Mathematics

Developing and Validating a Scalable, Classroom-focused Measure of Usable Knowledge for Teaching Mathematics: The Classroom Video Analysis Instrument

Principal Investigator: 
Nicole Kersting
This project focuses on developing a scalable, classroom-focused measure of usable mathematics teaching knowledge in three content areas: (a) fractions (grades 4 and 5), (b) ratio and proportions (grades 6 and 7); and (c) variables, expressions, and equations (grades 6 and 7). The project examines a variety of validity evidence for the new items and the reliability of scores to evaluate the overall construct validity.
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Discipline / Topic: 
Mathematics
Assessment
Disciplinary Content Knowledge
Target Audience: 
Elementary School
Middle School

Developing and Evaluating Assessments of Problem Solving (Collaborative Research: Bostic and Sondergeld)

Principal Investigator: 
Jonathan Bostic

Through DEAP, we have created three Problem-Solving Measures (PSMs) that address the Common Core State Math Content for grades 3, 4, 5, and 6 and built a robust validity argument for their use and score interpretations. We have also used vertical equating to link the PSMs with the already functioning middle-school PSMs (grades 6, 7, and 8). We are constructing a DEAP reporting system and investigating how the reporting system formatively informs teachers instructional decisions.

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Discipline / Topic: 
Mathematics
Assessment
Target Audience: 
Elementary School
Middle School

CAREER: Fraction Activities and Assessments for Conceptual Teaching (FAACT) for Students with Learning Disabilities

Principal Investigator: 
Jessica Hunt

This poster describes the outcomes, dissemination, and scaling of project work from "Fraction Activities and Assessment for Conceptual Teaching (FAACT)." We describe the results of a pilot study for FAACT, free curriculum materials, and how the work has been translated to a new game based project, Model Mathematics Education (ModelME). A link to an intro video for ModelMe's game based curriculum will be shared.

Co-PI(s): Matthew Marino and Michelle Taub, University of Central Florida

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Discipline / Topic: 
Mathematics
Assessment
Broadening Participation
Curriculum
Special Education
Target Audience: 
Elementary School
Middle School

CAREER: Designing and Enacting Mathematically Captivating Learning Experiences for High School Mathematics

Principal Investigator: 
Leslie Dietiker

This project explores how secondary mathematics teachers can design mathematically captivating learning experiences using the mathematical story framework to improve aesthetic opportunities with complex mathematical content. This study has developed and tested 28 MCLEs. By comparing captivating lessons with those that students describe as dull or boring, we have identified multiple characteristics of captivating mathematics lessons. Also, in addition to raising student interest, MCLEs positively impact teacher and student questioning.

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Discipline / Topic: 
Mathematics
Broadening Participation
Curriculum
Target Audience: 
High School

Anchoring High School Students in Real-Life Issues that Integrate STEM Content and Literacy

Principal Investigator: 
Amy Lannin

Through the integration of STEM content and literacy, this project studies the ways teachers implement literacy practices in the STEM classroom. Teachers will facilitate instruction using scenarios that present students with STEM-related issues, presented as scenarios. After reading and engaging with math and science content, students write a source-based argument in which they state a claim, support the claim with evidence from the texts, and explain the multiple perspectives on the issue.

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Discipline / Topic: 
Mathematics
Science
Technology
Assessment
Curriculum
Target Audience: 
Middle School
High School

Theory to Practice: Prospective Mathematics Teachers’ Recontextualizing Discourses Surrounding Collective Argumentation

Mathematics
Pedagogical Content Knowledge
Professional Development
High
Teacher education programs have a critical role in supporting prospective teachers’ connections between theory and practice. In this study, we examined three prospective secondary mathematics teachers’ discourses regarding collective argumentation during and after a unit of instruction addressing collective argumentation and ways they recontextualized their on-campus coursework (theory) into their student teaching (practice) as demonstrated by their support for students’ mathematical arguments during student teaching.
Access Link: 
https://link.springer.com/article/10.1007/s10857-021-09500-9#Ack1
Author/Presenter: 
Carlos Nicolas Gomez Marchant
Hyejin Park
Yuling Zhuang
Jonathan K. Foster
AnnaMarie Conner
Lead Organization(s): 
The University of Texas at Austin
University of Georgia (UGA)
Year: 
2021
Short Description: 

Teacher education programs have a critical role in supporting prospective teachers’ connections between theory and practice. In this study, authors examined three prospective secondary mathematics teachers’ discourses regarding collective argumentation during and after a unit of instruction addressing collective argumentation and ways they recontextualized their on-campus coursework (theory) into their student teaching (practice) as demonstrated by their support for students’ mathematical arguments during student teaching.

Backward Transfer Influences from Quadratic Functions Instruction on Students’ Prior Ways of Covariational Reasoning about Linear Functions

Algebra
Mathematics
High

The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. We conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of our study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions. The subjects were 57 students from two authentic algebra classrooms at two local high schools.

Access Link: 
https://www.sciencedirect.com/science/article/abs/pii/S0732312320300985?via%3Dih...
Author/Presenter: 
Charles Hohensee
Sara Gartland
Laura Willoughby
Matthew Melville
Lead Organization(s): 
University of Delaware (UD)
Year: 
2021
Short Description: 

The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. Authors conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of the study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions.

Cognitive Instructional Principles in Elementary Mathematics Classrooms: A Case of Teaching Inverse Relations

Algebra
Mathematics
Classroom Practice
Video
Elementary

Instructional principles gleaned from cognitive science play a critical role in improving classroom teaching. This study examines how three cognitive instructional principles including worked examples, representations, and deep questions are used in eight experienced elementary teachers’ early algebra lessons in the U.S. Based on the analysis of 32 videotaped lessons of inverse relations, we found that most teachers spent sufficient class time on worked examples; however, some lessons included repetitive examples that also included irrelevant practice problems.

Access Link: 
https://www.tandfonline.com/doi/full/10.1080/0020739X.2020.1749319
Author/Presenter: 
Meixia Ding
Ryan Hassler
Xiaobao Li
Lead Organization(s): 
Temple University
Year: 
2020
Short Description: 

This study examines how three cognitive instructional principles including worked examples, representations, and deep questions are used in eight experienced elementary teachers’ early algebra lessons in the U.S.

Understanding of the Properties of Operations: A Cross-Cultural Analysis

Algebra
Mathematics
Elementary
This study examines how sampled Chinese and U.S. third and fourth grade students (NChina=167,NUS=97) understand the commutative, associative, and distributive properties. These students took both pre- and post-tests conducted at the beginning and end of a school year. Comparisons between students’ pre- and post-tests within and across countries indicate different learning patterns. Overall, Chinese students demonstrate a much better understanding than their U.S. counterparts.
Access Link: 
https://sites.temple.edu/nsfcareerakt/files/2019/08/Ding-et-al_2019_Property.pdf
Author/Presenter: 
Meixia Ding
Xiaobao Li
Ryan Hassler
Eli Barnett
Lead Organization(s): 
Temple University
Year: 
2021
Short Description: 

This study examines how sampled Chinese and U.S. third and fourth grade students (NChina=167,NUS=97) understand the commutative, associative, and distributive properties.

Teaching Early Algebra through Example-based Problem Solving: Insights from Chinese and U.S. Elementary Classrooms

Algebra
Mathematics
Classroom Practice
Pedagogical Content Knowledge
Pedagogy
Teacher Practice
Elementary

Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS).

Access Link: 
https://www.routledge.com/Teaching-Early-Algebra-through-Example-Based-Problem-S...
Author/Presenter: 
Meixia Ding
Lead Organization(s): 
Temple University
Year: 
2021
Short Description: 

Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS).

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