Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification

A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students’ mathematical reasoning, we conduct design research where whole-class mathematical discussions triggered by exploratory tasks play a key role. We take mathematical reasoning as making justified inferences and we consider generalizing and justifying central reasoning processes. Regarding teacher actions, we consider inviting, informing/suggesting, supporting/guiding and challenging actions can be identified in whole-class discussions. This paper presents design principles for an intervention geared to tackle such reasoning processes and focuses on a whole-class discussion on a grade 7 lesson about linear equations and functions. Data analysis concerns teacher actions in relation to design principles and to the sought mathematical reasoning processes. The conclusions highlight teacher actions that lead students to generalize and justify. Generalizations may arise from a central challenging action or from several guiding actions. Regarding justifications, a main challenging action seems to be essential, while follow-up guiding actions may promote a further development of this reasoning process. Thus, this paper provides a set of design principles and a characterization of teacher actions which enhance students’ mathematical reasoning processes such as generalization and justification.     

The dynamics of connecting universities,non-governmental organizations and community members by means of academic projects directed at people in need

In this article we discuss an action research experience that took place from 2002 to 2015. We analyze the inception and progress of several project-based learning-centered academic courses that were aimed at developing the project management skills of graduate and undergraduate students. The experience involved approximately 1800 students from two universities and 40 community partners. The students developed real-life projects on behalf of institutions and non-governmental organizations located in the area that help people in need; we refer to these agencies as ‘community partners.’ We analyze the development of the course from a systemic perspective, making use of causal loop diagrams in order to understand the main driving dynamics. We discuss the results achieved by these projects and the benefits brought to the community partners. We also present testimony from the community partners themselves. We conclude by presenting the lessons we learned over the years we have been running this course.     

If I experience formative assessment whilst studying at university,will I put it into practice later as a teacher? Formative and shared assessment in Initial Teacher Education (ITE)

The aim of this article is to analyse whether having experience of formative assessment during their initial teacher education courses (ITE) influences graduates’ subsequent practice as teachers. That is, if the assessment methods that university students are subject to during their learning process are then actually employed by them during their professional practice as schoolteachers. To address this issue, questionnaires were issued and focus groups were held with a sample of ITE graduates. The main results of the study are that: (1) formative and shared assessment (FSA) is not used a great deal during ITE, but is highly valued; (2) some graduates have implemented FSA in their practice as teachers, following their experience on their ITE course; and (3) significant variables are found regarding the implementation of FSA in schools (possible resistance from colleagues and/or pupils’ parents, etc.).     

Application of a lexical-semantic intervention programme for students with Specific Language Impairment / Aplicación de un programa de intervención léxico-semántica en alumnado con Trastorno Específico del Lenguaje

The aim of this research has been to test the efficacy of an intervention programme on lexical-semantic problems in children with Specific Language Impairment (SLI). The sample consisted of 34 children diagnosed with SLI and 34 children with typical language development, all enrolled in different schools on the island of Tenerife (Canary Islands, Spain). For the selection of the sample, CELF-3, Peabody, ITPA Auditory Association and Visual Association subtests and the K-BIT IQ tests were used. The intervention programme consisted of 72 sessions of 30 minutes each, using noun and action naming activities along with conversation and categorization tasks in order to increase vocabulary and improve lexical semantic competence. Significant results were achieved in aspects related to the acquisition of vocabulary as well as in lexical semantics or related terms. The educational implications are clear insofar as lexical-semantic aspects are key in terms of activating other linguistic components and in improving the academic progress of SLI students.     

Handling math expressions in economics: recoding spreadsheet teaching tool of growth models

In the present paper, we develop a teaching methodology for economic theory. The main contribution of this paper relies on combining the interactive characteristics of spreadsheet programs such as Excel and Unicode plain-text linear format for mathematical expressions. The advantage of Unicode standard rests on its ease for writing and reading mathematical expressions. In this sense, our proposal allows incorporating an easily readable and writable methodology to cope with math expressions when interactive spreadsheets are used and designed in Economics teaching. The resulting nearly plain text can be used with few or no modifications in other numerical computing programs.     

School principals’ views of teacher evaluation policy: lessons learned from two empirical studies

Teacher evaluation accountability policies are emerging worldwide. This study examines principals’ perceptions of teacher evaluation in terms of commonalities and differences arising from two research projects conducted in Portugal and in the US. Perceptions of school principals in regard to a new policy on teacher evaluation as well as its perceived effects at school and conditions for its implementation will be analysed. Findings point to the challenges and successes of coping with mandated accountability measures in two different contexts. Principals balanced perceived conflicting goals, sought maintenance of positive teacher relationships and school culture and managed the tensions of policy implementation and the making sense of its effects at school. Implications of the findings are discussed.     

Stretching the academic harness: knowledge construction in the process of academic mobility in Chile

In this article, we analyse the impact of academic mobility on the construction of knowledge for Chilean scholars who have studied abroad. We conducted 41 semi-structured interviews with Chilean-born scholars in the social sciences and humanities, who accepted jobs at national research universities in Chile after receiving their doctorates abroad. Findings show that international academic mobility allowed these participants to question legitimised ways of doing knowledge, where they can stretch the academic harness that increasingly rules their knowledge construction. Our main argument is that knowledge construction process is neither linear nor unidimensional and it occurs as a rhizomatic process in a multidimensional space.     

Attitudes Toward Spanish and Code-Switching in Belize: Stigmatization and Innovation in the Spanish Classroom

Through the analysis of survey and interview data, we investigated the attitudes and perceptions of 32 multilingual teachers of Spanish in Belize, a code-switching (CS) context where Spanish is in intense contact with English and Belizean Kriol. More specifically, we examined teachers’ and students’ attitudes toward Spanish and CS and teachers’ perceptions vis-à-vis students’ attitudes toward Spanish instruction. The study revealed that whereas some teachers held negative views of Northern Belizean Spanish, they did not markedly perceive standard Spanish as “better” than the local variety of Belizean Spanish. The analysis also showed that most teachers had a positive predisposition to the use of CS as a pedagogical tool in their classrooms, a finding that suggests that ultra-normative attitudes toward Spanish varieties are not prevalent among these educators. In view of students’ attitudes, teachers concurred that students had overwhelmingly negative attitudes toward standard Spanish, in line with previous findings. We argue that educational reforms and status-planning efforts are vital to destigmatize Spanish and to promote its maintenance alongside Belizean Kriol and English.     

Honey-bee mating optimization (HBMO) algorithm for optimal reservoir operation

In recent years, evolutionary and meta-heuristic algorithms have been extensively used as search and optimization tools in various problem domains, including science, commerce, and engineering. Ease of use, broad applicability, and global perspective may be considered as the primary reason for their success. The honey-bee mating process has been considered as a typical swarm-based approach to optimization, in which the search algorithm is inspired by the process of real honey-bee mating. In this paper, the honey-bee mating optimization (HBMO) algorithm is presented and tested with a nonlinear, continuous constrained problem with continuous decision and state variables to demonstrate the efficiency of the algorithm in handling the single reservoir operation optimization problems. It is shown that the performance of the model is quite comparable with the results of the well-developed traditional linear programming (LP) solvers such as LINGO 8.0. Results obtained are quite promising and compare well with the final results of the other approach.     

Using Health Literacy in School to Overcome Inequalities

Health literacy has firmly established the links between literacy skills and health outcomes and is subsequently considered a key strategy for improving the health of disadvantaged populations and addressing social inequality. However, current research findings for improving health literacy have primarily focused on adults and actions within health and health care settings. Implementation studies outside the health sector are scarce. This study, a subset of the INCLUD-ED community- based project on social inclusion, reports on successful community-based approaches to health literacy. This article focuses on two schools that take advantage of the cultural intelligence of their students' family members, allowing them to make health literacy programmes more effective and useful for the participants. In addition, family involvement in educational activities addressed to children, including health programmes, has been found to improve the health literacy of the participating adults and their use of healthcare services. Findings indicate that schools in Europe can play a key role in breaking the cycle of health inequalities by promoting health literacy through education.