This paper reports a study on conceptions of assessment held by students and instructors. The conceptions of assessment are considered to be one of the four interrelated sets of conceptions which together constitute the conception of education. The three other sets are the conceptions of (1) knowledge, (2) learning, and (3) instruction. Conceptions of knowledge were measured using an adapted version of the Epistemic Beliefs Questionnaire (EBQ). Conceptions of learning and instruction were measured with the Teaching and Learning Conceptions Questionnaire (TLCQ) developed by Elliott (2002)1, and Chan (2004)2. Since no instrument was available to measure conceptions of assessment, an experimental Conceptions of Assessment Scale (CAS) was developed and tested. Students filled out a 32-item forced-choice version, while instructors filled out a 25-item version in a four-point rating format. On all three instruments a dichotomy was created to distinguish subjects with ‘traditional’ conceptions from the ones with more ‘constructivist’ views. Results indicate that students and instructors hold different conceptions of assessment. Students have more traditional conceptions of assessment than instructors. With regard to conceptions of knowledge, students are more traditional than instructors. The conceptions of teaching and learning also show students to be more traditional than instructors. With respect to the congruency of conceptions of education, students seem to be equally (in) consistent as the instructors. An important implication of the present study is to pay more attention to the alignment between the educational philosophy of an institute and the conceptions of education held by its students and instructors.

Purpose: Yerkish is an artificial language created in 1971 for the specific purpose of exploring the linguistic potential of nonhuman primates. The aim of this paper is to remind the research community of some important issues and concepts related to Yerkish that seem to have been forgotten or appear to be distorted. These are, particularly, its success, its promising aspects for future research and last but not least that it was Ernst von Glasersfeld who invented Yerkish: he coined the term “lexigrams,” created the first 120 of them and designed the grammar that regulated their combination. Design: The first part of this paper begins with a short outline of the context in which the Yerkish language originated: the original LANA project. It continues by presenting the language itself in more detail: first, its design, focusing on its “lexigrams” and its “correlational” grammar (the connective functions or “correlators” and the combinations of lexigrams, or “correlations”), and then its use by the chimpanzee Lana in formulating sentences. The second part gives a brief introduction to the foundation of Yerkish in Silvio Ceccato’s Operational Methodology, particularly his idea of the correlational structure of thought and concludes with the main insights that can be derived from the Yerkish experiment seen in the light of Operational Methodology. Findings: Lana’s success in language learning and the success of Yerkish during the past decades are probably due to the characteristics of Yerkish, particularly its foundation in operational methodology. The operation of correlation could be what constitutes thinking in a chimpanzee and an attentional system could be what delivers the mental content that correlation assembles into triads and networks. Research implications: Since no other assessment or explanation of Lana’s performances has considered these foundational issues (findings), a new research project or program should validate the above-mentioned hypotheses, particularly the correlational structure of chimpanzee thinking.

Key words: Yerkish, artificial language, correlational grammar, operational methodology, Silvio Ceccato, machine translation, animal communication

Abstract: Maker education is a new instantiation of the decades-old project of project-based, constructionist, inquiry-driven learning. However, unlike other past implementations, it offers many unique characteristics, makes possible novel educational outcomes, and challenges policy makers and teachers with new infrastructural needs. In this response, using examples from school and district-wide implementation, we address three categories of questions raised in the commentaries around maker education: the uniqueness of makerspaces and the artifacts produced within them (and how they differ from projects and artifacts produced in other educational environments), teacher professional development for this novel type of school environment, and new approaches to assessment. Our conclusions point to recommendations that could be useful for policy makers, teachers and educators working on the implementation of maker programs.

The paper builds on the “Predict-Observe-Explain” (POE) assessment method reported by Gunstone and White almost 30 years ago. Arguments based on radical constructivism are used to extend POE into the form of a teaching strategy with four components: Predict-Explain-Observe-Reflect (PEOR). It is argued that there are many opportunities for the use of this strategy in science teaching. To illustrate, the use of PEOR in a teacher education programme is reported. A risk of adopting sequenced teaching strategies is that they can become “menu-driven,” detached from their conceptual origins. The paper demonstrates how a radical constructivist perspective can provide a coherent rationale for the PEOR teaching strategy.

Constructivist educational principles suggest that educational environments should provide learners with personal control, authentic learning contexts, and diverse personal interactions including collaboration. How can such constructivist values be applied to mass Higher Education? Traditional methods cannot achieve it with large student numbers but computer‐based media are scaleable and may support constructivist learning. A new course for non‐science undergraduates provided an opportunity for a constructivist design using the World Wide Web, email, and video. The design of the course, its implementation and evaluation are described. Authentic assessment was critical. Web forms and e‐mail supported some necessary personal interactions, but collaborative work was problematical.

Excerpt: In this book, you will read about five overarching principles evident in constructivist classrooms. • Teachers seek and value their students’ points of view. Teachers who consistently present the same material to all students simultaneously may not consider students’ individual perspectives on the material to be important, may even view them as interfering with the pace and direction of the lesson. In constructivist classrooms, however, students’ perspectives are teachers’ cues for ensuing lessons. • Classroom activities challenge students’ suppositions. All students, irrespective of age, enter their classrooms with life experiences that have led them to presume certain truths about how their worlds work. Meaningful classroom experiences either support or contravene students’ suppositions by either validating or transforming these truths. • Teachers pose problems of emerging relevance. Relevance, meaning, and interest are not automatically embedded within subject areas or topics. Relevance emerges from the learner. Constructivist teachers, acknowledging the central role of the learner, structure classroom experiences that foster the creation of personal meaning. • Teachers build lessons around primary concepts and ‘‘big” ideas. Too much curriculum is presented in small, disconnected parts and never woven into whole cloth by the learner. Students memorize the material needed to pass tests. But many students, even those with passing scores, are unable to apply the small parts in other contexts or demonstrate understandings of how the parts relate to their wholes. Constructivist teachers often offer academic problems that challenge students to grapple first with the big ideas and to discern for themselves, with mediation from the teacher, the parts that require more investigation. • Teachers assess student learning in the context of daily teaching. Constructivist teachers don’t view assessment of student learning as separate and distinct from the classroom’s normal activities but, rather, embed assessment directly into these recurrent activities.

Purpose: This study aims to explore, illuminate and hence evoke further reflections on the implications of creating and conserving distinctions that inherently act as simplifications and limit appropriate action. Design/methodology/approach – The approach used was reflective regarding the chosen concept of designing and learning from the perspective of a constitutive epistemology. These were investigated as circularities and as distinctions in language. The variety of intended meanings and hence implicit entailments was examined from the perspective of implicit domains. Findings: A tendency to focus on the results of designing and learning rather than the processes was attributed to several factors including cultural relevance, tangibility, durability and observability. Further, it was found that result and process are arbitrary distinctions in a circular system. It was noted that lack of awareness of multiple domains encourages reification, and that distinctions inherently obscure what happens in the non-articulated aspects of living. However, expertise embraces an ability to attend to such “betweens”. This applies to expertise in the assessment of learning and designing. Originality/value – The most obvious value of the findings is for the field of education. The insights gained indicate that the path of individualized learning with an emphasis on attention to the processes, inclusive of those that are not distinguished and named but can, with reflective experience, be sensed and acted on, has deep epistemological roots. A further implication is that educators require expertise to effectively work with learners, and that effective assessment depends on recurrent conversational interactions between the educator and learner.

Key words: recursion, language, learning, education, epistemology.

In the past decade, there have been ample interests in the assessment of cognitive and affective processes and products for the purposes of meaningful learning. Meaningful measurement has been proposed which is in accordance with a humanistic constructivist information-processing perspective. Students’ responses to the assessment tasks are evaluated according to an item response measurement model, together with a hypothesized model detailing the progressive forms of knowing/competence under examination. There is a possibility of incorporating student errors and alternative frameworks into these evaluation procedures. Meaningful measurement drives us to examine the composite concepts of “ability” and “difficulty.” Under the rubric of meaningful measurement, validity assessment (i.e. internal and external validities) is essentially the same as an inquiry into the meanings afforded by the measurements. Reliability, measured in terms of standard errors of measurement, is guaranteed within acceptable limits if testing validity is secured. Further evidences of validity may be provided by indepth analyses of how “epistemic subjects” of different levels of competence and proficiency engage in different types of assessment tasks, where affective and metacognitive behaviors may be examined as well. These ways of undertaking MM can be codified by proposing a three-level conceptualization of MM, where reliability and validity are central issues for an explication of this conceptualization.

Key words: testing, philosophy, educational methods, constructivism, humanism, construct validity, scaling, cognitive processes, problem solving

Introduction:As the International Group for the Psychology of Mathematics Education (IG PME) grew up, so did constructivism. Reflecting over the role of constructivism in the history of mathematics education is a daunting task, but one which provides an opportunity to reflect on what has been accomplished, honor the contributions of scholars around the world, and identify what remains unfinished or unexplained. In undertaking this task, we divide our treatment into five major sections: (1) The historical precedents of constructivism during the first ten years (1976–85); (2) The debates surrounding the ascendancy of constructivism during the next ten years (1986–95); (3) Our own articulation of key principles of constructivism; (4) Thematic developments over the last ten years (1996-present); and (5) An assessment of and projection towards future work. Looking back, we hope we can share the excitement of this epoch period in mathematics education and the contributions to it which came from across the globe. Since its inception at the 1976 International Congress on Mathematical Education (ICME) in Karlsruhe, PME has addressed three major goals all addressing the need to integrate mathematics education and psychology. While PME clearly has welcomed and thrived on multiple theories of psychology, beginning with Skemp’s (1978) The Psychology of Learning Mathematics, it has preferred those with a cognitive, and to some extent, an affective orientation. Two major theories of intellectual development have been dominant, namely constructivism and socio-cultural perspectives. In recent years, these two theories have intermingled, but in this volume, they are separated as we trace their paths, overlapping and distinctive. We will not give in to the frequent temptation to cast constructivism and socio-cultural perspectives as a diametrically opposed where one is personal/individual and the other social; but rather track the evolution of the theory via the theorists and the perspectives that they assign to their work.

What follows is my attempt to explore some of the issues that emerge out of the constructivist perspective related to the issue of assessment. I have chosen the form of a “Galilean Dialogue” modeled after Galileo’s famous “Two Major Systems of the World” [see Jauch, 1973, for a more recent incarnation of this format]. The topic of Galileo ‘s dialogue was the comparison of the Ptolemaic and Copernican views of the universe. To some, a discussion of objectivist and constructivist views of assessment may seem trivial in comparison, but I would disagree. The issues raised here go to the heart of our world view, to the core of what we believe It means to be human. I have retained the names of the original participants (Salviati, Sagredo, and Simplicio), although their role in the dialogue is transformed to accommodate the issue at hand.