Mathematics

Simulations as a Tool for Practicing Questioning

In this chapter we discuss some of the affordances and constraints of using online teaching simulations to support reflection on specific pedagogical actions. We share data from a research project in which we implemented multiple iterations of a set of simulated teaching experiences in an elementary mathematics methods course. In each experience, preservice teachers contrasted the consequences of different pedagogical choices in response to a particular example of student thinking.

Author/Presenter: 
Corey Webel
Kimberly Conner
Wenmin Zhao
Lead Organization(s): 
Year: 
2018
Short Description: 
Authors discuss some of the affordances and constraints of using online teaching simulations to support reflection on specific pedagogical actions.

Scaling up innovative learning in mathematics: exploring the effect of different professional development approaches on teacher knowledge, beliefs, and instructional practice

Professional learning experiences (PLEs) provide teachers with opportunities to improve their understanding of mathematics content and teaching practices. However, PLEs are often conducted in person and in small groups—hence costly and localized. The purpose of the current study was to explore different ways for teachers to engage in PLEs and how these approaches might enable the field to scale up these efforts in a sustainable manner.

Author/Presenter: 
Daniel J. Heck
Courtney L. Plumley
Despina A. Stylianou
Adrienne A. Smith
Gwendolyn Moffett
Year: 
2019
Short Description: 
The purpose of the current study was to explore different ways for teachers to engage in Professional learning experiences (PLEs) and how these approaches might enable the field to scale up these efforts in a sustainable manner.
Resource Type: 
Publication

Patterns Linking Interpreting and Deciding How to Respond During the Launch of a Lesson: Noticing from an Integrated Perspective

Researchers have generated a powerful framework that identifies three aspects of noticing students’ mathematical thinking: attending to, interpreting, and deciding how to respond to student thinking. Previous research has tended to focus on evaluating how well teachers engaged in noticing, and how well they connected the different aspects of noticing. We describe a complementary way of studying the connections between different aspects of noticing, one that stresses the content of teachers noticing.

Author/Presenter: 
Rob Wieman
Corey Webel
Year: 
2019
Short Description: 
Authors describe a complementary way of studying the connections between different aspects of noticing, one that stresses the content of teachers noticing. They report on a study in which participants were shown depictions of students reacting to the launch of a complex task. Participants then chose among a variety of possible interpretations and teacher responses.

Clarifiable Ambiguity in Classroom Mathematics Discourse

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Author/Presenter: 
Blake E. Peterson
Keith R. Leatham
Lindsay M. Merrill
Laura R. Van Zoest
Shari L. Stockero
Year: 
2019
Short Description: 
In this article, authors argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Aligning Test Scoring Procedures with Test Uses: A Balancing Act

Test scoring procedures should align with the intended uses and interpretations of test results. In this paper, we examine three test scoring procedures for an operational assessment of early numeracy, the Early Grade Mathematics Assessment (EGMA). Current test specifications call for subscores to be reported for each of the eight subtests on the EGMA. This test scoring procedures has been criticized as being difficult for stakeholders to use and interpret, thereby impacting the overall usefulness of the EGMA for informing decisions.

Author/Presenter: 
Leanne Ketterlin Geller
Lindsey Perry
Linda Platas
Yasmin Sitabkhana
Year: 
2018
Short Description: 
Test scoring procedures should align with the intended uses and interpretations of test results. In this paper, we examine three test scoring procedures for an operational assessment of early numeracy, the Early Grade Mathematics Assessment (EGMA). Current test specifications call for subscores to be reported for each of the eight subtests on the EGMA. This test scoring procedures has been criticized as being difficult for stakeholders to use and interpret, thereby impacting the overall usefulness of the EGMA for informing decisions. We examine the psychometric properties including the reliability and distinctiveness of the results and usefulness of reporting test scores as (1) total scores, (2) subscores, and (3) composite scores. These test scoring procedures are compared using data from an actual administration of the EGMA. Conclusions and recommendations for test scoring procedures are made. Generalizations to other testing programs are proposed.

Curriculum and Instruction at Exemplar Inclusive STEM High Schools

In recent years, prominent organizations have released large-scale policy reports on the state of science, technology, engineering, and mathematics (STEM) education in the United States, with particular emphasis on curricula and instructional practices. The purpose of this paper was to examine the curriculum and instruction occurring at high performing STEM-focused high schools that have no academic conditions for student admission. This study conducted a cross-case analysis across eight case studies of contextually different but well-regarded inclusive STEM high school.
Author/Presenter: 
Erin Peters-Burton
Ann House
Ed Han
Sharon Lynch
Year: 
2018
Short Description: 
In recent years, prominent organizations have released large-scale policy reports on the state of science, technology, engineering, and mathematics (STEM) education in the United States, with particular emphasis on curricula and instructional practices. The purpose of this paper was to examine the curriculum and instruction occurring at high performing STEM-focused high schools that have no academic conditions for student admission. This study conducted a cross-case analysis across eight case studies of contextually different but well-regarded inclusive STEM high school. Common themes that emerged included different hierarchical levels of design and implementation (classroom-level, cross-cutting school level, school-wide) as well as responsive design of curriculum and instruction. Unique contextual differences are discussed as well as implications for replication of inclusive STEM school design.

How Viewers Orient Toward Student Dialogue in Online Math Videos

Online math videos for student learning are abundant; yet they are surprisingly uniform in their monologic, expository mode of presentation and their emphasis on procedural skill. In response, we created an alternative model of online math videos that feature the unscripted dialogue of secondary school students, who convey sources of confusion and resolve the dilemmas that arise during problem solving.

Author/Presenter: 
Joanne Lobato
Carren Walker
Lead Organization(s): 
Year: 
2019
Short Description: 
Authors describe an alternative model of online math videos that feature unscripted dialogue of secondary school students, who convey sources of confusion and resolve the dilemmas that arise during problem solving.

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