Humanizing Rational Numbers in Middle School

PurposeThis study aims to better understand how students’ academic strains and multilevel strengths relate to their math achievement, with a particular emphasis on underrepresented students of color and girls given the need to broaden science, technology, engineering and math (STEM) participation for these groups.Design/methodology/approachNational Education Longitudinal Study of 1988 data was used for a historical examination of the various student academic strains and multilevel strengths that relate to math achievement in high school. T-tests and chi-square tests were conducted to examine differences in strains and strengths across policy-relevant student subgroups. Ordinary least squares (OLS) regression was used to examine how students’ strains and strengths related to their math achievement and the relative importance of each of these factors.FindingsThe findings suggest that both the academic strains and multilevel strengths that students’ experience in middle school are related to their high school math achievement and the prevalence of these factors varies across different policy-relevant student subgroups. Furthermore, the relative importance of these factors on achievement differs.Originality/valueStudies which focus on either students’ academic challenges or their adaptive strengths fall short of a more nuanced discussion about how both factors relate to math outcomes. This study addresses this limitation and emphasizes that stakeholders who are interested in STEM diversity should consider holistic strategies for alleviating gender and racial/ethnic discrepancies in secondary math achievement.

Self-regulation, motivation, and math achievement in middle school: Variations across grade level and math context

Computational complexity of quantifier-free negationless theory of field of rational numbers

Math anxiety (MA) and math achievement are generally negatively associated. This study investigated whether and how classroom engagement behaviors mediate the negative association between MA and math achievement. Data were drawn from an ongoing longitudinal study that examines the roles of affective factors in math learning. Participants consisted of 207 students from 4th through 6th grade (50% female). Math anxiety was measured by self-report using the Mathematics Anxiety Scale for Children (Chiu & Henry, 1990, Measurement and valuation in Counseling and Development, 23, 121). Students self-reported their engagement in math classrooms using a modified version of the Math and Science Engagement Scale (Wang et al., 2016, Learning and Instruction, 43, 16). Math achievement was assessed using the Applied Problem, Calculations, and Number Matrices subtests from the Woodcock-Johnson IV Tests of Achievement (Schrank et al., 2014, Woodcock-Johnson IV Tests of Achievement. Riverside). Mediation analyses were conducted to examine the mediating role of classroom engagement in the association between MA and math achievement. Students with higher MA demonstrated less cognitive-behavioral and emotional engagement compared to students with lower MA. Achievement differences among students with various levels of MA were partly accounted for by their cognitive-behavioral engagement in the math classroom. Overall, students with high MA exhibit avoidance patterns in everyday learning, which may act as a potential mechanism for explaining why high MA students underperform their low MA peers.

Background/Context Because of the growing concern over the decline of bachelor degree recipients in the disciplines of science, technology, engineering, and math (STEM) in the U.S., several studies have been devoted to identifying the factors that affect students’ STEM major choices. A majority of these studies have focused on factors relevant to math and science. However, few studies have addressed the linkage between technology-or engineering-related factors and students’ STEM major selection. Purpose The purpose of this study was to investigate the extent to which 10th-grade students’ engagement in computer-based learning activities in math classrooms has an effect on student STEM major selection in 4-year postsecondary institutions. After controlling for student-and school-level variables, this study explored the effects of computer-based learning activities in math classrooms on students’ STEM major selections as mediated by either math self-efficacy or math performance. Research Design The data from this study were collected from the Educational Longitudinal Study of 2002/2006 (ELS: 2002/2006) conducted by the National Center for Education Statistics of the Institute of Education Sciences in the U.S. Department of Education. ELS: 2002/2006 included a nationally representative sample of young adults who had enrolled in 4-year colleges or universities by 2006. Considering the hierarchical structure of the ELS: 2002/2006, in which students are nested within schools, I used multilevel structural equation modeling (ML-SEM) rather than traditional SEM. Findings Students’ engagement in computer-based learning activities in math classrooms had a positive effect on their STEM major selection as mediated by math self-efficacy. Specifically, student computer-based learning activities had a larger effect on students’ STEM major selection than did individual- and lecture-based learning activities. In addition, at the school level, a marginal, but significant, relationship emerged between math teachers’ motivation and students’ math performance. Conclusions This study provided evidence that it is important to incorporate computer-based learning activities into math classrooms at the secondary level. Moreover, at the school level, the significant effect of teacher motivation on students’ math achievement scores suggests that motivating teachers is an important part of STEM education, particularly given the fact that teachers are responsible for designing and implementing progressive math curricula that are embedded in computer-based learning activities.

The National Academy of Engineering “Grand Challenges for Engineering” (GCE) initiative has inspired the introduction of humanitarian applications of engineering into middle school science and math classrooms. Two GCE case study instructional modules have been developed by an interdisciplinary research team and piloted at six participating middle schools during the 2011–12 school year. Each module employs realistic fictional scenarios to engage a broad spectrum of students through role-play as engineers. Students develop engineering skills by tackling specific problems inspired by societal needs. Relevant science and math content, based on state and national middle school standards, are embedded within the modules. Integration of engineering with science and math instruction is aligned with recommendations in the Framework for National K-12 Science Standards, recently published by the National Research Council. The pilot modules, “Improving Aging Infrastructure” and “Solar Energy,” were introduced to teachers at participating schools at a professional development workshop during Summer 2011. The success of this approach as a strategy to increase interest in STEM (science, technology, engineering and math) fields among all students, especially women and under-represented groups, is being evaluated through measurement of participating students' attitudes toward math, science and STEM-related occupations.

The relationship between phonological awareness, overall language, vocabulary, and nonlinguistic cognitive skills to decoding and reading comprehension was examined for students at 3 stages of literacy development (i.e., early elementary school, middle school, and high school). Students with histories of speech sound disorders (SSD) with and without language impairment (LI) were compared to students without histories of SSD or LI (typical language; TL). In a cross-sectional design, students ages 7;0 (years;months) to 17;9 completed tests that measured reading, language, and nonlinguistic cognitive skills. For the TL group, phonological awareness predicted decoding at early elementary school, and overall language predicted reading comprehension at early elementary school and both decoding and reading comprehension at middle school and high school. For the SSD-only group, vocabulary predicted both decoding and reading comprehension at early elementary school, and overall language predicted both decoding and reading comprehension at middle school and decoding at high school. For the SSD and LI group, overall language predicted decoding at all 3 literacy stages and reading comprehension at early elementary school and middle school, and vocabulary predicted reading comprehension at high school. Although similar skills contribute to reading across the age span, the relative importance of these skills changes with children's literacy stages.

Rational number conceptualization predicts mathematics achievement: Quantity matters

The way that students cope with the difficulties and setbacks they encounter daily in their academic work can make a material difference to their learning, school success, and capacity to re-engage with challenging educational activities. Because of their potential importance to students’ everyday academic resilience, educators and researchers are interested in the development of adaptive and maladaptive ways of coping—both how they improve or deteriorate over students’ educational careers and the factors that underlie their differential development. Using information on self-reports of 5 adaptive and 6 maladaptive ways of coping, collected from 1,018 American third through sixth graders in fall and spring of the same school year, this study examined (1) the normative progression of these 11 ways of coping across fall of third to spring of sixth grade, and (2) whether developmental patterns differed for students with differing motivational resources. A generally stable profile of constructive coping was evident during Grades 3 and 4 (in which adaptive strategies were high and maladaptive responses low), followed by modest improvements across fourth to fifth grades. Marked shifts were apparent across the transition to middle school. Compared to spring of fifth grade, students in fall of sixth grade reported lower levels of all adaptive and higher levels of all maladaptive ways of coping, and this trend persisted across the first year of middle school. Although motivational resources did not produce differing developmental trends, they did seem to organize coping. Highest levels of adaptive coping were found for students high in both personal and interpersonal assets, just as the highest levels of maladaptive coping were found for students high in both personal and interpersonal liabilities. Findings suggest that both motivational and developmental approaches are needed to fully account for patterns of age-graded trends in academic coping across late elementary and early middle school.

A disconnect may exist between the taught curriculum in middle school and the real-world applications of Science Technology Engineering and Mathematics (STEM) concepts, leaving students underprepared to envision themselves in future STEM roles. This two-cycle action research study investigated the connection between middle school STEM taught curriculum and student awareness of career opportunities within STEM fields within the Northeast of the United States. Cycle 1 participants included middle school STEM teachers who were interviewed about the middle school curricular expectations and opportunities to introduce STEM careers. Following two levels of in vivo coding, the themes identified in Cycle 1 were: STEM future roles may be hard to predict; teachers need materials that they can integrate into their programmatic curriculum; and middle schoolers need to be able to comprehend information about their STEM career options. This data informed the collaborative development of an action step: the creation of career-focused videos designed to connect curriculum and workforce realities for middle school teachers. Teachers were again the participants and stakeholders in the second cycle of research, while STEM professionals served as collaborators. A triangulated approach to evaluation incorporated data from teacher focus groups, student feedback, and YouTube commentary analysis to assess the action step's effectiveness. This study found that 1. Teachers close the circuit; they are crucial curricular informants and gatekeepers, 2. Student engagement depends on the availability of materials that are both relatable and tailored to their level of understanding, and 3. Connecting professionals to students requires innovative, multimodal, and classroom-ready materials to provide a meaningful entry point for professionals and bridge the gap between theory and real-world practice. Recommendations from this study suggest curriculum enhancements that may foster stronger connections between STEM learning and the vast array of career possibilities, specifically in connecting teachers and STEM professionals.--Author's abstract

Chapter 2 - Numbers

Rational number knowledge is critical in both current and future mathematical success. Despite its importance, there is a gap in understanding regarding how children process quantitative information from discretized non-symbolic fractions when salient surface features interfere with this process. This study examines five research questions aimed at addressing this gap in 3rd to 5th grade children in the US. First, how do children spontaneously organize non-symbolic discretized fractions? Second, does the pattern vary across grade levels? Third, we tested whether math anxiety predicts children’s non-symbolic organization. Fourth, we examined whether the pattern of discretized non-symbolic fraction conceptualization correlates with their conceptualization of symbolic rational numbers. Lastly, we examined whether the ways children organize non-symbolic discretized fractions predicted their math achievement. Our sample consisted primarily of high math-achieving students. The results showed that most children organized non-symbolic fractions based on quantity or surface features, with a higher proportion showing quantitative conceptualization in higher grades. Math anxiety was not related to children’s non-symbolic fraction organization. Non-symbolic fraction organization was significantly correlated with symbolic fraction organization. Quantitative conceptualization of non-symbolic rational numbers was associated with higher math achievement. These findings shed light on how children process the magnitude of discretized fractions and provide insights into the relation among non-symbolic fraction understanding, math achievement, and math anxiety.

People’s fear and anxiety about doing math—over and above actual math ability—can be an impediment to their math achievement. We show that when the math-anxious individuals are female elementary school teachers, their math anxiety carries negative consequences for the math achievement of their female students. Early elementary school teachers in the United States are almost exclusively female (>90%), and we provide evidence that these female teachers’ anxieties relate to girls’ math achievement via girls’ beliefs about who is good at math. First- and second-grade female teachers completed measures of math anxiety. The math achievement of the students in these teachers’ classrooms was also assessed. There was no relation between a teacher’s math anxiety and her students’ math achievement at the beginning of the school year. By the school year’s end, however, the more anxious teachers were about math, the more likely girls (but not boys) were to endorse the commonly held stereotype that “boys are good at math, and girls are good at reading” and the lower these girls’ math achievement. Indeed, by the end of the school year, girls who endorsed this stereotype had significantly worse math achievement than girls who did not and than boys overall. In early elementary school, where the teachers are almost all female, teachers’ math anxiety carries consequences for girls’ math achievement by influencing girls’ beliefs about who is good at math.

Paraeducators are foundational to the success of inclusive education programs, yet little is known about how students experience their support over time. The aim of the study was to determine the meaning of the physical and symbolic presence of paraeducator support in physical education across elementary (approximately ages 6–11), middle (ages 12–14), and high school years (ages 15–18) for students experiencing physical impairment. Using an interpretative phenomenological analysis and life story research approach, data were retrospectively gathered as the participants looked back on their school experiences. The thematic analysis of one-on-one semi-structured interviews of five participants (3 women and 2 men), aged 18–30 years (average age 23) generated three themes. The themes were (a) initially I didn’t question their (in)action, (b) over time, their presence created social interaction barriers, and (c) blurred boundaries of friendship, independence, and interdependence. Relational ethics provided the conceptual framework for the study. In elementary school, the participants reflected on their impoverished engagement in physical education as their paraeducators looked on. In early middle school, the physical presence and over protection of paraeducators thwarted social skill development leading to social dependence, distancing the participants from their peers. Toward late middle school, the participants found themselves negotiating relational boundaries to gain independence yet preserve beneficial interdependence. In high school the participants lamented the loss of their paraeducators as valuable communication conduits, leaving them feeling abandoned. The participants recommended that during the elementary years paraeducators provide meaningful strategies for participation. Further, during upper elementary and middle school years, paraeducator support should be discretionary, with students (and parents) determining support requirements, in anticipation of an increasing need for autonomy during high school years.

Prior research has demonstrated the scope and impact of adverse childhood experiences (ACEs) on health and wellbeing. Less is known about the trajectories from exposure to ACEs, such as witnessing family conflict and violence in the community, to teen dating violence perpetration, and the protective factors that buffer the association between early exposure to ACEs and later teen dating violence perpetration. Students (n = 1611) completed self-report surveys six times during middle and high school from 2008 to 2013. In early middle school, the sub-sample was 50.2% female and racially/ethnically diverse: 47.7% Black, 36.4% White, 3.4% Hispanic, 1.7% Asian/Pacific Islander, and 10.8% other. Youth were, on average, 12.7 years old. Latent transition analysis was used to assess how trajectories of exposure to parental conflict and community violence during middle school transition into classes of teen dating violence perpetration (e.g., sexual, physical, threatening, relational, and verbal) in high school. Protective factors were then analyzed as moderators of the transition probabilities. Three class trajectories of ACEs during middle school were identified: decreasing family conflict and increasing community violence (n = 103; 6.4%), stable low family conflict and stable low community violence (n = 1027; 63.7%), stable high family conflict and stable high community violence (n = 481; 29.9%). A three class solution for teen dating violence perpetration in high school was found: high all teen dating violence class (n = 113; 7.0%), physical and verbal only teen dating violence class (n = 335; 20.8%), and low all teen dating violence class (n = 1163; 72.2%). Social support, empathy, school belonging and parental monitoring buffered some transitions from ACEs exposure trajectory classes to teen dating violence perpetration classes. Comprehensive prevention strategies that address multiple forms of violence while bolstering protective factors across the social ecology may buffer negative effects of exposure to violence in adolescence.