objects and to problem solve.

The design and application of technology-based courses in the mathematics classroom

It is difficult to examine the effectiveness of technology-based courses (TBC) without understanding the design and application in classrooms. There is evidence of disconnects among the theory for designing, the theory used to apply TBCs in classrooms, and the theory used to research and evaluate TBCs [Hickey, D. T. (1997). Motivation and contemporary socio-constructivist instructional perspectives. Educational Psychologist, 32(3), 175-193]. Comments provided by administrators, teachers and students may lead researchers to determine whether or not the original TBC course goals have been attained. In this paper, we first discuss examples of theoretical disconnects found in other technology-based research [Aleven, V. E., Stahl, E., Schworm, S., Fischer, F., & Wallace, R. (2003). Help seeking and help design in interactive learning environments. Review of Educational Research, 73(3), 277-320; Hickey, D. T., & McCaslin, M. (2001). A comparative, sociocultural analysis of context and motivation. In S. Volet, & S. Jarvela (Eds.), Motivation in learning contexts: Theoretical advances and methodological implications (pp. 33-55). Elmsford, NY: Pergamon Press]. Then, we describe the course design of the mathematics TBC used in this study, the reasons the principal and the teachers believe the software will benefit their mathematics students, and the perceptions of mathematics students regarding the effectiveness of the technology in their classroom. In conclusion, we will discuss how this preliminary qualitative data shaped our future research questions.