Mathematics

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.

Explaining Differences in One Teacher’s Instruction Across Multiple Tracked Fifth‐Grade Classes

In this article, we describe the case of “Keri,” a fifth-grade teacher who had completed an Elementary Mathematics Specialist (EMS) certification program. Drawn from a larger study investigating the knowledge, beliefs, and practices of EMSs, Keri's case was unique in that she was teaching mathematics to four classes in a departmentalized structure, where students were placed into different classes according to perceived mathematics ability. Observations from the larger study revealed that Keri's instructional practices did not align with her reported beliefs and knowledge.

Author/Presenter

Corey Webel

Kimberly A. Conner

Christina Sheffel

Lead Organization(s)
Year
2021
Short Description

In this article, we describe the case of “Keri,” a fifth-grade teacher who had completed an Elementary Mathematics Specialist (EMS) certification program. Drawn from a larger study investigating the knowledge, beliefs, and practices of EMSs, Keri's case was unique in that she was teaching mathematics to four classes in a departmentalized structure, where students were placed into different classes according to perceived mathematics ability. Observations from the larger study revealed that Keri's instructional practices did not align with her reported beliefs and knowledge. To explore this deviation, we conducted a case study where we observed Keri's instruction across multiple classes and used interviews to explore reasons for Keri's instructional decisions in terms of her perceived professional obligations.

National Council of Supervisors of Mathematics 54th NCSM Annual Conference; Anaheim, CA

Event Date
-

Learn more at https://www.mathedleadership.org/pl/54th-ncsm-annual-conference/.

DRK-12 Presentations

  • Supporting Success in Algebra for Underprepared Ninth Graders (Presenters: June Mark and Deborah Spencer)
  • Video Coaching Clubs (Presenters: Ryan Gillespie, Jen Kruger, and Stephanie Martin)
Discipline/Topic
Event Type

Beyond the Basics: A Detailed Conceptual Framework of Integrated STEM

Given the large variation in conceptualizations and enactment of K-12 integrated STEM, this paper puts forth a detailed conceptual framework for K-12 integrated STEM education that can be used by researchers, educators, and curriculum developers as a common vision.

Author/Presenter

Gillian H. Roehrig

Emily A. Dare

Joshua A. Ellis

Elizabeth Ring-Whalen

Year
2021
Short Description

This paper puts forth a detailed conceptual framework for K-12 integrated STEM education that can be used by researchers, educators, and curriculum developers as a common vision