Reasonable or Not? A Study of the Use of Teacher Questioning to Promote Reasonable Mathematical Answers from Sixth Grade Students

In this action research study of my sixth grade mathematics class, I investigated the influence a change in my questioning tactics would have on students’ ability to determine answer reasonability to mathematics problems. During the course of my research, students were asked to explain their problem solving and solutions. Students, amongst themselves, discussed solutions given by their peers and the reasonability of those solutions. They also completed daily questionnaires that inquired about my questioning practices, and 10 students were randomly chosen to be interviewed regarding their problem solving strategies. I discovered that by placing more emphasis on the process rather than the product, students became used to questioning problem solving strategies and explaining their reasoning. I plan to maintain this practice in the future while incorporating more visual and textual explanations to support verbal explanations.

Review of The Elemental Prairie: Sixty Tallgrass Plants (Watercolors and introduction) by George Olson

The Elemental Prairie provides a general discussion of the Great Plains and the tallgrass prairie for the general reader. Its botanically accurate plant drawings render a beautiful and artistic view into prairie plants. George Olson writes a compelling introduction about "Prairie Elements," painting a graphic verbal description about his trip into the prairie with noted prairie author John Madson. The introduction draws readers into the book and prepares them for John Madson's essay "The Running Country," an eloquent portrayal of the history of the tallgrass prairie. We are led into the hearts and minds of the pioneers who crossed the immense expanse of the Great Plains. Madson's descriptions of prairie plants help us visualize how the Great Plains looked prior to settlement, stirring us to see not only the allure of the prairies, but also the solitude and sometimes the loneliness. Madson mixes his personal experiences with current scientific theory of the formation of the prairies across the region, offering a way of seeing how the present fits into the past.

Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

THE ROLE OF INDUSTRY IN DEVELOPING NEW MATERIALS FOR VERTEBRATE PEST CONTROL

In the first paper presented to you today by Dr. Spencer, an expert in the Animal Biology field and an official authority at the same time, you heard about the requirements imposed on a chemical in order to pass the different official hurdles before it ever will be accepted as a proven tool in wildlife management. Many characteristics have to be known and highly sophisticated tests have to be run. In many instances the governmental agency maintains its own screening, testing or analytical programs according to standard procedures. It would be impossible, however, for economic and time reasons to work out all the data necessary for themselves. They, therefore, depend largely on the information furnished by the individual industry which naturally has to be established as conscientiously as possible. This, among other things, Dr. Spencer has made very clear; and this is also what makes quite a few headaches for the individual industry, but I am certainly not speaking only for myself in saying that Industry fully realizes this important role in developing materials for vertebrate control and the responsibilities lying in this. This type of work - better to say cooperative work with the official institutions - is, however, only one part and for the most of it, the smallest part of work which Industry pays to the development of compounds for pest control. It actually refers only to those very few compounds which are known to be effective. But how to get to know about their properties in the first place? How does Industry make the selection from the many thousands of compounds synthesized each year? This, by far, creates the biggest problems, at least from the scientific and technical standpoint. Let us rest here for a short while and think about the possible ways of screening and selecting effective compounds. Basically there are two different ways. One is the empirical way of screening as big a number of compounds as possible under the supposition that with the number of incidences the chances for a "hit" increase, too. You can also call this type of approach the statistical or the analytical one, the mass screening of new, mostly unknown candidate materials. This type of testing can only be performed by a producer of many new materials,that means by big industries. It requires a tremendous investment in personnel, time and equipment and is based on highly simplified but indicative test methods, the results of which would have to be reliable and representative for practical purposes. The other extreme is the intellectual way of theorizing effective chemical configurations. Defenders of this method claim to now or later be able to predict biological effectiveness on the basis of the chemical structure or certain groups in it. Certain pre-experience should be necessary, that means knowledge of the importance of certain molecular requirements, then the detection of new and effective complete molecules is a matter of coordination to be performed by smart people or computers. You can also call this method the synthetical or coordinative method.