Levels in Learning

In 1957, Van Hiele published his study on levels in learning mathematics. In this article we present an elaboration of the theory on levels in learning and an illustration of this theory based on empirical results. We distinguish between three levels: The first is the formation of an image out of a range of familiar examples or experiences. Second, on the basis of the image a schema can be built, which includes all kinds of interrelated details. Third, a theory can be developed with basic assumptions, definitions, and logical inferences. Before entering the next level, the learner should be sufficiently experienced on the actual level. It is shown that the theory on levels in learning can be integrated with other learning principles, such as notions from constructivism.     

HF: Working on mathematics education

First an impression will be given of the way Freudenthal worked on mathematics education during the period after WW II, until the early seventies. The sequence of events of that time form the leading principle of that period when important didactic concepts were being developed. In the following section the chronological order is set aside in an attempt to show how Freudenthal approached research, both in education and into mathematics education. In the next two sections two core themes are dealt with in detail: learning mathematics and developing mathematics education. Earlier didactic concepts are completed and further developed into key notions of a science of mathematics instruction.     

Actor social networks as knowledge sharing mechanisms in multi-stakeholder processes: a case of coffee innovation platforms of Uganda

Purpose: This study examined knowledge sharing mechanisms in coffee IPs and their effect on actor linkages in four districts of Uganda.

Design/methodology/approach: Thirty one respondents from the public and private sector were interviewed using a qualitative approach. Data were analyzed using the Atlas ti qualitative software version 7.5.18 to generate themes for information sources, types and channels. Social network analysis was used to measure the actor centrality positions and influence in the IP network.

Findings: Results revealed seven main categories of actors in the Coffee IPs who shared information on coffee inputs, agronomic practices, processing and markets through three main channels. Level of cohesion was less than 10% which had negative implications on the knowledge flow, trust and collaboration among the actors. Influential positions were occupied by the processors and farmer leaders in IPs in the southern districts of Luwero and Rakai, while nursery operators were most influential in IPs of the western districts of Ntungamo and Bushenyi. Weak linkages within the social networks indicated that initiatives of the actors were fragmented, as each actor acted as an individual detached from the platform activities limiting inter-actor knowledge sharing.

Practical implications: Innovation intermediaries should focus on integrated systemic and innovative approaches to strengthen actor social linkages for knowledge sharing and better platform performance.

Theoretical implications: Actor positions and relationships in innovation networks are critical tenets for fostering knowledge exchange and performance. In an innovation platform, diverse actors are multiple sources for accessing information within a given social and institutional context.

Originality/value: The study contributes to existing debate and knowledge on institutional change in agricultural innovation systems.     

Le diagnostic du potentiel d’apprentissage par LPAD: Une etude de la fidélité

The present study was intended to test some of the psychometric properties of Feuerstein’s Learning Potential Assessment Device (LPAD), in particular the reliability of the Set Variations II, considered to assess modificability or learning capacity. Thirty 10-year-old children were studied: an experimental group (N=20) submitted to two training sessions with Set Variations II and a control group (N=10). Both groups were administered three times the Standard Progressive Matrices (SPM). The experimenter’s interventions during training were semi-standardized, based on an examination guide, and the helps given were classified in four types. Analyses dealt with the number and type of helps provided as well as with errors during training. Correlations between these indices for the two sessions of training were rather low, indicating weak stability, in particular with respect to the helps provided. Correlations were also computed between the gains in SPM for the three administrations, indicating low stability in amount of progression. Further, it was also noted that the experimental group did not progress more than the control group. Conclusions are drawn with respect to reliability and validity of the Set Variations Test, as well as, on a more theoretical level, with respect to the concept of cognitive modifiability.     

Prospective elementary teachers' prior knowledge about light

This article reports on a study that was designed to describe prospective elementary teachers' prior verbal and diagrammatic knowledge about various aspects of light, seeing, shadows, and mirror images. Data were collected through individual interviews using simple apparatus (light bulb, objects, screen, and plane mirror). Included are some inferences about how students' ideas may have emerged from their interpretations of everyday experiences. The article concludes with a section that provides an example of a conceptual change instructional strategy that was based on the research results reported here.