Number Sense Mediated by Mathematics Self-Concept in Impacting Middle School Mathematics Achievement

The purpose of the current study was to extend the research on number sense to the middle school level and to simultaneously consider socioemotional elements related to the construct at this developmental stage. Its genesis was initially rooted in an ongoing and dramatic emphasis by U.S. policymakers, researchers, and educators on improving mathematics achievement in order to compete globally in technology and innovation. Despite debates about optimal curriculum and instruction, tremendous support exists for the construct of number sense. However, middle school research examining the phenomena has been limited to intervention protocols targeting specific skillsets and better measurement of its domains. Concomitantly, educational research has produced ample evidence of the decline in student mathematics motivation over time, and the corresponding literature establishes a link between mathematics self-concept and mathematics achievement, particularly during adolescence. The Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 provides a sample of 4,425 U.S. eighth graders for the present study, assessed directly and indirectly in cognitive, demographic, and affective domains. Multiple regression analyses confirmed the hypotheses that number sense predicts both mathematics self-concept and mathematics achievement at the middle school level, when controlling for gender, race, socioeconomic status, and special education services. Additionally, a path analysis with Statistical Analysis Software (SAS) and the Sobel test revealed that mathematics self-concept mediates the relationship between number sense and mathematics achievement. This indirect effect, when combined with the direct effect of number sense, results in a significant, medium total effect value of .35 for the model. By incorporating this knowledge regarding the interconnection of these three constructs into mathematics curriculum and instruction, as well as teacher education, the United States can move closer to bringing about equity of opportunity and motivating students to pursue more complex mathematics coursework and subsequently professions

Evaluating technology-based strategies for enhancing motivation in mathematics

Background, context, and purpose of study: During the middle school years, students frequently show significant declines in motivation toward school in general and mathematics in particular. One way in which researchers have sought to spark students’ interests and build their sense of competence in mathematics and in STEM more generally is through the use of technology. Yet evidence regarding the motivational effectiveness of this approach is mixed. Here we evaluate the impact of three brief technology-based activities on students’ short-term motivation in math. 16,789 5th to 8th grade students and their teachers in one large school district were randomly assigned to three different technology-based activities, each representing a different framework for motivation and engagement and all designed around an exemplary lesson related to algebraic reasoning. We investigated the relationship between specific technology-based activities that embody various motivational constructs and students’ engagement in mathematics and perceived competence in pursuing STEM careers. Article available under a Creative Commons Attribution 4.0 License

Street Stops and Police Legitimacy in New York

Police-initiated citizen encounters in American cities often are non-neutral events. Encounters range from routine traffic stops to police interdiction of pedestrians during their everyday movements through both residential and commercial areas to aggressive enforcement of social disorder offenses. As a crime detection and control strategy central to the “new policing,” these encounters often are unproductive and inefficient. They rarely result in arrest or seizure of contraband, and often provoke ill will between citizens and legal authorities that discourages citizen cooperation with police and compliance with law. In this chapter, we describe the range of potentially adverse reactions or harms that SQF or ‘street’ policing may produce. We next link those harms to a broader set of normative concerns that connect dignity, harm and police legitimacy. In the third section we review the evidence that connects citizen views of police – as well as their experience with police – to their perceptions of the legitimacy of the police and criminal legal institutions generally. We also review the evidence that links those perceptions to how citizens behave with respect to law, and identify the consequences of adverse reactions of citizens to harsh forms of street policing. We discuss alternative frameworks for regulation and democratic control of the new policing to link police legitimacy with guardianship of communities

Noncognitive skills in the classroom

This book provides an overview of recent research on the relationship between noncognitive attributes (motivation, self efficacy, resilience) and academic outcomes (such as grades or test scores). We focus primarily on how these sets of attributes are measured and how they relate to important academic outcomes. Noncognitive attributes are those academically and occupationally relevant skills and traits that are not “cognitive”—that is, not specifically intellectual or analytical in nature. We examine seven attributes in depth and critique the measurement approaches used by researchers and talk about how they can be improved.Publishe

The Effects of Digital Game-Based Learning on Algebraic Procedural and Conceptual Understanding and Motivation Towards Mathematics

This study examined the impact of digital game-based learning (DGBL) on procedural and conceptual understanding of algebraic expressions and equations and the motivation of students towards classroom mathematics. The mixed-methods sequential explanatory design was used in this study to collect data to determine the effectiveness of DGBL in a 7th grade STEM class. Following a pre-test and pre-motivation survey, students were assigned to either the DGBL group or the non-gaming computer applications as supplemental to mathematics instruction. In order to address both procedural targets and conceptual targets students would be using the technology interventions in addition to traditional math instruction as part of their daily math class, and a problem-based unit taught as part of their STEM class. Following the treatment, a post-test, post-motivation survey, and a conceptual assessment were administered, as well as a digital questionnaire. No significant differences were detected between their understanding of procedural or conceptual problems, nor was there a significant impact to their motivation towards mathematics based on the quantitative data gathered. Students displayed an enthusiastic response to the DGBL environment based on their transcripts from the follow-up questionnaire. The results of the study imply that there is a need for further development of DGBL systems and scaffolded supports to assist students in making connections from the digital environment to classroom mathematics. It further indicates that enjoyment of the DGBL environment does not necessarily transfer to motivation to learn the subject matter in the non-digital environment

STUDENT CENTERED MATHEMATICS INSTRUCTION: DEVELOPING A TEACHER AND STUDENT SURVEY AND UNDERSTANDING STUDENTS’ EXPERIENCES

Over the past thirty years, policies have been enacted at the local and state levels to reform mathematics instruction to be student-centered (see Cohen & Ball, 1990; Resnick, Stein, & Coon, 2008). Despite the wave of instructional reforms, several critical gaps remain in our understanding of student-centered mathematics instruction. First, the field lacks a conceptual framework that relates the underlying theories with student-centered instructional practice in mathematics. Second, there has been very little systematic and large-scale research on the implementation and effects of student-centered mathematics instruction. Third, we know very little about how students experience and respond to the implementation of student-centered instructional reform. The dissertation studies aimed to bridge these gaps with two mixed methods studies. Study 1 proposes a conceptual framework of student-centered mathematics instruction and uses a combination of literature review, feedback from experts, and data from a large sample of urban and suburban youth (n= 2,536 students) and their mathematics teachers (n = 34) to validate a student and teacher survey of student-centered mathematics instruction. Study 2 investigates seventh grade adolescents’ experiences of their mathematics teachers implementing a reform to student-centered instruction. Specifically, the study examines the emotional experience of getting stuck in their algebra coursework and how the frequency and nature of these emotions vary by student characteristics and how students’ emotional experiences influence their sense of competence in math. The studies have important implications for our understanding of student-centered mathematics instruction. In particular, the studies suggest that students’ perspective and experiences could be important to both the implementation and effects of student-centered mathematics instruction. The studies also suggest mechanisms for differential experiences and effects of student-centered instruction for minority, low-income, and female students. Study findings are discussed in terms of implications for education research, practice, and theory

All-boy mathematics classes in middle school.

A comparative case study focused on six mathematics teachers of all-boy classes in three middle schools. Each school chose to experiment with gendered classes to improve specific, yet somewhat different, outcomes. A purpose of this study was not to compare single-gender schooling with coeducation, but rather, to focus on each school\u27s implementation process and to identify school and classroom factors that seemed to contribute to success of the single-gender program. Another purpose was to examine mathematics teaching. Observational analysis used as a framework the Five Strands of Mathematics Proficiency. Related areas of inquiry were classroom time allocation, textbook selection and use, and mathematics beliefs. Results indicated many differences in the nature of the mathematics teaching for the six teachers of the study. Additionally, teacher use of a non-traditional textbook did not relate to non- traditional teacher practices. Overall findings suggested one school to be more successful than the other two in implementing a single-gender program and in using the all-boy mathematics classes to improve student outcomes. Four school-level phenomena that seemed particularly important were as follows: the faculty bought-in to the belief that a single-gender program could improve learning for their students; teacher retention was high; teachers possessed a high sense of collective teacher efficacy; and the principal served effectively as an instructional leader. Additionally, the teacher participants at this school most frequently implemented strategies for boys and exhibited the most characteristics of teaching for mathematics proficiency. In teaching all-boy mathematics classes, classroom management was a first priority. Secondly, teachers of the study found they could engage and motivate boys by using teaching strategies that work for boys and by building relationships with their students. Strategies identified in this study as being successful with boys included games and competition; drama and jokes; the scaffolding of lessons and tasks; and assistance in developing organizational skills. Once, classroom management structures were operational and boys were engaged, teachers reported that boys sustained their engagement in mathematics activities and problems. Thirty-one middle school boys were interviewed, and all reported that they enjoyed mathematics and perceived it as useful for current and future pursuits

An investigation into supporting the teaching of calculus-based senior mathematics in Queensland

David Chinofunga investigated student participation in calculus-based senior secondary mathematics in Queensland and pedagogical resources that enhance teaching of mathematics. Trend analysis reveal a high dropout rate. David also found that pedagogical resources that comprise procedural flowcharts and concept maps can enrich mathematics teaching and promote student participation and engagement

An Expansive Framing Intervention and its Influence on Nursing Students\u27 Perceptions of Value for Mathematics

Nurses regularly use mathematics on the job, yet they often do not view their work as mathematical. This may indicate a lack of transfer from the nursing school mathematics context to nursing practice. Further, nursing students often perceive very little usefulness and relevance for learning mathematics beyond simple calculations. Expansive Framing (EF) is a theory and instructional technique that has been shown to foster transfer by establishing intercontextuality, or connections made between disparate contexts. This research explored whether creating intercontextuality created through broad framing also improved perceptions of mathematics value and transferability, and how intercontextuality functioned as the driver of changes in perceptions of mathematics value and transferability. This embedded case study mixed-methods analysis investigated these constructs by collecting qualitative and quantitative data from undergraduate nursing students in a College Algebra course. Data were analyzed using descriptive statistics, a Wilcoxon Signed Rank test, and reflexive thematic analysis. Results varied; while quantitative analyses showed slight declines in positive value perceptions and a slight increase in negative value perceptions, the results were not statistically significant. Mixed and qualitative-focused analyses showed that participants experienced improved perceptions due to expansively framed activities in the course. The form of EF varied; while webinars showed mixed effectiveness, other expansively framed activities were identified as highly valuable for both groups. Overall, intercontextuality was an apparent motivator of changes in value and transferability perceptions. Based on this research, I recommend that instructors seek opportunities to create intercontextuality by framing broadly across context during instruction, but also by applying EF to classroom activities through curricular integration of content. Future research across multiple classrooms, age groups, and cultural settings, is warranted to investigate the extent to which intercontextuality is the motivator of perception changes versus other factors and to further disentangle the individual roles of connecting settings versus student authorship in effective EF