Development of a Framework to Characterise the Openness of Mathematical Tasks

Educators usually mean different constructs when they speak of open tasks: some may refer to pure-mathematics investigative tasks while others may have authentic real-life tasks in mind; some may think of the answer being open while others may refer to an open method. On the other hand, some educators use different terms, e.g. open and open-ended, to mean the same construct, while others distinguish between these terms. It is difficult to hold a meaningful discussion or to define clearly an area of research on open tasks if the idea of what constitutes the construct of openness is vague. Moreover, what students learn depends on the types of tasks that they are given, and different kinds of tasks place differing cognitive demands on students. Thus, the objectives of this article are to clarify the types of mathematical tasks and develop a framework to characterise their openness based on five task variables: goal, method, task complexity, answer and extension; and to discuss how different types of tasks and openness may affect student learning. The openness framework can help teachers to design or select more appropriate tasks to cater to students with different abilities in order to develop in them various kinds of mathematical thinking processes, and it can also make it easier for researchers to study the interaction between different types of openness and student learning.     

A test-retest analysis of the Vanderbilt Assessment for Leadership in Education in the USA

The Vanderbilt Assessment for Leadership in Education (VAL-ED) is a 360-degree learning-centered behaviors principal evaluation tool that includes ratings from the principal, supervisors, and teachers. The current study assesses the test-retest reliability of the VAL-ED for a sample of seven school districts as part of multiple validity and reliability assessments based on various samples of real users of the VAL-ED. We administered the VAL-ED twice and examined the correlations and mean differences between time 1 and time 2. We find that the principal and teacher ratings from time 1 and time 2 have large, positive, and significant correlations. Additionally, for both time points, principals are rated as being at least satisfactorily effective. Principals rate themselves slightly higher at time 2, while teachers rate principals slightly higher at time 1.     

Subgroups of adult basic education learners with different profiles of reading skills

The purpose of this study was to identify subgroups of adult basic education (ABE) learners with different profiles of skills in the core reading components of decoding, word recognition, spelling, fluency, and comprehension. The analysis uses factor scores of those 5 reading components from on a prior investigation of the reliability and construct validity of measures of reading component skills (MacArthur, Konold, Glutting, & Alamprese, 2010). In that investigation, confirmatory factor analysis found that a model with those 5 factors fit the data best and fit equally well for native and non-native English speakers. The study included 486 students, 334 born or educated in the United States (native) and 152 not born nor educated in the US (non-native) but who spoke English well enough to participate in English reading classes. The cluster analysis found an 8-cluster solution with good internal cohesion, external isolation, and replicability across subsamples. Of the 8 subgroups, 4 had relatively flat profiles (range of mean scores across factors <0.5 SD), 2 had higher comprehension than decoding, and 2 had higher decoding than comprehension. Profiles were consistent with expectations regarding demographic factors. Non-native speakers were overrepresented in subgroups with relatively higher decoding and underrepresented in subgroups with relatively higher comprehension. Adults with self-reported learning disabilities were overrepresented in the lowest performing subgroup. Older adults and men were overrepresented in subgroups with lower performance. The study adds to the limited research on the reading skills of ABE learners and, from the perspective of practice, supports the importance of assessing component skills to plan instruction.     

Cowboys,Angels, and Demons: American Exceptionalism and the Frontier Myth in the CW's Supernatural

The CW network series Supernatural (2005–) draws its text from the horror and fantasy genres as well as religious mythology. Concurrently, it transmits a core “American” mythos. As its protagonists keep watch along a supernatural frontier and eradicate threats to the American way of life, this program both reinforces and alters aspects of the frontier myth and the myth of American exceptionalism by depicting its main characters as representations of America writ large whose mission has grown from an appointment by God to being equals to God. In this manner, Supernatural forwards a new American exceptionalism through the notion that America is exceptional because it is not just divinely appointed by God, but is divine itself.     

Eco‐Webbing: A Teaching Strategy to Facilitate Critical Consciousness and Agency

Eco‐webbing is a teaching strategy that can be used to help counselor educators integrate a social justice focus into their courses. Preliminary data indicated increased critical consciousness and social justice agency as a result of using eco‐webbing with counseling students (N = 17). The authors provide implications for counselor educators and future research.     

A Subtle Tyranny: Rediscovering the Purpose of the Liberal Arts

Discord in the academy currently manifests in divisions over political correctness, the content of the canon and the defects of modernity. As scholarly and intellectual matters these concerns arise exclusively from the domain of the liberal arts. At their core, these controversies arguably develop from deep epistemic roots reflecting fundamental differences concerning the nature, purpose and value of the liberal arts. At issue is the integrity of the liberal arts and understanding the nature, purpose and value of these fields depends upon appreciating the distinction between professional, theoretical, and moral studies. One can begin to understand these distinctions by considering the contrast in ordinary language between knowledge and wisdom. For it is arguable that while the notion of wisdom is presumably irrelevant to production or dissemination of knowledge in all other disciplines, it is demonstrably central to the purpose and value of both research and teaching in each and every liberal art. If this can be shown then it is possible to understand why emphasis on expertise and professionalism, on knowledge for its own sake undermines commitment to common purposes and concerns. By institutionalizing new patterns of behavior, stress on professionalism changes the nature and conception of liberal arts scholarship in ways that produce deep confusions about meaning and value in these fields. The object of this article is to show that unlike other disciplines the liberal arts depend upon shared purposes and concerns such that participation of in a common moral discourse is essential to the integrity and worth of each field.     

Reasons for Utilizing Mental Health Services as Predictors of College Students’ Alcohol Risk

The authors examined college student drinkers’ (n = 153) reasons for seeking counseling services and risk for alcohol problems. Students seeking help for impulse‐ or anger‐related issues and depression were at heightened risk for alcohol problems. Only 10% of students sought alcohol‐related help despite high rates of hazardous alcohol use (80%) and dependence (39%). Targeted screening and intervention in college counseling centers may enable providers to effectively identify and treat students in need of alcohol treatment.     

Monitoring Reading Growth: Goal Setting,Measurement Frequency,and Methods of Evaluation

This study examined effects of goal setting, frequency of progress monitoring, and method of evaluating progress on the number of instructional change prompts generated by reading‐curriculum‐based measurements (CBM). Participants were 31 high‐incidence special education students in grades 2–6 selected from 8 schools. Following baseline measurements, researchers administered grade‐level CBM passages every 2 weeks for 8 weeks. Comparisons included 3 goal levels (0.5, 1.0, or 1.5 word growth per week), 3 monitoring/evaluation schedules (every 2, 4, or 8 weeks), and 2 methods for evaluating progress (points below the aim line or slope). Overall, more ambitious goals, less frequent monitoring, and using slope to evaluate progress generated more instructional change prompts. Results favored less frequent monitoring and using slope to evaluate progress.