Conceptual and Procedural Knowledge During Strategy Construction: A Complex Knowledge Systems Perspective

ABSTRACT

This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated for decades. Recently, there has been mounting empirical evidence that conceptual and procedural knowledge can develop by mutual bootstrapping in a bidirectional and iterative fashion (e.g., Rittle-Johnson & Schneider, 2014 Rittle-Johnson, B., & Schneider, M. (2014). Developing conceptual and procedural knowledge of mathematics. In R. C. Kadosh & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1102–1118). Oxford: Oxford University Press. [Google Scholar]). However, the very constructs of conceptual and procedural knowledge (especially procedural knowledge) have been critiqued for inconsistency in definition and lack of operationalization (Star, 2007 Sherin, B. L. (1996). The symbolic basis of physical intuition A study of two symbol systems in physics instruction (Doctoral dissertation). University of California, Berkeley. [Google Scholar]). The analysis in this article addresses this critique by modeling the diverse forms of conceptual and procedural knowledge needed to implement a strategy as a complex knowledge system: a strategy system. Furthermore, the strategy system model is used to elaborate processes of mutual bootstrapping between conceptual and procedural knowledge at a moment-by-moment time scale. The strategy system model builds upon the Knowledge in Pieces epistemological perspective (diSessa, 1993 diSessa, A. A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10(2–3), 105–225. doi:10.1080/07370008.1985.9649008[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and coordination class theory in particular (diSessa & Wagner, 2005 diSessa, A. A., & Wagner, J. F. (2005). What coordination has to say about transfer. In J. P. Mestre (Ed.), Transfer of learning from a modern multidisciplinary perspective (pp. 121–154). Greenwich, CT: Information Age Publishing. [Google Scholar]). Both the theoretical notion of a strategy system and the bidirectional model of mutual bootstrapping between conceptual and procedural knowledge are illustrated using data from a case study of a pre-algebra student who iteratively refined a procedure for solving algebra word problems. The strategy system model highlights the complexity of both strategies and concepts and offers a window into what can be learned by students during strategy construction processes.     

Transpersonal Psychology: Defining the Past,Divining the Future

Retrospective analysis of definitions published over some 35 years suggests the major subject areas of the field can be summed up in three themes: beyond-ego psychology, integrative/holistic psychology, and psychology of transformation. Theme frequency analysis reveals that early emphasis on alternative states of consciousness has moderated into a broader approach to human transcendence, wholeness, and transformation. This expanded definition of transpersonal psychology suggests the field has much in common with integral psychology. As a comprehensive, historically based content summary, this tripartite definition contributes a small but vital piece to the foundation of a transpersonal vision that is spreading across the globe. While transpersonal psychology still needs to embody the inclusiveness and diversity that it represents, its vision is one of great relevance to the contemporary human condition.     

International Genetic Counseling Students’ Perspective on Their Training Experience in the United States

International students face social, psychological and academic challenges upon moving to a foreign country to pursue higher education. Clinical disciplines such as genetic counseling present additional challenges adapting to an unfamiliar health care system and different interactions and expectations with patients and colleagues. This study used semi-structured interviews to identify challenges that international genetic counseling students face during training in the United States. Eight international genetic counseling alumni who graduated from U.S.-accredited programs were interviewed. Participants stated that the U.S. academic system was unfamiliar—class participation and paper-writing required the greatest adjustment. There was a need for help in understanding social norms in academic settings. Clinically, they were unfamiliar with the dynamics and communication style of U.S. families. Non-native English speakers experienced greater difficulty in all areas. Most participants reported that they were uncomfortable asking for help in transitioning to life, study and work. Participants identified mentorship programs for international students as potentially useful in clarifying expectations in academic and clinical settings. These results may assist international students preparing to study genetic counseling in the U.S. and may help genetic counseling training programs identify the academic and clinical challenges faced by international students.     

On the learnability of frequent and infrequent word orders: An artificial language learning study

Most languages have a basic or "canonical" word order, which determines the relative positions of the subject (S), the verb (V), and the object (O) in a typical declarative sentence. The frequency of occurrence of the six possible word orders among world languages is not distributed uniformly. While SVO and SOV represent around 85% of world languages, orders like VSO (9%) or OSV (0.5%) are much less frequent or extremely rare. One possible explanation for this asymmetry is that biological and cognitive constraints for structured sequence processing make some word orders easier to be processed than others. Therefore, the high frequency of these word orders would be related to their higher learnability. The aim of the present study was to compare the learnability of different word orders between groups of adult subjects. Four artificial languages with different word orders were trained: two frequent (SVO, SOV) and two infrequent (VSO, OSV). In a test stage, subjects were asked to discriminate between new correct sentences and syntax or semantic violations. Higher performance rates and faster responses were observed for more frequent word orders. The results support the hypothesis that more frequent word orders are more easily learned.     

Congruence of the Marital Relationship During Transition to Parenthood: A Study with Couples Who Conceived Spontaneously or Through Assisted Reproductive Technologies

In this study we examined the congruence between partners’ perceptions of their marital relationship during the transition to parenthood and the effect of depression during pregnancy on couples’ congruence during the early postpartum period. Thirty-one couples who conceived spontaneously, along with thirty-five who conceived through assisted reproductive technologies (ART), provided data on their marital relationship and depression at their 24th pregnancy week and four months after the partum. All couples reported a decrease in marital congruence. Couples who conceived through ART reported lower marital congruence. For these subjects, women’s depression was associated with lower congruence. Interventions that focus on strengthening the marital relationship across the transition to parenthood should assess and promote couples’ congruence.     

Communication between domestic dogs and humans: effects of shelter housing upon the gaze to the human

It is widely known that gaze plays an essential role in communicative interactions. Domestic dogs tend to look at the human face in situations of conflict and uncertainty. This study compares the gaze of shelter and pet dogs during acquisition and extinction phases in a situation involving a reward in sight but out of reach. Even though no significant differences between the groups were recorded during acquisition, gaze duration decreased in both groups during extinction, with shelter dogs showing a significant shorter duration. This could be related to their different living conditions and to the fact that through their ordinary everyday interactions, pet dogs have more opportunities to learn to persist in their communicative responses when they do not get what they want. These results highlight the relevance of learning experiences during ontogeny, which would therefore modulate communicative responses.