Preservice teachers’ creation of dynamic geometry sketches to understand trigonometric relationships

Dynamic geometry software can help teachers highlight mathematical relationships in ways not possible with static diagrams. However, these opportunities are mediated by teachers' abilities to construct sketches that focus users' attention on the desired variant or invariant relationships. This paper looks at two cohorts of preservice secondary mathematics teachers and their attempts to build dynamic geometry sketches that highlighted the trigonometric relationship between the angle and slope of a line on the coordinate plane. We identify common challenges in the construction of these sketches and present examples for readers to interact with that highlight these issues. Lastly, we discuss ways that mathematics teacher educators can help beginning teachers understand common pitfalls in the building of dynamic geometry sketches, which can cause sketches not to operate as intended

Applying Quantitative Reasoning to Clarify Arc Measurements

The importance of reasoning quantitatively is reflected in both mathematics education research and mathematical standards for K-12 students. In this article, we detail how a quantitative reasoning framework can be used to help differentiate two quantities we have found students often struggle with: arc length and the measure of a central angle. We argue that taking the time to define all four components of a quantity can support students’ understanding of theorems involving these quantities

Constructing Kites to Integrate Mathematics and Arts Concepts

This article describes a tetrahedral kite activity that was implemented with grade 9 students (age 14-15). We detail how the three-part lesson provided opportunities to integrate mathematics and art concepts, with potential to also weave in science and engineering ideas. The first part primed students to consider tetrahedral kites, their cultural and historical significance, and the materials needed for constructing the kite. The second part had students create a prototype using nets of tissue paper decorated with mark making techniques. The third part had students create a tetrahedron kite containing cultural and geographical mark making techniques on the tissue paper sides before flying the kites at a community event. We conclude the article with recommendations to help other teachers integrate mathematics and visual arts topics through tetrahedral kites

Researching from a Distance: Using Live Web Conferencing to Mediate Data Collection

When faced with the challenge of limited resources and participants that span state and institutional borders, researchers still have technological options available to them for data collection. This presentation summarizes how I conducted video interviews with these types of participants using the internet software Elluminate. This presentation highlights the possibilities for research using this methodology and the critical aspects for successful implementation

Students\u27 Perceived Utility of Precision Taught Calculus

The last decade of calculus research has showed students learn best when lecture is supplemented with thoughtful use of technology and group work; however, educators are given little direction of how they are to balance the already full first semester calculus class. Precision teaching is an instructional model that employs formative assessment to provide information on what topics are understood by students as well as indicate troublesome concepts. With this information, the instructor can adjust class time accordingly by incorporating supplemental activities most beneficial to students. The purpose of this interview study was to explore the perceived utility of precision teaching by eight students earning to see if further exploration of this topic was warranted. Although precision teaching requires more work for the instructor, students\u27 high perceived utility makes precision teaching a valuable method of undergraduate instruction because they claim to study more, understand material better, and earn higher grades

Sustainability Education and Organizational Change: A Critical Case Study of Barriers and Change Drivers at a Higher Education Institution

Integrating sustainability within institutions of higher education can have a tremendous impact on students, faculty, and the larger community. Sustainability efforts also experience many barriers to implementation within higher education contexts. A change management perspective can help characterize these barriers and ways to overcome them. In this critical case study, we use a process model to examine the kinds of barriers Kennesaw State University (KSU) has faced regarding implementation of academic sustainability and to evaluate change drivers that can advance sustainability during a time of leadership change. The process model evaluates barriers and change drivers according to published frameworks, and provides a way for higher education institutions to identify the most difficult barriers, easily surmountable barriers, and areas where change drivers can have the most impact. At KSU, the process model identified the self-determination of middle-tier change drivers as the most important way to advance sustainable development in higher education institutions (SD in HEI) until new leadership emerges. The process model is iterative and modifiable, because the specific frameworks used in the process model may vary depending upon the needs of each HEI and stage of progression toward SD

Impacts of STEM Professional Development on Teachers' Knowledge, Self-Efficacy, and Practice

Research frameworks outline key aspects of STEM (science, technology, engineering, mathematics) integration for teachers, but translating this research into productive changes in teachers' classroom practices remains a challenge, particularly in schools without an emphasis on STEM integration. In this article, we detail how a STEM education descriptive framework was used to design and enact a year-long professional development with eight middle and secondary teachers at non-STEM focused schools in Southeast USA. We examined the professional development impact on teacher content knowledge, self-efficacy, and practice using pre- and post-test scores on a content exam, pre- and post-test scores on a self-efficacy instrument, and self-reported STEM integration efforts. We found teachers improved in their self-efficacy and made productive changes in their classroom practices, though no significant gains in content knowledge was detected. We conclude with how this STEM education descriptive framework can be helpful in designing effective professional development for teachers at non-STEM focused schools

Identifying and supporting teachers’ robust understanding of proportional reasoning

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Noticing before responding

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.Accepted manuscrip