Education

The goal of the study was to reconstruct and dismantle a sequence of events that preceded an insight solution to a challenging problem by a ninth-grade student. A three-week long solution process was analysed by means of the theory of shifts of attention. We argue that concurrent focusing on what, how and why the student attends to when working on the problem can adequately explain his insight.

The goal of the case study presented in this paper was to examine a student's perspective on creative products in project-based learning. In this paper we dismantle, by means of the theory of shifts of attention, a two-month long sequence of events that preceded an unexpected invention made by a ninth-grade student: the student invented a new mathematical symbol, and valued this invention higher than his solution to a complex mathematical problem.
Key Words: Sense of creativity, shifts of attention, unusual sign, PBL, sequences

Mathematics education practitioners and researchers have long debated best pedagogical practices for introducing new concepts. Our design-based research project evaluated a heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives (grounding) and formal mathematical rules (generalizing). We compared student performance under conditions of working with stark (acontextual) vs. iconic (situated) manipulatives. We summarize findings from analyzing 20 individually administered task-based semi-structured clinical interviews with Grade 4 – 6 participant students. We found tradeoffs of situatedness: Whereas iconic objects elicit richer narratives than stark objects, these narratives may detrimentally constrain the scope of potential sensorimotor schemes students develop in attempt to solve manipulation problems.

There is a famous tale about the schoolboy Gauss, who was able to compute the sum of the first 100 integers with great rapidity. Mathematics teachers and educators frequently use the tale to demonstrate to their students what insight in mathematical problem solving may look like. Hayes (2006) collected and analysed more than a hundred versions of the tale. In all the versions, a pivotal part of the young Gauss's insight is described as noticing the pattern 1 + 100 = 2 + 99 = 3 + 98 and so on. However, there is no agreement on what " the method of Gauss " could be. Hayes (2006) found that the most widespread interpretations of the method are folding, double row and average, which correspond to the formulas respectively (see Hayes, 2006, and Tall et al., 2012, for additional approaches to the problem). The three formulas are algebraically equivalent, but the ways of attending to the string of the first n integers leading to each of them are different. We will never know which method young Gauss used and how he noticed the pattern. In this article, however, we make empirically-based suggestions about how the pattern was found by a 15-year-old student Ron, when he sought, with his classmate Arik, a formula for the sum of the first n integers. Ron and Arik needed to find a formula in order to accomplish a solution to a challenging problem that they had chosen for their research project in mathematics. In an attempt to account for the three-week long sequence of events that preceded Ron's (seemingly) serendipitous invention of the Gauss formula [1], we use the lenses provided by the Mason's (1989, 2008, 2010) theory of shifts of attention. Accordingly, our goal for this article is to reveal the potential of this theory as an analytical tool that can (at least partially) explain the course of the exploration towards the insight solution.

Mathematics education practitioners and researchers have long debated best pedagogical practices for introducing new concepts. Our design-based research project evaluated a heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives (grounding) and formal mathematical rules (generalizing). We compared student performance under conditions of working with stark (acontextual) vs. iconic (situated) manipulatives. We summarize findings from analyzing 20 individually administered task-based semi-structured clinical interviews with Grade 4 – 6 participant students. We found tradeoffs of situatedness: Whereas iconic objects elicit richer narratives than stark objects, these narratives may detrimentally constrain the scope of potential sensorimotor schemes students develop in attempt to solve manipulation problems.

Rhythm is a means of production—a scheme for coordinating the enactment of real or imagined physical movements over time, space, material resources, and concerting participants. In activities requiring the coordination of two or more continuous motor actions, rhythmic re-assembly of the actions creates a goal event structure mediating the enactment. Yet building that structure requires first unitizing continuity. Unitizing could thus be conceptualized as a cultural– historical strategy for supporting mundane routines by parsing, distributing, and codifying activity as a sequence of iterated actions of equivalent magnitude. Ipso facto, unitizing shifts us from naive to disciplinary activity: articulated rhythm is an ontogenetic achievement driving cognitive growth. We present empirical data of a student spontaneously measuring continuous actions as her means of organizing the enactment of a bimanual task designed for proportions.

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students’ attention. We present and compare various examples of how auxiliary elements can be introduced in various problems and proofs and characterize their auxiliary quality. Some auxiliary elements unite previously unrelated components of the original diagram; others divide a given complex entity into manageable ones. Implications for further educational research and mathematics instruction are proposed.

This article concerns the purpose, function, and mechanisms of students' rhythmic behaviors as they solve embodied-interaction problems, specifically problems that require assimilating quantitative information structures embedded into the environment. Analyzing multimodal data of one student tackling a bimanual interaction design for proportion, we observed the (1) evolution of coordinated movements with stable temporal–spatial qualities; (2) breakdown of this proto-rhythmic form when it failed to generalize across the problem space; (3) utilization of available resources to obtain greater specificity by way of measuring spatial spans of movements; (4) determination of an arithmetic pattern governing the sequence of spatial spans; and (5) creation of a meta-rhythmic form that reconciles continuous movement with the arithmetic pattern. The latter reconciliation selectively retired, modified, and recombined features of her previous form. Rhythmic enactment, even where it is not functionally imperative , appears to constitute a tacit adaptation goal. Its breakdown reveals latent phenomenal properties of the environment, creating opportunities for quantitative reasoning, ultimately supporting the learning of curricular content.

The goal of this study was to develop and test a theoretical model of Strategies for Coping with Career Indecision (SCCI). The proposed model consists of 14 categories that represent three major coping clusters—Productive coping, Support-seeking, and Nonproductive coping. The major concepts of the model were adopted from coping theories (Frydenberg & Lewis, 1993; Skinner, Edge, Altman, & Sherwood, 2003) and adapted to the context of career decision making. To test the proposed model, the SCCI questionnaire was developed and refined using data from 10 samples (N = 3,081). Study 1 reports the development of the SCCI and its psychometric properties using an additional sample of Israelis young adults deliberating about their career decisions (N = 460). Study 2a presents the results of a confirmatory factor analysis, based on American (N = 386) and Israeli (N = 819) samples of young adults. Study 2b tests the concurrent validity of the SCCI. The results from both the American and the Israeli samples supported the hypothesized distinction among the three major coping clusters; however, Support-seeking was associated partially with Productive coping and partially with Nonproductive coping. The implications for future research and career counseling are discussed. Career decisions are among the most important decisions individuals make throughout life (Lancaster, Rudolph, Perkins, & Patten, 1999). However, making such decisions is not only complex but also a stressful and confusing experience. Although some young adults make career decisions without any apparent problems, many others face difficulties during the decision-making process (Amir & Gati, 2006). Such difficulties can delay initiating the process, stop it in the middle, or lead to making a less than optimal decision (Gati, Krausz, & Osipow, 1996). Several studies have focused on various aspects of career decision-making difficulties, such as cognitive, emotional, and personality-related aspects,

The goal of the present research was to test the convergent and divergent validity of the Strategies for Coping with Career Indecision (SCCI) model and questionnaire, which comprises three main coping styles—Productive coping, Support-seeking, and Nonproductive coping—using three samples of young adults deliberating about their career choice. Study 1 tested the association between the SCCI and career decision-making profiles, using a sample of 390 young adults. Study 2 tested the relations between the SCCI and emotional and personality-related career decision-making difficulties, using a sample of 454 young adults. Finally, Study 3 tested the associations between the SCCI and career decision self-efficacy as well as the five dimensions of the Big Five Inventory, using a sample of 451 young adults. All three studies also tested the SCCI's incremental validity by assessing its ability to predict individuals' stages in the career decision-making process over and above the other measures. The results supported the convergent and divergent validity and partially supported the incremental validity of the SCCI. The theoretical and counseling implications are discussed and suggestions for future research are presented. Keywords career assessment, career indecision, career coping strategies, career decision-making profiles, emotional and personality-related career decision-making difficulties, career decision self-efficacy, the Big Five personality inventory Making educational and career decisions is often a complex and demanding task. This decision has become even more challenging in the 21st-century world of work, which offers a broad range of career opportunities, a rapidly changing and unpredictable job market, career uncertainty, and economic instability (Nota & Rossier, 2015). These drastic changes require the individual to become more resourceful and to exercise career adaptive self-management behaviors (Lent & Brown, 2013; Savickas,

The goal of the present research was to test a model of strategies for coping with career indecision during the college-to-work transition and its accompanied measure (the Strategies for Coping with Career Indecision–College-to-Work Transition Questionnaire [SCCI-CWTQ]), as predictors of career choice-related outcomes. Study 1 (N ¼ 522) supported the psychometric properties of the SCCI-CWTQ in a sample of college seniors and confirmed the model's hierarchical structure with three coping styles: productive, support-seeking, and nonproductive styles. Study 2 (N ¼ 659) tested the concurrent and incremental predictive validity of the SCCI-CWTQ. The results showed that productive coping style was positively associated with a sense of coping efficacy, career decision status, and career choice satisfaction 1 year following graduation, whereas using a nonproductive coping style was negatively related to those outcomes and positively associated with career deci-sional distress. Theoretical as well as practical implications pertaining to career decision-making during the college-to-work transition are suggested. The college years comprise a period when young adults are involved in extensive exploration of new options and in decisions about their future career without the pressures of having to commit to firm decisions (Lane, 2016). Thus, the senior year of college represents a critical developmental transition , during which individuals prepare to leave behind the freedom of the college experience and to

In this paper we report on a multi-method study that seeks to explore the scope, nature and purposes of FB interactions between secondary school teachers and their students explore if, how and why secondary teachers use FB to interact with their students. Issues of privacy, authority, and even abuse have fueled socio-political debates on the desirability of teacher-student FB contact, leading some authorities to curtail or even prohibit such contact. However, little is known about the actual FB interactions between teachers and their (under-aged) students, the scope and the nature of these interactions, and the reasons why teachers choose (not) to interact with their students through this platform. Combining survey data as well as in-depth interviews, this study then makes a first step in this direction.