Visualizing geometrical counterexamples using digital tools

In my study about pre-service secondary mathematics teachers’ (PSMTs) understanding about the nature of theorems in geometry, I noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. The use of the dragging feature of some digital tools, such as The Geometer’s Sketchpad (GSP), in teaching and learning proof and reasoning has been widely discussed and become an ongoing research trend. In this conference session presentation, I will introduce the background of the use of dragging feature in dynamic geometry environment and present two examples showing how this feature could be useful in helping the learners find counterexamples for the two geometrical statements, and thus enhance their understanding about the meaning and usage of counterexamples in geometrical reasoning. The session is potentially beneficial to pre-service/in-service secondary math teachers and teacher educators

Incorporating the Dragging Feature of Dynamic Geometry Environments in Teaching and Learning College Geometry

In a study about pre-service secondary mathematics teachers’ (PSMTs) understanding about the nature of theorems in geometry, the researcher noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. Meanwhile, the use of the dragging feature of dynamic geometry environments (DGEs), such as the Geometer’s Sketchpad and GeoGebra, in teaching and learning proof and reasoning has been widely discussed and become an ongoing research trend. In this paper, the researcher and her colleague will present a research design aimed at investigating PSMTs’ conceptions of counterexamples in geometric reasoning when using the dragging feature of DGEs. Expected results of the study are potentially beneficial to pre-service/in-service secondary math teachers as well as teacher educators

How to Be a Mathematician: Complexifying Mathematical Smartnesses

This presentation was given at the Twelfth Annual Georgia Association of Mathematics Teacher Educators Conference

Pre-Service K-8 Teachers’ Learning of Measurement Unit Conversion Problems

This presentation was given at the Twelfth Annual Georgia Association of Mathematics Teacher Educators Conference

Using Google Forms to Inform Teaching Practices

Kay and LeSage (2009) conducted a literature review of research on use of student response systems in university courses (typically Science, Technology, Engineering, and Mathematics courses) and categorized benefits into classroom environment, learning, and assessment. The objectives of the proposed session are to discuss how using Google Forms will benefit those three above categories. Examples of Google Forms used to gather data, receive in-themoment feedback to students and instructors, engage students’ learning, and assess their learning will be shared throughout the paper. Limitations of Google Forms will also be discussed. This session can be beneficial to all KCollege educators

Using Google Forms to Inform Teaching Practices

Kay and LeSage (2009) conducted a literature review of research on use of student response systems in university courses (typically Science, Technology, Engineering, and Mathematics courses) and categorized benefits into classroom environment, learning, and assessment. The objectives of the proposed session are to discuss how using Google Forms will benefit those three above categories. Examples of Google Forms used to gather data, receive in-the-moment feedback to students and instructors, engage students’ learning, and assess their learning will be shared throughout the paper. Limitations of Google Forms will also be discussed. This session can be beneficial to all K-College educators

Using Google Forms to Inform Teaching Practices

Do you need a quick way to assess your student learning and identify misconceptions? Are you tired of collecting and/or grading papers? Google Forms can help, especially with some newly added features such as checkbox grids, intelligent response validation, and automatic grading. Through interactive activities during this talk, participants will hear about several uses of Google Forms to gather data, engage student learning, and create and score assessments. Additionally, participants will learn how to shorten an URL link with a desired name and generate a QR code for instant access to the link. This session can be beneficial to all K-College educators

Student Conceptions of Counterexample in Dynamic Geometry Environments

As an important aspect of mathematical reasoning and proof, disproof by counterexample, can be used as an effective instructional tool in helping students generate conjectures. Studies have shown using the dragging feature supported by dynamic geometry environments (DGEs) can promote student understanding and reasoning ability in learning geometry. I designed a set of DGE-incorporated geometry tasks and conducted a case study through individual task-based interviews with six undergraduate math major students. The goal is to unpack students’ conceptions of counterexample using the DGE-incorporated tasks and provide suggestions on the use of DGEs in the design of geometry tasks and lessons