Mathematical Modeling in the Elementary Grades: Developing and Testing an Assessment

Mathematical modeling is a high-leverage topic, critical for college and career readiness, participation in STEM education, and civic engagement. Mathematical modeling involves connecting real-world situations, phenomenon, and/or data with mathematical models, and in this way applies across various STEM disciplines, including mathematics, engineering, and science. Although research has begun to explore mathematical modeling instruction in the elementary grades, questions remain about how to assess student learning at the elementary level. We addressed this need by designing an assessment of mathematical modeling competencies for students in grades 3 through 5. Informed by international research, our assessment includes a hybrid structure to assess mathematical modeling competencies holistically (as students engage in the complete modeling process) and atomistically (as students engage in different components of the modeling process, including making sense of phenomena and real-world situations, setting up and operating on mathematical models, and interpreting results in relation to the real-world context). We conducted student interviews, followed by two rounds of pilot testing to inform item development and ensure acceptable psychometric properties. The final assessment included 13 items (9 multiple choice, 3 open-response, and 1 complete modeling task). We describe our assessment development process, and provide sample assessment items and detailed coding rubrics. We summarize quantitative analyses which established high reliability and low standard error for our assessment, supporting its use for grades 3 to 5. Implications of our framework and assessment for mathematical modeling instruction and future research on STEM learning are discussed.

     

Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability

The purpose of this study is to introduce a measure of standards-based mathematics teaching practices, the Mathematics Scan (M-Scan), and to examine its validity and score reliability. First, we define standards-based mathematics teaching practices based on eight dimensions that have emerged in recent conceptualizations by researchers and in the context of existing observational measures. Second, we present three sources of validity evidence: content review by experts, analysis of response processes of coders, and convergent and discriminant patterns with existing observational measures. Third, we provide evidence of inter-coder (or inter-rater) reliability through analyses of variance components and calculation of reliability coefficients, using the framework of generalizability theory. Results show the M-Scan holds promise as a useful tool in mathematics education research, measuring indicators of standards-based teaching practices unique to the subject of mathematics.     

Adoptive Gay Father Families: Parent–Child Relationships and Children's Psychological Adjustment

Findings are presented on a U.K. study of 41 gay father families, 40 lesbian mother families, and 49 heterosexual parent families with an adopted child aged 3–9 years. Standardized interview and observational and questionnaire measures of parental well‐being, quality of parent–child relationships, child adjustment, and child sex‐typed behavior were administered to parents, children, and teachers. The findings indicated more positive parental well‐being and parenting in gay father families compared to heterosexual parent families. Child externalizing problems were greater among children in heterosexual families. Family process variables, particularly parenting stress, rather than family type were found to be predictive of child externalizing problems. The findings contribute to theoretical understanding of the role of parental gender and parental sexual orientation in child development.     

The road to self-assessment: exemplar marking before peer review develops first-year students’ capacity to judge the quality of a scientific report

Lack of clarity about assessment criteria and standards is a source of anxiety for many first-year university students. The Developing Understanding of Assessment for Learning (DUAL) programme was designed as a staged approach to gradually familiarise students with expectations, and to provide opportunities for the development of the skills required to successfully complete assessment tasks. This paper investigated the students’ perceptions of the first two components of the DUAL programme, which assist first-year biology students to engage with stated assessment criteria and standards in order to develop their capacity to make judgements about scientific report exemplars, their peers’ scientific reports and ultimately their own. The study found strong evidence (96% of responses) that the marking and discussion of exemplar reports with peers and demonstrators clarified expectations of scientific report writing. A key feature of this element of DUAL was the opportunity for structured discussion about assessment criteria and standards between peers and markers (demonstrators). During these discussions, students can clarify explicit statements and develop a tacit knowledge base to enhance their ability to judge the quality of others’ work and their own. The peer review exercise (the second element of DUAL) was not rated as highly, with 65% of students finding the process helpful for improving their report. The negative reactions by a sizeable minority of students highlight the need to clearly communicate the expectations and benefits of peer review, with a focus on how the process of giving feedback to peers might benefit a student as much as receiving feedback on their own report.     

Exploring the Impact of Television Watching on Vocabulary Skills in Toddlers

With the rising incidence of television consumption in children, the aim of the present study was to investigate the impact of such habits on vocabulary skills in young children. Very little research has targeted a key cognitive skill—vocabulary—during the toddler years, which represent a critical developmental period. We recruited toddlers, aged two to three, from British child care centers. Parents indicated the television watching habits of their children in different genres (educational, cartoons, baby DVDs, adult entertainment) in order to investigate potential differential effects. We also included other key variables linked to vocabulary acquisition: short-term memory (verbal and visuo-spatial) and reading habits (fiction and educational books). The findings indicated that television did not impact vocabulary scores, either positively or negatively. Instead, reading educational books and short-term memory skills predicted vocabulary performance.     

Delivering the Discourse—Urban Adolescents' Perceptions of Physical Education

abstract

This study investigates how National Curriculum policy for England and Wales has been translated into practice as perceived by the pupils who are its recipients. Results suggest that pupil entitlement as enshrined in the National Curriculum rationale is at best being provided at the level of access to activity and pupil experiences are differentiated sharply by activity, by gender and by school. The paper suggests that the physical education National Curriculum already advantages certain pupil groups rather than others, and that changes in the discourse of physical education, exemplified by the texts of the latest official publications, will, if translated into practice, militate further against access to a curriculum relevant to all pupils.     

Do as we do and not as we say: teacher educators supporting student teachers to learn on teaching practice

This paper reports data from a larger study into the ways in which Physical Education Teacher Education (PETE) students engaged in professional learning during teaching practice (TP) in Ireland. The study comprised one umbrella case study of Greendale University, schools and PETE students that consisted of five individual cases: tetrads of PETE student teacher, cooperating teacher (CT), University tutor (UT) and School Principal (SP). Each tetrad was defined as a unique community of practice located within the wider structures of school, education and university policies on teacher education. Data were collected over one academic year using qualitative research methods and grounded theory as a systematic data analysis tool.

Findings indicate that in each of the five cases, support for PETE student learning was, to some degree, dysfunctional. In particular, it became evident that there were two conflicting teacher-learning curricula in operation. The official curriculum, expressed in policy and by SPs, UTs and CTs (also referred to as mentors), valued a PETE student who cared for pupils, had a rich pedagogical content knowledge, knew how to plan for and assess pupils’ learning, valued reflection, and was an active member of a community of practice. The unofficial but essentially more powerful enacted curriculum, encouraged PETE students to draw upon their own resources to learn pedagogical content knowledge in an isolated and unsupported manner.

The data highlight the force of the unofficial curriculum and the ways in which PETE students were guided to the core of the dysfunctional community of practice by untrained CTs (mentors) and untrained UTs. PETE students in this study learned to survive in a largely unsupportive professional learning environment and, just as theories of social reproduction intimate, indicated that they would reproduce this practice with PETE students in their care in the future.

The findings suggest that in cases similar to those studied, there is a need for teacher educators in Ireland, (in both universities and schools) to critically interrogate their personal practices and implicit theories of teacher education and to engage in training for their role. There is also evidence to suggest that PETE students in Ireland could benefit from the development of school–university partnerships that act as fundamental units of high quality professional learning. In the cases studied, this may have led to a stronger focus on the intended or official curriculum of TP, led by the revised maxim: ‘Do as we say and as we do’.     

Sagittal plane motion of the lumbar spine during ergometer and single scull rowing

Lumbar spine injury in rowers is common and ergometer rowing has been cited as a risk factor for this injury. The purpose of this study is to compare lumbar kinematics between ergometer and single scull rowing and to examine the effect of fatigue on kinematics. The sagittal lumbar spine motion of 19 elite male rowers (lumbar spine injury free in the previous six months) was measured with an electrogoniometer during a ‘step test’ on an ergometer and in a single sculling boat. Maximum range of lumbar flexion was recorded in standing for reference. Power output and heart rate were recorded during the ergometer tests. Heart rate was used as a surrogate for power output in the sculling test. Maximum lumbar flexion increased during the step test and was significantly greater on the ergometer (4.4° ± 0.9°change), compared with the boat (+1.3° ± 1.1°change), (3.1°difference, p = 0.035). Compared to the voluntary range of motion, there is an increase of 11.3% (ergometer) and 4.1% (boat). Lumbar spine flexion increases significantly during the course of an ergometer trial while changes in a sculling boat were minimal. Such differences may contribute to the recent findings linking ergometer use to lower-back injury.     

Muscular Fatigue Curves of Boys and Girls

Abstract

Exponential fatigue curves for dynamic work of the forearm muscles were obtained from 200 boys arid girls ranging from 8 through 17 years of age. The fatigue parameters analyzed in relation to initial strength were fatigable strength, steady-state equilibrium strength, and relative rate of strength loss per contraction. Older children were stronger and exhibited greater fatigue. When their strength loss and steady-state levels were considered in relation to their initial strength-capacity, there were no age differences in fatigability, and sex differences were either absent or very small. At age eight, boys and girls had equal rates of strength loss per muscle contraction. Older boys, since they exerted more strength initially, tended to reach the fatigue level more rapidly than younger children. Older girls reached their fatigue level more slowly.