Learning Statistics Through Exemplars

This paper implements recent proposals for enhancing the learning of mathematics by developing statistics instruction and assessment for eighth grade students that c^italizes on the use of exemplars. The goal of instruction was for small groups to learn about statistics by engaging in hands-on activities as well as to ^ply their knowledge and skills by creating statistics projects tfiat involved designing, conducting, and presenting a mini-experimeni. Performance criteria which reflected the statistical concepts taught in the instruction were explained to students to ensure their understanding of the task (i.e., project). Groups were assigned to two treatments-exemplars and nonexemplars?Av'hich differed in the degree to which criteria modeled the processes of hypothesis generation, data collection, data analysis, and graphic representation. The effectiveness of elaborating on criteria through examples and text (i.e., exemplars) or just text (i.e., nonexemplars) for enhancing learning was examined. Both treatments demonstrated significant performance gains from pretest to posttest. However, students' understanding of representative sampling was significantly better as a result of receiving the exemplars treatment than the nonexemplars treatment. Making criteria more elaborate through examples of performance can thus enhance students' understanding of more abstfact statistical concepts such as sampling

Crop pests and predators exhibit inconsistent responses to surrounding landscape composition

The idea that noncrop habitat enhances pest control and represents a win–win opportunity to conserve biodiversity and bolster yields has emerged as an agroecological paradigm. However, while noncrop habitat in landscapes surrounding farms sometimes benefits pest predators, natural enemy responses remain heterogeneous across studies and effects on pests are inconclusive. The observed heterogeneity in species responses to noncrop habitat may be biological in origin or could result from variation in how habitat and biocontrol are measured. Here, we use a pest-control database encompassing 132 studies and 6,759 sites worldwide to model natural enemy and pest abundances, predation rates, and crop damage as a function of landscape composition. Our results showed that although landscape composition explained significant variation within studies, pest and enemy abundances, predation rates, crop damage, and yields each exhibited different responses across studies, sometimes increasing and sometimes decreasing in landscapes with more noncrop habitat but overall showing no consistent trend. Thus, models that used landscape-composition variables to predict pest-control dynamics demonstrated little potential to explain variation across studies, though prediction did improve when comparing studies with similar crop and landscape features. Overall, our work shows that surrounding noncrop habitat does not consistently improve pest management, meaning habitat conservation may bolster production in some systems and depress yields in others. Future efforts to develop tools that inform farmers when habitat conservation truly represents a win–win would benefit from increased understanding of how landscape effects are modulated by local farm management and the biology of pests and their enemies

Minimum Information about a Biosynthetic Gene cluster

A wide variety of enzymatic pathways that produce specialized metabolites in bacteria, fungi and plants are known to be encoded in biosynthetic gene clusters. Information about these clusters, pathways and metabolites is currently dispersed throughout the literature, making it difficult to exploit. To facilitate consistent and systematic deposition and retrieval of data on biosynthetic gene clusters, we propose the Minimum Information about a Biosynthetic Gene cluster (MIBiG) data standard.Chemistry and Chemical Biolog

Authentic assessment : a library of exemplars for enhancing statistics performance

This manuscript incorporates recent proposals for enhancing the learning of mathematics by developing authentic statistics instruction and assessment for eighth grade students based on a cognitive apprenticeship approach. The goal of instruction was for small groups to create statistics projects that addressed a meaningful research question. To ensure that criteria for assessing such performance were understood, groups were assigned to two treatments--library of exemplars and text--which differed in the degree to which criteria were explicit. The effectiveness of elaborating on criteria through examples (i.e., library) or text (i.e., text) for enhancing learning was examined. Both treatments demonstrated significant performance gains from pretest to posttest. However, students' understanding of representative sampling was significantly better as a result of receiving the library treatment than the text treatment. Making criteria more elaborate through examples of performance can thus enhance students' understanding of more abstract statistical concepts such as sampling

Project-based investigations for producing and critiquing statistics

This study was designed to address the need for learning opportunities that enable adolescents to become producers and critics of statistics. The producer/critic model (Palinscar & Brown, 1984) was adapted to the context of statistical investigation where questions are formulated and data are subsequently collected, analyzed, and represented to address this question (Graham, 1987). In the producer phase learners design, conduct, and present a group investigation to peers. In the critic phase, groups evaluate investigations produced by unknown peers which are presented in a computer-based learning environment, Critiquing Statistics (CS). The critic phase served as the intervention and was expected to yield three positive outcomes: (1) sophisticated statistical reasoning; (2) a strong understanding of statistical investigation; and (3) a close alignment of evaluations between learners and experts due to successful internalization of criteria. However, the effects of the intervention were also expected to be mediated by the types of questions investigated and the nature of group collaborations. These outcomes were assessed by comparing groups that participated in the critic phase (intervention) with those that did not (control). Investigations produced and evaluated from the first to the second producer phase provided the basis for this comparison. Six groups of three students participated in the study. The descriptive analyses yielded mixed results. As expected, the types of questions investigated and the nature of group collaborations interacted with reasoning and understanding. These two factors accounted for the quantity and quality of reasoning that were higher initially in the control than in the intervention. How groups defined the task based on their questions explained the larger amount of understanding initially found in the intervention compared to the control. However, the intervention's effect was to enhance the quality of understanding on more aspect

Statistical reasoning of middle school children engaged in survey inquiry

The case study examined two groups of grade 7 students as they engaged in four inquiry phases: posing a question and collecting, analyzing, and representing data. Previous studies reported analyses of statistical reasoning on a single inquiry phase. Our goal was to identify the modes of statistical reasoning displayed during group discussions in all phases as children designed and conducted their own inquiry. A content analysis of audio and video recorded discussions yielded 10 statistical reasoning modes: six relate to Garfield and Gal’s [Garfield, J., Gal, I. (1999). Teaching and assessing statistical reasoning. In L. V. Stiff, & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12. 1999 Yearbook (pp. 207–219). Reston, VA: National Council of Teachers of Mathematics] statistical reasoning types involved in the collection, analysis, and representation of data and four modes deal with an aspect of inquiry not exclusively focused upon in the literature on statistical reasoning—i.e., the problem-posing phase. Although students’ reasoning reflected an incomplete understanding of statistics they serve as building blocks for instruction

Communicating performance criteria to students through technology

A project that uses computer and video technology to help students understand the criteria used to evaluate their statistics projects is describe

Empowering children in the use of statistics

Statistics pervade our society, yet the understanding of statistics has remained the domain of a select few. Although the majority of the literature has focused on the adult learner, there is a movement toward teaching statistics to children. This article addresses the ways in which the study of statistics has been examined in the elementary and secondary schools in terms of content, readiness of children to learn, pedagogy, and assessment. A proposal is presented of how a cognitive apprenticeship model can be developed from the empirical research findings in order to build more effective instructional and assessment methods for statistics education