Investigating peer-assessment strategies for mathematics pre-service teacher learning on formative assessment

Formative assessment practices for secondary mathematics have been advocated as valuable for students, but difficult for teachers to learn. There have been calls in the literature to increase the emphasis on formative assessment in mathematics teacher preparation courses. This study explored the use of peer-assessment strategies for helping pre-service secondary mathematics teachers (PSTs) cultivate formative assessment principles and practices for assessing school students. Twenty-seven PSTs participated in a peer-assessment cycle comprised of: sourcing a rich mathematics task; constructing an assessment rubric for it; and collecting and analysing a selection of secondary student responses to the task. Each PST then provided written and verbal feedback to a peer on his/her rubric and student solution assessments. We draw on theoretical conceptions of Teacher Assessment Literacy in Practice to characterize the PSTs’ perceptions of their experience of formative assessment processes for learning to assess school students, in terms of cognitive and affective dimensions of their conceptions of assessment. The cohort evidenced a wide range of levels of confidence with the various aspects of formative assessment practices but on average less confidence in assessing school student task responses themselves than in assessing peer work. In addition to highlighting specific changes to different types of assessment knowledge, the PSTs also evidenced an awareness of shifts in their attitudes, in coming to view student task responses with more appreciation and humility.

     

Overcoming visual obstacles with the aid of the Supposer

This paper presents research about the effect of intensive work with diagrams on high school students' use of diagrams in geometry. It identifies three obstacles, culled from previous research, which students must overcome when examining and interpreting diagrams: Diagrams are particular; common usage confuses certain standard diagrams with the classes of objects to which they belong; and a single diagram can be viewed and described in different ways. The paper outlines the resources of the Geometric Supposer, a set of microcomputer software tools which were designed to aid students in overcoming these obstacles. The bulk of the paper presents evidence from students' papers and classroom comments indicating that over the course of a year's work students using the Supposer became more facile in their use of diagrams and were able to overcome each of the three obstacles.The preparation of this paper was supported in part by the National Academy of Education's Spencer Fellowship program.     

Admission to Higher Education in Israel and the Role of the Psychometric Entrance Test: Educational and political dilemmas

This paper describes the admissions process to higher education in Israel, which is frequently debated in public. It presents the historical background, outlines the psychometric considerations, summarises the extensive research data gathered in validity and evaluation studies, and provides the social and political perspectives. The paper points to how developments in the volume and importance of higher education have affected the way upper-secondary certificates mediate university entrance. Particular reference is made as to how far the pressures are changed by the use of a psychometric entrance test. Two laws, dealing with admissions to higher education, that are currently being put to vote in the Israeli parliament, are described and discussed.     

Contribution of a contralateral hearing aid to perception of consonant voicing, intonation, and emotional state in adult cochlear implantees

Binaural hearing in cochlear implant (CI) users can be achieved either by bilateral implantation or bimodally with a contralateral hearing aid (HA). Binaural-bimodal hearing has the advantage of complementing the high-frequency electric information from the CI by low-frequency acoustic information from the HA. We examined the contribution of a contralateral HA in 25 adult implantees to their perception of fundamental frequency-cued speech characteristics (initial consonant voicing, intonation, and emotions). Testing with CI alone, HA alone, and bimodal hearing showed that all three characteristics were best perceived under the bimodal condition. Significant differences were recorded between bimodal and HA conditions in the initial voicing test, between bimodal and CI conditions in the intonation test, and between both bimodal and CI conditions and between bimodal and HA conditions in the emotion-in-speech test. These findings confirmed that such binaural-bimodal hearing enhances perception of these speech characteristics and suggest that implantees with residual hearing in the contralateral ear may benefit from a HA in that ear.     

Stage theory of the development of alternative conceptions

A systematic study of children's ideas on motion of macroscopic objects was carried out with the participation of 631 subjects in Grades 2–12 (ages 7–8 through 17–18). An open-ended, four-part questionnaire was administered to the subjects. The responses were categorized according to the level of sophistication of the answer. The results were analyzed using a mathematical model that was first applied to the development of Piagetian stages (Eckstein & Shemesh, 1992, in press). For three of the questions, the responses change as the children mature, and it appears that the children pass through distinct, successive stages with respect to their conceptual understanding of these questions. The mathematical model predicts that the proportion of subjects at each stage is a linear combination of decreasing exponentials. The model fits the experimental data well. Characteristic times for transition between stages were calculated. If teaching strategies to overcome misconceptions are to be effective, then they must be appropriate to the particular misconception prevalent at each stage.     

Do dyslexic individuals present a reduced visual attention span? Evidence from visual recognition tasks of non-verbal multi-character arrays

A controversy has recently developed regarding the hypothesis that developmental dyslexia may be caused, in some cases, by a reduced visual attention span (VAS). To examine this hypothesis, independent of phonological abilities, researchers tested the ability of dyslexic participants to recognize arrays of unfamiliar visual characters. Employing this test, findings were rather equivocal: dyslexic participants exhibited poor performance in some studies but normal performance in others. The present study explored four methodological differences revealed between the two sets of studies that might underlie their conflicting results. Specifically, in two experiments we examined whether a VAS deficit is (a) specific to recognition of multi-character arrays as wholes rather than of individual characters within arrays, (b) specific to characters’ position within arrays rather than to characters’ identity, or revealed only under a higher attention load due to (c) low-discriminable characters, and/or (d) characters’ short exposure. Furthermore, in this study we examined whether pure dyslexic participants who do not have attention disorder exhibit a reduced VAS. Although comorbidity of dyslexia and attention disorder is common and the ability to sustain attention for a long time plays a major rule in the visual recognition task, the presence of attention disorder was neither evaluated nor ruled out in previous studies. Findings did not reveal any differences between the performance of dyslexic and control participants on eight versions of the visual recognition task. These findings suggest that pure dyslexic individuals do not present a reduced visual attention span.     

Instrument Development and Validation of the Infant and Toddler Assessment for Quality Improvement

Research Findings: There is a growing need for accurate and efficient measures of classroom quality in early childhood education and care (ECEC) settings. Observational measures are costly, as their administration generally takes 3–5 hr per classroom. This article outlines the process of development and preliminary concurrent validity testing of the Assessment for Quality Improvement (AQI), a new measure of global quality. The AQI is a classroom-level measure of structural and process quality. It consists of 24 items on a 5-point scale designed for use in ECEC infant and toddler classrooms. At between 60 and 90 min per room, the AQI is a relatively efficient measure. Item response theory modeling was used to ensure logical and coherent ordering of subitems. Exploratory factor analysis supported the use of the AQI total score and the Interactions section as a stand-alone measure. Correlations between the Infant and Toddler versions of the AQI and the Infant/Toddler Environment Rating Scale–Revised were moderate, providing preliminary support for the concurrent validity of both versions. Practice or Policy: Our results suggest that the AQI is a promising, efficient measure of global quality in infant and toddler ECEC environments. This may be especially relevant for Quality Rating and Improvement Systems, for which the observational component is a major cost driver.     

Professional development of mathematics teachers toward the facilitation of small-group collaboration

Collaborative work in small groups is often a suitable context for yielding substantial individual learning outcomes. Indeed, small-group collaboration has recently become an educational goal rather than a means. Yet, this goal is difficult to attain, and students must be taught how to learn together. In this paper, we focus on how to prepare teachers to become facilitators of small-group collaboration. The current case study monitors a group of six prospective teachers and their instructor during a one-semester course. The instructor was a skilled mathematics teacher with strong beliefs about what is entailed in establishing a mini-culture of learning to learn together and about how to facilitate student group work in problem-solving situations. We describe the learning path followed by the instructor, including the digital environment. The findings show that by the end of the course, the students became more competent facilitators of learning to learn together.     

Signifying the accumulation graph in a dynamic and multi-representation environment

The present study focuses on the accumulation process involved in the integration of a single-variable function. Observing the work of two high-school calculus students who had not yet learned any other integral-related ideas, we analyze the emergence of the semiotic relationship between personal and mathematical meanings, as expressed through the understanding of mathematical signs in integration tasks. Adopting Radford's educational perspective whereby learning is defined as a process of objectification, we identify a three-stage evolution of the double semiotic meaning of the lower boundary and of its role in the definition of the accumulation graph: (1) objectifying a zero accumulation in relation to the lower limit, (2) objectifying zero as marking the zero sum of accumulated areas, and (3) objectifying the accumulation graph as dependent on the lower-limit value. This evolution is marked by semiotic changes related to the pivotal role of the “zeros” in the accumulation graph.     

Non-abandonment as a foundation for inclusive school practice

The authors of this article describe an essential feature of inclusive educational practice: non-abandonment. When students’ needs and difficult behavior are overwhelming, teachers may abandon them emotionally as a defensive reaction to their own experience of emotional distress and helplessness. Non-abandonment represents a constructive strategy for dealing with these students based on the psychodynamic concepts of containing and holding. The authors provide a theoretical grounding for the processes of abandonment and non-abandonment, and then illustrate how these two processes play themselves out in school practice, drawing on action research conducted with educators in Israeli schools. They then describe eight elements in an active strategy of non-abandonment. These are: (1) make a conscious choice to assume professional responsibility for these students; (2) “stand by” students whose behaviour leads others to abandon them; (3) reframe self-defeating ways of thinking to open new avenues for action; (4) attempt to understand students’ real needs, including emotional ones; (5) adapt teaching practice to meet these needs, even going beyond traditional pedagogy; (6) create school frameworks in which teachers can systematically reflect on and improve practice; (7) address teachers’ emotional needs by making their own negative feelings openly discussable; and (8) promote teamwork and supportive relations among school faculty based on honest feedback and mutual non-abandonment.