Diversity, identity and belonging in e-learning communities: some theories and paradoxes Teaching in Higher Education

It is often assumed that online collaborative learning is inclusive of diversity. In this exploratory paper I challenge this notion by developing a theory which proposes that inclusion occurs through congruence between learners’ social identities and the identities implicitly supported through the interactions in a particular community. To build identity congruence, e-learning communities need spaces for both commonality and diversity and I present three paradoxes which underlie the aims of online learners and teachers to embrace diversity online. I illustrate these with some examples from online learning and teaching. The ability to ‘listen’ to each other online offers a way forward and the paper ends with some future possibilities about how we can ensure that e-learning communities benefit from diversity

Gender issues in computer‐supported learning: What we can learn from the gender; science and technology literature

This paper is a response to the article, ‘Gender issues in computer‐supported learning’, in Alt‐J 10 (1). I argue that the studies presented in the original paper could be enhanced by a more rigorous approach to gender that avoids universalizing identity, recognizes gender as a construction and which builds on previous research from gender, science and technology studies

Towards a personal best : a case for introducing ipsative assessment in higher education

The central role that assessment plays is recognised in higher education, in particular how formative feedback guides learning. A model for effective feedback practice is used to argue that, in current schemes, formative feedback is often not usable because it is strongly linked to external criteria and standards, rather than to the processes of learning. By contrast, ipsative feedback, which is based on a comparison with the learner's previous performance and linked to longterm progress, is likely to be usable and may have additional motivational effects. After recommending a move towards ipsative formative assessment, a further step would be ipsative grading. However, such a radical shift towards a fully ipsative regime might pose new problems and these are discussed. The article explores a compromise of a combined assessment regime. The rewards for learners are potentially high, and the article concludes that ipsative assessment is well worth further investigation. © 2011 Society for Research into Higher Education

A Glimpse into Secondary Students’ Understanding of Functions

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students’ intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so. Instead, these students tend to represent the physical characteristics of the situation. In addition, we discovered that middleschool students had sophisticated ideas of dependency and covariance. All the students were able to use their models of the situation to generalize and make predictions. These findings suggest that secondary students have the ability to describe covariant and dependent relations and that their models of functions tend to be more intuitive than mathematical-even for the students in algebra II and calculus. Our work suggests a possible framework that begins describing a way of analyzing students’ understanding of functions

Assessing Teacher Attentiveness to Student Mathematical Thinking

This article illustrates an argument-based approach to presenting validity evidence for assessment items intended to measure a complex construct. Our focus is developing a measure of teachers’ ability to analyze and respond to students’ mathematical thinking for the purpose of program evaluation. Our validity argument consists of claims addressing connections between our item-development process and the theoretical model for the construct we are trying to measure: attentiveness. Evidence derived from theoretical arguments in conjunction with our multiphased item-development process is used to support the claims, including psychometric evidence of Rasch model fit and category ordering. Taken collectively, the evidence provides support for the claim that our selected-response items can measure increasing levels of attentiveness. More globally, our goal in presenting this work is to demonstrate how theoretical arguments and empirical evidence fit within an argument to support claims about how well a construct is represented, operationalized, and structured

Statewide Mathematics Professional Development: Teacher Knowledge, Self-Efficacy, and Beliefs

We examined the impact of a state mandated K-12 mathematics professional development course on knowledge, self-efficacy and beliefs of nearly 4,000 teachers and administrators. Participants completed the Mathematical Thinking for Instruction course, emphasizing student thinking, problem-solving, and content knowledge specific to mathematics instruction. Inventories utilizing items fromthe Learning Mathematics for Teaching project (2005) measured changes in participants’ Mathematical Knowledge for Teaching (MKT) and an end-of-course self-evaluation enabled analysis of changes in MKT, self-efficacy and beliefs. Statistically significant changes were found in all three variables. This study adds to our understanding of the potential usefulness of mandating professional development as a policy vehicle for influencing educators’ mathematics knowledge and beliefs

Analysis of Students’ Proportional Reasoning Strategies

Proportional reasoning is key to students’ acquisition and application of complex mathematics and science topics. Research is needed regarding how students’ progress towards and come to demonstrate key developmental understandings within proportional reasoning. To this end we created and administered assessment items to 297 middle grades students. We categorized student solution processes qualitatively, followed by Rasch analysis to examine item difficulty and strategy use in relation to an anticipated trajectory. Our findings indicate that different strategies manifest themselves in a hierarchical manner, providing initial confirmation of categories based on strategy efficiency and emphasizing the importance of teacher (and researcher) analysis of classroom assessments from a student cognition perspective

Influence of Proportional Number Relationships on Item Accessibility and Students’ Strategies

Extensive evidence points to the need for mathematics instruction to tap into students’ informal understandings in order to conceptually develop formal mathematical ideas (Ahl, Moore, & Dixon, 1992; Freudenthal, 1973, 1991; Treffers, 1987). Contextual problems are a common means of helping students access their informal mathematical ideas (Lamon, 1993; Moore & Carlson, 2012). However, to successfully use context in this manner, we must ensure these problems are accessible to students and have the potential to promote connections to deeper or more formal mathematics (Jackson, Garrison, Wilson, Gibbons, & Shahan, 2013; Stein, Smith, Henningsen, & Silver, 2000). There is thus a need for research to identify what characteristics make contextual tasks accessible to students as a point of entry and useful for educators in analyzing and pressing students’ thinking

Identity and belonging in social learning groups : the importance of distinguishing social, operational and knowledge-related identity congruence

Collaborative learning has much to offer but not all learners participate fully and peer groups can be exclusive. The paper examines how belonging or 'congruence' in learning groups is related to identities of gender, age, ethnicity and socio-economic status. A study of student experiences of collaborative learning on three different blended learning courses illustrated how learners negotiate identity congruence with peer groups to belong and engage. An analytical framework that distinguishes social, operational and knowledge-related identity congruence has emerged. Contrary to received wisdom, the social aspect appears least important for learner engagement while knowledge-related identity congruence is fundamental. Some of the consequences of identity incongruence, particularly concerning gender and maturity, are discussed and the paper points towards the pedagogies which might enable identities of group members to shift so that collaborative learning can flourish

Immune sensing of Candida albicans requires cooperative recognition of mannans and glucans by lectin and Toll-like receptors

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