# Mathematics

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

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.

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

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

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

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.

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

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.

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

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

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.

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

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.

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

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

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).

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).