The functional use of a mathematical sign

The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both as an object with which to communicate (like a word is used) and as an object on which to focus and to organise her or his mathematical ideas (again as a word is used) even before she or he fully comprehends the meaning of this sign. Through this sign usage, I claim that the mathematical concept evolves for that learner so that it eventually has personal meaning, like the meaning of a new word does for a child; furthermore, because the usage is socially regulated, I claim that the concept evolves for the learner so that its usage concurs with its usage in the mathematical community. In line with Vygotsky, I call this usage of the mathematical sign before mature understanding, ‘functional use’. I demonstrate ‘functional use’ of signs (manipulations, imitations, template-matching and associations) through an analysis of an interview in which a mathematics university student engages with a ‘new’ mathematical sign, the improper integral, using pedagogically designed tasks and a standard Calculus textbook as resources.     

The Efficacy of Preschool Developmental Indicators as a Screen for Early Primary School-Based Literacy Interventions

Literacy success lays the foundation for children's later educational, health, and well-being outcomes. Thus, early identification of literacy need is vital. Using data from New Zealand's national preschool health screening program for fiscal years 2010/2011–2014/2015, demographic and health variables from 255,090 children aged 4 years were related to whether they received a literacy intervention in early primary school. Overall, 20,652 (8.1%) children received an intervention. Time-to-event analysis revealed that all considered variables were significantly related to literacy intervention (all p < .01), but the full model lacked reasonable predictive power for population screening purposes (Harrell's c-statistic = .624; 95% CI [.618, .629]). Including more direct literacy measures in the national screening program is likely needed for improvement.     

Building an understanding of heat transfer concepts in undergraduate chemical engineering courses

Understanding the distinctions among heat, energy and temperature can be difficult for students at all levels of instruction, including those in engineering. Misconceptions about heat transfer have been found to persist, even after students successfully complete relevant coursework. New instructional methods are needed to address these misconceptions. This pilot study examined whether researcher-developed and inquiry-based activities could increase conceptual understanding of heat transfer and alter common misconceptions. Twenty-two undergraduate chemical engineering students were assessed before and after instruction with inquiry-based activities using a ten-item concept inventory. Concept inventory questions were developed to assess students＇ performance on questions closely related to the inquiry-based activities and questions applying concepts in new contexts. Participants significantly improved their overall scores from pre-test to post-test. An examination of performance on individual items revealed significant improvement on half of those questions closely related to the instructional activities and half of those applying concepts in new but related contexts. Results are examined in light of the assessment and inquiry activities that were used, as well as the difficulty of the concepts. Educational implications and suggestions for future research are discussed.     

Book Reviews

This study examined the teaching of games via a tactical approach (also known as teaching games for understanding) from the theoretical perspective of social constructivism. A pilot study (of student teachers (STs) and pupils) informed the ‘main’ study which included collecting data on 49 STs, 58 cooperating teachers (CTs) and 1177 pupils. ST data were collected through videotaping (lessons), interviews and questionnaires; CT data through interviews and questionnaires; and pupil data through questionnaires. Data analysis techniques included systematic coding of teaching behaviours through computer software, using constant comparison to code open-ended question responses, and computing frequencies of Likert-scale question responses. T-tests were used to compare pre- and post-CT workshop data. Findings suggest that STs’ teaching of the tactical approach was in line with a social constructivist perspective, in part because lessons were student-centred. Overall student activity was 53% of all lessons taught, and STs facilitated pupil learning through several question and answer scenarios. Pupils wrote that they enjoyed playing games in what amounted to ‘authentic’ settings. Their responses also suggest that learning took place through ‘legitimate peripheral participation in communities of practice’ and this facilitated pupil movement through the ‘zone of proximal development’. There were indications that pupil experiences were mediated by ST competence. CTs reported that an in-service workshop on the tactical approach and mentoring was beneficial and subsequent pairings with STs elicited positive feelings from both parties.     

Connecting Urban Youth with their Environment: The Impact of an Urban Ecology Course on Student Content Knowledge, Environmental Attitudes and Responsible Behaviors

This study explores the impact of an urban ecology program on participating middle school students?? understanding of science and pro-environmental attitudes and behaviors. We gathered pre and post survey data from four classes and found significant gains in scientific knowledge, but no significant changes in student beliefs regarding the environment. We interviewed 12 students to better understand their beliefs. Although student responses showed they had learned discrete content knowledge, they lacked any ecological understanding of the environment and had mixed perceptions of the course??s relevance in their lives. Students reported doing pro-environmental behaviors, but overwhelmingly contributed such actions to influences other than the urban ecology course. Analyses indicated a disconnect between the course, the environment, and the impact on the students?? lives. Consequently, this suggests the importance of recognizing the implications of context, culture, and identity development of urban youth. Perhaps by providing explicit connections and skills in urban environmental programs through engaging students in environmental scientific investigations that stem from their own issues and questions can increase student engagement, motivation, and self-efficacy of environmental issues.     

Teacher perspectives on factors facilitating implementation of whole school approaches for resolving conflict

While social–emotional learning programmes in schools often have positive outcomes, many such initiatives are not well implemented and maintained. This paper reports on teacher reflections on the process of planning and implementing a whole school social–emotional learning (SEL) programme with a conflict resolution focus, called Enhancing Relationships in School Communities (ERIS). Ten primary schools participated in an 18‐month professional development programme offered by the researchers to assist schools to develop a whole school approach to handling interpersonal issues using a cooperative problem‐solving approach. Implementation (core) teams of three to five members, including principal or assistant principal and relevant teachers, attended workshops and managed the change process. In individual interviews, 29 core team members described the most significant changes that had taken place, what factors facilitated those changes and what assisted in overcoming barriers. A synthesised model of facilitators of implementation was developed on the basis of these interviews. The major components of the model included ensuring a whole school vision and process; pre‐programme engagement confirming commitment and alignment of researcher and teachers' visions; facilitative programme structure and processes such as linking the current programme to existing programmes and processes in the school; leadership and support for staff in the change process, for example, through the implementation team; the nature of the programme content; and monitoring and feedback processes to sustain motivation and inform on needs and outcomes.     

‘Does it answer the question or is it French fries?’: an exploration of language supports for scientific argumentation

ABSTRACT

Reform initiatives around the world are reconceptualising science education by stressing student engagement in science practices. Yet, science practices are language-intensive, requiring students to have strong receptive and productive language proficiencies. It is critical to address these rigorous language demands to ensure equitable learning opportunities for all students, including English language learners (ELLs). Little research has examined how to specifically support ELL students’ engagement in science practices, such as argumentation. Using case-study methodology, we examined one middle school science teacher's instructional strategies as she taught an argumentation-focused curriculum in a self-contained ELL classroom. Findings revealed that three trends characterized the teacher’s language supports for the structural and dialogic components of argumentation: (1) more language supports focused on argument structure, (2) dialogic interactions were most often facilitated by productive language supports, and (3) some language supports offered a rationale for argumentation. Findings suggest a need to identify and develop supports for the dialogic aspects of argumentation. Furthermore, engaging students in argumentation through productive language functions could be leveraged to support dialogic interactions. Lastly, our work points to the need for language supports that make the rationale for argumentation explicit since such transparency could further increase access for all students.