Developing a Learning Progression for Curriculum,Instruction, and Student Learning: An Example from Mathematics Education

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked understanding of students learning over time through careful articulation of a curricular framework and progression, instructional sequence, assessments, and levels of sophistication in student learning. Under this broadened conceptualization, we advance a methodology for developing and validating learning progressions, and advance several design considerations that can guide research concerned with engendering forms of mathematics learning, and curricular and instructional support for that learning. We advance a two-phase methodology of (a) research and development, and (b) testing and revision. Each phase involves iterative cycles of design and experimentation with the aim of developing a validated learning progression. In particular, we gathered empirical data to revise our hypothesized curricular framework and progression and to measure change in students. thinking over time as a means to validate both the effectiveness of our instructional sequence and of the assessments designed to capture learning. We use the context of early algebra to exemplify our approach to learning progressions in mathematics education with a focus on the concept of mathematical equivalence across Grades 3-5. The domain of work on research on learning over time is evolving; our work contributes a broadened role for learning progressions work in mathematics education research and practice.     

Mental health consequences of weight cycling in the first-year post-treatment for breast cancer

Objectives: Weight cycling is linked with advanced breast cancer diagnosis, increased risk of cancer reoccurrence and cancer-related mortality. While women treated for breast cancer report challenges with navigating their post-treatment body shape and weight, the effects of weight cycling on body image and mental health have not been elucidated. This study examined associations between weight changes and weight cycling on psychological health (i.e. weight-related guilt, shame and depressive symptoms) among women in the first-year post-treatment.

Design and Outcome Measures: Self-reported assessments of pre-cancer weight cycling, post-treatment weight-related guilt, shame and depressive symptoms, and objective assessments of weight were assessed in a longitudinal sample of 173 women treated for breast cancer (M_age = 55.01 ± 10.96 years).

Results: Based on findings from multilevel models, women experienced the most weight-related shame when their weight was heavier than their personal average. Additionally, heavier weight was associated with worse psychological health, particularly for women with a history of stable (vs. cycling) weight pre-cancer.

Conclusions: Weight cycling pre-cancer and post-treatment weight change have important implications for psychological well-being. Due to the potential psychological consequences associated with a history of weight cycling, targeted strategies are needed to improve overall health outcomes for women’s survivorship after breast cancer.     

It is written all over your face: Socially rejected people display microexpressions that are detectable after training in the Micro Expression Training Tool (METT)

Social rejection is a powerful negative emotional experience, yet rejected people often appear stoic and unmoved. That is, their macroexpressions of emotion are not accurate reflections of their emotional states. Yet, there is reason to believe that rejected people exhibit involuntary microexpressions of negative emotion. We contrasted people's macroexpressions of emotion with their microexpressions subsequent to an acceptance or rejection experience. Observers coded microexpressions after being trained with the Micro Expression Training Tool. Rejected participants expressed more sad and angry microexpressions than did accepted participants. This research demonstrates that socially rejected people display negative microexpressions that are detectable by observers trained in the Micro Expression Training Tool.     

Sex differences and the effect of instruction on reorientation abilities by humans

This study examined whether differences in the amount of information provided to men and women, in the form of verbal instruction, influenced their encoding during a reorientation task. When a navigator needs to orient, featural (e.g., colour or texture) and geometry (e.g., metric information) are used to determine which direction to begin traveling. The current study used a spatial reorientation task to examine how men and women use featural and geometric cues and whether the content of the task’s instructions influenced how these cues were used. Participants were trained to find a target location in a rectangular room with distinctive objects situated at each corner. Once the participants were accurately locating the target, various tests manipulating the spatial information were conducted. We found both men and women encoded the featural cues, and even though the features provided reliable information, participants generally showed an encoding of geometry. However, when participants were not provided with any information about the spatial aspects of the task in the instructions, they failed to encode geometry. We also found that women used distant featural cues as landmarks when the featural cue closest to the target was removed, whereas men did not. Yet, when the two types of cues were placed in conflict, both sexes weighed featural cues more heavily than geometric cues. The content of the task instructions also influenced how cues were relied upon in this conflict situation. Our results have important implications for our understanding of how spatial cues are used for reorientation.     

Shared Communities: A Multinational Qualitative Study of Immigrant and Receiving Community Members

Community psychology is central to understanding how immigrants and more established residents of their new settings join together to develop a shared sense of community and membership. In our present study, we explored how newer (i.e., first‐ and second‐generation immigrants) and more established community members form multiple positive psychological sense of community (PSOC) with one another. We conducted a multinational, qualitative study of PSOC through interviews with 201 first‐ and second‐generation immigrants and third generation or more “receiving community members” in three contexts (Baltimore‐Washington corridor of the U.S.; Torino, Italy; Lecce, Italy). Results indicated numerous similarities among the ways in which participants constructed PSOC in shared and nonshared communities, regardless of immigration/citizenship status, length of community residence, city, country, age, or gender. Small, proximal, and salient communities were often particularly important to building positive PSOC, which was formed around diverse membership boundaries. As intersectional beings, members converged and diverged on many characteristics, providing multiple opportunities for members to bring diversity to their communities while sharing other characteristics deemed essential to membership. Nonetheless, findings point to significant, structural challenges rooted in power and privilege that must be confronted to bridge the community‐diversity dialectic and build strong, shared sense of community.     

Capturing a More Complete View of Employees’ Lives Outside of Work: The Introduction and Development of New Interrole Conflict Constructs

This research introduces 4 new constructs that reflect interrole conflict (i.e., work‐to‐personal, personal‐to‐work, family‐to‐personal, and personal‐to‐family conflict) and provide a more complete view of the roles and responsibilities employees experience outside of work. An integration of interrole conflict literature and research on work and nonwork roles or domains highlights the importance of considering an individual's personal domain, which includes activities one pursues because of his or her own interests (e.g., friends, hobbies, community). Unfortunately, without conflict measures pertaining to this new role, researchers cannot clearly understand how roles other than family interfere with individuals’ work role including how interrole conflict impacts employees who do not have significant responsibilities in the family domain. Five phases of research across 4 separate samples were conducted in order to develop measures for the 4 new conflict constructs and to examine relationships with important work, family, life, and health outcomes. Findings from multisource data, including self‐rated, coworker‐rated, as well as single and nonsingle participants, show that the 4 new forms of interrole conflict have significant implications for employees and organizations.     

An Approach‐Inhibition Model of Employee Silence: The Joint Effects of Personal Sense of Power and Target Openness

When employees consciously withhold potentially important suggestions or concerns from those who may be able to act on that information, it can have serious implications for organizational performance. Yet there is research suggesting that, when faced with the choice of whether or not to raise an issue, employees often choose to remain silent. Our objective in this paper is to expand current theoretical understanding of why employees often remain silent and of situational factors that can lessen this tendency. Drawing on the approach‐inhibition theory of power, we argue that an employee's personal sense that he or she is lacking in power in relation to others at work is a key factor contributing to the decision to remain silent but that this effect is moderated by perceived target openness. We took a multimethod approach, testing these relationships across 3 studies: a laboratory experiment, a survey study of healthcare workers, and a survey study of employees working across a wide range of industries. Our findings suggest that, although silence is indeed rooted in the psychological experience of powerlessness, perceived target openness mitigates this relationship, encouraging employee to speak up when they would not otherwise do so.     

A first grade student’s exploration of variable and variable notation / Una alumna de primer grado explora las variables y su notación

Abstract

This paper presents a case study of a first grade student to illustrate the diversity of her understandings related to variables and variable notation. While prior research has documented secondary school students’ difficulties with variables and variable notation, we identify many productive understandings in this much younger student, leading us to question the prevailing argument that students might have difficulties with variables due mostly to their own limitations. We draw our data from a teaching experiment that explored functional relationships. Individual interviews were carried out with a subset of the students in the experiment prior to, as well as mid-way through and at the end of the experiment. This paper focuses on a set of three interviews with one of the first grade students. We illustrate the shifts that occurred in the student’s understandings about variables and variable notation across as well as within each of the three interviews.