Hollylynne S. Lee

IDEA: Identifying Design Principles in Educational Applets.

The Internet is increasingly being used as a medium for educational software in the form of miniature applications (e.g., applets) to explore concepts in a domain. One such effort in mathematics education, the Educational Software Components of Tomorrow (ESCOT) project, created 42 miniature applications each consisting of a context, a set of questions, and one or more interactive applets to help students explore a mathematical concept. They were designed by experts in interface design, educational technology, and classroom teaching. However, some applications were more successful for fostering student problem-solving than others. This article describes the method used to mine a subset (25) of these applets for design principles that describe successful learner-centered design by drawing on such data as videos of students using the software and summaries of written student work. Twenty-one design principles were identified, falling into the categories of motivation, presentation, and support for problem solving. The main purpose of this article is to operationalize a method for post hoc extraction of design principles from an existing library of educational software, although readers may also find the design principles themselves to be useful.

Characterising and Developing Teachers’ Knowledge for Teaching Statistics with Technology

Developing the pedagogical expertise needed to effectively engage students in learning statistics with technology requires teachers to have a depth of knowledge about statistics, technological tools for exploring statistical ideas, and of pedagogical issues related to teaching and learning statistics with technology. In this chapter, a framework for a specialised knowledge that is called technological pedagogical statistical knowledge (TPSK) is presented and examples of how aspects of this type of knowledge may assist a teacher are provided. Implications for training teachers are described.

Research on Teaching and Learning Probability

Research in probability education is now well established and tries to improve the challenges posed in the education of students and teachers. In this survey on the state of the art, we summarise existing research in probability education before pointing to some ideas and questions that may help in framing a future research agenda.

New Standards Require Teaching More Statistics: Are Preservice Secondary Mathematics Teachers Ready?

Mathematics teacher education programs often need to respond to changing expectations and standards for K-12 curriculum and accreditation. New standards for high school mathematics in the United States include a strong emphasis in statistics. This article reports results from a mixed methods cross-institutional study examining the preparedness of preservice secondary mathematics teachers to teach statistics and identifying factors and experiences that influence their preparedness. Our results suggest that the cohort of teachers entering secondary mathematics classrooms in 2015-2016 were not well prepared to teach statistics. Specific suggestions are given for how teacher education programs must rise to the challenge of preparing their graduates to teach statistics.

Probability Concepts Needed for Teaching a Repeated Sampling Approach to Inference

This paper uses theoretical and empirical perspectives to articulate what learners should understand about a repeated sampling approach to inference that emphasizes a process of randomizing data, repeating through simulation, and rejecting any model with observed data in the extreme of a distribution that does not fit the model. Key probability concepts, such as a probability model and data distributions, are identified and discussed as to why and how they can assist learners in developing richer understandings and capabilities to a repeated sampling approach to inference.

Statistics Learning Trajectories

Statistics curricula and pedagogy are changing rapidly in response to a growing body of research findings involving students’ reasoning processes, technology capability, attention to underpinning conceptual infrastructure, and new ways of statistical practice. Because many of the statistical ideas being considered are currently not in the curriculum, many researchers in statistics education have investigated students’ reasoning processes through the use of learning trajectories in conjunction with design-based research methods. In this chapter, we outline the characteristics of learning trajectories and exemplify how learning trajectories have been used in three case studies in statistics education. Commonalities and differences across the learning trajectories are discussed as well as recommendations for future research.

Factors that influence secondary mathematics teachers' integration of technology in mathematics lessons

Abstract While many studies describe the use of technology in the mathematics classroom, few explore the factors that influence teacher decisions around its use. The participants in this study were 21 early career secondary mathematics teachers who had completed an undergraduate mathematics teacher preparation program in the USA with a strong emphasis on the use of technology to teach mathematics. In this qualitative study, interview data were collected and analyzed with attention toward why teachers choose to use technology to teach mathematics, what tools they chose to use and why, as well as the general factors they consider when selecting particular technology tools. Findings indicate that one of the most important factors when deciding whether to use technology was how well it aligned with the goals of a lesson. The range of technology used spanned mathematical action tools, collaboration tools, assessment tools, and communication tools. When selecting particular tools teachers most heavily considered ease of use for both themselves and their students. These findings suggest that when considering how to infuse technology into teacher education programs we suggest that it is important to focus more broadly on types of tools, ways teachers can position them, and how particular activities align with specific mathematics learning objectives.

Validation of Scores From the High School Version of the Self-Efficacy to Teach Statistics Instrument Using Preservice Mathematics Teachers

Recently adopted state standards for middle grades and high school mathematics content have an increased emphasis on statistical topics. With this change, teacher education programs may need to adapt how they prepare preservice secondary mathematics teachers (PSMTs) to teach statistics and require measures related to statistics teaching to assess the impact of programmatic changes and track teacher growth. Using responses from a sample of 290 PSMTs from 20 institutions across the United States, this study presents validity and reliability evidence for the high school version of the Self-Efficacy to Teach Statistics (SETS-HS), which could be used to assess statistics teaching efficacy. Confirmatory factor analysis results via Rasch modeling support the use of three subscales, which exhibit adequate reliabilities and correspond to the three levels in the Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education endorsed by the American Statistical Association. Item and rating scale analyses indicate that the 46 items and the six-category scale employed in the SETS-HS perform as intended.