Supporting primary-level mathematics teachers’ collaboration in designing and using technology-based scenarios

In this article, we address how the design of educational scenarios can support teachers’ adoption of both technology and open-ended projects indorsing creativity and innovation. We do that by describing how groups of teachers develop digital learning environments supporting using a combination of GeoGebra and Google sites. Both teachers and pupils work with the concept of “game” as something they design, and furthermore, the pupils immerse themselves into the scenarios that the teachers create in a way similar to “playing a game.” We investigate teachers participation in collaborative development and testing through qualitative means, aiming to describe the teachers’ appropriation of (1) GeoGebra as a tool for doing and teaching mathematics, and (2) game as a metaphor supporting open-ended projects addressing creativity and innovation in the classroom. The data from the project suggest that the notion of “game” can support collaborative scenario design is a viable way of introducing technology and open-ended projects to primary school teachers.     

Basic school teachers’ perspective to digital teaching and learning in Ghana

This study proposes a model for describing the situation of Digital Teaching and Learning (TD-TaL) in Ghanaian schools using the perspectives of basic school teachers. The Digital Teaching and Learning model was developed based on the theories of Valsiner’s Zone of Free Movement (ZFM) and Zone of Promoted Action (ZPA) and Vygotsky’s Zone of Proximal Development (ZPD). The model proposes to look at the effects of ZFM in schools (comprising Digital environment factors and Personal attitudinal and Digital Culture factors) and ZPA (comprising Teacher Training factor) on the Teachers’ Digital Knowledge, Competence and Action ( TDKCA) factors to influence teachers in their Zone of Proximal Development. The model was tested in Ghana’s case using the survey data collected from 256 teachers from 45 schools across six districts in the Western Region of Ghana. The findings from Regression path analysis revealed that Personal and Digital Culture factors, but most of all teachers’ Digital Attitudes effected directly on Teachers’ Digital Activities they claimed to be doing, whereas from Environmental factors only Schools’ Digital Agenda was impacting Teachers’ Digital Action both directly and indirectly through Teachers’ Digital Training (ZPA). The model specifically highlighted that in observed Ghanaian schools the ZFM factors Digital Infrastructure and Digital Support to Digital Teaching did not associate with the ZPA factor Digital Teacher Training and overall to Teachers’ Digital Knowledge, Competence and Action factors.     

Improving Professional Practice through Practice-Based Research: V<Emphasis Type="Italic">a</Emphasis>KE (Values <Emphasis Type="Italic">and</Emphasis> Knowledge Education) in University-Based Teacher Education

Evidence suggests that in the professional education of teachers the moral goals are currently a neglected topic in favor of the subject matter and knowledge. The constructivist instructional approach VaKE (Values and Knowledge Education) addresses this problem by combining the moral and epistemic goals through the discussion of moral dilemmas. The main research question of this practice-based study was whether teacher educators can improve their instructional practice by using VaKE. We describe an empirical study of a teacher educator who used VaKE in order to (i) facilitate pre-service teachers to solve moral conflicts which they are faced with in their workplace learning and to (ii) increase the moral climate in his course. 58 pre-service teachers who formed two classes participated in the study. The study consisted of three research phases: In the first research phase the types of the pre-service teachers’ moral conflicts were examined. In the second research phase the most frequent types of moral conflicts were used as a basis for an explorative quasi-experimental pre-posttest study. This study investigated the effects of VaKE compared to a traditional case-analysis approach with regard to the pre-service teachers’ application of discourse-oriented actions for conflict resolution. In the third phase, a case study method was used comprising a random sample of seven pre-service teachers chosen from each class to investigate the perceived learning climate during the intervention. The results indicate that VaKE provides the possibility to combine the moral and epistemic goals of the professional education of teachers.     

Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers?

This study employed content analysis to examine 3 popular middle-grades mathematics curricula in the USA on the support they provide for teachers to implement concepts associated with variables in school mathematics. The results indicate that each of the 3 curricula provides some type of support for teachers, but in a varied amount and quality. More specifically, whereas the University of Chicago School Mathematics Project (UCSMP) curriculum provides support for teachers on several aspects of using variables in school mathematics, the support found in the Connected Mathematics 2 and the Math Connects curricula focused mainly on one conception of variables—namely, the use of variables as quantity that varies in the Connected Mathematics 2 curriculum and the use of variables as specific unknowns in the Math Connects curriculum. Overall, the UCSMP curriculum provides the most support for teachers, followed by the Connected Mathematics 2 curriculum, with the Math Connects curriculum recording the least support for teachers to enact variable concepts. It is worth pointing out that, although the 3 curricula collectively provide guidance for teachers to implement variable ideas within meaningful real-world contexts, the supports identified in the respective curriculum were not sufficient in addressing all of the areas that are essential for teaching the many concepts associated with variables in school mathematics effectively. Recommendations for curriculum developers and for international researchers with interest in the roles of variables in school mathematics are provided.     

From resource to document: scaffolding content and organising student learning in teachers’ documentation work on the teaching of series

We examine teachers’ use of resources as they prepare to teach the topic of numerical series of real numbers, in order to identify how their personal relationship with mathematical content—and its teaching—interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a term coined in the Anthropological Theory of the Didactic (ATD, Chevallard, 2003), in terms of documentation work (resources, aims, rules of action, operational invariants), a key construct from the documentational approach (DA, Gueudet & Trouche, in Educational Studies in Mathematics, 71, 199–218, 2009). We do so in the case of five post-secondary teachers who use the same textbook as a main resource for teaching the topic. Documentational analysis of interviews with the teachers led to the identification of their aims and rules of action (the what and how of their resource use as they organise their teaching of the topic) as well as the operational invariants (the why for this organisation of their teaching). We describe the teachers’ documentation work in two sets of aims/rules of action: scaffolding mathematical content (series as a stepping stone to learning about Taylor polynomials and Maclaurin series), and organising student learning about series through drill exercises, visualisation, examples, and applications. Our bridging (networking) of theoretical constructs originating in one theoretical framework (personal relationship, ATD) with the constructs of a different, yet compatible, framework (documentation work, DA) aims to enrich the latter (teachers’ documentation work) with the individual agency (teachers’ personal relationships with the topic) provided by the former.     

Pre-service teachers’ experiences of scaffolded learning in science through a computer supported collaborative inquiry

Scaffolding helps the novice to accomplish a task goal or solve a problem that otherwise would be beyond unassisted efforts. Scaffolding firstly aims to support the learner in accomplishing the task and secondly in learning from the task and improving future performance. This study has examined pre-service teachers’ experiences of technologyenhanced/computer-supported collaborative inquiry learning when studying the anatomy of fish. The study investigated pre-service teachers’ experiences of scaffolded use of a Wiki in structuring a dissection inquiry activity combined with scaffolded use of digital imaging to support problematizing during the sense making process. Quantitative data on the benefits experienced by the pre-service teachers in using the Wiki and in digital imaging were collected through responses to questions posted through an online questionnaire. Structure equation modeling was used to investigate the relationship between scaffolding with the Wiki and the experienced benefits of using technology. The use of structural scaffolding with the Wiki was not seen to be directly related to the experienced benefits. In encouraging knowledge acquisition and supporting deeper thinking on the topic, digital imaging had the strongest positive relationship to the experienced benefits of the technology, but there was no direct relationship with the use of the Wiki. However, scaffolding by structuring the activity with the Wiki had meditational, indirect, effects through visualizations and peer support to intentional and active participation and thus the scaffolds were working during the inquiry synergistically. For teacher education this means that pre-service teachers may recognize the benefits of using technology only through a significant experience and thus under value the role of the technology itself.     

中国地区孢子丝菌临床分离株的分子鉴定(英文)简

In this study, we investigated the molecular phylogeny of 64 clinical isolates which were identified as Sporothrix schenckii sensu lato by morphological identification. All of the strains were isolates from patients from several provinces in China. The phylogeny was inferred by DNA sequence analyses based on datasets of the ribo- somal internal transcribed spacer （ITS） and a combined ITS and partial 13-tubulin region. Reference sequences were retrieved from GenBank. Results showed that all of the isolates were clustered in a distinct clade with a type of Spo- rothrix globosa. Our analysis showed that S. globosa is the causal agent of the tested sporotrichosis in China, rather than S. schenckii that was generally believed to be the case. The existence of S. schenckii in China remains to be confirmed. This study improved our understanding of the distribution of the species in S. schenckii complex.     

Linking Science and Statistics: Curriculum Expectations in Three Countries

This paper focuses on the curriculum links between statistics and science that teachers need to understand and apply in order to be effective teachers of the two fields of study. Meaningful statistics does not exist without context and science is the context for this paper. Although curriculum documents differ from country to country, this paper uses extracts from three countries: Australia, New Zealand and the USA. The statistical ideas from the Australian Curriculum: Mathematics, the New Zealand Mathematics and Statistics Curriculum and the US Common Core State Standards for Mathematics are linked to the relevant parts of the Australian Curriculum: Science, the New Zealand Science Curriculum and the US Next Generation Science Standards for States, by States. Teachers of mathematics need to be aware of the potential of science to provide meaningful contexts within which to set statistical investigations. Similarly, teachers of science, who are developing methods for implementing investigations and experiments in their classrooms, need to be aware of the close ties to statistical tools for decision-making.     

Making Space for Consuming Practices

This empirically driven paper is about workplace learning with specific focus on the ‘work’ of consuming practices. By consuming we refer to the eating, and the drinking, and (at times) to the smoking that workers, in most organisations, do on a daily basis. Indeed, it is the quotidian nature of consuming, coupled with its absence from workplace learning research that make them noteworthy practices to explore. In using the term practice we draw on the recent tranche of practice based theorisations: notably Schatzki (1996, Organization Studies, 26(3), 465-484, 2005, Organization Studies, 27(12), 1863-1873, 2006) and Gherardi (Human Relations, 54(1), 131-139, 2001, 2006, Learning Organization, 16(5), 352-359, 2009). The paper frames consuming practices as ‘dispersed’ (general) practices and, illustrated through empirical data from multiple projects, we progressively outline how these contribute to the learning of ‘integrative’ (specialized work) practices. Our overall aim is to (re)position consuming practices from prosaic, to having much relevance for research on workplace learning.     

Change or Durability? The Contribution of Metaconceptual Awareness in Preservice Early Childhood Teachers’ Learning of Science Concepts

This longitudinal study examined the role of metaconceptual awareness in the change and the durability of preservice teachers’ conceptual understandings over the course of several months. Sixteen preservice early childhood teachers participated in the study. Semi-structured interviews were conducted to reveal the participants’ conceptual understandings of lunar phases (pre, post, and delayed-post) and level of metaconceptual awareness (delayed-post only). Based on the change and stability in participants’ conceptual understandings from pre to post and from post to delayed-post interviews, participants’ conceptual understandings were assigned into three groups that described the profile of their long-term conceptual understandings: “decay or stability”, “continuous growth”, and “growth and stability”. The results indicated that participants in the “continuous growth” and “growth and stability” groups had significantly higher metaconceptual awareness scores than participants in the “decay or stability” group. The results provided evidence that metaconceptual awareness plays a more decisive role in the restructuring of conceptual understandings than the durability of conceptual understandings.     

Teachers’ professional growth through engagement with lesson study

Lesson study is highly regarded as a model for professional learning, yet remains under-theorised. This article examines the professional learning experiences of teachers and numeracy coaches from three schools in a local network of schools, participating in a lesson study project over two research cycles in 2012. It maps the interconnections between their experiences and their beliefs and practices, using Clarke and Hollingsworth’s (Teach Educ 18(8):947–967, 2002) Interconnected Model of Professional Growth. Analysis of interview data and video-recordings of planning meetings, research lessons, and post-lesson discussions reveals the development of teachers’ collaborative planning skills, increased attention to students’ mathematical thinking, use of orchestrated whole-class discussion based on anticipated student solutions and focused questioning, and the enhancement of collaborative practices for teacher inquiry. Our findings illuminate the interplay between the External Domain, the Personal Domain, the Domain of Practice, and the Domain of Consequence, in the teaching and learning change environment, and the mediating processes of enactment and reflection. Changes in the domains across the period of the lesson study provide evidence of teachers’ professional growth, with the iterative processes of enactment and reflection being critical in mediating this professional growth.     

A comparative examination of Canadian and American pre-service teachers’ self-efficacy beliefs for literacy instruction

This study explored Canadian and American pre-service elementary teachers’ self-efficacy beliefs for literacy instruction, as well as the contextual factors (i.e., course and field experiences) that contribute to these self-efficacy beliefs. Survey data were collected over a two-year period at the beginning and end of a required elementary literacy methods course that assessed pre-service teachers’ self-efficacy for literacy instruction. A content analysis of the American and Canadian literacy methods course syllabi was also conducted. Paired t test results showed no significant difference in pre-service teachers’ literacy teaching self-efficacy scores from pre-test to post-test; however, there was a significant difference in the pre-service teachers’ literacy efficacy beliefs related to oral reading from the beginning to the end of the course. A weak negative correlation was found between the Canadian pre-service teachers’ total Teachers’ Sense of Efficacy for Literacy Instruction (TSELI; Tschannen-Moran & Hoy, 2011) scores and their teaching experience specific to literacy instruction, r = ? .1, p = .04. There was a positive correlation between Canadian pre-service teachers’ self-efficacy scores related to engagement and differentiated instruction and their volunteer and work experiences. A positive correlation existed between Canadian and American pre-service teachers’ self-efficacy for reading/writing connections and university coursework related to literacy instruction. Implications for literacy teacher educators and recommendations for literacy instruction are discussed.     

Investigating Flow Experience and Scientific Practices During a Mobile Serious Educational Game

Mobile serious educational games (SEGs) show promise for promoting scientific practices and high engagement. Researchers have quantified this engagement according to flow theory. This study investigated whether a mobile SEG promotes flow experience and scientific practices with eighth-grade urban students. Students playing the game (n = 59) were compared with students in a business-as-usual control activity (n = 120). In both scenarios, students worked in small teams. Data measures included an open-ended instrument designed to measure scientific practices, a self-report flow survey, and classroom observations. The game players had significantly higher levels of flow and scientific practices compared to the control group. Observations revealed that game teams received less whole-class instruction and review compared to the control teams. Game teachers had primarily a guide-on-the-side role when facilitating the game, while control teachers predominantly used didactic instruction when facilitating the control activity. Implications for these findings are discussed.     

Teachers’ use of Facebook and teacher quality: developing a ‘Facebook Effect Scale on Teacher Quality (FESTQ)’ from the perspective of PCK,TPACK, and lifelong learning frameworks

The main purpose of the study is to develop a Facebook Effect Scale on Teacher Quality (FESTQ) based on the pedagogical content knowledge, technological pedagogical content knowledge and lifelong learning frameworks. Study participants comprised 556 teachers. Explanatory factor analysis and confirmatory factor analysis were conducted in the development and testing of the FESTQ. The results showed that the FESTQ is reliable and valid to measure Facebook effect on teacher quality. The FESTQ consists of 40 positive six-point Likert-type items along with six factors, instructional knowledge for in-class applications, general culture knowledge, individual characteristics, instructional knowledge related to student characteristics, instructional knowledge for preparing an assessment tool and special content area knowledge. The psychometric properties of the FESTQ, the study limitations and suggestions for future studies are discussed.     

Points at Which Continuous Functions Have the Same Height

As an easy application of the intermediate value theorem, one can show that for any continuous function f: [0, 1] → ? with f (0) = f (1), there are points a, a + 1/2 both in [0, 1] such that f (a) = f (a + 1/2). In this note, we show that this property holds with 1/2 replaced by any number of the form 1/n for a positive integer n. More interestingly, we show that this is false for every number not of the form 1/n.     

The ontology of science teaching in the neoliberal era

Because of ever stricter standards of accountability, science teachers are under an increasing and unrelenting pressure to demonstrate the effects of their teaching on student learning. Econometric perspectives of teacher quality have become normative in assessment of teachers’ work for accountability purposes. These perspectives seek to normalize some key ontological assumptions about teachers and teaching, and thus play an important role in shaping our understanding of the work science teachers do as teachers in their classrooms. In this conceptual paper I examine the ontology of science teaching as embedded in econometric perspectives of teacher quality. Based on Foucault’s articulation of neoliberalism as a discourse of governmentality in his ‘The Birth of Biopolitics’ lectures, I suggest that this ontology corresponds well with the strong and substantivist ontology of work under neoliberalism, and thus could potentially be seen as reflection of the influence of neoliberal ideas in education. Implications of the mainstreaming of an ontology of teaching that is compatible with neoliberalism can be seen in increasing marketization of teaching, ‘teaching evangelism’, and impoverished notions of learning and teaching. A shift of focus from teacher quality to quality of teaching and building conceptual models of teaching based on relational ontologies deserve to be explored as important steps in preserving critical and socially just conceptions of science teaching in neoliberal times.     

Encouraging Students with Different Profiles of Perceptions to Pursue Science by Choosing Appropriate Teaching Methods for Each Age Group

This research aimed at identifying student profiles of perceptions by means of a clustering method using a validated questionnaire. These profiles describe students’ attraction to science and technology (S&T) studies and careers as a variable driven by school S&T self-concept and interest in school S&T. In addition to three rather predictable student profiles (confident enthusiast, average ambitious, and pessimistic dropout), the fourth fairly well-populated profile called confident indifferent was produced. Our second and third research questions allowed us to describe each profile in terms of the instructional methods to which their population was exposed (including the degree to which they were actively involved) and the instructional methods to which they would like more exposure. An analysis of the evolution of the profiles’ population over time is also presented. The results suggest that pedagogical variety and active involvement in the decision to pursue S&T are important. The perception of the utility and importance of S&T both in and out of school may also play an important role in these decisions. Minor pedagogical preferences were also found in certain age groups.     

On a Problem of Alaoglu and Erdős

Starting with an elementary problem that appeared in the Putnam mathematics competition, we proceed to discuss some techniques of transcendental number theory and prove the following result. If p, q, r are distinct primes and if c is a real number with the property that p^c, q^c, r^c are integers, then c must be a non-negative integer. The tools used are some linear algebra and complex analysis. The zero-density estimate method discussed here was used by Alan Baker to prove his celebrated theorem on linear forms in logarithms. The question as to whether we can replace three primes by two primes is an open question.