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.

     

Does slow and steady win the race?: Clustering patterns of students’ behaviors in an interactive online mathematics game

Educational technology research and development - Online educational games have been widely used to support students’ mathematics learning. However, their effects largely depend on...     

A Campus-Wide Study of STEM Courses: New Perspectives on Teaching Practices and Perceptions

At the University of Maine, middle and high school science, technology, engineering, and mathematics (STEM) teachers observed 51 STEM courses across 13 different departments and collected information on the active-engagement nature of instruction. The results of these observations show that faculty members teaching STEM courses cannot simply be classified into two groups, traditional lecturers or instructors who teach in a highly interactive manner, but instead exhibit a continuum of instructional behaviors between these two classifications. In addition, the observation data reveal that student behavior differs greatly in classes with varied levels of lecture. Although faculty members who teach large-enrollment courses are more likely to lecture, we also identified instructors of several large courses using interactive teaching methods. Observed faculty members were also asked to complete a survey about how often they use specific teaching practices, and we find that faculty members are generally self-aware of their own practices. Taken together, these findings provide comprehensive information about the range of STEM teaching practices at a campus-wide level and how such information can be used to design targeted professional development for faculty.     

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.     

RELIABILITY AND STRUCTURAL VALIDITY OF THE TEACHER RATING SCALES OF EARLY ACADEMIC COMPETENCE

Currently, there are few strengths‐based preschool rating scales that sample a wide array of behaviors believed to be essential for early academic success. The purpose of this study was to assess the factor structure of a new measure of early academic competence for at‐risk preschool populations. The Teacher Rating Scales of Early Academic Competence (TRS‐EAC) includes two broad scales (Early Academic Skills and Early Academic Enablers) and was completed by 60 teachers for 440 children enrolled in Head Start and public preschool classrooms. Evidence from two exploratory factor analyses supported a five‐factor solution for the Early Academic Skills Scale (Creative Thinking, Critical Thinking Skills, Numeracy, Early Literacy, and Comprehension) and a five‐factor solution for the Early Academic Enablers Scale (Approaches to Learning, Social and Emotional Competence, Fine Motor Skills, Gross Motor Skills, and Communication). TRS‐EAC scores also demonstrated good to excellent reliability and were related to children's performance on direct measures of early academic skills.     

Envisioning Equitable Classrooms That Enhance All Students’ Wonderful Ideas: A Duckworth Perspective

This synopsis centers on Eleanor Duckworth’s ideas about the relationship between education and intellectual development. Specifically, Duckworth described the essence of intellectual development as the “having of wonderful ideas” and the essence of pedagogy as the creation of occasions to “have wonderful ideas.” As opposed to accepting the persistent, pernicious educational belief that there is a single, best way to understand and a single, best way of explaining this understanding, Duckworth determined that all children can come to comparable, equally satisfactory, wonderful understandings when provided occasions to do so.     

Quality of Life Assessment for Physical Activity and Health Promotion: Further Psychometrics and Comparison of Measures

Despite the clear relationship between physical activity and quality of life, few sound, relevant quality of life measures exist. Gill and colleagues developed a 32-item quality of life survey, and provided initial psychometric evidence. This study further examined that quality of life survey in comparison with the widely used short form (SF-36) health survey. Participants (n = 446) completed the quality of life survey, short form (36) health survey, World Health Organization quality of life measure, satisfaction with life scale, and the Godin physical activity measure. All quality of life survey scales (emotional, social, spiritual, physical, activities of daily living, cognitive, integrated) were internally consistent (alpha .79–.95) and test–retest correlations ranged from .68 to .82. The SF-36 had similar internal consistency, slightly lower test–retest correlations, and weaker relationships with satisfaction with life scale. Quality of life survey scales correlated with matching SF-36 and World Health Organization quality of life measure subscales supporting convergent validity. The quality of life survey reflects positive health models better than the SF-36, and is more appropriate for research and programs that focus on physical activity and health promotion.     

Lower limb moments differ when towing a weighted sled with different attachment points

Sprinting while towing a sled improves sprinting parameters, however, only kinematic and temporal–spatial variables have been reported. The purpose of this study was to determine how lower extremity joint moment impulses alter when towing a sled compared to normal walking. Twelve participants walked normally, walked while towing a sled with a 50% body weight load attached at the waist, and with a 50% body weight load attached at the shoulders. Joint moment impulses were calculated for the hip, knee, and ankle. A mixed-model ANOVA with a between-subject factor of limb and repeated measures of condition was used to compare differences between limbs and towing conditions for each joint. Towing a sled increased joint moment impulses at the hip, knee, and non-dominant ankle. When compared with normal walking waist attachment increased hip extension moment impulse by 214.5% ( ? 3.31 vs. ? 10.41 Nms/kg), and shoulder attachment increased knee extension moment impulse by 166.9% (4.62 vs. 12.33 Nms/kg). The dominant limb produced greater knee extension moment impulse (p < 0.001), while the non-dominant limb produced greater hip extension (p < 0.001) and ankle plantarflexion moment impulse (p < 0.001) across all conditions. Results suggest that walking while towing may increase hip and knee extension strength.     

Reliability of power output measurements during repeated treadmill sprinting in rugby players

The non-motorized treadmill system initially reported by Lakomy in 1984 has been used extensively to assess sprinting performance. However, there has been limited research into the reliability of power output measurement using such systems. The aim of this study was to design a system and protocol capable of measuring treadmill sprinting performance in rugby players and to assess the reliability of this system for measuring power output. Twenty-seven rugby players, all of whom were familiar with treadmill sprinting, performed three maximal 6 s sprints with 2 min recovery between sprints, on two occasions 1 week apart. Both tests were performed on a non-motorized Woodway tramp treadmill, interfaced to a data acquisition system. There were no significant differences ( P > 0.05) between power output for repeated trials on the same day (between trials) or for repeated trials on different days (between days). Limits of agreement for maximum average power (the average of 100 readings per second) were 4 - 98 and 30 - 157 W for between trials and between days, respectively. When reported as ratio limits of agreement, these were 1.07 (*/ 1 1.12) and 1.03 (*/ 1 1.16), respectively. The limits of agreement for maximum instantaneous power (the highest of 100 readings per second) were 51 - 464 and 105 - 588 W for between trials and between days, respectively. When reported as ratio limits of agreement, these were 1.02 (*/ 1 1.20) and 1.04 (*/ 1 1.21) for between trials and between days, respectively. The coefficients of variation for all measures of power output were less than 9.3%. Hence, the treadmill system and protocol developed in this study provide a reliable measure of power output for rugby players.