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Rasch models for fundamental measurement in the psychological sciences are derived from the principle of specific objectivity, the requirement that the parameter value representing each component in a test situation be independent of the other components. The dichotomous Rasch model for two-faceted analysis, applicable to conventional paper-and-pencil tests, is constructed. The many-faceted Rasch model is also derived by means of a three-faceted example, comprising judges, examinees, test items, and a rating scale, which is applicable to many judging situations. Any other particular form of the many-faceted model may also be derived in a similar manner. (Author/TJH)

Although numerous research studies have shown that viewing educational television results in significant gains in preschool and school-age children's academic knowledge or skills, there is less consistent evidence regarding transfer of learning, the application of knowledge or skills learned in one context to a new problem or situation. This paper is a first attempt to provide a theoretical basis for transfer from educational television and to describe factors that can be built into educational television programs to maximize the possibility of transfer. The paper takes several factors that are common across many existing theories of transfer and applies them to the context of educational television. In addition, the paper draws upon the literature on children's learning from educational television and on the capacity model, which describes some of the processing underlying comprehension of educational content on television. Three factors viewed as critical to transfer of learning are examined: (1) the viewer's initial learning or comprehension; (2) the nature of the viewer's mental representation of the content; and (3) the transfer situation, the novel problem to which the content is subsequently applied. The paper concludes by asserting that the likelihood with which transfer will occur is a function of the characteristics of the viewer (such as developmental differences in metacognition and ability to draw inferences), the program (such as the distance between the narrative and educational content), and the transfer situation (including the relationship between the narrative and the underlying educational context). It is noted that although many unanswered questions remain, this paper provides a starting point for discussion and research. (Contains 55 references.) (KB)

The purposes of this paper are to identify common errors made by researchers when dealing with reliability coefficients and to outline best practices for reporting and interpreting reliability coefficients. Common errors that researchers make are: (1) stating that the instruments are reliable; (2) incorrectly interpreting correlation coefficients; (3) not reporting reliability coefficients for their own sample; (4) conducting tests of statistical significance on reliability coefficients; and (5) failing to report the reliability of difference scores when examining gain scores. It is recommended that researchers report reliability coefficients for their own data and that they interpret confidence intervals around reliability coefficients, considering that reliability coefficients should be reported not only for the full sample at hand but also for each subgroup. A heuristic example is used for the two-sample case (i.e., t-test) to illustrate how comparing subgroups with different reliability coefficients can affect statistical power. (Contains 3 tables and 36 references.) (Author/SLD)

Researchers consistently fail to report reliability estimates for data used in their studies. This lack of reporting hinders appropriate evaluation and interpretation of data and may lead to inappropriate conclusions. Because reliability is inured to scores obtained from a test, and not the test itself, it is important to report score reliability in both measurement and substantive studies. Failure to report reliability estimates is a practice that plagues social science research and may undermine results across studies. Reliability generalization (RG) is a meta-analytic method that looks at the reliability of scores from tests and helps to determine what is causing measurement error across studies. RG has the potential to help researchers use specific tests more accurately and to help identify specific sample characteristics and other factors that influence and affect score data. The purpose of this paper is to discuss the sample dependency of score reliability, emphasize the importance of measurement, even in substantive studies, and explain the premises and procedures of RG. (Contains 1 figure, 1 table, and 29 references.) (Author/SLD)

This paper describes how one researcher's understanding of life history research evolved while conducting research with a high school English teacher. The life history examined the history and evolution of the teacher's beliefs about literacy and how those beliefs related to her teaching practices throughout her career. The paper begins by explaining what life history research is, then it elaborates on two experiences that helped make sense of life histories for the researcher. The first experience was around the issue of life history as an artistic interpretation (following an experience in an art museum). The second experience was a troubling conversation with a former mentor about what constituted educational research and why life history research was controversial as a topic. The paper suggests that life history and narrative research can be as robust as or more robust than quantitative studies in terms of trustworthiness, and it notes that it can produce knowledge or insights that could be generalized to other teachers. The paper concludes by arguing for the importance of life history research. (Contains 58 references.) (SM)

The purpose of this paper is to describe (a) multivariable calculus students' meanings for the domain and range of single and multivariable functions and (b) how they generalize their meanings for domain and range from single-variable to multivariable functions. We first describe how students think about domain and range of multivariable functions as inputs and outputs, independent and dependent quantities, and as associated with particular variables. We then use an actor-oriented transfer framework to describe the ways in which students identify similarities between domain and range in single- and multivariable functions, and how they use these similarities to generalize their meanings for domain and range. [For the complete proceedings, see ED597799.]

The purpose of this paper is to explore teachers' ability to explain student reasoning in linear and non-linear patterns and in different types of generalization tasks. A questionnaire consisting of student responses to different types of generalization tasks was developed and then given to a sample of 91 in-service mathematics teachers from 20 schools in Lebanon. Analysis of data shows that teachers' explanations exhibited variations in the extent to which they identified the elements and relationships found in students' responses. The results showed that teachers' ability to explain students' reasoning of linear tasks seemed to be higher than that of non-linear patterns. The findings also showed that teachers' explanations of students' reasoning for far generalization tasks exhibited a larger amount of data (elements and relationships) compared to the explanations for near generalization tasks. [For the complete proceedings, see ED597799.]

Over the last three decades, there has been increased attention on the collection and interpretation of "response processing data" to inform claims of learners' knowledge and skills (e.g., see Ercikan et al., 2010; Kobrin & Young, 2003; see also, Leighton, 2004). Response processing data are perhaps most consequential in the development of validation arguments to support claims or inferences about test-takers (see AERA, APA & NCME, 2014). However, these data may also serve to inform test development and encourage dialogue on fair student assessment of 21st century skills. One challenge is that methods for collecting response processing data vary in non-trivial ways and must be employed judiciously depending on the cognition of interest being measured. Thus, the objective of the paper is to highlight how two methods -- cognitive labs and think alouds -- can and should be used adaptively to inform distinct goals in test development, validity arguments, and to further the credibility of claims made about test-takers.

We investigate generalizability of face-based detectors of mind wandering across task contexts. We leveraged data from two lab studies: one where 152 college students read a scientific text and another where 109 college students watched a narrative film. We automatically extracted facial expressions and body motion features, which were used to train supervised machine learning models on each dataset, as well as a concatenated dataset. We applied models from each task context (scientific text or narrative film) to the alternate context to study generalizability. We found that models trained on the narrative film dataset generalized to the scientific text dataset with no modifications, but the predicted mind wandering rate needed to be adjusted before models trained on the scientific text dataset would generalize to the narrative film dataset. Additionally, we analyzed generalizability of individual features and found that the lip tightener and jaw drop action units had the greatest potential to generalize across task contexts. We discuss findings and applications of our work to attention-aware learning technologies. [For the full proceedings, see ED596512.]

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer Science and Technology at Tsinghua University; and Dr. Ron Cole, President of Boulder Learning Inc. The main conference invited contributions to the Research Track and Industry Track. 122 submissions were received (71 full, 47 short, 4 industry). 18 full papers papers were accepted (25% acceptance rate) and 32 short papers for oral presentation (42% acceptance rate) and an additional 39 for poster presentations, 3 demonstrations. The industry track includes all 4 submitted industry papers and 1 paper initially submitted as a full paper. The EDM conference provides opportunities for young researchers, and particularly Ph.D. students, to present their research ideas and receive feedback from the peers and more senior researchers. This year, the Doctoral Consortium features 6 such presentations. In addition to the main program, the conference includes 3 workshops: (1) Graph-based Educational Data Mining (G-EDM 2017); (2) Sharing and Reusing Data & Analytics Methods with LearnSphere; and (3) Deep Learning with Educational Data; and 2 tutorials: (1) Why Data Standards are Critical for EDM and AIED; and (2) Principal Stratification for EDM Experiments. [For the 2016 proceedings, see ED592609.]

This paper demonstrates a method for constructing long variables using items that elicit partically correct responses across ages. Long variables may be defined by students at different ages (year levels) attempting common items within a test containing other items considered to be appropriate for each age or year level. A developmental model of understanding is described in the form of vertically equating a student's response with expectations for increasing sophistication in the response range. A unit from the Victorian Social Education Study on the long variable of "cultural understanding" is provided to exemplify the technique. The paper demonstrates the use of the Rasch partial credit model for mapping student responses onto this continuum of cultural understanding. Stimulus material, items, sample responses, and the analysis are all outlined in detail. (EH)

This study examined discussions centered on precise mathematical language use in two fifth grade classrooms. Drawing on episodes from lessons in which teachers focused on encouraging mathematics reasoning, our analysis examines the relationship between precise language use and mathematical justifying. We present three classroom episodes that illustrate facets of the relationship between precise language use and mathematical argument, and explore how blurring the borders of two types of pedagogical tools (attention to precise mathematical language and engagement of students in justifying) promotes enculturation of students into mathematics. [For the complete proceedings, see ED583608.]

Mathematics education practitioners and researchers have long debated best pedagogical practices for introducing new concepts. Our design-based research project evaluated a heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives (grounding) and formal mathematical rules (generalizing). We compared student performance under conditions of working with stark (acontextual) vs. iconic (situated) manipulatives. We summarize findings from analyzing 20 individually administered task-based semi-structured clinical interviews with Grade 4-6 participant students. We found tradeoffs of situatedness: Whereas iconic objects elicit richer narratives than stark objects, these narratives may detrimentally constrain the scope of potential sensorimotor schemes students develop in attempt to solve manipulation problems. [For the complete proceedings, see ED583608.]

This paper reviews evidence of the success of behavior intervention approaches which teach students with challenging behaviors alternative functional communication behaviors. Research supporting the view that challenging behavior is a form of nonverbal communication is reviewed, noting the importance of identifying what such individuals are "saying" with their behavior problems. Functional communication training is described as providing the consequences originally maintaining the target behavior with a new more appropriate behavior. Specific interventions which used functional communication to reduce such behavior problems as aggression, self-injurious behavior, and stereotyped or self-stimulatory behaviors are reviewed. Factors affecting the initial effectiveness of functional communication training include matching responses to functions of the challenging behavior and ensuring that the appropriate behavior is more response efficient than the inappropriate behavior. Factors affecting generalizability and maintenance include response acceptability, recognizability of the communicative response, and communicative context. Recommendations for implementation stress home-school collaboration, teamwork, and development of secondary prevention strategies. Other recommendations address development of a comprehensive model of behavior, development of assessment procedures, improved use of augmentative communication strategies, and primary prevention of serious behavior problems. (Contains 73 references or suggested resources.) (DB)

To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of 3 different multiplicative concepts participated. This paper reports on the 6 students with the most basic multiplicative concept, who were also pre-fractional in that they had yet to construct the first genuine fraction scheme. These students' emerging iterating operations facilitated their algebraic activity, but the lack of a disembedding operation was a significant constraint in developing algebraic equations and expressions. [For the complete proceedings, see ED584829.]

This paper maintains that the best approach to writing across the curriculum is one that focuses on thinking and writing strategies that cut across a number of subject areas. The paper describes some methods and classroom tested activities found to be successful in teaching students the complex thinking skills involved in making and supporting generalizations, producing arguments in a composition, and creating extended definitions. The paper includes sample materials involving a variety of different subject areas to provide ideas about activities that work with students at a variety of ability and grade levels. In three main sections, the paper presents four activities to develop the ability to make and support generalizations, four activities to promote argumentation skills, and three activities to develop the skills involved in extended definitions. The paper contends that focusing instruction on such activities will enable students to learn these important thinking strategies. The paper maintains that if the activities are interesting, engage students in using the target strategies, provide repeated practice of the strategies in a variety of situations that are sequenced with more structure at the beginning and move to student independence at the end, and require students to contend with the immediate demands of a real audience in small group and whole class discussions, then students will be able to think and write more effectively across the curriculum. (Forty-eight references are attached, and appendixes contain 20 pages of student activity sheets.) (SR)

Findings from a study to develop and validate an instrument for the measurement of principals' attitudes toward visionary leadership are presented in this paper. Two leadership styles--visionary and managerial--were measured by a 35-item five-point Likert attitude scale. Questionnaires mailed to a random sample of 250 K-12 Nebraska and 250 California principals yielded 387 completions, a 77 percent response rate. Factor analysis confirmed that factors corresponding to the two leadership styles were implicit in the instrument design and supported the instrument's validity for measuring attitudes toward the conceptualization of visionary leadership. The instrument may be used for empirical substantiation of a generalization of visionary leadership style, for diagnostic purposes, and as a screening tool. Two tables, including a statistical analysis of the survey item results are provided. (11 references) (LMI)

This paper describes some methods found to be successful in helping students learn two major thinking strategies: making and supporting generalizations, and argumentation. The paper includes sample materials involving a variety of different subject areas to provide ideas about activities that work with students at a variety of ability and grade levels. In two main sections, the paper presents activities to develop the ability to make and support generalizations, and activities to promote argumentation skills. The paper maintains that such activities will enable students to learn these important thinking strategies, particularly if the activities are interesting; engage students in using the target strategies; provide repeated practice of the strategies in a variety of situations that are sequenced with more structure at the beginning and move to student independence at the end; and require students to contend with the immediate demands of a real audience in small group and whole class discussions. (Thirty-seven references are attached, and appendixes contain 20 pages of student activity sheets.) (SR)

This paper examines the tension in the process of designing student surveys between the methodological requirements of good survey design and the institutional needs for survey data. Building on the commonly used argumentative approach to construct validity, I build an interpretive argument for student opinion surveys that allows assessment of the inferences and assumptions underlying the claim that an opinion survey item is a valid measure of a construct. I then evaluate the content validity of measures of program satisfaction and academic growth in Utah Valley University's 2010 Graduated Alumni Survey and 2009 Graduating Student Survey, surveys designed to maximize conformity with existing and legacy institutional priorities and demands. Using analytical assessment and empirical tests including response change across surveys, inter-item correlation, and factor analysis I show that UVU's surveys--and by implication, all surveys developed with primarily institutional validity in mind--are subject to grave challenges to the construct validity. I conclude by suggesting that effective operationalization of institutional priorities can bring together construct and institutional validity. AIR Forum Powerpoint Presentation is appended. (Contains 9 tables and 4 footnotes.)

Literature shows that most researchers are unaware of some of the characteristics of reliability. This paper clarifies some misconceptions by describing the procedures, benefits, and limitations of reliability generalization while using it to illustrate the nature of score reliability. Reliability generalization (RG) is a meta-analytic method developed "to characterize the mean measurement error variance across studies [using a particular instrument] and also the sources of variability of these variances across studies" (Vacha-Haase, 1998, p. 6). Like all meta-analyses, RG uses studies, rather than individuals, as the unit of analysis to help researchers find which study characteristics to predict or explain variability in observed score reliability coefficients.

The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on materials called "object boxes," then created sets of their own object box materials. Each algebra rules object box contained materials to illustrate and describe four different algebraic generalizations, or "rules." The variables "n" and "z" were used in each of the generalizations. For each generalization, there was a set of objects attached to a piece of mat board that showed three cases of the generalization for different values of "n." Two sets of cards accompanied these objects, giving word problems, defining variables, stating equations, and explaining the algebraic generalizations. Students matched word problems to the object sets, defined variables and checked their work, then wrote algebraic generalizations for the object sets and used the reverse sides of the equation cards to check their work. Projects were graded with a rubric. Students were then surveyed about their difficulties. Results of the analysis showed that students were able to make an assortment of authentic materials in a variety of contexts and enjoyed the creative aspects of the project, but found the algebraic content challenging. The most common mathematical difficulties were being able to define the variable, and identify the pattern. Examples of effective student materials are provided. (Contains 4 tables and 16 figures.) [This paper was presented at the: (1) Annual Conference of the New York State Association of Teacher Educators (NYSATE) (Saratoga Springs, New York, April 28) [Conference presentation title: Preservice Elementary Candidate Assessment of Algebraic Understanding for Accreditation]; and (2) Annual Conference of the Association of Mathematics Teachers of New York State (AMTNYS) (Saratoga Springs, New York, October 26-28) [Conference presentation title: Using Hands-On Materials to Write Algebraic Generalizations (Grades 5-8)].]

In this paper we focus on the role of signs in students' perceptive processes underpinning the generalization of numeric-geometric patterns. Based on a videotaped Grade 9 classroom group activity undertaken by three students and framed by a cultural-semiotic theoretical perspective, we carry out a microgenetic analysis of an elementary form of mathematical generalization termed "factual". We present a detailed analysis of the dynamics between oral speech and gestures. Two main results are: the detection of intra-personal and inter-personal synchronizations between different semiotic systems; and the individuation of the key role played by objectifying iconic gestures. (Contains 5 figures.) [For complete proceedings, see ED496851.]

The 9th International Conference on Educational Data Mining (EDM 2016) is held under the auspices of the International Educational Data Mining Society at the Sheraton Raleigh Hotel, in downtown Raleigh, North Carolina, in the USA. The conference, held June 29-July 2, 2016, follows the eight previous editions (Madrid 2015, London 2014, Memphis 2013, Chania 2012, Eindhoven 2011, Pittsburgh 2010, Cordoba 2009 and Montreal 2008). The EDM conference is the leading international forum for high-quality research that leverages educational data, learning analytics, and machine learning to answer research questions that shed light on the learning processes. This year's conference features three invited talks by: Rakesh Agrawal, President and Founder of Data Insights Laboratories; Marcia C. Linn, Professor of the University of California at Berkeley; and Judy Kay, Professor of the University of Sydney. Judy Kay's invited paper entitled "Enabling people to harness and control EDM for lifelong, life-wide learning" is also presented in the proceedings. Together with the "Journal of Educational Data Mining" ("JEDM"), the EDM 2016 conference supports a "JEDM" Track that provides researchers a venue to deliver more substantial mature work than is possible in a conference proceedings and to present their work to a live audience. The papers submitted to this track followed the "JEDM" peer review process; three papers have been accepted to the track and were presented at the conference. The abstracts of the invited talks, panels and accepted "JEDM" Track papers can be found in these proceedings. [For the 2015 proceedings, see ED560503.]

The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was conducted with two classes of students with an average of eight years and six months. From the results it seems that the use of unmeasured quantity models in conjunction with number models does assist students focus on the underlying generalizations inherent in the models presented. (Contains 1 table and 1 figure.) [For complete proceedings, see ED489597.]

In this report, we will consider in-service elementary school teachers' noticing of the mathematical practice: justification. This study is part of a larger project evaluating the efficacy of a three year professional development built around attending to student thinking and promoting mathematical habits of justifying, generalizing and making sense. Noticing justification is a complex task requiring attention to both the (1) mathematical content and strategies and (2) the nature of the argument provided by a student. We have found that teachers' struggle to attend to both aspects simultaneously and offer a framework for considering teacher noticing of mathematical practices. [For the complete proceedings, see ED583989.]

In this paper, the theory of variation in the tradition of phenomenographic research approach is placed in the context of Dynamic Geometry Environment (DGE). Central concepts of discernment, variation, simultaneity and space of learning in the theory of variation are discussed for simple dragging episodes in DGE to illustrate the potential partnership between the two enterprises. Implications for further research will be discussed at the end. (Contains 6 figures.) [For complete proceedings, see ED500858.]

This paper explores the role of open-ended realistic division problem in the development of algebraic reasoning. A written test was administered to 672 students. From the results of this test students were selected for semi-structured interviews. The students were interviewed in pairs and were asked to explain to each other how they would solve the problem. The results of the written tests and the semi-structured interviews indicated that both students understanding of division and the real world context of the problem played an important role in abstracting generalisations. (Contains 2 tables.) [For complete proceedings, see ED500859.]

Although mathematics deals with generalizations relating abstract ideas, very little attention has been given in the mathematics education literature to the role of abstraction and generalization in the development of mathematical knowledge. In this paper, the meanings of "abstraction" and "generalization" are first explored by examining various definitions given by mathematics educators and others. These concepts are illustrated by reference to the author's research on children's understanding of angle concepts. The question of how mathematics teaching would be affected if more explicit attention were given to abstraction and generalization in the classroom is then considered. Finally, some recent experiments in "teaching for abstraction" are presented and discussed. (Contains 29 references.) (Author/MM)