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The three phases (finding seventh and eighth grade mathematically talented students, studying them, and helping them educationally) of the Study of Mathematically Precocious Youth (SMPY) are detailed, and examples of the superiority of educational acceleration over educational enrichment are pointed out. Results of standardized intelligence tests are seen to be less helpful than scores on the mathematics part of the College Entrance Examination Board's Scholastic Aptitude Test in identifying gifted students for SMPY. Four types of enrichment (busy work, irrelevant academic, cultural, and relevant academic) are described and contrasted with academic acceleration. Presented is the case of 11 1/2-year-old boy who was helped educationally by entering college before completing high school. Stressed is the need for flexibility that makes a variety of educationally accelerative possibilities (such as grade skipping and college courses for credit) available for the student. (SBH)

PLAN is a computer-managed individualized learning program with two major goals: to provide each child with an individualized program of studies in the language arts, mathematics, science, and social studies and to involve students in making decisions and assuming responsibility for their own learning. A computer assists the teacher by scoring and analyzing tests, recording student progress, and providing daily objectives for learning. Teachers spend most of their time tutoring and counseling students on a one-to-one basis or in small groups, during which time Teaching Learning Units (TLU's) are introduced. A TLU states the objective the child will work toward, lists the materials he or she will use, and prescribes the activities he or she will perform in order to achieve the objective. Some learning activities require students to work in small groups, while others require them to work alone. When a child feels that he or she has mastered the objective of a TLU, the child is tested individually and measured against his or her own potential. (LL)

This paper reports a study in which eighteen structural and linguistic variables were identified, defined and used in an attempt to determine which variables accounted for a significant amount of the observed variance in the difficulty level of items on two different conditional reasoning tests administered to high school and college students. The use of regression analysis identified a tentative subset of variables which accounted for a significant amount of variance in the proportion of correct judgments of verbal simple deductive arguments of the conditional type. (PEB)

A study involving 20 emotionally disturbed boys (9- to 11-years-old) was conducted to determine the effects of tactile and verbal reinforcement on attention to task and accuracy. Ss were given arithmetic problems to work during 16 20-minute sessions under four conditions: tactile reinforcement (intermittent touch pressure applied to Ss shoulders as they worked); verbal reinforcement (intermittent praise by the teacher); a combination of tactile and verbal reinforcement; and control treatment (no reinforcement cues). At the end of each period, scores were calculated for each S on both attention to task and accuracy of performance. Results showed that the combination treatment was most effective in producing high attention to task and high accuracy in problem solving; that tactile and verbal reinforcement alone ranked second and third in effectiveness; and that combination, verbal, and tactile treatments were all superior to the control with the exception that verbal reinforcement alone failed to produce higher problem solving accuracy. (Author/SB)

To determine possible implications of sex differences that might be useful for educators planning accelerated programs for mathematically gifted students, four measures of values and career-related interests were administered to three groups (totaling 78 Ss) of gifted seventh grade girls and boys. Results indicated that male Ss showed strong theoretical and investigative orientations compatible with scientific pursuits and academic acceleration in mathematics, that female Ss exhibited stronger interests in social and aesthetic values and careers, and that female Ss were considerable less rejecting of "masculine" careers than were male Ss of "Feminine" careers. It was also found that female Ss were characterized by feelings of conflict when presented with opportunities for educational acceleration in theoretical and investigative pursuits, suggesting that gifted girls should be taught by socially oriented female mathematicians, that their course content should relate theoretical mathematics to applied problems with a social interest appeal, that they should be offered career counseling that relates classroom experience to future jobs, and that special program opportunities for mathematically gifted adolescent girls should involve a sufficient number of female students to minimize feelings of social stigma associated with appearing "different" or "unfeminine." (LH)

Reported are results of a study comparing the incidence and characteristics of male and female mathematically gifted junior high students, and suggested are ways to encourage female participation in science and mathematics. It is explained that the Study for Mathematically Precocious Youth identified significantly more males than females with outstanding mathematical reasoning ability and also noted differing attitudes (such as greater social values and less inclination to seek out mathematical experiences) on the part of highly gifted girls. An accelerated class for girls only is reported to have been moderately effective in promoting mathematical achievement among girls. It is concluded that the observed sex differences may be biologically based or due to such environmental variables as less parental encouragement for mathematically gifted girls. (DB)

The relationships between use of specific tutorial skills and pupil outcomes is the domain of the present paper, the third of three studies of mathematics tutoring designed and conducted using three populations of tutors--teachers, paraprofessionals, and students. The other two studies individually address the effects of tutoring on the achievement and attitudes of fourth and/or fifth grade pupils, and the effects of training in tutorial skills on the achievement and attitudes of fourth and/or fifth grade pupils. Minicourse 5, Individualizing Instruction in Mathematics, is used as the training vehicle for each of the three studies, although the materials are adapted for use with the student tutors. Regression analysis procedures are proposed in order to investigate the relationship of the tutoring skills and interpersonal behaviors to pupil outcomes. The data which forms the basis of the regression analyses consists of frequency counts indicating the number of times that a particular skill is used in the tutorial setting. A more appropriate question in these analyses might have concerned itself not with the quantity of skill usage, but with the quality or appropriateness of a particular skill being used. (Author/AM)

Thirty-eight teachers and 96 low achieving students from 10 elementary schools were involved in a study designed to evaluate the effects of an inservice training course, "Tutoring in Mathematics", on teachers in mainstreaming settings. Course effects were defined in terms of specific tutoring skills and teacher attitudes about working with mainstreamed students. Changes in student math achievement and attitudes toward math were also examined. Experimental teachers took the 6-week course while control teachers received no training. A videotape of a tutoring session was taken before and after training. Three of the nine tutoring skills (specific verbal praise, negative comments, and teacher declarations) reached statistical significance at posttest for the experimental teachers; control teachers did not exhibit significant gains in tutoring skills. Significant gains were also achieved on the total attitude scale and two attitude subscales for experimental teachers only. Pre-post math attitude and math achievement scores were collected for the students. Students of experimental teachers showed significant gains in total math achievement particularly in addition, subtraction, and multiplication subscales, whereas students of control teachers did not exhibit similar gains. Data on student attitude toward math indicated no significant increase or decrease for both student samples. (Author/SB)

This paper examines consumer education choices over variables affecting the quality and the costs of differing educational outcomes. For ten years, the city of Milwaukee, Wisconsin, has pursued a policy of open enrollment. Transfer figures for the 1974-75 school year at the city's 15 high schools are analyzed according to schoolwide racial data, street mile distances, percent of black students in each school, average class size, percent of teachers having M.A. degrees, and tenth-grade math scores. A separate regression was run for each school, with the percentage of students transferring as the dependent variable and the five selected characteristics of the other schools as independent variables. The following tentative conclusions emerge: (1) it is appropriate to conceive of a school system as a market; (2) families do take distance costs into account in making educational purchases, but less than they do benefits from such school attributes as student test scores; and (3) no strong support for racial prejudice controlling educational purchases of either race could be found. (Author/MLF)

The practice of utilizing mathematics instruction, in which only practical engineering applications and not the pure mathematical proofs are stressed, is questioned. Three cases are presented in which students made erroneous conclusions concerning an engineering topic. In each situation, the student violated a mathematical principle which was not evident to him because his instruction had dwelled only on the practical applications of the formulae. (CP)

The Michigan Department of Education implemented a large-scale social action program through its Compensatory Education School Aid Act of SY 1971-72. Schools received $200 per pupil and were held accountable for pupil achievement. This paper describes the educational delivery systems in three urban schools, the evaluation of pupil achievement, and the state validation process. The results showed that the downward trend in achievement among inner-city students was reversed, and that promising educational practices were documented and replicated. The success of the programs has resulted in the continuation and recent large increase in funding for Michigan schools. (Author)

A model of an evaluation process for a college level mathematics course using management procedures is described. It is suggested that by designing the evaluation process as part of a management procedure, data useful for making policy decisions will be generated and the success of the instructional process will be insured. The foundation of the system is the development of a procedures manual that generates questions about policies that affect the administration, the students, and the operation and effectiveness of the staff and the program. The second phase of evaluation involves data analysis concerning questions of staff size, program structure, attendance requirements, grading procedures, and program costs. Data collection, the third phase, provides a record of student progress and weekly cumulative reports. Quarterly reviews and tutor evaluations are also part of the procedure used. The final phase of evaluation is dissemination of reports to the staff, administrative units, and agencies outside the university. The reports range from one-page summaries to full-scale reports documenting procedures and student achievement. It is suggested that the management approach to evaluation evolved because the success of this program for mathematics depended upon efficient program management as well as quality instruction and materials. The evaluation components of the model are viewed as having a large effect on the success of these programs. (Author/SF)

Discussed are some issues and queries about research in language and language acquisition. In particular, the area of inquiry is the logic subjacent to communication. In question here are the foundations of communication. What, if anything, underlies language? The unorthodox position developed in this paper has ambitious assumptions and slim empirical foundation. Nevertheless, it has strong links with some classical intellectual theories. The general argument to be made runs roughly as follows: The human animal is, to a great extent, characterized by the mathetic capacity. This innate capacity, which is related to the primal abilities of classifying and rule-generating and following, is essentially mathematical in nature and underlies all cognitive activity including language. Relative to their own sets of assumptions, human beings tend to be logical or consistent beings. A rich and not well-developed area for understanding the nature of language and its acquisition, and intellectual growth in general, is the study of children in situations where their implicit sets of rules or assumptions become clear. The clarity, precision, and power of certain elementary mathematical structures make them ideal vehicles for the study of the mathetic capacity and its manifestations. (Author/MK)

The influence of sex-role identity on academic achievement behaviors and attitudes is just beginning to be understood. This paper examines two subject areas, mathematics and English, which have traditionally been sex-typed as male and female domains, respectively. Two mechanisms by which sex-role identity may affect achievement behaviors--value of task and self-perceptions--are also explored. The instrument used in this study includes a list of activities shown to be sex-typed. The respondents rated these activities as to their importance for girls and boys. The ratings were used to assess the degree to which students stereotype the activities of boys and girls. Results showed boys as expressing more stereotypical views in general. As for the effect of sex-role identity on achievement attitudes, it was greatest for girls on their attitudes toward math; for boys toward both math and English. The androgynous personality seemed to have the most positive attitudes toward math and English. (Author/GK)

The study investigated the development of 48 gifted adolescents' competencies and achievement related cognitions in mathematical skill development and examined the effects of school achievement level and sex. Ss completed a self instructional packet on mathematical residues (remainders) and were periodically assessed on perceived ability, task difficulty, effort, general expectancy, and perceived efficacy. Compared with Ss who performed well in school, underachievers judged ability, general expectancy, and perceived efficacy lower, and rated task difficulty and effort higher. Contrary to prediction, there were no sex differences on any measure. Three possible reasons for the lack of sex differences were noted. (Author/CL)

Five papers, three panels, and descriptions of six technical assistance workshops are presented from a national conference for sex equity coordinators and directors of vocational education for each state. The first section contains the five papers addressing the topics of vocational education's role in reindustrialization from one of five perspectives: historical, economic, planning, evaluation, and business. Papers focus on a history of working women, economic trends, critical issues in planning, developing criteria for sex equity programs, and economic/business recovery and education. A fact sheet following each paper summarizes major points. The second section includes three panel discussions expanding on two topics--planning and political perspectives. Titles of the first two are Implementing State Planning (4 presentations) and The Political Perspective on Reindustrialization (4 presentations). The third panel presents comments from the State Directors of Vocational Education. The third section presents descriptions of six technical assistance workshops (with information and materials used). Topics include mathematics as a basis of vocational education; promoting race and handicap equity; funding, implementing, and monitoring effective sex equity programs; survival strategies for postsecondary vocational education programs; political, social, and economic factors influencing progress of sex equity; and effective use of available state vocational education data. The agenda is appended. (YLB)

Investigated with 26 gifted seventh-grade girls was the influence of an experimental summer mathematics acceleration program on later mathematics course-taking behavior. Classes were designed to provide social stimulation through such methods as using a woman teacher and assistants for role models, informal structure, organization for small group and individualized instruction, stressing cooperative activities, and emphasizing ways in which mathematics could be used to solve social problems. Among conclusions after a 3-year follow-up were that the course-taking behavior of gifted girls can be modified by early intervention, and that career interest appears to be more difficult to influence. (IM)

Reported are methods of accelerating and individualizing science and mathematics curricula for extremely gifted junior high school students as developed by the Study of Mathematically Precocious Youth (SMPY) and the Intellectually Gifted Child Study Group. Given are examples of acceleration such as allowing the student to take more advanced courses in the standard sequence, taking advanced placement courses, taking special out of class college level courses, or receiving tutoring through the Oxford-Cambridge Tutorial Preceptory System of SMPY. A question is raised regarding the amount of laboratory work that is necessary for highly gifted science students. Sources of further information are provided. (DB)

Reading the language of mathematics textbooks is very different from reading the narrative in traditional basal textbooks, and children should be taught how to read in a mathematics course; teachers should not assume a transfer of skills will occur. Specific skills, such as noting details, following directions, and seeing relationships, should be taught. Students should be shown how to modify their flexible narrative reading styles to one of great deliberation, in order to understand mathematics reading material. The specialized vocabulary of mathematics and the special mathematical symbols must also be specifically taught, beginning with concrete examples when possible. Suggestions for instruction include getting the students to discuss the expository material or the verbal problem, in order to understand their thinking processes; being careful, as an instructor, not to talk too much; being sure that students understand the technical vocabulary; and preparing short-answer, multiple-choice tests to use as pretests before instruction in a particular concept. (MKM)

In this study, two experiments indicate that modification of the method of scoring in the EQUATIONS game enhances achievement in learning specific mathematical ideas. The experimental scoring method (4+ scoring) which allows learners to obtain bonus points for constructing more complex solutions was introduced into year-long instructional gaming tournaments in two classrooms: a seventh-grade class in an inner-city school and an eighth-grade class in a suburban university-community school. The results in the experimental classes were compared with those in corresponding classes taught by the same teachers in which the conventional scoring method was used. The mean difference in pretest/posttest results was nearly three times as great in the experimental class as in the control class in the eighth-grade group, and nearly double in the seventh-grade group. The results seem to have implications for the potential for improving learning processes by channeling attention appropriately. (Author/VT)

An experiment involving 30 sixth graders with learning disabilities in mathematics tested the hypothesis that participation in goal setting enhances achievement outcomes. Ss received subtraction training that included instruction and practice opportunities over several sessions. Some Ss set proximal performance goals each session, others had goals assigned, and others received training but no goals. Although proximal goals promoted motivation more than no goals, participation in goal setting led to the highest self efficacy and subtraction skill. It is suggested that participation in goal setting may help promote more active task engagement. (Author/CL)

The Survival Skills Center described in this report operates at Columbia College, CA, to provide individualized instruction in basic reading, writing, and math skills using a series of modules which focus on problems commonly encountered in everyday life. After discussing the need for such instruction among nontraditional students, the paper describes five booklets written by Center staff: (1) "Your Health," which covers topics including first aid, safety, drug and alcohol abuse, and birth control; (2) "Your Community," which focuses on government and community services, the legal system, and public transportation; (3) "Your Money," which considers personal budgeting, banking, credit, taxes, and insurance; (4) "You as a Consumer," which concentrates on finding a place to live, buying a car, shopping, and energy needs; and (5) "Your Job," which centers around assessing personal interests and finding and keeping a job. The remainder of the paper discusses administrative and operational factors that are basic to the Center's success. These factors include: the familiarity of the staff with the abilities and problems of the students; the utilization of well-qualified instructional aides who are sensitive to students' social and emotional problems; the use of a variety of instructional materials; the selective and individualized employment of diagnostic tests; and the availability of nontransferable credit for completing courses at the Center. (JP)

Teachers' perceptions about the nature of their discipline are important factors in their curricular decisions, behavior in the classroom, and interpretations and reactions to classroom events. It is not an easy task to access one's beliefs nor stimulate genuine dialogue about them. Errors can provide both the motivations and the means for engaging in valuable mathematical explorations and reflections about the nature of mathematics as a guide for an analysis of the subject. The first part of the paper concerns the rationale behind the use of errors. Then a report and an in-depth analysis of a specific experience conducted in a graduate mathematics course is discussed along with a brief description of additional units organized around the study of error. Sections included in the paper are: (1) "Introduction"; (2) "Rationale of the Strategy"; (3) "Using Errors as Springboards for Reflections on the Nature of Mathematics"; (4) "Analyzing Incorrect Definitions of 'Circle': An Illustration"; (5) "Other Applications of the Strategy"; and (6) "Conclusions." References are listed. (RT)

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces that students leave when they interact, either individually or collaboratively, with learning management systems, interactive learning environments, intelligent tutoring systems, educational games or when they participate in a data-rich learning context. The types of data therefore range from raw log files to eyetracking devices and other sensor data. Being hosted in London, UK the theme of the conference is "Big Data--Big Ben--Education Data Mining for Big Impact in Teaching and Learning". In this seventh year of EDM conferences, it is clear that the field is continuing to grow at a rapid pace. With renewed focus on education driven by big data learning analytics has put the EDM field in the center of growing interest. Traditional educational technologies, intelligent tutoring systems, educational games, and learning management systems all continue to generate growing amounts of data that are becoming available for analysis. The new interest in MOOCs and their promise to reach thousands or even hundreds of thousands of students per class requires techniques for feedback and grading that are being researched in the EDM domain. The conference submissions this year also continue to grow. A tremendous amount of work has gone into bringing this conference together, and the following are presented: (1) The Field of EDM: Where We Came from and Where We're Going (Joseph Beck); (2) Generative Adaptivity for Optimization of the Learning Ecosystem (Zoran Popovic; (3) 150K+ Online Students at a Time: How to Understand What's Happening in Online 4 Learning (Daniel Russell); (4) Adaptive Practice of Facts in Domains with Varied Prior Knowledge (Jan Papoušek, Radek Pelánek and Vít Stanislav); (5) Alternating Recursive Method for Q-Matrix Learning (Yuan Sun, Shiwei Ye, Shunya Inoue and Yi Sun); (6) Application of Time Decay Functions and the Elo System in Student Modeling (Radek Pelánek); (7) Causal Discovery with Models: Behavior, Affect, and Learning in Cognitive Tutor Algebra (Stephen Fancsali); (8) Choice-Based Assessment: Can Choices Made in Digital Games Predict 6th-Grade Students' Math Test Scores? (Min Chi, Daniel Schwartz, Kristen Pilner Blair and Doris B. Chin); (9) Comparing Expert and Metric-Based Assessments of Association Rule Interestingness (Diego Luna Bazaldua, Ryan Baker and Maria Ofelia San Pedro); (10) Different Parameters - Same Prediction: An Analysis of Learning Curves (Tanja Käser, Kenneth Koedinger and Markus Gross); (11) Discovering Gender-Specific Knowledge from Finnish Basic Education Using PISA Scale Indices (Mirka Saarela and Tommi Kärkkäinen); (12) EduRank: A Collaborative Filtering Approach to Personalization in E-Learning (Avi Segal, Ziv Katzir, Kobi Gal, Guy Shani and Bracha Shapira); (13) Exploring Differences in Problem Solving with Data-Driven Approach Maps (Michael Eagle and Tiffany Barnes); (14) General Features in Knowledge Tracing: Applications to Model Multiple Subskills, Temporal Item Response Theory, and Expert Knowledge (José González-Brenes, Yun Huang and Peter Brusilovsky); (15) Generating Hints for Programming Problems Using Intermediate Output ( Barry Peddycord III, Andrew Hicks and Tiffany Barnes); (16) Integrating Latent-Factor and Knowledge-Tracing Models to Predict Individual Differences in Learning (Mohammad Khajah, Rowan Wing, Robert Lindsey and Michael Mozer); (17) Interpreting Model Discovery and Testing Generalization to a New Dataset (Ran Liu, Elizabeth A. McLaughlin and Kenneth R. Koedinger); (18) Learning Individual Behavior in an Educational Game: A Data-Driven Approach (Seong Jae Lee, Yun-En Liu and Zoran Popovic); (19) Predicting Learning and Affect from Multimodal Data Streams in Task-Oriented Tutorial Dialogue (Joseph Grafsgaard, Joseph Wiggins, Kristy Elizabeth Boyer, Eric Wiebe and James Lester); (20) Sentiment Analysis in MOOC Discussion Forums: What does It Tell Us? (Miaomiao Wen, Diyi Yang and Carolyn Rose); (21) The Effect of Mutual Gaze Perception on Students' Verbal Coordination (Bertrand Schneider and Roy Pea); (22) The Opportunities and Limitations of Scaling Up Sensor-Free Affect Detection (Michael Wixon, Ivon Arroyo, Kasia Muldner, Winslow Burleson, Cecil Lozano and Beverly Woolf); (23) The Problem Solving Genome: Analyzing Sequential Patterns of Student Work with Parameterized Exercises (Julio Guerra, Shaghayegh Sahebi, Peter Brusilovsky and Yu-Ru Lin); (24) Trading Off Scientific Knowledge and User Learning with Multi-Armed Bandits (Yun-En Liu, Travis Mandel, Emma Brunskill and Zoran Popovic); (25) Vertical and Stationary Scales for Progress Maps (Russell Almond, Ilya Goldin, Yuhua Guo and Nan Wang); (26) Visualization and Confirmatory Clustering of Sequence Data from a Simulation- Based Assessment Task (Yoav Bergner, Zhan Shu and Alina von Davier); (27) Who's in Control?: Categorizing Nuanced Patterns of Behaviors within a Game- Based Intelligent Tutoring System (Erica Snow, Laura Allen, Devin Russell and Danielle McNamara); (28) Acquisition of Triples of Knowledge from Lecture Notes: A Natural Language Processing Approach (Thushari Atapattu, Katrina Falkner and Nickolas Falkner); (29) Towards Assessing Students' Prior Knowledge from Tutorial Dialogues (Dan Stefanescu, Vasile Rus and Art Graesser); (30) Assigning Educational Videos at Appropriate Locations in Textbooks (Marios Kokkodis, Anitha Kannan and Krishnaram Kenthapadi) (31) Better Data Beats Big Data (Michael Yudelson, Stephen Fancsali, Steven Ritter, Susan Berman, Tristan Nixon and Ambarish Joshi); (32) Building a Student At-Risk Model: An End-to-End Perspective (Lalitha Agnihotri and Alexander Ott); (33) Can Engagement be Compared? Measuring Academic Engagement for Comparison (Ling Tan, Xiaoxun Sun and Siek Toon Khoo); (34) Comparison of Algorithms for Automatically Building Example-Tracing Tutor Models (Rohit Kumar, Matthew Roy, Bruce Roberts and John Makhoul); (35) Computer-Based Adaptive Speed Tests (Daniel Bengs and Ulf Brefeld); (36) Discovering Students' Complex Problem Solving Strategies in Educational Assessment (Krisztina Tóth, Heiko Rölke, Samuel Greiff and Sascha Wüstenberg); (37) Discovering Theoretically Grounded Predictors of Shallow vs. Deep-Level Learning (Carol Forsyth, Arthur Graesser, Philip I. Pavlik Jr., Keith Millis and Borhan Samei); (38) Domain Independent Assessment of Dialogic Properties of Classroom Discourse (Borhan Samei, Andrew Olney, Sean Kelly, Martin Nystrand, Sidney D'Mello, Nathan Blanchard, Xiaoyi Sun, Marci Glaus and Art Graesser); (39) Empirically Valid Rules for Ill-Defined Domains (Collin Lynch and Kevin Ashley); (40) Entropy: A Stealth Measure of Agency in Learning Environments (Erica Snow, Matthew Jacovina, Laura Allen, Jianmin Dai and Danielle McNamara); (41) Error Analysis as a Validation of Learning Progressions (Brent Morgan, William Baggett and Vasile Rus); (42) Exploration of Student's Use of Rule Application References in a Propositional Logic Tutor (Michael Eagle, Vinaya Polamreddi, Behrooz Mostafavi and Tiffany Barnes); (43) Exploring Real-Time Student Models Based on Natural-Language Tutoring Sessions (Benjamin Nye, Mustafa Hajeer, Carolyn Forsyth, Borhan Samei, Xiangen Hu and Keith Millis); (44) Forum Thread Recommendation for Massive Open Online Courses (Diyi Yang, Mario Piergallini, Iris Howley and Carolyn Rose); (45) Investigating Automated Student Modeling in a Java MOOC (Michael Yudelson, Roya Hosseini, Arto Vihavainen and Peter Brusilovsky); (46) Mining Gap-Fill Questions from Tutorial Dialogues (Nobal B. Niraula, Vasile Rus, Dan Stefanescu and Arthur C. Graesser); (47) Online Optimization of Teaching Sequences with Multi-Armed Bandits (Benjamin Clement, Pierre-Yves Oudeyer, Didier Roy and Manuel Lopes); (48) Predicting MOOC Performance with Week 1 Behavior (Suhang Jiang, Adrienne Williams, Katerina Schenke, Mark Warschauer and Diane O'Dowd); (49) Predicting STEM and Non-STEM College Major Enrollment from Middle School Interaction with Mathematics Educational Software (Maria Ofelia San Pedro, Jaclyn Ocumpaugh, Ryan Baker and Neil Heffernan); (50) Quantized Matrix Completion for Personalized Learning (Andrew Lan, Christoph Studer and Richard Baraniuk); (51) Reengineering the Feature Distillation Process: A Case Study in Detection of Gaming the System (Luc Paquette, Adriana de Carvahlo, Ryan Baker and Jaclyn Ocumpaugh); (52) SKETCHMINER: Mining Learner-Generated Science Drawings with Topological Abstraction (Andy Smith, Eric N. Wiebe, Bradford W. Mott and James C. Lester); (53) Teachers and Students Learn Cyber Security: Comparing Software Quality, Security (Shlomi Boutnaru and Arnon Hershkovitz); (54) Testing the Multimedia Principle in the Real World: A Comparison of Video vs. Text Feedback in Authentic Middle School Math Assignments (Korinn Ostrow and Neil Heffernan); (55) The Importance of Grammar and Mechanics in Writing Assessment and Instruction: Evidence from Data Mining (Scott Crossley, Kris Kyle, Laura Allen and Danielle McNamara); (56) The Long and Winding Road: Investigating the Differential Writing Patterns of High and Low Skilled Writers (Laura Allen, Erica Snow and Danielle McNamara); (57) The Refinement of a Q-Matrix: Assessing Methods to Validate Tasks to Skills Mapping (Michel Desmarais, Behzad Beheshti and Peng Xu); (58) Tracing Knowledge and Engagement in Parallel in an Intelligent Tutoring System (Sarah Schultz and Ivon Arroyo); (59) Tracking Choices: Computational Analysis of Learning Trajectories (Erica Snow, Laura Allen, G.Tanner Jackson and Danielle McNamara); (60) Unraveling Students' Interaction Around a Tangible Interface Using Gesture Recognition (Bertrand Schneider and Paulo Blikstein); (61) A Predictive Model for Video Lectures Classification (Priscylla Silva, Roberth Pinheiro and Evandro Costa); (62) Accepting or Rejecting Students' Self-Grading in their Final Marks by using Data Mining (Javier Fuentes, Cristobal Romero, Carlos García-Martínez and Sebastián Ventura); (63) Analysis and extraction of behaviors by students in lectures 329 Eiji Watanabe, Takashi Ozeki and Takeshi Kohama (64) Analysis of Student Retention and Drop-Out Using Visual Analytics (Jan Géryk and Lubomír Popelínský); (65) Automatic Assessment of Student Reading Comprehension from Short Summaries (Lisa Mintz, Dan Stefanescu, Shi Feng, Sidney D'Mello and Arthur Graesser); (66) Building an Intelligent PAL from the Tutor.com Session Database Phase 1: Data Mining (Donald Morrison, Benjamin Nye, Borhan Samei, Vivek Varma Datla, Craig Kelly and Vasile Rus); (67) Building Automated Detectors of Gameplay Strategies to Measure Implicit Science Learning (Elizabeth Rowe, Ryan Baker, Jodi Asbell-Clarke, Emily Kasman and William Hawkins); (68) Challenges on Applying BKT to Model Student Knowledge in Multi-Context Online Learning Environment (Wolney Mello Neto and Eduardo Barbosa); (69) Combination of Statistical and Semantic Data Sources for the Improvement of Software Engineering Courses (Michael Koch, Markus Ring, Florian Otto and Dieter Landes); (70) Comparing Learning in a MOOC and a Blended On-Campus Course (Kimberly Colvin, John Champaign, Alwina Liu, Colin Fredericks and David Pritchard); (71) Cost-Effective, Actionable Engagement Detection at Scale (Ryan Baker and Jaclyn Ocumpaugh); (72) Data Mining of Undergraduate Course Evaluations (Sohail Javaad Syed, Yuheng Helen Jiang and Lukasz Golab); (73) Data Sharing: Low-Cost Sensors for Affect and Cognition (Keith Brawner) (74) Diagnosing Algebra Understanding via Inverse Planning (Anna Rafferty and Thomas Griffiths); (75) Discovering and Describing Types of Mathematical Errors (Thomas McTavish and Johann Larusson); (76) Discovering Prerequisite Relationships Among Knowledge Components (Richard Scheines, Elizabeth Silver and Ilya Goldin); (77) Dynamic Re-Composition of Learning Groups Using PSO-Based Algorithms (Zhilin Zheng and Niels Pinkwart); (78) Educational Data Mining and Analyzing of Student Learning Outcomes from the Perspective of Learning Experience (Zhongmei Shu, Qiong-Fei Qu and Lu-Qi Feng); (79) Using EEG in Knowledge Tracing (Yanbo Xu, Kai-Min Chang, Yueran Yuan and Jack Mostow); (80) Exploring Engaging Dialogues in Video Discussions (I-Han Hsiao, Hui Soo Chae, Manav Malhotra, Ryan Baker and Gary Natriello); (81) Exploring Indicators from Keyboard and Mouse Interactions to Predict the User Affective State (Sergio Salmeron-Majadas, Olga C. Santos and Jesus G. Boticario); (82) Extracting Latent Skills from Time Series of Asynchronous and Incomplete Examinations (Shinichi Oeda, Yu Ito and Kenji Yamanishi); (83) Generalizing and Extending a Predictive Model for Standardized Test Scores Based On Cognitive Tutor Interactions (Ambarish Joshi, Stephen Fancsali, Steven Ritter, Tristan Nixon and Susan Berman); (84) How Patterns in Source Codes of Students Can Help in Detection of Their Programming Skills? (Štefan Pero and Tomáš Horváth); (85) A Preliminary Investigation of Learner Characteristics for Unsupervised Dialogue Act Classification (Aysu Ezen-Can and Kristy Elizabeth Boyer); (86) Improving Retention Performance Prediction with Prerequisite Skill Features (Xiaolu Xiong, Seth Adjei and Neil Heffernan); (87) Indicator Visualization for Adaptive Exploratory Learning Environments (Sergio Gutierrez Santos, Manolis Mavrikis, Alex Poulovassilis and Zheng Zhu); (88) Learning Aid Use Patterns and Their Impact on Exam Performance in Online Developmental Mathematics (Nicole Forsgren Velasquez, Ilya Goldin, Taylor Martin and Jason Maughan); (89) Learning to Teach like a Bandit (Mykola Pechenizkiy and Pedro A. Toledo); (90) Matching Hypothesis Text in Diagrams and Essays (Collin Lynch, Mohammad Falakmasir and Kevin Ashley); (91) Matrix Factorization Feasibility for Sequencing and Adaptive Support in Intelligent Tutoring Systems (Carlotta Schatten, Ruth Janning, Manolis Mavrikis and Lars Schmidt-Thieme); (92) Microgenetic Designs for Educational Data Mining Research (Taylor Martin, Nicole Forsgren Velasquez, Ani Aghababyan, Jason Maughan and Philip Janisiewicz); (93) Mining and Identifying Relationships among Sequential Patterns in Multi-Feature, Hierarchical Learning Activity Data (Cheng Ye, John Kinnebrew and Gautam Biswas); (94) Mining Coherent Evolution Patterns in Education through Biclustering (André Vale, Sara C. Madeira and Claudia Antunes); (95) Mining Multi-Dimensional Patterns for Student Modelling (Andreia Silva and Claudia Antunes); (96) Mining Reading Comprehension Within Educational Objective Frameworks (Terry Peckham and Gordon McCalla); (97) Mining Students' Strategies to enable Collaborative Learning (Sergio Gutierrez-Santos, Manolis Mavrikis and Alexandra Poulovassilis); (98) Modeling Student Socioaffective Responses to Group Interactions in a Collaborative Online Chat Environment (Whitney Cade, Nia Dowell, Art Graesser, Yla Tausczik and James Pennebaker); (99) Now We're Talkin': Leveraging the Power of Natural Language Processing to Inform ITS Development (Laura Allen, Erica Snow and Danielle McNamara); (100) Peer Assessment in the First French MOOC: Analyzing Assessors' Behavior (Matthieu Cisel, Rémi Bachelet and Eric Bruillard); (101) Peer Influence on Attrition in Massively Open Online Courses (Diyi Yang, Miaomiao Wen and Carolyn Rose); (102) Predicting Students' Learning Achievement by Using Online Learning Patterns in Blended Learning Environments: Comparison of Two Cases on Linear and Non-Linear Model (Jeong Hyun Kim, Yeonjeong Park, Jongwoo Song and Il-Hyun Jo); (103) Predictive Performance of Prevailing Approaches to Skills Assessment Techniques: Insights from Real vs. Synthetic Data Sets (Behzad Beheshti and Michel Desmarais); (104) Recent-Performance Factors Analysis (April Galyardt and Ilya Goldin); (105) Refining Learning Maps with Data Fitting Techniques: Searching for Better Fitting Learning Maps (Seth Adjei, Douglas Selent, Neil Heffernan, Zach Pardos, Angela Broaddus and Neal Kingston); (106) Relevancy Prediction of Micro-Blog Questions in an Educational Setting (Mariheida Cordova-Sanchez, Parameswaran Raman, Luo Si and Jason Fish); (107) Singular Value Decomposition in Education: A Case Study on Recommending Courses (Fábio Carballo and Claudia Antunes); (108) The Predictive Power of SNA Metrics in Education (Diego García-Saiz, Camilo Palazuelos and Marta Zorrilla); (109) Data-Driven Curriculum Design: Mining the Web to Make Better Teaching Decisions (Antonio Moretti, Jose Gonzalez-Brenes and Katherine McKnight); (110) Towards IRT-Based Student Modeling from Problem Solving Steps (Manuel Hernando, Eduardo Guzmán, Sergey Sosnovsky, Eric Andres and Susanne Narciss); (111) Towards Uncovering the Mysterious World of Math Homework (Mingyu Feng); (112) Towards Using Similarity Measure for Automatic Detection of Significant Behaviors from Continuous Data (Ben-Manson Toussaint, Vanda Luengo and Jérôme Tonetti); (113) Using Data Mining to Automate ADDIE (Fritz Ray, Keith Brawner and Robby Robson); (114) Using Multimodal Learning Analytics to Study Learning Mechanisms in Hands-on Environments (Marcelo Worsley and Paulo Blikstein); (115) Using Problem Solving Times and Expert Opinion to Detect Skills (Juraj Nižnan, Radek Pelánek and Jirí Rihák); (116) Toward Collaboration Sensing: Multimodal Detection of the Chameleon Effect in Collaborative Learning Settings (Bertrand Schneider); (117) The Use of Student Confidence for Prediction & Resolving Individual Student Knowledge Structure (Charles Lang); (118) Nonverbal Communication and Teaching Performance (Roghayeh Barmaki); (119) Data-Driven Feedback Beyond Next-Step Hints (Michael Eagle and Tiffany Barnes); (120) E3: Emotions, Engagement and Educational Games (Ani Aghababyan); (121) MOOC Leaner Motivation and Learning Pattern Discovery--A Research Prospectus Paper (Yuan Wang); and (122) Personalization and Incentive Design in E-learning Systems (Avi Segal). Workshops presented include: (1) Graph-based Educational Data Mining (G-EDM) (Collin F. Lynch, Tiffany Barnes); (2) Non-Cognitive Factors & Personalization for Adaptive Learning (NCFPAL@EDM) (Steven Ritter, Stephen E. Fancsali); (3) Approaching Twenty Years of Knowledge Tracing: Lessons Learned, Open Challenges, and Promising Developments (Michael Yudelson, José P. González-Brenes, Michael Mozer); and (4) Feedback from Multimodal Interaction in Learning Management Systems (Lars Schmidt-Thieme, Arvid Kappas, Carles Sierra, Emanuele Ruffaldi). References are included in each presentation.

This paper explores the correlation between mental calculation performance and the frequency of using written algorithms in mental calculation tasks. Mental calculation is a mathematical tool used in everyday life situations during and after our formal education. After presenting an overview of the professional literature on this topic, the paper will present calculation methods and show how represented they are in the Curriculum. For the empirical part of the research, a total of 233 Croatian students aged 10 to 22 years were tested and interviewed. The previously mentioned correlation was then analyzed. An overview of the interview results will be presented as well. It was found that school mathematics does not always contribute to the development and flexibility in using mental calculation strategies because of the student preference for acquired written algorithms. Definitely, recommendation is shifting the focus from written calculation and procedures to the mental, discussing the associated strategies and different concepts of number. In this way, formal education could contribute to what students really need later on, in both private and professional situations in which they may find themselves on a daily basis. [ABSTRACT FROM AUTHOR]

The use of Digital Twins (DTs) or the digital replicas of physical entities has provided benefits to several industry sectors, most notably manufacturing. To date, the application of DTs in the healthcare sector has been minimal, however. But, as pressure increases for more precise and personalized treatments, it behooves us to investigate the potential for DTs in the healthcare context. As a proof-of-concept demonstration prior to working with real patients, we attempt in this paper, to explore the potential for creating and using DTs. We do this in a synthetic environment at this stage, making use of data that is all computer-generated. DTs of synthetic present patients are created making use of data of synthetic past patients. In the real world, the clinical objective for creating such DTs of real patients would be to enable enhanced real-time clinical decision support to enable more precise and personalized care. The objective of the numerical experiment reported in this paper, is to envisage the possibilities and challenges of such an approach. We attempt to better understand the strengths and weaknesses of applying DTs in the healthcare context to support more precise and personalized treatments. [ABSTRACT FROM AUTHOR]

Proceedings of Annual Research Forum. 34 studies. Cultural Awareness in Secondary Spanish (Amy Allen), Writing in Mathematics (Lindsey L. Bakewell), Homework: Assignment Methods and Student Engagement (Lia Beresford), Current Events and Social Studies (Jennie Marie Biser), Authentic Assessments in Social Studies (Carl Boland), Assessment in High School Mathematics (Katie Bradley), Teacher Positivity and Student Engagement (Brianna Brown), Socioscientific Issues in High School Biology (Erin Campbell), Note Taking in Social Studies (Amber Carter), How High School Students Solve Linear Equations (Jennifer Cipriano), Teacher Use of Classroom Discussion (John Compton), Student Engagement (Jessica Rose Conley), Teachers' Use of Verbal Irony (Megan Connor), Calculator Use (Christina M. Cook), Student-Centered Projects in World History (Sarah Cooper), Text Length and Student Engagement (Amanda Ferris), Oral Proficiency Development in Spanish (Ana Ginorio), Teaching Elections through Technology (Katie Gulledge), Higher Order Thinking in Social Studies (Kristina Hanley), Student Motivation in Chemistry (Casie Hermes), Teacher Time-Management and Student Engagement (Melissa Johnson), Reading Instruction in Spanish (Kelsey Lentz), Real Life Connections in Algebra (Sarah E. Lovejoy), Digital Primary Sources (Alex Massengale), Content Terminology (Sarah Weis Neggers), Inquiry in Biology (Leslie Parker), Oral Proficiency in French (Robbie Richwine), Teacher Actions and Student Enthusiasm (Sean Sexton), Students Experience SMART Board through Constructivist Values (Andrew J. Smith ), Students' Understanding of Linear Regression (Matthew J. Smith), The Effect of Teacher Question Type on Student Engagement (WT (Ted) Stille IV), Teacher Gender, Student Gender, and Verbal Interaction (Mary Beth White), Oral Proficiency in Spanish (Gregory Williams), and Formative Assessment in Science (Kristy Younker). (Contains 10 tables, 20 figures, and 1 graph.)

The development of mathematics stands as one of the most important achievements of humanity, and the development of the calculus, both the differential calculus and integral calculus is one of the most important achievements in mathematics. Differential calculus is about finding the slope of a tangent to the graph of a function, or equivalently, differential calculus is about finding the rate of change of one quantity with respect to another quantity. On the other hand, integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Integrals and derivatives became the basic tools of calculus, with numerous applications in science and engineering. Category theory is a mathematical approach to the study of alge-braic structure that has become an important tool in theoretical computing science, particularly for semantics-based research. The notion of a limit in category theory generalizes various types of universal constructions that occur in diverse areas of mathematics. In our paper we show how to represent some parts of infinitesimal calculus in categorical structures. [ABSTRACT FROM AUTHOR]

In a pilot study conducted at a correctional training center, it was determined that a score of 70% or better on an informal reading inventory, based on the textbook used in a vocational shop program, was an accurate predictor of an applicant's success in the program. On the basis of the pilot study, inventories were administered to applicants for numerous shop programs; a score of 70% or better entitled an applicant to enter a shop program. Applicants who scored below 70% attended daily reading and math classes to prepare for entrance. Preliminary results indicated that most shops had a perfect correlation between test achievement and academic success in the shop. Mathematics computation tests were also administered to program applicants, but no extensive study was performed to determine the relationship of these scores to vocational shop success. (The paper includes directions for constructing and scoring informal reading inventories and provides a sample test.) (GW)

This discussion of the Basic Skills Improvement Program (BSIP) formulated by the United States Congress strongly urges educators to develop programs that demonstrate the effectiveness of teaching basic skills in a comprehensive curriculum integrating reading, writing, speaking, and mathematics. The major functions of BSIP are explained as screening program ideas submitted, validating the effectiveness of promising practices and processes among elementary and secondary school students and functionally illiterate adults, and coordinating basic skills efforts at the federal, state, and local levels. Plans for dispersing the funds budgeted for the program and the process for submitting project proposals for funding are outlined. The last section of the paper discusses the implications that BSIP may have for already existing basic communications programs and defines key issues in developing programs in the future. (AEA)

Some general suggestions for the teaching of mathematics study skills are provided in this paper. The suggestions offered are as follows: (1) teach the specialized mathematical vocabulary directly, (2) show students how the mathematical symbol system works, (3) give practice in understanding graphics, (4) give practice in spotting unstated assumptions, and (5) show how to make use of patterns commonly used in mathematics textbooks in developing mathematical concepts and principles. The paper also describes several approaches that may be used to help students learn problem solving techniques; these include providing students with a general heuristic, or model of attack, that they can use in all mathematics textbook assignments and helping students associate assigned problems with other similar problems. (GT)

This research involved the observation and audio-recording of 30 ninth-grade mathematics students recommended as being outstanding by their mathematics teachers. Each student was presented with five different problem situations for which he or she was to make mathematical conjectures. During the interview, the students thought aloud and all of their manipulative moves were recorded. The primary focus of this paper is an analysis of creativity factors exhibited by the five highest-scoring students on a particular geometric problem. The comparisons and analyses showed that these five students had much in common even though each student was highly individualistic. (MP)

The paper describes the Interactive Model for Professional Action and Change for Teachers (IMPACT), a collaborative project based on a consulting teacher model which provides inservice classroom based inservice training for teachers and individualized instruction for high school students with mild handicapping conditions. The model incorporates three levels of inservice teacher training: workshops (arranged by the consulting teachers in response to the basic competency areas identified by groups of teachers); courses (offered for graduate credit by the consulting teachers in areas which include learning strategies, curriculum development, and behavior management); and consultation (provided in the form of team teaching between regular and special educators). The IMPACT program in an English department and in a math department exemplified competency training and use of the workshop for inservice training. It is concluded that the model of collaboration between regular and consulting teachers utilized five components in inservice training (theory, demonstration, practice, feedback, and coaching) and resulted in both effective staff development and actual change in the classroom. (SB)

The document contains the texts of three presentations from a conference on financial support of the sciences and humanities in West Germany and the United States. The first paper explains financial support of the sciences and the humanities in West Germany. Awards and uses of funds are primarily determined by the scholarly community, which also receives most of the funds. Humanities receives only about 17% of the total expenditure, but it has an important role in the educational system. Humanities in West Germany includes Roman law, philosophy, economics, philology, and linguistics. Scientific research is carried out by universities, government-sponsored institutes, and industry. The second paper explores the rationale and structure of support for the humanities in the United States. Humanities in the United States includes history, literature, philosophy, religion, and ancient and modern languages. Support comes from universities, libraries, museums, learned societies, and the publishing industry. Private foundations recently have not given consistently strong support for the humanities. Federal and industrial support of the sciences in the United States are reviewed in the third paper. Basic research, applied research, and development have been strongly supported since the 1950s to increase national defense, and in private industry, to create future profits. The Congressional debate system over science policy issues is described in detail. (AV)

This paper describes the materials, processes, and effects of three individualized compensatory courses in reading, writing, and mathematics. Each course was outlined separately and evaluated according to student performance in selected transfer-level courses. Follow-up studies for each course show that the performance level of former developmental-skills students in the transfer-level courses was equal to, or higher than, that of the students who had not been enrolled in compensatory courses. In addition, the dropout rate among developmental-skills students was less than, or equal to, that of the other students in each class. (MAI)

This document presents papers delivered at a symposium held to discuss the problems associated with excessive specialization in contemporary education and of ways of counterbalancing this trend. Papers were presented in the areas of mathematics, fine arts, science, literature, philosophy, psychology, social sciences, and integrative education. (SL)

Within the context of the developments in mathematics and computer science, this paper argues that the emergence of the microcomputer gives mathematics the opportunity to survive as a viable and healthy discipline. Section I traces the development of the computer and the position of established mathematics on the sidelines of this development. Section 2 discusses some ironies in the synchronous development of computers, with their potential for transforming mathematics education via an emphasis on the computational content of mathematics, and the development of the Bouraki movement in mathematics, which stressed the syntax and structure of mathematics. Section 3 describes the Bouraki years (1945-1975), which focused on abstract formalism coupled with an exclusive mentality, and resulted in alienated client departments, aggravated employment problems, and isolation of the discipline. Section 4 considers the roots of mathematics, looking at three schools of classical mathematics and modern theoretical developments. Section 5 proposes a tetrahedron model of mathematical sciences, in which pure mathematics stands at the apex and applied mathematics, statistics, and computer science stand at its base, and sections 6 and 7 look at the implications of this model for curriculum development with respect to the three classical schools of mathematics. Finally, section 8 suggests ways of revitalizing the mathematics curriculum through, for example, using the computer to provide a graphical or computational component in every math course. (AYC)

These Proceedings document an educational research forum held at Wake Forest University (Winston-Salem, North Carolina) on December 8, 2004. Table of contents and 26 research studies of high school teaching are included. Studies include: The Use of Authentic Materials in the K-12 French Program (Katherine Elizabeth Baird), Surveying Students: What Classroom Styles They Enjoy and Think Work Best (David Bennett); Teachers' Perceptions of the Use of Student to Student Interaction in Social Studies Classrooms (Cynthia Bertram); Effective Writing in Secondary English Classrooms (Alan Brown); Teaching Styles and Student Preferences: Is There a Mismatch? (Tucker Campbell); One-on-One Interactions in the English Classroom (Emily Dolim); The Effects of Group Work on Student Achievement (Kathleen Eckersley); Opening Salvos: The First Five Minutes of Class (Marcus Jestfield Eure); Language Departures: Teacher Response to Nonstandard Language in the English Classroom (Mary Beth Fay); The Effect of Individualized Oral Feedback on Perceived Classroom Engagement (Melanie A. Fehrenbacher); Teacher Beliefs and Practice: Consistency or Inconsistency in the High School Social Studies Classroom? (Leslie Goelz); Student Preferences for Teaching Styles: Gender, Student Achievement Levels, and Ethnicity (Jeanine Greydanus); Secondary Social Studies Teachers' Usage of Reading Comprehension Techniques in Inclusive Classrooms (Amanda Renee Houver); Teaching Culture in the K-12 Spanish Program (Tamara Darcel Hughes); Developing Writing Proficiency in the Secondary Spanish Classroom (Deborah K. Jackson); Teacher Beliefs and Practices with Respect to Culturally Relevant Teaching (Erik Johnson); Contemporary Allusions in the English Classroom (Rebecca Johnson); The Use of Discussion in the Secondary Social Studies Classroom (Victor Lindsay); Differences in Teacher Practices between Standard and Honors Level History Classes (R. Laymarr Marshall); The Effect of Culturally-Responsive Pedagogy on Student Engagement (G. William Perry); Maximizing Discourse: An Assessment of Male/Female Student Response in the Classroom (Connie Pullum);The Last Five Minutes of Class in Secondary English Classrooms (Jennifer Rawlings); Native Speakers of Spanish in the K-12 Spanish Program (Meredith Rymer); The Effect of Teacher Instruction and Teacher Behaviors on Student Participation (Maureen Stanford); Teaching Outside of the Box (Angela Watkins); A Study of Attitude toward Mathematics and Its Relationship to Ethnicity and Gender (Olivia Williams). Each paper contains a literature review, methodology, results, conclusions, and references.

In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both confirm and extend the work of Hadamard on the inventive process. In addition, the results also speak to the larger context of "doing" and learning mathematics. [For complete proceedings, see ED489538.]

This document contains the third volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics. Conference presentations are centered around the theme "Inclusion and Diversity". A total of 65 research reports are presented here: (1) A Teacher's Model of Students Algebraic Thinking About Equivalent Expressions (Jean E. Hallagan); (2) On Motivational Aspects of Instructor-Learner Interactions in Extra-Curriculum Activities (Stefan Halverscheid); (3) Development of Understanding and Self-Confidence in Mathematics, Grades 5-8 (Markku S. Hannula, Hanna Maijala, and Erkki Pehkonen); (4) Mathematics Teachers' Knowledge Base: Preliminary Results (Guershon Harel and Kien H. Lim); (5) The Role of Tool and Teacher Mediations in the Construction of Meanings for Reflection (Lulu Healy); (6) The Proving Process in Mathematics Classroom--Method and Results of a Video Study (Aiso Heinze); (7) Structure Sense in High School Algebra: The Effect of Brackets (Maureen Hoch and Tommy Dreyfus); (8) Explaining Variability in Retrieval Times for Addition Produced by Students with Mathematical Learning Difficulties (Sarah L. Hopkins and Michael J. Lawson); (9) Early Gender Differences (Marj Horne); (10) Perceptual and Symbolic Representations as a Starting Point of the Acquisition of the Derivative (Markus Hahkioniemi); (11) Implementation of a Model Using Authentic Investigative Activities for Teaching Ratio & Proportion in Pre-Service Teacher Education (Bat-Sheva Ilany, Yaffa Keret, and David Ben-Chaim); (12) Mathematicians and the Selection Task (Matthew Inglis and Adrian Simpson); (13) Insight into Pupils' Understanding of Infinity in a Geometrical Context (Darina Jirotkova and Graham Littler); (14) Textual Differences as Conditions for Learning Processes (Marit Johnsen Hoines); (15) Students' Gender Attitudes Towards the Use of Calculators in Mathematics Instruction (L. M. Kaino and E. B. Salani); (16) Teaching Arithmetic and Algebraic Expressions (K. Subramakhi Banerjee); (17) An Introduction to the Profound Potential of Connected Algebra Activities: Issues of Representation, Engagement and Pedagogy (James J. Kaput and Stephen J. Hegedus); (18) The Tension between Teacher Beliefs and Teacher Practice: The Impact of the Work Setting (M. Kerem Karaagac and John Threlfall); (19) What a Simple Task Can Show: Teachers Explore the Complexity of Children's Thinking (Heather Kelleher, Cynthia Nicol, and Carole Saundry); (20) Constructing Knowledge about the Bifurcation Diagram: Epistemic Actions and Parallel Constructions (Ivy Kidron and Tommy Dreyfus); (21) Experiencing Research Practice in Pure Mathematics in a Teacher Training Context (Eva Knoll, Paul Ernest, and Simon Morgan); (22) Enhancing Mathematical Literacy with the Use of Metacognitive Guidance in Forum Discussion (Bracha Kramarski); (23) The Impact of Developing Teacher Conceptual Knowledge on Students' Knowledge of Division (Janeen Lamb and George Booker); (24) Kinds of Arguments Emerging While Exploring in a Computerized Environment (Ilana Lavy); (25) Using Solo to Analyse Group Responses (Christine Lawrie and Chris Reading); (26) Connections between Qualitative and Quantitative Thinking about Proportion: The Case of Paulina (Elena Fabiola Ruiz Ledesma and Marta Elena Valdemoros Alvarez); (27) Towards High Quality Geometrical Tasks: Reformulation of a Proof Problem (Roza Leikin); (28) Mathematical Thinking & Human Nature: Consonance & Conflict (Uri Leron); (29) The Mathematics Pedagogical Values Delivered by an Elementary Teacher in Her Mathematics Instruction: Attainment of Higher Education and Achievement (Yuh-Chyn Leu and Chao-Jung Wu); (30) Visual Reasoning in Computational Environment: A Case of Graph Sketching (Allen Leung and King Wah Chan); (31) Elementary School Students' Use of Mathematically-Based and Practically-Based Explanations: The Case of Multiplication (Esther Levenson, Dina Tirosh, and Pessia Tsamir); (32) Mathematical Discovery: Hadamard Resurrected (Peter Liljedahl); (33)Supporting Teachers on Designing Problem-Posing Tasks as a Tool of Assessment to Understand Students' Mathematical Learning (Pi-Jen Lin); (34) Prospective Elementary School Teachers' Solution Strategies and Reasoning for a Missing Value Proportion Task (Jane Lo); (35) Introduction of Calculus in 12th Grade: The Role of Artefacts (Michela Maschietto); (36) The Critical Role of Institutional Context in Teacher Development (Kay McClain and Paul Cobb); (37) Students' Perceptions of Factors Contributing to Successful Participation in Mathematics (Andrea McDonough, Peter Sullivan, and Robyn Turner Harrison); (38) The Cognitive--Motivational Profiles of Students Dealing with Decimal Numbers and Fractions (Kaarina Merenluoto); (39) The Number Line as a Representation of Decimal Numbers: A Research with Sixth Grade Students (Niki Michaelidou, Athanasios Gagatsis, and Demetra Pitta-Pantazi); (40) Preservice Teachers Conceptions of Mathematics-Based Software (James Middleton, Terri Kurz, and H. Bahadir Yanik); (41) Helping Children to Model Proportionally in Group Argumentation: Overcoming the "Constant Sum" Error (Christina Misailidou and Julian Williams); (42) Abstraction in Mathematics and Mathematics Learning (Michael Mitchelmore and Paul White); (43) Reflective Symmetry in Construction and Proving (Takeshi Miyakawa); (44) Students' Improper Proportional Reasoning: The Case of Area and Volume of Rectangular Figures (Modestina Modestou, Athanasios Gagatsis, and Demetra Pitta-Pantazi); (45) Abstraction and Consolidation (John Monaghan and Mehmet Fatih Ozmantar); (46) Critical Sense in Interpretations of Media Graphs (Carlos Monteiro and Janet Ainley); (47) Between Affect and Cognition: Proving at University Level (Francesca Morselli and Fulvia Furinghetti); (48) An Aspect of Mathematical Understanding: The Notion of "Connected Knowing" (Judith Mousley); (49) Algebraic and Geometric Approach in Function Problem Solving (Nikos Mousoulides and Athanasios Gagatsis); (50) Children's Development of Structure in Early Mathematics (Joanne Mulligam, Anne Prescott, and Michael Mitchelmore); (51) On the Fragile, Yet Crucial, Relationship between Mathematicians and Researchers in Mathematics Education (Elena Nardi and Paola Iannone); (52) Students' Preference of Non-Algebraic Representations in Mathematical Communication (Dorit Neria and Miriam Amit); (53) Learning to See in Mathematics Classrooms (Cynthia Nicol and Sandra Crespo); (54) Students' Ways of Interpreting Aspects of Chance Embedded in a Dice Game (Per Nilsson); (55) The Impact of State-Wide Numeracy Testing on the Teaching of Mathematics in Primary Schools (Steven Nisbet); (56) "The Poetry of the Universe": New Mathematics Teachers' Metaphoric Meaning-Making (Andrew Noyes); (57) What Students Do When Hearing Others Explaining (Kazuhiko Nunokawa and Satoshi Ohzeki); (58) Changes in Teachers' Practices While Assuming New Leadership Roles (Jo Clay Olson); (59) Students' Structuring of Rectangular Arrays (Lynne Outhred and Michael Mitchelmore); (60) Construction of Mathematical Definitions: An Epistemological and Didactical Study (Cecile Ouvrier-Buffet); (61) Mathematical Abstraction through Scaffolding (Mehmet Fatih Ozmantar and Tom Roper); (62) The Use of Diagrams in Solving Non Routine Problems (Marilena Pantziara, Athanasios Gagatsis, and Demetra Pitta-Pantazi); (63) Designing for Local and Global Meanings of Randomness (Efi Paparistodemou and Richard Noss); (64) Integrating the History of Mathematics in Educational Praxis: An Euclidean Geometry Approach to the Solution of Motion Problems (Theodorus Paschos, Vassilike Farmaki, and Nikos Klaudatos); and (65) The Magic Circle of the Textbook--An Option or an Obstacle for Teacher Change (Leila Pehkonen). (Individual papers contain references.)

This document summarizes the content and conclusions of a workshop focusing on the transformation of traditional science, mathematics, engineering, and technology (SME&T) lectures and laboratories into more active learning environments. Presenters described innovative undergraduate courses in a range of SME&T disciplines. Using information technology (IT), these courses have been transformed in ways that appear to enhance learning for a diverse spectrum of undergraduate students, but workshop participants noted that the full educational potential of IT has not yet been realized. Several factors, including the difficulty of assessing student learning in technology-rich environments, the state of current technology, and cultural and institutional factors could pose barriers to rapid deployment of technology in SME&T classrooms. Many workshop participants thought that it is both possible and essential to begin planning for what the future might hold. The first section of the report, Innovations in Pedagogy and Technology, presents case studies of innovative courses and discusses evaluation and assessment challenges and cultural and institutional constraints to IT use. The second section, Planning for Uncertainty, summarizes steps that should be taken to make the best use of IT for future course development and the improvement of SME&T education. Four appendixes contain the background paper sent to participants before the workshop, the agenda, a list of participants, and biosketches of planning group members. (Contains 5 tables, 1 figure, and 58 references.) (SLD)

Research pertaining to the small number of female students in the sciences and mathematics is examined. This research shows that, compared to males, females are not as likely to develop interests in mathematics and science at an early age, are not encouraged by parents and teachers to seek careers in these areas, and have fewer appropriate feminine role-models. (MH)

The authors describe a one-quarter, undergraduate teacher education experience that involved a high level of personal freedom and synergy in an attempt to develop humanistic teachers. Twenty-three juniors and seniors were involved in the program, which took the form of an unstructured block of courses in mathematics, science, and social studies. Three instructors were in charge of the block and taught both individually and in teams. Eleven goals were outlined for the course, the first two of which had to be student-initiated. The balance were devoted to viewing math, science, and social studies as human endeavors for which appropriate psychological, philosophical, and practical bases had to be developed. The result hoped for was that each student (and the three teachers) would develop skills that would make the curriculum and/or classroom evolve in a synergetic rather than competitive fashion. Personal freedom was retained to the maximum level to allow students to pursue the stated goals of the course and also to develop their own journals to reflect their readings in the field, personal reactions to the course, evaluations of self, teachers, and program, and miscellany at the students' discretion. Both student and professorial reaction to the program was highly positive, with an emerging concensus that students and teachers were more capable of honest, open relationships and the pursuit of educational goals in a setting of interpersonal cooperation and personal freedom. (MB)

The study presented here examines whether an ethnographic approach to the study of teaching yields new insight into the teaching-learning process. Two-hundred teachers, who differed in measured effectiveness, were recruited from thirteen school districts in the state of California. Each teacher taught two experimental teaching units (ETU's) of two-weeks duration. Each ETU included an introduction to the teacher, giving a rationale for the unit; performance objectives; pre- and post-examinations for students; and a variety of instructional materials and activities. After test data were collected, posttest scores were regressed on pretest scores for each grade level. Based on class pretest means, three strata were created: low, middle, and high-achieving classrooms within each subject area and grade level. Twelve observers were selected and trained. This included learning to read educational ethnographies, practicing in classrooms, and observing films of classrooms. The ethnographers were trained to provide both reading and mathematics protocols each day; give informal protocols based on observations during recess, talks with principals, and conversations with peers; and asked to give a summary protocol emphasizing important anthropological concepts useful for studying education. Six raters were brought together for two weeks to read a pair of protocols a day, describing a more effective and less effective classroom. They were asked to describe as many ways as possible that the two classrooms differed using any desired terminology. They generated 211 dimensions. This list was revised to 61 variables and used to do a more extensive study involving 20 raters using specially constructed rating forms. (DMT)

The Generic Skills project is a research study being conducted in Canada to determine those overt and covert behaviors which are fundamental to the performance of many tasks and sub-tasks performed in a wide range of occupations. Data aimed at determining the needs for adult education and training have been obtained in two surveys. In the first, 340 workers and their 340 supervisors in 27 different occupations answered questions related to mathematics and communications skills. In the second survey, 490 workers and 480 supervisors in 37 occupations, 18 of which were repeated from the first survey, completed questions related to mathematics, communications, interpersonal, and reasoning skills. From the data, certain core skill requirements for work performance appear evident. All occupations require reading and listening at least the literal level of comprehension--reading forms and writing words/phrases on forms. Most of the skills of one-to-one conversation are common requirements and all occupations require instructional communication, the ability to demonstrate and instruct. Complete data are presented in tabular form and conclusions and implications are discussed. (TO)

A survey of computer use was conducted in 1974 in a small, nonrandom sample of Massachusetts colleges and universities. Allowing for inflation, but adjusting for the increase in computer power per dollar, it is clear that significantly more computer power is being devoted to instruction--both "with" and "about" the computer. The percentage of computer-using courses teaching "with" the computer is estimated to be about 70 to 75 percent of the total number of courses using computers. In particular, physical sciences, social sciences, business, and mathematics have increased their computer use. The bulk of the application is in drill and practice, problem-solving, games, and simulations. Each of these applications is found in most of the departments reporting use of the computer. By contrast, there are very few instances of tutorial or inquiry and retrieval uses. (Author/WCM)

The establishment and validation of a learning hierarchy for use in the teaching of selected principles and strategies was useful in judging a conditional argument in the familiar content domain. Preservice elementary teachers were instructed in two basic skills: (1) translating a simple argument from verbal to symbolic form, and (2) judging the validity of a simple argument given in symbolic form. Several sequences, with and without a Gagne guided thinking component, were investigated. Subjects attained the first skill readily, while the sequence providing the learning of the second skill prior to the first appeared to be the better one. The guided thinking information appeared to have no significant influence on the attainment of the terminal objective, judging a simple conditional argument presented in verbal form. (Author/SM)

This research investigated the effects of employing fixed, variable, and extended token exchange periods for back-ups on the completion and accuracy of daily assignments for a total fifth and sixth-grade class. The results indicated that, in general, a higher percentage of assignments was completed when the number of days between point exchanges was variable, and that performance was maintained when the number of school days between point exchanges was gradually increased. The overall accuracy on assignments was high, but variable and did not appear to be under the systematic control of the experimental procedures. Data for two selected pupils indicated that there were individual differences as to the effects of the various token (point) exchange procedures. Thus, the variable sequencing of the number of days should be an important consideration in any effort to maintain the positive effects of token-reinforcement systems within classroom settings. (Author/ED)

The Radio Mathematics Project is being undertaken in Masaya, Nicaragua, to assess the feasibility and effectiveness of radio as the medium of instruction for primary school mathematics in the developing nations. The curriculum is based upon a series of segments, each of which contains several conceptual or topical strands. Thus, for example, one segment of the first-grade curriculum contains four strands, Number Concepts, Addition, Subtraction, and Application. Behavioral objectives are established for each strand. Student responses are both oral and written. Class observation and pupil response data will be used to revise the lessons currently being tested. Each segment will be considered individually and in relation to the entire curriculum. Preliminary work is underway in the analysis of lesson scripts. The dimensions of the broadcasts to be analyzed are: (a) attitude of the sender, (b) expected behavior of the receiver, (c) language and codes through which the message is expressed, (d) the subject of the message, (e) the contact established between the sender and the receiver, and (f) the form of the message. (DC)

With reference to data from a Swedish investigation into learning difficulties in mathematics, an analysis is presented of models and taxonomies applied to special education problems. The author suggests that such developmental cognitive theories as those of J. Bruner, J. Piaget, and R. Gagne are suitable as a starting point for a taxonomy in mathematics for low achievers but contain inconsistencies. Proposed is a three dimensional model which relates the child's stage of development, instructional objectives and activities, and mathematics content categories. (Author/DB)