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.

     

Leg Muscle Metabolism in Trained and Untrained Men

The purpose of this study was to describe substrate changes in blood and muscles during submaximal exercise and to look at the relationship of these changes to some enzyme activities important in lipid and carbohydrate metabolism. A group of six trained and six untrained men were exercised for 1 hour at 50% [Vdot]O₂ max; three from each group cycled and the rest ran on a treadmill. During the exercise, blood-free fatty acid (FFA) levels increased twofold, glycerol by 3.6 times, triglyceride (TG) by 11/100 ml, and glucose by a mean 11 mg/100 ml in the trained men. In the untrained subjects, however, FFA increased 1.8 fold, glycerols 1.6 fold, and TG by a mean 24/100 ml. Glucose fell in every subject by an average 5 mg%. Muscle glycogen depletion averaged 34 mmoles/kg in the untrained and 23 mmoles/kg in the trained group. The activities of succinic acid dehydrogenase (SDH), malic acid dehydrogenase (MDH), and carnitine palmityl transferase (CPT) were greater by 177%, 93%, and 64%, respectively, in the trained group than in the untrained subjects. The results indicated that at the same percent [Vdot]O₂ max, the trained men seemed to “preferentially” use FFA as an energy source, possibly due to a well developed Krebs cycle and increased CPT activities. This preference would tend to inhibit the major rate-limiting enzymes of glycolysis, thus slowing even further the use of carbohydrates as an energy source. The differences in response to exercise were independent of fiber type and indicate that these catabolic responses were primarily due to aerobic training.     

Obscenity and fabrication in equity and widening participation methodologies

Equity and widening participation (EWP) initiatives in Australia are increasingly reimagined in policy as sites where participants are constructed as competitor-individuals, with education considered only in terms of employability, social mobility and nation-state market competition. In the context of EWP outreach, and with school students in particular, this can transpire into demands for narrow forms of ‘legitimate’ aspirations. Goffman defines obscenity as when (1) the very intimate is forced into the public sphere, while (2) the humanising dimensions or contexts are stripped away, with an example being pornography—where intimate encounters are reproduced as de-contextualised acts while being made public. This article argues that dominant approaches to practicing and evaluating EWP risk obscene consequences if they force community members to present static future-oriented valuations of intimate, fluid aspirations and experiences of education against a backdrop of increasingly individuated, competitive and standardised educational institutions. In this article, firstly we detail the context to establish a foundation for theorising consequences of particular socio-educational discursive practices. Secondly, we engage with notions of frame, keying and fabrication as a toolbox to reveal some of the unintended (obscene) dynamics risked via certain approaches to programmatic practice and evaluation. Thirdly, we review the diversity of approaches to evaluation (and their attendant debates), highlighting the importance of these debates and diversities, making a case against methodological imperialism.     

Methodological concerns: the feeling-of-knowing task affects resolution

In traditional feeling-of-knowing procedures, participants make judgments on unrecalled items only (e.g. Hart 1965). However, many researchers elicit feeling-of-knowing judgments (FOKs) on all items. When FOKs are made on all items, participants may use recall as a basis for judgments, leading to higher magnitude judgments for recalled items, but causing a relative floor effect for judgments for unrecalled items. We suspected that resolution (relative accuracy) would be better when FOKs are made on all items than when they are made on unrecalled items only. We examined the issue by comparing across studies, reanalyzing data from another experiment, and by conducting an original experiment. In the literature review, we included 83 conditions across 52 studies. We found that feeling-of-knowing judgments made on all items showed higher resolution than feeling-of-knowing judgments made on unrecalled items. This was replicated in the reanalysis of existing data of a single study that used both methods. In the original experiment, we collected feeling-of-knowing judgments for general-information questions. The experiment confirmed that resolution for predicting recognition was higher when feeling-of-knowing judgments were made on all items than when they were made only on unrecalled items. We discuss both methodological and theoretical implications of these data.     

Paul F-Brandwein 2004 Lecture: Regarding the Ecology of Science Education: Connections to Environmental and Distance Education

Paul F-Brandwein was a visionary who looked at education broadly. He left us with an insightful view of the ecology of education in which he identified three ecological systems: school–family–community, postsecondary, and cultural. The first part of this lecture, by Dean B. Bennett, examines Brandwein's ideas related to environmental education and explores the relationship of environmental education with science teaching in the K-12 school–family–community ecosystem. Focusing particularly on the middle-secondary level, evidence suggests that the goals of environmental education, since their emergence in the late 1960s, are today strongly evident in science curricula, instructional resources, educational assessment, and teacher education. But the author points out that more must be done and provides some fundamental suggestions. The second part of the lecture, by Sheila K. Bennett, examines the role of distance education in the teaching of science in the postsecondary ecosystem and addresses its value as a viable tool in promoting scientific literacy. The lecture focuses on a successful statewide, interdisciplinary laboratory science course delivered by interactive television, the Internet, and computer network. Now in its ninth year, the course reflects Brandwein's thinking about effective classroom teaching and is based on national standards for scientific literacy.     

University staff mental health literacy,stigma and their experience of students with mental health problems

Despite high rates of mental disorders in university students, very few seek professional help. University teaching staff are well placed to connect students with mental health care. However, little is known about university staff attitudes to and knowledge about mental health problems, or whether these factors influence their experience with and assistance of students with these problems. A total of 224 teaching staff members at the Australian National University, Canberra completed an anonymous online survey via an email link (16.4% response rate from N ~ 1370). Measures included demographic and professional information, experiences with student mental health, knowledge of depression (literacy) and attitudes to depression (stigma). Strength of stigmatising attitude did not predict whether a teaching staff member would approach a student to assist with mental health problems. Teaching staff with higher levels of depression literacy (OR = 1.14, p = 0.007) were more likely to feel sufficiently informed to help students with mental health problems. Ensuring staff complete mental health literacy training and have adequate skills to respond appropriately to students with mental health problems may help in connecting young people to appropriate care in a university context.     

Social transmission of information about multiflavored foods

We fed demonstrator rats diets made by adding three, four, or five different flavorants to powdered Purina Rat Chow. We then allowed each of these demonstrator rats to interact with a naive observer rat for 30 min. We found that (1) observers exhibited enhanced preferences for many of the individual flavorants in the multiflavored diets that their respective demonstrators had eaten and (2) the probability of an observer exhibiting enhanced preference for an individual flavorant in its demonstrator’s diet decreased as the number of flavorants in that diet increased. In Experiment 2, the individual members of pairs of subjects were each fed one of two different four-flavored diets. The subjects in each pair interacted for 30 min, then each chose between two single-flavored diets. One of these single-flavored diets contained a flavorant in the four-flavored food that a subject had itself eaten; the other single-flavored diet contained a flavorant in the four-flavored diet that a subject’s partner had eaten. The subjects showed enhanced preferences for six of eight flavorants in the four-flavored diets that their respective partners had eaten.     

Behavioral profiles of children with epilepsy: Parent and teacher reports of emotional,behavioral, and educational concerns on the BASC‐2

The Behavior Assessment Scale for Children – Second Edition (BASC‐2) was administered to 108 parents and 37 teachers of children with epilepsy (mean age of 10.6 years; 51% female, 49% male). Results demonstrated high mean scores on the Atypicality, Attention Problems, Withdrawal, and Adaptive Skills scales and a high percentage of At‐Risk or Clinically Significant scores on the majority of scales. Ratings were correlated with level of functioning, age of onset, and number of antiepileptic medications. In addition, children with poor seizure control had higher ratings on the Depression, Somatization, and Withdrawal scales, and children with temporal lobe seizures had higher scores on the Depression scale. These results confirm a high rate of behavioral concerns in children with epilepsy. © 2008 Wiley Periodicals, Inc.     

Childhood acquired brain injury: the knowledge and training needs of special educational needs coordinators

The aim of this study was to further explore Special Educational Need Co-ordinators' (SENCos) knowledge of childhood acquired brain injury (ABI) and if they have received training on how to effectively support children and young people (CYP) with an ABI in school. SENCos from Nottinghamshire were asked to complete a survey face-to-face or online. Data reported by Howe and Ball (Support for Learning, 32, 1, 85–100), was also used to allow comparisons between different counties in the UK for knowledge of childhood ABI. Results indicated that SENCos from Nottinghamshire hold numerous uncertainties about childhood ABI, although less uncertainties than SENCos from the West Midlands. A majority SENCos from Nottinghamshire had not received training about childhood ABI. Additional challenges in supporting CYP with an ABI were also identified. The findings show a clear need for more training on childhood ABI across UK schools. It is also apparent that obtaining funding for CYP with an ABI can be a challenge for SENCos. However, further research is needed to determine what these barriers to funding are.