I will describe children’s mathematical learning and sociopolitical beliefs/constructs (e.g., oppression, power, privilege) for children with cancer. I depict how robotics incited students to connect to political issues and contribute to how, why, and when mathematics is done while making significant conceptual growth across mathematical domains.

Session Type: Brief Research Report

We report on the development of teacher noticing in a math content course for preservice teachers. Participants submitted writing assignments about a mathematical task followed by analyzing and interpreting student solutions of that task. Results have implications for co-developing teacher noticing with specialized content knowledge for teaching.

Session Type: Brief Research Report

The purpose of this study was to begin examining differences in instructional delivery methods in the flipped mathematics classroom and their influence on elementary preservice teachers’ mathematics anxiety and anxiety about teaching mathematics.

Session Type: Brief Research Report

Beliefs about the nature of mathematical ability are deeply tied to learners’ perceptions of their own potential. The case studies presented here of mathematics learners from mixed-race backgrounds shed light on how racial ideologies reify prevailing perceptions of mathematical ability as innate and fixed.

Session Type: Brief Research Report

Preservice middle and secondary grades teachers’ determination of the directly and inversely proportional relationships, the types of strategies they used to solve given hands-on and real-world mathematical problems, and the difficulties they faced while working on those problems will be discussed.

Session Type: Brief Research Report

There is much research on problem solving in mathematics education. There is much less research concerning problem posing. We share findings from 6 middle-grades classrooms on the kinds of problems students posed, the frequency with which we observed various types of problem posing, and consider circumstances that support problem posing.

Session Type: Brief Research Report

Students' perspectives can enrich our conceptions of how they understand mathematics. The framework, Student-Generated Processes for Understanding Mathematics, illustrates how students generated and expressed key processes which contributed to their mathematical understanding and empowered them in reforming their identity as mathematical learners.

Session Type: Brief Research Report

Research on student-centered approaches to teaching proof can identify practices that support meaningful learning of proof. Undergraduates in an inquiry-based introduction to proof course perceived that communicative activities such as discussion, presentation, and critique of peers’ arguments were crucial to developing an understanding of proof.

Session Type: Brief Research Report

Design-Based Implementation Research (DBIR) is an approach to research and development that can support district-level efforts to improve teaching and expand opportunities for all students to learn. DBIR is organized around problems of practice, and researchers collaborate with teachers and district leaders to design and test innovations. In this presentation, we will describe the principles of DBIR. In addition, we will describe how we are applying these principles to support and study Denver Public Schools’ efforts to expand all students’ opportunities to gain access to rigorous mathematics tasks and build teacher leadership in the district.

Session Type: Plenary Sessions

We share results from a design research study by which we identified a trajectory in grades K–2 children’s understanding of variable and variable notation as they explored functional relationships. Our findings suggest that even young children can begin to think in quite sophisticated ways about these core algebraic concepts.

Session Type: Brief Research Report

Teachers in a professional development project are becoming skilled in using the NCTM (2014) teaching practices as an instructional framework. In order to evaluate the impact of the project, student and teacher perceptions surveys were developed and administered to assess the implementation of these constructs of mathematics teaching practice.

Session Type: Brief Research Report

Interviews with five preservice elementary teachers elicited their views of nine mathematical arguments at two points in time, near the beginning of a course emphasizing mathematical argumentation and after its completion. Qualitative analysis revealed substantial changes in the arguments they preferred and their reasons for selecting them.

Session Type: Brief Research Report

While reforms stress equitable practices, teachers lack the support to attend to equity. Our purpose was better to understand equitable practices through exploring teacher noticing. Through interview analysis of three secondary math teachers, we found although they practice equitable teaching, teachers varied in what they attended to.

Session Type: Brief Research Report

This investigation explores the ways in which the four principles of productive disciplinary engagement (Engle & Conant, 2002) may be used as a tool for informing the design of the norms, structures, and classroom features that combine to form a learning environment.

Session Type: Brief Research Report

This paper reports on middle-grades teachers’ learning about formative assessment in FACETS, a two-year PD program designed to promote an understanding of FA as a comprehensive cycle of instruction and to provide supports for teachers during development of FA classroom practices. Both teacher successes and challenges will be discussed.

Session Type: Brief Research Report

This session will focus on elementary teachers’ development of rational number learning trajectories. We will share observations of their difficulties with setting goals, sequencing the trajectory, selecting appropriate tasks correlated with instances on the trajectory, and discuss supporting them in demonstrating mathematics teaching practices.

Session Type: Brief Research Report

This study investigates the perspectives that secondary math teachers committed to teaching math for social justice bring to their work. Interviews with fifteen teachers from urban cities across the U.S. addressed teachers’ opportunities and challenges developing critical math pedagogies, as well as their visions for improving math education.

Session Type: Brief Research Report

In this study, we explore student-centered approaches to mathematics instruction in high school, examine the relationship between implementation of these approaches and instructional context, and investigate the relationship between student-centered instruction and student (a) engagement and (b) skill in problem solving.

Session Type: Brief Research Report

This report focuses on concepts and strategies exhibited by a large sample of elementary, middle, and secondary students using a hypothetical learning trajectory (LT) for length measurement (Authors). Results address a critical outstanding question about how an LT for length measurement extends into the middle and secondary grades.

Session Type: Brief Research Report

Researchers highlight the development of flowcharts to score video-based assessments of professional noticing capacities to increase coding efficiency and reliability across a large team. The measurement process in this research has potential to refine strategies for assessment of responsive teaching with respect to noticing frameworks and beyond.

Session Type: Brief Research Report

The MYTEAM project investigated the decline in mathematics engagement and achievement in Australian middle-years students using a series of quantitative and qualitative studies. This presentation tracks one investigative pathway through the five studies that highlights the critical role of individual student differences.

Session Type: Brief Research Report

This study examines high school students’ (n=18) use of academic language in formal written mathematical solutions. We discuss students' use of linking words, mathematical vocabulary, and syntactic complexity and how these relate to indicators associated with content understanding.

Session Type: Brief Research Report

In this study, we focus on how grades 3-5 teachers make sense of and interpret artifacts of students’ multiplicative thinking, namely the written work that students produce on multiplication and division problems.

Session Type: Brief Research Report

This study examined the impact of the order of teaching approaches on student abilities. Group 1 (n=22) received multiple representations followed by traditional algorithms. Group 2 (n=21) received these in reverse order. Results indicated ability gains for both groups however comparisons of effect size found larger growth gains for Group 1.

Session Type: Brief Research Report

We will report on an expert teaching study designed to characterize responsive teaching—instruction that is continually adjusted in response to children’s mathematical thinking. We will highlight the teaching moves and decision making involved in responsive teaching when skilled teachers of grades 4–5 engaged with children’s fractional thinking.

Session Type: Brief Research Report

This interview study investigated 4th through 12th grade students’ use and understanding of the commutative property of multiplication. Students produced a range of justifications from appeals to authority, to examples, to more analytic justifications. Students’ conceptions of the property were classified as either syntactic or structural.

Session Type: Brief Research Report

Other fields have identified a list of Grand Challenges as a way to prioritize the most pressing problems that research should address. In a recent JRME issue, the NCTM Research Committee wrote a research commentary that argues for initiating this approach for mathematics education. If the field of mathematics education were to identify a list of Grand Challenges, what might the list include? How could we initiate a process to generate that list? What are the associated risks? We invite you to learn about this new NCTM initiative, provide ideas, and engage in a discussion about the future of this endeavor.

Session Type: Research Symposium

This study investigates whether performance on an alternative mode of assessment may provide a means to identify mathematical capabilities that are not captured on conventional measures of mathematics achievement. This alternative mode would identify a broader diversity of talented students who might otherwise be denied access to STEM studies.

Session Type: Brief Research Report

We examine whether three teacher/classroom characteristics that research has shown influence curriculum implementation, also influence curriculum effects. Across the contexts examined, we find one standards-based and one conventional curriculum are equally effective, and either as effective or more effective than the other two curricula studied.

Session Type: Brief Research Report

A researcher and teacher at a diverse urban school partnered to enact a 7th grade unit where students analyzed and designed visualizations of public city data. We analyze students’ engagement with math content and mathematical agency, and identify supports that promoted mathematical depth. The talk will include classroom video and student work.

Session Type: Brief Research Report

This session will report on a student's participation in a 12-week teaching experiment. This session will focus on how Jace solved open numbers sentences with integer addition and subtraction in four different individual interviews. Results provide more robust descriptions of conceptual models for integers and provide a developmental perspective.

Session Type: Brief Research Report

This report uses data from four projects to highlight aspects of curricular noticing, which theorizes how teachers make sense of the complexity of curricular materials. We will engage participants in considering how curricular noticing may support mathematics teacher educators in supporting preservice teachers’ engagement with curricular materials.

Session Type: Brief Research Report

This study investigated inquiry-based teaching of algebra based on the thinking and practice of exemplary mathematics teachers. Findings based on interviews and classroom observations include 3 inquiry-oriented perspectives that engage students in unique ways of learning algebra and 4 aspects of teachers’ thinking that support these perspectives.

Session Type: Brief Research Report

This brief research report describes the results of implementing High-Impact Practices (HIP)into graduate statistics for the social sciences utilizing a quasi-experimental two-group research design for comparing graduate students' average statistics efficacy, leadership skills, and research ethics. NCTM Principles to Actions and HIP are compared.

Session Type: Brief Research Report

In this study, I measured AP Calculus students' understandings of functions at the end of the school year, and compared their understandings to their performance on the AP Calculus Exam.

Session Type: Brief Research Report

Making mathematical practices explicit while still providing students authentic opportunities to engage in these practices can make instruction more equitable. This study compares how experienced and beginning teachers make mathematical practices explicit in discourse and what this might reveal about the knowledge and skills entailed in doing so.

Session Type: Brief Research Report

Video usage has grown in teacher preparation programs, but little is known about what prospective teachers really see and focus on when they watch their own teaching videos. This report will present a study where prospective teachers made video observations after a peer microteaching lab experience, and provide opportunities for discussion.

Session Type: Brief Research Report

In this session we will discuss results of a research study designed to investigate the extent to which elementary teachers support the beliefs expressed in NCTM’s Principles to Actions and to understand how teachers interpret the statements made by NCTM.

Session Type: Brief Research Report

The purpose of this study was to examine how preservice elementary teachers’ visions of mathematics instruction developed during their teacher preparation program. Nineteen participants were interviewed multiple times. We will share a trajectory of how visions of mathematics instruction developed and discuss implications for teacher educators.

Session Type: Brief Research Report

This research targets children’s informal strategies and knowledge of fractions through their creation and interpretation of multiple representations when solving fractions tasks. Analyses of clinical interviews with grades 2-6 children suggest variation across models of the whole and conflicts between informal and rule-based knowledge.

Session Type: Brief Research Report

A survey with classroom vignettes was developed and used to evaluate novice teachers' orientation to teaching mathematics. 52 teachers from traditional and alternative preparation programs at one university were surveyed. Response patterns reveal opportunities for preparing teachers to engage in productive teaching practices in high need schools.

Session Type: Brief Research Report

We present video clips and analyses of three individual interviews with a kindergarten student, a first grade student, and a second grade student working through a function task. These three cases highlight how arithmetic and algebra are mutually supporting ventures in the mathematical education of young students.

Session Type: Brief Research Report

This research examines the relations between co-regulation and self-regulation strategies, help-seeking behaviors, perceptions of teacher support, and the mathematics achievement of African American middle school students (n = 440). Structural equation modeling was used to analyze the data.

Session Type: Brief Research Report

This presentation examines pre-service secondary teachers' interpretations of student work. Participants reasoned mathematically, pedagogically, and with comparisons to personal solutions. Results showed relationships between the interpretations and MKT. There are implications for supporting teachers to implement practices in Principles to Actions.

Session Type: Brief Research Report

This investigation examined German middle school students’ changes in motivation to learn mathematics. Student motivation levels were assessed relative to specific psychological needs of students based on the motivational theoretical framework of Self-Determination Theory.

Session Type: Brief Research Report

Improving tasks used in methods courses can encourage better development of high-leverage practices among prospective teachers. We examined the effects of modifications to a video-critique task assigned in a methods course. We will present the improvements in student work found as result of the changes and discuss implications for other tasks.

Session Type: Brief Research Report

Students with disabilities continue to lack access to and achievement in rich mathematics. This presentation describes a research project that examined shifts in teacher discourse during a series of professional learning sessions focused on the use of Universal Design for Learning framework in advancing equity in mathematics education

Session Type: Brief Research Report