Mathematics

Coaching from a Distance: Exploring Video-based Online Coaching

This study explored an innovative coaching model termed video-based online video coaching. The innovation builds from affordances of robot-enabled videorecording of lessons, accompanied by built-in uploading and annotation features. While in-person coaching has proven effective for providing sustained support for teachers to take up challenging instructional practices, there are constraints. Both logistical and human capacity constraints make in-person coaching difficult to implement, particularly in rural contexts.

Author/Presenter

Cynthia D Carson

Jeffrey Choppin

Lead Organization(s)
Year
2021
Short Description

This study explored an innovative coaching model termed video-based online video coaching.  As part of an NSF-funded project, we studied nine mathematics coaches over four years as they engaged in video-based coaching with teachers from geographically distant, rural contexts.

Examining the Use of Video Annotations in Debriefing Conversations during Video-Assisted Coaching Cycles

This study examined how mathematics coaches leverage written annotations to support professional discourse with teachers about important classroom events during synchronous debriefing conversations. Coaches and teachers created the annotations while asynchronously watching video of an implemented lesson as part of online video-assisted coaching cycles. More specifically, this project examined the extent to which a coach and teacher discussed the annotations during a debrief conversation in a coaching cycle.

Author/Presenter

Ryan Gillespie

Julie M. Amador

Jeffrey Choppin

Year
2021
Short Description

This study examined how mathematics coaches leverage written annotations to support professional discourse with teachers about important classroom events during synchronous debriefing conversations. Coaches and teachers created the annotations while asynchronously watching video of an implemented lesson as part of online video-assisted coaching cycles. More specifically, this project examined the extent to which a coach and teacher discussed the

annotations during a debrief conversation in a coaching cycle. We present a rationale for needing new knowledge about the relationships between video annotations and professional discourse as well as the potential implications of such knowledge.

Synchronous Online Video-based Professional Development for Rural Mathematics Coaches

In this project, we have designed, implemented, and started to research an innovative fully online video-based professional development model for mathematics coaches in rural contexts. Coaches in rural areas often lack access to professional development available in more populated areas, fueling the need for an online model that bridges geographic barriers (Howley & Howley, 2005; Maher & Prescott, 2017). The intent of the poster will be to share the professional development model and describe the research processes that are currently in progress.

Author/Presenter

Julie M. Amador

Jeffrey Choppin

Cynthia Callard

Cynthia Carson

Ryan Gillespie

Lead Organization(s)
Year
2021
Short Description

In this project, we have designed, implemented, and started to research an innovative fully online video-based professional development model for mathematics coaches in rural contexts. The intent of the poster will be to share the professional development model and describe the research processes that are currently in progress.

A Three-Part Synchronous Online Model for Middle Grade Mathematics Teachers’ Professional Development

In this chapter, we describe a three-part fully online model for the professional development of middle school mathematics teachers. While the model could be applied to any context, we created it for rural mathematics teachers to provide them access to high-quality professional development and to demonstrate that we could move face-to-face experiences to an online context without losing interactional qualities or intellectual rigor. We describe the model and how we researched it.

Author/Presenter

Julie Amador

Cynthia Callard

Cynthia Carson

Ryan Gillespie

Jennifer Kruger

Stephanie Martin

Genie Foster 

Year
2021
Short Description

In this chapter, we describe a three-part fully online model for the professional development of middle school mathematics teachers. This chapter contributes to understanding how online contexts provide opportunities to collect and analyze data in ways that would be difficult to accomplish in face-to-face settings.

A Three-Part Synchronous Online Model for Middle Grade Mathematics Teachers’ Professional Development

In this chapter, we describe a three-part fully online model for the professional development of middle school mathematics teachers. While the model could be applied to any context, we created it for rural mathematics teachers to provide them access to high-quality professional development and to demonstrate that we could move face-to-face experiences to an online context without losing interactional qualities or intellectual rigor. We describe the model and how we researched it.

Author/Presenter

Julie Amador

Cynthia Callard

Cynthia Carson

Ryan Gillespie

Jennifer Kruger

Stephanie Martin

Genie Foster 

Year
2021
Short Description

In this chapter, we describe a three-part fully online model for the professional development of middle school mathematics teachers. This chapter contributes to understanding how online contexts provide opportunities to collect and analyze data in ways that would be difficult to accomplish in face-to-face settings.

Second and Fifth Graders’ Use of Knowledge-Pieces and Knowledge-Structures When Solving Integer Addition Problems

In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. Fifty-one out of 102 second graders and 90 out of 102 fifth graders read or used negative signs at least once across the 11 problems. Among second graders, one of their most common strategies was subtracting numbers using their absolute values, which aligned with students’ whole number knowledge-pieces and knowledge-structure.

Author/Presenter

Mahtob Aqazade

Laura Bofferding

Lead Organization(s)
Year
2021
Short Description

In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. For both grade levels, the order of the numerals, the location of the negative signs, and also the numbers’ absolute values in the problems played a role in students’ strategies used. Fifth graders’ greater strategy variability often reflected strategic use of the meanings of the minus sign. Our findings provide insights into students’ problem interpretation and solution strategies for integer addition problems and supports a blended theory of conceptual change.

The Development and Assessment of Counting-based Cardinal Number Concepts

The give-n task is widely used in developmental psychology to indicate young children’s knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and the cardinal-count concept, which she argued is a more advanced cardinality concept that underlies the counting-out process required by the give-n task with larger numbers.

Author/Presenter

Arthur J. Baroody

Menglung Lai

Year
2022
Short Description

The give-n task is widely used in developmental psychology to indicate young children’s knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and the cardinal-count concept, which she argued is a more advanced cardinality concept that underlies the counting-out process required by the give-n task with larger numbers. One aim of the present research was to evaluate Fuson’s disputed hypothesis that these two cardinality concepts are distinct and that the count-cardinal concept serves as a developmental prerequisite for constructing the cardinal-count concept. Consistent with Fuson’s hypothesis, the present study with twenty-four 3- and 4-year-olds revealed that success on a battery of tests assessing understanding of the count-cardinal concept was significantly and substantially better than that on the give-n task, which she presumed assessed the cardinal-count concept.

Secondary Mathematics Teachers’ Use of Students’ Incorrect Answers in Supporting Collective Argumentation

This study illustrates how two secondary mathematics teachers used students’ incorrect answers as they supported students’ engagement in collective argumentation. Three ways of supporting argumentation when students contributed incorrect answers are exemplified, and the structures of these arguments are investigated. Then, by focusing on the correctness of argument components as represented by the diagrams, we developed a potential model of levels of validity in classroom-based argumentation.

Author/Presenter

Yuling Zhuang

AnnaMarie Conner

Year
2022
Short Description

This study illustrates how two secondary mathematics teachers used students’ incorrect answers as they supported students’ engagement in collective argumentation.

Teachers’ Pedagogical Content Knowledge in Mathematics and Science A Cross-Disciplinary Synthesis of Recent DRK-12 Projects

This review synthesized insights from 27 NSF-funded projects, totaling $62 million, that studied pedagogical content knowledge (PCK) in STEM education from prekindergarten (PreK) to Grade 12, split roughly equally across mathematics and science education. The projects primarily applied correlational/observational and longitudinal methods, often targeted teaching in the middle school grades, and used a wide variety of approaches to measure teachers’ PCK.

Author/Presenter

David Miller

Isabella Pinerua

Jonathan Margolin

Dean Gerdeman

Year
2022
Short Description

This review synthesized insights from 27 NSF-funded projects, totaling $62 million, that studied pedagogical content knowledge (PCK) in STEM education from prekindergarten (PreK) to Grade 12, split roughly equally across mathematics and science education. The projects primarily applied correlational/observational and longitudinal methods, often targeted teaching in the middle school grades, and used a wide variety of approaches to measure teachers’ PCK. The projects advanced substantive knowledge about PCK across four major lines of research, especially regarding the measurement and development of PCK.

Mathematical and Scientific Argumentation in PreK-12: A Cross-Disciplinary Synthesis of Recent DRK-12 Projects

This review synthesizes insights from 23 NSF-funded projects, totaling $40 million, that studied mathematical and scientific argumentation in STEM education from prekindergarten (PreK) to Grade 12. The projects reported on both studies of argumentation interventions and naturalistic observations in “business-as-usual” settings. The projects advanced substantive knowledge about how to support student argumentation.

Author/Presenter

Eben Witherspoon

David Miller

Isabella Pinerua

Dean Gerdeman

Year
2022
Short Description

This review synthesizes insights from 23 NSF-funded projects, totaling $40 million, that studied mathematical and scientific argumentation in STEM education from prekindergarten (PreK) to Grade 12. The projects reported on both studies of argumentation interventions and naturalistic observations in “business-as-usual” settings. The projects advanced substantive knowledge about how to support student argumentation. In particular, the projects highlighted the importance of making an argument’s structure explicit and facilitating student-to-student discourse, especially with technological tools.