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

An Autoethnography of Transitioning Mathematics Content Courses for K-8 Preservice Teachers to Online Learning during COVID-19

The following autoethnography is completed by a group of mathematics teacher educators (MTEs) after transitioning their mathematics content courses for K-8 Preservice Teachers (PSTs) from face-to-face to online due to COVID-19 in Spring 2020. The MTEs present their perceptions of the shift to online teaching and learning by describing (a) how they typically teach their classes, (b) how they redesigned classes to support student learning when the pandemic started, (c) their PSTs\u27 perceptions of which course components we effective (or not) in helping them adjust to the new online learning environment, and (d) next steps in teaching and research

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

K-8 Preservice Teachers\u27 Numeracy (Number Sense) Knowledge

The Georgia Numeracy Project Individual Knowledge Assessment of Number (IKAN) written assessment is a video-based assessment used in Georgia to assess Grades 4-8 numeracy mastery. IKAN written pre/post assessment data were collected spring and fall 2021 and spring 2022 semesters at a Georgia instituion of higher education in a Foundations of Numbers and Operations course to assess K-8 preservice teachers mathematics numeracy knowledge. Students\u27 numeracy knowledge increased during the course but almost all students did not complete the course with the highest possible stage scores. These data support the assertation a content course can positively impact student knowledge. These data also show that more focused work is needed in content courses that prepare future K-8 preservice teachers in order for these teachers to teach Grades 4-8 numeracy knowledge