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From checklists, to processes, to models, information literacy (IL) instructors have sought to better teach students how to evaluate the information they encounter, increasingly through critical information literacy (CIL) pedagogies. CIL engages high-impact pedagogical practices as students direct their learning through dialogue and problem-posing, but there are persistent barriers to implementing CIL pedagogies at scale. Drawing from motivational design can empower librarians to advance CIL and empower students to critically evaluate information. Although many evaluation pedagogies employ general motivational strategies, there is a gap in the literature exploring the application of one specific component of motivation: "confidence." This conceptual and exploratory study aims to: 1) determine the connections between motivational design and IL pedagogy, specifically related to confidence-building strategies and critical approaches to evaluating information; and 2) map the integration of confidence-building design and CIL practices to provide suggestions for practical application. The researchers employ a crosswalk analysis to demonstrate how IL instructors can overcome barriers to implement CIL instructional practices through confidence-building design that illuminates students' abilities to learn and make a meaningful impact. In taking a confidence-building, critical focus to designing evaluation instruction, IL instructors reframe information evaluation as a participatory place for critical questioning, exploration, creative expression, and dialogue.

Service-learning models serve as noteworthy curriculum paradigms that can help students engage with their communities while continuously learning. This article recounts the implementation of a service-learning model within a student initiative aimed to help combat vaccine hesitancy and promote the uptake of vaccinations within the Rhode Island community. Through a collaborative effort between students, faculty, and the university, the student initiative was able to construct a credit-bearing course to help assess and alleviate vaccine hesitancy within Rhode Island. This article highlights the journey the organization took to develop a service-learning model within the course, the project details, and the impact of their project on the community. A detailed analysis of the service-learning model's impact on students as well as key takeaways of the project are also highlighted below.

Current educational research demonstrates the importance of equipping students to be active participants in their own learning. However, more work is needed to provide students with the metacognitive skills necessary to engage in Self-Regulated Learning (SRL). Feedback is a crucial component of the learning process and can be used by students to develop these skills but remains a source of dissatisfaction for students and educators. We contend that this is a result of a gap in students' understanding of the feedback process and the lack of dialogue between students and educators. This paper presents a methodology to conduct a feedback workshop as a means to improve the feedback experience while equipping students with the metacognitive skills needed to facilitate SRL. The methodology was evaluated in four workshops conducted with students from engineering and business at a university in the United Kingdom. In each workshop (excluding the pilot) students were requested to complete pre and post-workshop questionnaires and there was also opportunity for group discussion and reflection. Results demonstrate the potential benefits of such workshops in deepening the student understanding of the process and use of feedback.

In recent years, professional organizations in the United States have suggested undergraduate mathematics shift away from pure lecture format. Transitioning to a student-centered class is a complex instructional undertaking especially in the proof-based context. In this paper, we share lessons learned from a design-based research project centering instructional elements as objects of design. We focus on how three high leverage teaching practices (HLTP; established in the K-12 literature) can be adapted to the proof context to promote student engagement in authentic proof activity with attention to issues of access and equity of participation. In general, we found that HLTPs translated well to the proof setting, but required increased attention to navigating between formal and informal mathematics, developing precision around mathematical objects, supporting competencies beyond formal proof construction, and structuring group work. We position this paper as complementary to existing research on instructional innovation by focusing not on task trajectories, but on concrete teaching practices that can support successful adaption of student-centered approaches.

This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well they supported active and broad student participation. By guiding student exploration of a few key example groups and structuring the exploration to identify recurrent structure, students formulate key lemmas that they can combine to prove Lagrange's theorem.

Objective: We investigated the preliminary efficacy of a tailored human papillomavirus (HPV) vaccination on-line intervention designed to increase HPV vaccination intention. Participants: Female college students (N = 101; 18-26 years), who have not received the HPV vaccine. Methods: Participants were randomized to either a control group to read standard Center for Disease Control information or a narrative intervention group to read two narrative messages about HPV/HPV vaccination that were tailored based on the individual's sexual history and told from the perspectives from a peer and an expert. Participants were assessed at baseline (T1) and immediately after the intervention (T2). Results: The narrative intervention group reported a greater increase from T1 to T2 in vaccination intention compared with control group. Both groups reported increases in knowledge, positive attitude, self-efficacy, social norm, and perceived susceptibility to HPV from T1 to T2. Conclusions: A narrative intervention is promising to effectively increase HPV vaccination intention.

This article offers the construct "unitizing predicates" to name mental actions important for students' reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a universal set into examples and nonexamples. This explains the cognitive work that supports students to unify various statements with the same logical form, which is conventionally represented by replacing parts of statements with logical variables p or P(x). Using data from a constructivist teaching experiment with two undergraduate students, we document barriers to unitizing predicates and demonstrate how this activity influences students' ability to render mathematical statements and proofs as having the same logical structure.

The COVID-19 pandemic has had broad ranging impacts on the delivery of education at universities. In this context, hybrid-flexible teaching, or HyFlex (HF), has been offered at my university as a mode of delivery ostensibly suitable to what is ultimately a disrupted teaching environment. HF involves the delivery of a subject simultaneously in three modes: synchronous face-to-face, synchronous online and asynchronous. In this article I adopt a 'small data' research approach and examine my personal memos documenting my own implementation of a HF version of one undergraduate subject in two consecutive iterations. Existing research on HF is clear that students appreciate the convenience afforded, and while there is some general mention of the impact of HF on teacher workload, I set out to develop detailed insights by documenting and reflecting on my own experiences. Conclusions I reach are that attendance becomes complex and problematic in HF subjects, impacting curriculum design, teacher confidence and workload. Also, it is not practically possible to adapt existing synchronous subjects to HF without significant redesign, and this is to develop timely feedback interventions and create a sense of belonging for students. Hybrid-flexible learning is predicted to continue and expand in higher education, making the detailed account outlined here a valuable example.

The American Association of School Librarians (AASL) recently released standards to guide the practice of school librarians. The "National School Library Standards for Learners, School Librarians, and School Libraries" (2018) were put forward as a single text with integrated frameworks. One year later, the "ALA/AASL/CAEP School Librarian Preparation Standards" (2019) were adopted to inform the preparation of school librarians. Using a one-way crosswalk analysis, this study explores the alignment of the "AASL Standards Framework for School Librarians" from the AASL Standards with the "ALA/AASL/CAEP Preparation Standards" to determine consistencies in expectations as well as identify noted gaps. Findings will assist educators of school librarians to develop meaningful coursework and pre-service experiences

There is an uncomfortable moment in the podcast, "The Ballad of Billy Balls," that prompted me to think about a podcasting course I teach, and my approach to the emotional aspects of some of my students' own non-fiction stories. This article reflects on the course's first iteration from the perspective of Boler's pedagogies of discomfort and emotion. What became clear is that providing opportunities for students to engage with emotion and discomfort aids the development of their personal growth; yet, my approach to ethics in this course was preventing students from engaging with emotional aspects of their stories. After establishing the value of discomfort and emotion, this article presents teaching activities for the second iteration of the course. These activities are developed from my reflection and, following practitioners of speculative practice, they are designed to encourage students' exploration of emotion and discomfort and my own pedagogical experimentation in the classroom.

This article details how reading and literacy fit into the "2019 ALA/AASL/CAEP School Librarian Preparation Standards." It outlines the differences between the 2010 and 2019 standards and discusses how other standards influenced the development of the school librarian preparation standards.

This theoretical paper sets forth two "aspects of predication," which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logical structure. These aspects of predication are (1) "populating" the way students generate sets of examples of the property, and (2) "testing membership" how one tests whether or not a given object has a specific property. Using data from two teaching experiments in which undergraduate students read proofs of theorems about the discrete concept of multiple relations, we illustrate the nature of these aspects of predication and demonstrate how they help explain student interpretations of the proofs. We argue that these particular properties from number theory likely have correlates in many other discrete mathematics topics because of the role of computation/algorithms for defining and testing properties as well as the role of iteration and recursion in populating examples. We anticipate that these constructs will be useful to teachers and researchers of discrete mathematics to foster and assess student understanding of various mathematical properties. They provide tools for thinking about what it means to understand properties in a rich and coherent way that supports understanding complex lines of inference and generalizations.

This study was conducted to examine the preparation of school librarians around intellectual freedom issues. The pilot study was conducted with school librarian students at three universities. A gap analysis was used by the researchers to measure the gap between prior knowledge about intellectual freedom that students believed they possessed upon entering a school library preparation program and the knowledge they believed they possessed when leaving the school library preparation program. A survey was administered that was divided into the three aspects of self-awareness, education, and willingness to take action. The educational gaps are focused on in this article with recommendations to continue to analyze the data in further publications. Additionally, the researchers provide suggestions for improving school librarians' preparation in the area of intellectual freedom.

Objective: A measure was recently developed which assesses self-efficacy to resist NSSI across differing contexts. The aim of this study was to examine how self-efficacy to resist NSSI across contexts interacts with NSSI-related outcome expectancies when differentiating NSSI history. Participant: 501 Australian college students aged 17-40 years (M = 21.21, SD = 2.36). Method: Participants completed online questionnaires. Results: Self-efficacy to resist NSSI when in contexts considered to be protective or of high risk moderated the relationships between NSSI-related outcome expectancies and recent engagement in NSSI. Participants who expected NSSI to result in communication were more likely to have recently engaged in NSSI if they held weak self-efficacy to resist NSSI in protective contexts. Expecting NSSI to result in diminished self-worth was protective against weak self-efficacy to resist NSSI. Conclusion: Results support the application of Social Cognitive Theory to NSSI and provide future avenues for exploring NSSI-specific cognitions.

Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks connect three topics ubiquitous to such courses: logic, proof techniques, and sets. In particular, we were motivated by recent research showing that focusing on sets is propitious to novice students' ability to reason about logic and construct valid arguments. Our objectives were to (1) analyze examples of how these connections were made in relation to what is known about student thinking and learning in TTP courses and also to (2) identify situations in these texts in which there are opportunities for such connections to be made that could benefit students' learning. We focus on how logic was used to explain ideas related to sets and proof techniques, and how sets were used to explain ideas in the other domains. In addition to providing examples from our textbook sample illustrating instances in which connections were (or potentially could be made), we suggest several key recommendations TTP instructors can leverage in their unit(s) on sets.

The aim was to establish which postural and physical activity outcomes are comparable across different accelerometer brands worn on the thigh when processed using open-source methods. Twenty participants wore four accelerometers (Axivity, ActiGraph, activPAL, GENEActiv) for three free-living days. Postural and physical activity outputs (average acceleration, intensity gradient, intensity of the most active 30 min, 60 min, and 8 h) were generated. "Postural outputs": Mean absolute percent errors (MAPEs) were low, reliability excellent, and equivalency within the 5% zone across all monitor pairings for sitting/lying and upright times, but not specific lying postures. "Physical activity outputs": MAPEs were higher and reliability lower than for sitting/lying and upright time. However, the majority of the outcomes were within the 10% equivalency zone for Axivity/GENEActiv and Axivity/ActiGraph pairings. Total sitting/lying and upright times show strong potential for harmonization across studies utilizing different thigh-worn accelerometers. The majority of acceleration outcomes compare well for Axivity, GENEActiv, and ActiGraph.

This article documents differences between novice and experienced undergraduate students' processes of reading mathematical proofs as revealed by moment-by-moment, think-aloud protocols. We found three key reading behaviors that describe how novices' reading differed from that of their experienced peers: alternative task models, accrual of premises, and warranting. "Alternative task models" refer to the types of goals that students set up for their reading of the text, which may differ from identifying and justifying inferences. "Accrual of premises" refers to the way novice readers did not distinguish propositions in the theorem statement as assumptions or conclusions and thus did not use them differently for interpreting the proof. Finally, we observed variation in the type and quality of "warrants," which we categorized as illustrate with examples, construct a miniproof, or state the warrant in general form.

In this paper we analyze common solutions that students often produce to isomorphic tasks involving proportional situations. We highlight some key distinctions across the tasks and between the different equations students write within each task to help elaborate the different interpretations of equivalence at play: numerical, transformational, and descriptive. We use this opportunity to further explore the value of operationalizing these interpretations in both research and instruction.

Objectives: According to Social Cognitive Theory, the anticipated consequences of a behavior (outcome expectancies), coupled with our belief in our ability to successfully perform the behavior (self-efficacy), determine the likelihood of engagement in a behavior. We explored whether the relationship between nonsuicidal self-injury outcome expectancies and self-injury was moderated by self-efficacy to resist nonsuicidal self-injury. Participants: Five hundred and sixteen college students aged 18-26 years (M=20.60, SD=1.86). Methods: Self-report measures were completed online. Results: The relationship between expecting self-injury would result in pain or emotion regulation and engaging in self-injury was moderated by a belief in the ability to resist self-injury. People who had never self-injured were more likely to believe that self-injury would cause physical pain and believe they could resist self-injury. A belief in the ability to resist self-injury countered expectations that self-injury would result in emotion regulation. Conclusion: Results may inform college-based prevention and intervention efforts.

The value of some university mathematics courses gets characterized within a liberal arts course of study in terms of supporting "critical thinking skills" or some other phrase for generally improved reasoning. This can be seen as an application of the millennia old "Theory of Formal Discipline" that claims that mathematics learning fosters generally improved reasoning. This is ostensibly done by providing students with access to aspects of mathematical epistemology, which are taken to have some value beyond mathematics itself. The evidential basis both for learning mathematical epistemology and for its influence beyond the mathematics classroom are relatively thin, in part because they are hard to define and operationalize for research. In this paper, I will identify some challenges inherent in studying whether mathematical epistemology might contribute to productive reasoning beyond mathematics and proffer particular aspects of mathematical epistemology that could be useful for instruction and research thereupon. Given that mathematicians and many policy makers believe in the power of mathematical epistemology to improve people's general reasoning, this appears a worthwhile avenue for investigation, even if the challenge is daunting.

This study compares the relative influence of syntax, semantics, and pragmatics in university students' interpretation of multiply quantified statements in mathematics, both before and after instruction. Like previous studies, results show that semantics plays a heavy role in student interpretation, especially before instruction. Unlike previous studies, our data suggests that the patterns of student interpretation rely more upon the mathematical context than upon the order of the quantifiers. We operationalize two of Grice's (1975) pragmatic Maxims to evaluate whether they help explain which interpretations are harder for students to adopt for various statements. Our data support the claim that students find it easier to construct relevant interpretations, but do not support the claim that students find it easier to construct interpretations that render the statement true. Finally, based on our sample from six Transition to Proof classes across the US, we observe that after their experiences in such courses students became more sensitive to syntax in their interpretation of the statements.

In this paper, we provide an in-depth account of traditional IBL instruction. Understanding the nature and effects of this form of instruction is of growing importance due to the strength and breadth of the IBL movement and its connections to other forms of inquiry in undergraduate mathematics. In this case study of one real analysis course taught by a very experienced instructor and leader in the IBL community, we identify the primary goals this professor set forth for his students and the instructional strategies he employed to help them attain these goals. We observe that many of these practices seek to manage the double bind of proving in the classroom (Herbst "Journal for Research in Mathematics Education," 33(3), 176-203, 2002). Accordingly, we relate and categorize student storylines in the course according to their goal orientation and their level of buy-in to the IBL learning environment. We operationalize orientation and buy-in according to the double bind of the didactic contract by observing whether students focused more on the professor's obligation to provide resources for students to successfully complete the work of the course (and earn good grades) or on his obligation to provide an authentic experience in mathematical proving. Students' with different goal orientation and buy-in profiles took advantage of different aspects the professor's instructional strategies to engage in the course in ways that were productive for them.

The authors focus on the strategies employed in the recent renovation of the William Johnston Building at Florida State University, in which the historical exterior was preserved, while the interiors were adapted to new functions as classrooms, study centers, and common spaces with intentionally undefined purposes. The building's various use capacities, together with the flexibility of its interior environments, makes it a "building of requirement." The paper reveals how the building's historical interior layouts and architectural elements defined the approach to realizing a postmodern and future-oriented building while fostering new encounters and forming new user familiarities, thereby contributing to the evolution of the structure as living history.

In spite of numerous calls for action, e.g., Executive Office of the President (2010), there have been few efforts nationally to promote engineering education in the elementary grades. Of these, hardly any have targeted underrepresented populations (National Academy of Engineering, 2009, p. 74). The collaboration described in this paper is a significant exception, which could provide important lessons for those seeking to broaden the reach and scope of K-5 engineering education. We will argue for an interdisciplinary approach, which integrates engineering, math, science, literacy and art, and that engages a school and a university as equal partners. Neither of these components has been prominent in the literature on K-12 engineering education.

This paper sets forth a construct that describes how many undergraduate students understand mathematical terms to refer to mathematical objects, namely that they only refer to those objects that satisfy the term. I call this students' pronominal sense of reference (PSR) because it means they treat terms as pronouns that point to objects, like "that." The paper compares this account of reference with those assumed in common mathematical logic instruction. I demonstrate how propositional logic imposes unnatural uses of language on students while predicate logic is more natural to naïve language use and mathematical language use, when developed properly.

I am a lecturer with professional marketing experience, and this study was motivated by my dismay at university about what I have perceived as oversights in colleagues' typical use of mass email (emailing a single message to a large group of subscribers) for content delivery, in comparison to the communication strategies of major industries (for example, retail and public administration). I examine non-academic research about mass email best-practise, as implemented in industry communications; then I perform a systematic review of academic research on mass email for content delivery. My review of 19 studies confirms academics are behind the industry when it comes to mass email evaluation and optimisation strategies. Finally, I outline tactics necessary for more effective mass emails at university, the most salient being systematically analysing a range of email metrics, and testing and optimising emails. Also, included in this study is my identification of current obstacles to more effective mass email at university, and these include the technological limitations of learning management systems (LMS), and the limited expertise of teaching staff.

Whilst early childhood educators are well aware of the importance of meeting the needs of individual children when teaching "struggling readers", finding the time for frequent one-on-one support is difficult. Studies have established that with a well developed and structured tutoring programme, as well as high quality training and supervision, volunteers can be used to provide tutoring in a one-on-one early intervention reading programme. The current study suggests that there is an opportunity for preservice teachers to gain valuable information to increase their knowledge of the reading process, while providing effective support to schools as trained tutors. The small-scale exploratory study examines the skills and knowledge gained by preservice teachers while employed as trained tutors in an early intervention reading programme. (Contains 1 table and 1 figure.)

This study examines the institutional visibility of the university governing body amongst staff, as an unexplored factor influencing the effectiveness of the body in performing stewardship and strategic responsibilities on behalf of the university. A constructionist view of governance is taken in order to examine the enactment of governing body institutional visibility within the spaces of the university, from the formal projection of its legal and constitutional duties, to communication of the decisions made at governing body meetings, through to governors' informal encounters and engagement with staff. An institutional visibility spectrum was developed based on governing body 'apparency', 'transparency' and 'engagement', prior to interviewing secretaries and clerks as key actors in the governance system. It was found that governor visibility through engagement and interaction with a range of staff outside the 'boardroom' was perceived as a contributor to governing body effectiveness, including governors' knowledge-building and ability to contribute to strategic initiatives in the host university.

One challenge faced by many writing teachers is meeting the needs of students with varying skill and confidence levels. This article describes strategies used in a Composition and Rhetoric I course to meet the needs of basic and college-level writers. Sample assignments focusing on the theme of literacy and learning are provided, including an effective prewriting strategy called the Literacy Lifeline. The practices described are supported by Bartholomae and Petrosky's course framework in "Facts, Artifacts, and Counterfacts" (1986) in addition to other sources.

Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how logic emerges within students' mathematical activity. This activity entails reflecting on and systematizing their own language use across diverse semantic content. We present categories of students' untrained strategies for assessing the truth-values for mathematical disjunctions. Students' initial reasoning heavily reflected content-specific and pragmatic factors in ways inconsistent with the norms and conventions of mathematical logic. Despite this, all student groups reinvented the standard truth-functional definition for simple disjunctions. We demonstrate how this learning depended upon particular forms of reasoning about logic. We also contrast various strategies for assessing quantified disjunctions and their different affordances in students' mathematical activity.

We address previous hypotheses about possible factors influencing the gender gap in attainment in physics. Specifically, previous studies claim that scaffolding may preferentially benefit female students, and we present some alternative conclusions surrounding this hypothesis. By taking both student attainment level and the degree of question scaffolding into account, we identify questions that exhibit real bias in favor of male students. We find that both multidimensional context and use of diagrams are common elements of such questions.

"The Childhood Autism Rating Scale, Second Edition" (CARS2; 2010) includes two rating scales; the CARS2-Standard Version (CARS2-ST) and the newly developed CARS2-High Functioning Version (CARS2-HF). To assess the diagnostic agreement between the CARS2 and DSM-IV-TR versus DSM-5 criteria for Autism Spectrum Disorder (ASD), clinicians at community based centers of the University of North Carolina TEACCH Autism Program rated participants seen for a diagnostic evaluation on symptoms of autism using both the DSM-IV-TR and DSM-5 criteria and either the CARS2-HF or the CARS2-ST. Findings suggest that overall, the diagnostic agreement of the CARS2 remains high across DSM-IV and DSM-5 criteria for autism.

This paper demonstrates how questions of "provability" can help students engaged in reinvention of mathematical theory to understand the axiomatic game. While proof demonstrates how conclusions follow from assumptions, "provability" characterizes the dual relation that assumptions are "justified" when they afford proof of appropriate results. I provide examples of students' learning in teaching experiments connected to an advanced, undergraduate, neutral axiomatic geometry course. Students used "provability" relations to choose definitions, develop the notion of independence, and understand the relationship between axioms and theorems. I argue that provability promotes cognitive need for systematization, allaying concerns that geometric proof lacks illuminative value.

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

This study presents how the introduction of a metaphor for sequence convergence constituted an experientially real context in which an undergraduate real analysis student developed a property-based definition of sequence convergence. I use elements from Zandieh and Rasmussen's (2010) Defining as a Mathematical Activity framework to trace the transformation of the student's conception from a non-standard, personal concept definition rooted in the metaphor to a concept definition for sequence convergence compatible with the standard definition. This account of the development of the definition of sequence convergence differs from prior research in the sense that it began neither with examples or visual notions, nor with the statement of the formal definition. This study contributes to the Realistic Mathematics Education literature as it documents a student's progression through the definition-of and definition-for stages of mathematical activity in an interactive lecture classroom context. (Contains 4 figures and 2 tables.)

Weber and Alcock's (2004, 2009) syntactic/semantic framework provides a useful means of delineating two basic categories of proof-oriented activity. They define their dichotomy using Goldin's (1998) theory of representation systems. In this paper, I intend to clarify the framework by providing criteria for classifying student reasoning into different types of representation systems, especially pertaining to students' language use. I also suggest an extension to the framework by incorporating Goldin's (1998) construct of competencies. I demonstrate the analytical utility of these extensions to the framework in relation to a case study of two students' proving activity in an undergraduate geometry course.

Content knowledge and pedagogical practices are of particular concern to middle school science instructors teaching density. First introduced in elementary grades with the ideas of floating and sinking, density taught in middle school is geared toward understanding through the use of mathematical formulas. Using a lesson-plan study design, the authors identified preservice teachers' content understandings regarding density and how those understandings influenced their teaching practices. The results indicated that, although teacher candidates had developed reasonable, intuitive understandings of density, many experienced difficulty connecting those understandings to the mathematical relationships involved. Therefore, university science educators must carefully examine the levels at which their students understand density so that these future educators have the necessary conceptual knowledge to teach this concept effectively. (Contains 1 table and 1 figure.)

Learning communities are becoming increasingly popular in the quest for enhancing student learning. The purpose of this study is to examine the impact of the "Healthy Youth" Learning Community on student learning outcome measures. In this study, the authors compared student learning outcome measures of students enrolled in those sections of HED 332 that were involved in the Health Youth Learning Community with those who were not. The outcome measures used were: midterm exam, final exam, lesson plan, lesson plan presentation, and overall course average. Results indicate a statistically significant difference on midterm and final exam scores. (Contains 1 table.)

Learning communities continue to be at the heart of teaching and learning today. The purpose of this study is to examine the extent of the impact of the Freshman Academy/Learning Community program on student progress at a historically Black university. The authors also looked at the extent to which students engaged in their learning as a result of strategies developed and implemented based on the quality enhancement plan of "Strengthening the Quality of the Freshman-Year Experience through Student Engagement and Active Learning." Finally the extent of engagement and satisfaction with the program as reported by students were compared. The results showed some interesting differences in these core practices: active learning, integrated assignment, co-curricular and service learning activities. Performance was measured by analyzing student progression at the course, program, and university levels. The results are being used as feedback for program improvement. (Contains 6 tables.)