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Students' construction, coordination, and abstraction of units underlie success across multiple mathematics domains. Structures for coordinating units underscore notions of numbers as composite units (e.g., five is a unit of five and five units of one). In this working group, we seek to facilitate collaboration amongst researchers and educators concerned with units construction and units coordination. The aim for this working group is two-fold: (1) to extend our research around units construction and coordination to new grade levels; and (2) to collaborate with researchers who investigate students with learning differences in school settings to determine diverse students' mathematics learning trajectories. [For the complete proceedings, see ED606556.]

We, five math teacher educators (MTEs), share how multimodal microanalysis has the potential to contribute to rehumanizing mathematics education by expanding what counts as evidence of students’ knowings. We define multimodal microanalysis as the detailed examination and interpretation of minute interactions between various sensory modalities and mathematical representations at a granular level. Using mathematics cognitive interview videos, we share our research design and analysis processes and discuss how multimodal microanalysis can contribute to rehumanizing mathematics teaching and learning. [ABSTRACT FROM AUTHOR]

The Complex Connections: Reimagining Units Construction and Coordination working group has been running since PMENA in 2018. Previous years have focused on developing a website to share research articles and share completed work and facilitating collaboration between researchers and educators regarding students' units construction and coordination. This goal aligned with Steffe's (2017) call for work focused collaboration between researchers and educators to advance units construction and coordination for all learners. The group has grown beyond the initial topic of individuals' units coordination in whole number and fraction settings to discuss units coordination in algebraic and covariational reasoning. [ABSTRACT FROM AUTHOR]

In this manuscript we, six math teacher educators (MTEs), share a collaborative self-study investigation into increasing our embodiment-focused noticing. Initially, we individually viewed cognitive interview videos and recorded our embodiment-focused noticings. Next, we met as a group to share, compare, and merge our noticings. We used the merged noticings to develop an exemplar and a rubric. We will discuss how layering an embodiment lens over our noticings can contribute to rehumanizing mathematics. [ABSTRACT FROM AUTHOR]

The Complex Connections: Reimagining Units Construction and Coordination working group began at PMENA 2018, with the aim of facilitating collaboration amongst researchers and educators sharing Steffe's (2017) concerns about units construction and coordination for all learners. This working group made dramatic progress in their ability to conceptualize their work and impact the mathematics education field in the form of publications and task development. [ABSTRACT FROM AUTHOR]

Given the most recent need for virtual teaching, many mathematics teacher educators have taught pre-service teachers with virtual manipulatives, which often stood in for physical manipulatives. This brief considers the theoretical framing for pre-service teachers’ actions with physical Cuisenaire rods before considering benefits and limitations virtual Cuisenaire rod features afford when making such a transition to virtual Cuisenaire rods. In particular, we seek to consider the theoretical question: what is gained and lost when trying to replicate preservice teachers' ’se of physical Cuisenaire rods with virtual Cuisenaire rods [ABSTRACT FROM AUTHOR]

In this study, we collected data from 48 middle school girls who attended a five-day residential summer mathematics program. At the program beginning and end, the girls wrote a brief “Dear Math” letter to share their thoughts and feelings about mathematics, and they were asked to draw a picture of themselves doing math and to explain it. Participant data were analyzed into themes, and pre- and post-program data were compared to look for evidence of change. The data show favorable movement, particularly in viewing mathematics as being more collaborative and less procedural. [ABSTRACT FROM AUTHOR]

A powerful aspect of using neo-Piagetian frames to examine students' construction and coordination of units is their potential to apply across mathematical domains. This working group aims to facilitate collaborations between scholars of algebraic and covariational reasoning, with the particular aim of extending research on units coordination and construction across these contexts. An ultimate goal of this working group will be to develop a Special Issue. [ABSTRACT FROM AUTHOR]

This brief report describes the initial results of The Fractions as Measures for Prospective Elementary School Teachers (PTs) Study. Research shows that PTs' conceptions of fractions on a part-whole understanding may be problematic when teaching children about improper fractions. We created an instructional lesson sequence for PTs focused on using unitizing, iterating, and partitioning to think of fractions as measures in multiple situations. Initial results from this ongoing study indicate that PTs' manipulations of unpartitioned rod manipulatives supported both their construction of more powerful fractions schemes and their ability to verbally justify their reasoning. [ABSTRACT FROM AUTHOR]

An interpretive framework for organizing and reducing data from a whole class teaching experiment for further analysis is described. Design research typically generates extensive data and can become potentially unmanageable for analysis. The framework described in this paper uses a situated cognitive perspective: Meaning making arises out of activity within the context of the classroom. Each layer affords and constrains each other. Data from a whole class teaching experiment illustrates how the framework was used to reduce and catalog the data for further analysis. The framework can be adapted by anyone who is engaging in design research. [ABSTRACT FROM AUTHOR]

This report describes a framework used as a communication tool to reflect and adapt instruction to support student learning. Specifically, this framework was used as a bridge for collaboration between the classroom teacher and the researcher to reflect on daily lessons. The goal of this preliminary project was to adapt teaching and tasks to support seventh-grade students' learning of algebraic expressions and equations. The framework was used to document and summarize what occurred during the lesson on a daily basis and to identify learning goals for the subsequent lessons. The reflection process was helpful for the teacher to trace where students had been in their learning and to make decisions about how to foster learning in the following lessons. The framework served useful and made it easier for the teacher to adjust her instructional practices to support student learning in the classroom. [ABSTRACT FROM AUTHOR]

Students’ construction, coordination, and abstraction of units underlie success across multiple mathematics domains. This working group aims to facilitate collaboration between researchers and educators with the particular aim of extending research on units coordination and construction across numerical contexts and constructs. [ABSTRACT FROM AUTHOR]

Students' construction, coordination, and abstraction of units underlie success across multiple mathematics domains. This working group aims to facilitate collaboration between researchers and educators with the particular aim of extending research on units coordination and construction across age groups, learning differences, and mathematical contexts. [ABSTRACT FROM AUTHOR]

The article discusses a study which examined self-selected social positioning by mathematics students in the U.S. The study cited the case of a student who experienced frustration during her mathematics class. The results revealed that, rather then engaging in social positioning, students participated in mathematics discourse.

The article discusses a study on the intent that fourth grade students in the U.S. understand magnitude. The study created a curriculum unit in order to determine students' understanding of magnitude. It analyzed the mathematical discourse of the participants that focused on what to label the parts. The results showed that the students did not pay attention to the indication of 1 unit and labeled the ruler incorrectly.