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There is an educational expectation that children's natural drawing will develop into proficient mathematical representations and formal diagrams, yet there is little research available to guide the assessment and development of children's mathematical drawing skills. The aim of this paper is to explore how Year 2 children (approx. 7 years) chose to represent their interpretations of a simple story that is suggestive of the take-away subtraction process, and what changes occurred when the drawing task was repeated 6 months later. Analysis of 13 pairs of drawings revealed changes in what the children drew (categories of number representations) and how they drew it (style). The findings suggest that substantial change in children's representational ability can occur in within 6 months.

This research aimed to develop a valid and reliable test to be used to detect sixth grade students' misconceptions and errors regarding the subject of fractions. A misconception diagnostic test has been developed that includes the concept of fractions, different representations of fractions, ordering and comparing fractions, equivalence of fractions, representation of fractions on the number line, and addition, subtraction, multiplication and division of fractions. Studies in the literature on misconceptions in fractions were examined and 22 misconceptions were listed. An open-ended test consisting of 23 questions was created in which students justified their answers to the questions. The developed test was applied to 215 sixth grade students studying in a public secondary school in Istanbul. The average item difficulty index of the test was calculated as 0.37. The test was found to be of average difficulty. The average discrimination index of the test was measured as 0.69. This value shows that the test items are quite successful in distinguishing between students who know and those who do not. In addition, when the discrimination values of the test items were taken into consideration separately, there was no need for item removal or item change since there were no items below 0.30. The KR-20 reliability coefficient was calculated for the first stage of the test and was calculated as 0.93. A graded classification system was used for the first part and second part of the test. To determine that the two stages work in harmony, the Cronbach Alpha reliability coefficient was calculated and found to be 0.95. These results prove that the developed test is highly valid and reliable. [This paper was published in: "EJER Congress 2023 International Eurasian Educational Research Congress Conference Proceedings," Ani Publishing, 2023, pp. 255-272.]

Studies on math learning programs are lacking that consider a wide set of outcome variables, and students' practice behavior. Therefore, we investigated whether an adaptive arithmetic learning program fosters students' math performance (addition and subtraction), math self-concept, and a reduction of math anxiety, and how practice behavior (practiced tasks and practiced weeks) affect the investigated variables. We used a pre-post control group design with a total of 366 fifth grade German students. Randomization took place on the class level. Students in the experimental condition used the program for 22 weeks. Math self-concept only improved in the experimental group. Students' subtraction performance improved as a function of practiced tasks, and addition performance improved as a function of practiced weeks.

Drawing on research around the utility of worked examples, we examine how 29 first- and 27 third-grade students made sense of integer subtraction worked examples and used those examples to solve similar problems. Students first chose which of three worked examples correctly represented an integer subtraction problem and used the example to solve a similar problem. Later, we presented only the correct worked example and had them solve another similar problem. Our results highlight how their initial ideas around which worked example was correct supported or constrained their later interpretation and use of the correct worked example. Students were attuned to the number of jumps shown in the examples; however, they sometimes misinterpreted the jumps' direction. Students' visual answers were correct more than their written answers, suggesting further attention to visuals could support students' reasoning. [For the complete proceedings, see ED630060.]

National and state standards in the US have emphasized the importance of solving and posing word problems in students' mathematics learning for decades. Therefore, it is essential for prospective teachers (PTs) to have the mathematical knowledge necessary to teach these skills to their future students. Unfortunately, little research has investigated how PTs develop problem-posing skills. By employing thematic qualitative text analysis, the researchers identified nine distinct patterns in errors identified in K-8 PTs' posing of two-step addition and subtraction word problems, in the context of a collegiate teacher education course. These results were used to inform the initial design of an interventional task to bring awareness of common errors to PTs. [For the complete proceedings, see ED630060.]

This book contains a compilation of papers presented at the International Psychological Applications Conference and Trends (InPACT) 2018, organized by the World Institute for Advanced Research and Science (W.I.A.R.S.). Modern psychology offers a large range of scientific fields where it can be applied. The goal of understanding individuals and groups (mental functions and behavioral standpoints), from this academic and practical scientific discipline, aims ultimately to benefit society. The International Conference seeks to provide some answers and explore the several areas within the Psychology field, new developments in studies and proposals for future scientific projects. The goal is to offer a worldwide connection between psychologists, researchers and lecturers, from a wide range of academic fields, interested in exploring and giving their contribution in psychological issues. We take pride in having been able to connect and bring together academics, scholars, practitioners and others interested in a field that is fertile in new perspectives, ideas and knowledge. We counted on an extensive variety of contributors and presenters, which can supplement the view of the human essence and behavior, showing the impact of their different personal, academic and cultural experiences. This is, certainly, one of the reasons there are nationalities and cultures represented, inspiring multi-disciplinary collaborative links, fomenting intellectual encounter and development. InPACT 2018 received 386 submissions, from more than 35 different countries from all over the world, reviewed by a double-blind process. Submissions were prepared to take form of Oral Presentations, Posters, Virtual Presentations and Workshops. 126 submissions (overall, 32% acceptance rate) were accepted for presentation in the conference. The conference also includes a keynote presentation by Dr. Saima Löfgren (BSc(Hons), MSc, DClinPsy, Clinical Psychologist, Visiting Lecturer at the Universities of Nottingham and Leicester, United Kingdom); and two Special Talks, one by Prof. Dr. Michael Wang (Professor of Clinical Psychology, University of Leicester, United Kingdom), and the other by Prof. Dr. Pedro Oliveira (MSc on Anthropology and Child Development, PhD in Social Anthropology, Clinical Psychologist, Member of the Portuguese Order of Psychologists, Portugal). We would like to express our gratitude to all our invitees. The Conference addresses different categories inside Applied Psychology area and papers fit broadly into one of the named themes and sub-themes. The conference program includes six main broad-ranging categories that cover diversified interest areas: (1) Clinical Psychology: Emotions and related psychological processes; Assessment; Psychotherapy and counseling; Addictive behaviors; Eating disorders; Personality disorders; Quality of life and mental health; Communication within relationships; Services of mental health; and Psychopathology. (2) Educational Psychology: Language and cognitive processes; School environment and childhood disorders; Parenting and parenting related processes; Learning and technology; Psychology in schools; Intelligence and creativity; Motivation in classroom; Perspectives on teaching; Assessment and evaluation; and Individual differences in learning. (3) Social Psychology: Cross-cultural dimensions of mental disorders; Employment issues and training; Organizational psychology; Psychology in politics and international issues; Social factors in adolescence and its development; Social anxiety and self-esteem; Immigration and social policy; Self-efficacy and identity development; Parenting and social support; Addiction and stigmatization; and Psychological and social impact of virtual networks. (4) Legal Psychology: Violence and trauma; Mass-media and aggression; Intra-familial violence; Juvenile delinquency; Aggressive behavior in childhood; Internet offending; Working with crime perpetrators; Forensic psychology; Violent risk assessment; and Law enforcement and stress. (5) Cognitive and Experimental Psychology: Perception, memory and attention; Decision making and problem-solving; Concept formation, reasoning and judgment; Language processing; Learning skills and education; Cognitive Neuroscience; Computer analogies and information processing (Artificial Intelligence and computer simulations); Social and cultural factors in the cognitive approach; Experimental methods, research and statistics; and Biopsychology. (6) Psychoanalysis and Psychoanalytical Psychotherapy: Psychoanalysis and psychology; The unconscious; The Oedipus complex; Psychoanalysis of children; Pathological mourning; Addictive personalities; Borderline organizations; Narcissistic personalities; Anxiety and phobias; Psychosis; Neuropsychoanalysis. This book contains the results of the different researches conducted by authors who focused on what they are passionate about: to study and develop research in areas related to Psychology and its applications. It includes an extensive variety of contributors and presenters that are hereby sharing with us their different personal, academic and cultural experiences. We would like to express thanks to all the authors and participants, the members of the academic scientific committee, and of course, to the organizing and administration team for making and putting this conference together. [These proceedings were published by InScience Press. Abstract modified to meet ERIC guidelines. For the 2017 proceedings, see ED604951.]

Within the broad area of whole number operations, understanding and solving word problems continues to be an important area of inquiry. In the present study we draw on the framework of representational fluency to examine conceptual and procedural understandings that are exhibited by a group of Malaysian seven-year-olds as they attempted to solve 2-digit addition and subtraction word problems. Preliminary results show that the range of representations that were constructed by the participants as they searched the problem space was limited as was their ability to translate representations. Implications of these findings for further work about using representations are discussed.

This paper provides insight about the development of addition and subtraction strategies for nearly 22,000 Australian primary school children in 2016. The children were each assessed by their teacher using a task-based assessment interview that identified the strategies they used to mentally perform addition and subtraction, and matched these to a growth point framework. The findings highlight the broad distribution of strategies used by children in each grade level and suggest that few children, including those in Grade 6, reach Growth Point 6 that involves the mental calculation of two-digit and three-digit numbers. These findings have important implications for classroom teaching and professional learning.

The language that students use with whole numbers can be insufficient when learning integers. This is often the case when children interpret addition as "getting more" or "going higher." In this study, we explore whether instruction on mapping directed magnitudes to operations helps 88 second graders and 70 fourth graders solve addition and subtraction problems with negative numbers. Further we explore to what extent having prior training with directed magnitude language (as opposed to just more and less language, without a direction specified) prepares students to benefit from the instruction. Our data shows that students, regardless of which language training they had, improved, and second graders, even with less initial knowledge, were able to make the same gains as fourth graders, suggesting that having initial exposure to negatives earlier could help students reach proficiency by the time the standards expect it. [For the complete proceedings, see ED583608.]

This paper investigates how the selected three East Asian countries--Japan, Korea, and Taiwan-- introduce and develop ideas related to fractions and fraction addition and subtraction compared to the Common Core State Standards of Mathematics and EngageNY. Looking at curricular approaches used across countries can provide a better picture of what is of importance in instruction aimed at developing students' mathematical proficiency. Understanding how the aforementioned three Eastern Asian materials treat fractions will offer both mathematics teachers and teacher educators some concrete images of the visions of the Common Core State Standards of Mathematics and specific ideas on teaching and learning of fractions. [For the complete proceedings, see ED583989.]

This submission contains the Proceedings of the 2015 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Université de Moncton in Moncton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, an elder talk memoire, panel discussions, working group reports, topic sessions, new PhD reports, and summaries of ad hoc and poster sessions. Papers include: (1) Diversité, variabilité et convergence des pratiques enseignantes/Diversity, Variability, and Commonalities Among Teaching Practices (Éric Roditi) [Written in French]; (2) Connections: Mathematical, Interdisciplinary, Electronic, and Personal (Deborah Hughes Hallet); (3) Task Design and Problem Posing (Ami Mamolo and John McLoughlin); (4) Indigenous Ways of Knowing in Mathematics (Lisa Lunney Borden and Florence Glanfield); (5) Theoretical Frameworks in Mathematics Education Research/Les cadres théoriques dans la recherche en didactique des mathématiques (Jérôme Proulx and Anna Sierpinska) [Written in English and French]; (6) Early Years Teaching, Learning and Research: Tensions in Adult-Child Interactions Around Mathematics (Ann Anderson and Helena P. Osana); (7) Innovations in Tertiary Mathematics Teaching, Learning and Research/Innovations au post-secondaire pour l'enseignement, l'apprentissage et la recherché (Taras Gula and Denis Tanguay) [Written in English and French]; (8) Some Thoughts on Mathematics as the Alien Word (Richard Barwell); (9) Interaction Between a Mathematics Department in a University and the School System/Interaction entre un département de mathématiques universitaire et le système scolaire (Paul Deguire) [Written in English and French]; (10) Building Thinking Classrooms: Conditions for Problem Solving (Peter Liljedahl); (11) Growing Mathematical Understanding and Folding Back: The Individual, the Collective, the Teacher (Lyndon Martin); (12) De la « clochette de vigilance » au changement de posture: Quelques questions issues de la didactique des mathématiques et étudiées depuis la didactique du sens commun/From the Use of an "Alert Bell" to a Change of Posture: Some Questions Emerging from the Didactics of Mathematics Being Studied by the Didactics of Common Sense (Sophie René de Cotret) [Written in French and English]; (13) Secondary School Mathematics Teacher Candidates' Research, Pedagogical, and Content Knowledge (Alexander Antropov); (14) Étude des significations de la multiplication pour différents ensembles de nombres dans un contexte de géométrisation…et un aperçu de quelques réflexions d'ordre épistémologique (Raquel Isabel Barrera Curin) [Written in French]; (15) The Role of Drawing in Arithmetic Word Problem Solving: Microanalysis of the Subject/Material Dialectic (Élysée-Robert Cadet); (16) Histoire des mathématiques dans la formation des enseignants du secondaire : Une narration polyphonique sur la fragilité, l'adversité et l'empathie--Résumé de thèse/History of Mathematics in a Preservice Teacher's Training Context: A Polyphonic Narration on Fragility, Adversity and Empathy--Thesis Summary (David Guillemette) [Written in French and English]; (17) Improving Mathematics Teaching Through Professional Learning Groups (Jennifer Holm); (18) Mathematics Problems and Thinking Mathematically in Undergraduate Education (Asia R. Matthews); (19) Understanding Learning in Mathematics Through the Metaphor of Authoring (P. Janelle McFeetors); (20) How Elementary Students Learn to Mathematically Analyze Word Problems: The Case of Addition and Subtraction (Elena Polotskaia); (21) Le concept de variabilité chez des enseignants de mathématiques au secondaire (Sylvain Vermette) [Written in French]; (22) Lesson and Learning Study: Collaborative Learning Structures for Preservice Teacher Education (Diana Royea); and (23) Hear My Voice: Teachers' Stories (Ann Kajander and Jennifer Holm). Individual papers contain references. [For the 2014 proceedings, see ED581042.]

Kayla was a 15 years old girl with Down syndrome attending a special education school in Indonesia. A modification of Wright et al.'s (2006) approach to assessment documented her number knowledge and arithmetical strategies. This paper discusses the assessment process and the results focusing on her ability to solve number problems. Results show that Kayla's stages in early arithmetical learning and base ten arithmetical strategies are the same as those of typical developing students of a much younger age. This supports the notion that a student with Down syndrome may be capable of learning arithmetic similar to that learned by typical developing children, but their speed of learning appears to be much slower.

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using standard written algorithms: addition with or without carrying and subtraction with or without borrowing. Her mental calculation strategies were influenced by the taught standard written algorithms. These algorithms seem to be counter-productive. However, with appropriate supports, she might have a potential to be an accurate and flexible mental calculator.

Fifteen elementary and secondary teacher candidates solved sixteen integer addition and subtraction problems during think-aloud interviews. Investigators further probed participants' solution strategies as well as what they noticed first when starting a new problem. Task analyses of participants' solutions led to the creation of two distinct maps detailing the procedural relations among and conceptual elements underlying the six problem types. The task analysis results indicate that participants relied on procedural knowledge and had weak strategic knowledge with little focus on number values in their four main solution strategies. These findings highlight possible areas for instruction to support conceptual understanding. [This research was funded by a Purdue Research Foundation Year-long Grant. For the complete proceedings, see ED584443.]

The data from the national tests such as the National Assessment Program Literacy and Numeracy (NAPLAN) and its precursor Victorian Achievement Improvement Monitor (AIM) are an important resource. The 2006 Year 3 AIM assessment included two subtraction items that are similar in content, and which are presented without text or images. The detailed, novel analysis of the children's responses presented here provides insight into children's fluency and understanding of these items.

The longitudinal progress of 42 Grade 1 students who participated in a 10-20 week Extending Mathematical Understanding (EMU) intervention program was examined to evaluate the effectiveness of the program for enhancing and accelerating mathematics learning. Overall the students made accelerated progress during Grade 1 and their learning was maintained after the six-week summer break and also when they were assessed 12 months later. However, the rate of progress for many students was less during Grade 2 when they participated only in regular classroom lessons. [The research reported in this paper was funded by the Australian Government as part of the "Bridging the Numeracy Gap in Low SES and Indigenous Communities" Project.]

The "Extending Mathematical Understanding" (EMU) Program is a specialised mathematics program that aims to accelerate the learning of Grade 1 students who struggle with learning school mathematics. Forty-two students participated in an EMU Program in 2010 as part of the "Bridging the Numeracy Gap" (BTNG) project. Analysis of students' mathematics knowledge at the beginning of the EMU Program highlighted how diverse was this group of students. The students' mathematics knowledge was assessed again at the beginning of the following year in order to evaluate the effectiveness of the program for accelerating learning. Overall the students made very good progress and their learning was maintained. [The research reported in this paper was funded by the Australian Government as part of the "Bridging the Numeracy Gap in Low SES and Indigenous Communities" Project.]

This study investigates the influence of teacher understanding on student understanding through teacher practice. Three elementary school teachers participated in a university course that discussed mathematical and pedagogical knowledge regarding addition and subtraction word problems. The data from this study were analyzed qualitatively to describe the nature of the teachers' understandings, the ways teachers used their understandings in their practice, and the nature of their students' understandings. I hypothesize that teachers used their understanding to create and implement tasks at a high level of cognitive demand, maintaining that demand over time, which affected student understanding. [For the complete proceedings, see ED585874.]

Relating natural language to mathematical language is an important component of elementary mathematics education. This paper describes new steps toward a computerized database of addition and subtraction word problems that could provide teachers and students with access to critical natural language terms and expressions for mathematical relationships. On the basis of new results from a computer simulation that is sensitive to slight changes in problem wording, the suggestion is that a database of word problems that reflects a relative order of difficulty is not only feasible but essential if researchers in this area are to increase the practical dissemination of research results. A collection of math stories sensitive to children's text comprehension skills and mathematical development is the foundation of an ongoing effort to implement a knowledge-building environment that can facilitate children's discussions of why one math story is more difficult than another, as well as encourage communities of students to build their own database of stories. An appendix contains an example simulation of EDUCE and SELAH solving a static-non-relational (combine 5) problem. Contains 64 references. (Author/MKR)

The purpose of this study was: (a) to develop a learning hierarchy for rational number subtraction using intraconcept analysis, and (b) to validate that hierarchy using the Walbesser technique and pattern analysis. Skills required to complete tasks within the hierarchy were operationally defined and ordered from both a mathematical and psychological point of view. A test utilizing an item for each level in the hierarchy was administered to a sample of 200 children in grades four through eight. The final hierarchy generated and important implications for prescriptive instruction relative to subtraction of rationals are discussed. The specific tasks used in the study are appended. The initial hypothesized ordering of these tasks and the empirically determined hierarchy are presented. (Author/SD)

This study was presented at the 1979 meeting of the American Education Research Association (AERA), San Francisco. It investigated the relationship between the structure of simple addition and subtraction problems and the types of processes children use to solve them prior to receiving formal arithmetic instruction. Specific strategies which young children use to carry out addition and subtraction computations were also studied. Forty-three first-grade children were individually administered 20 problems representing 10 different problem types. Results showed that before receiving instruction, children: (1) can successfully solve addition and subtraction problems; (2) use solution processes which model the structural problem type; and (3) rely on a variety of counting strategies for computation. (Author/HM)

The present experiment tested the hypothesis that effort attribution given for prior achievement is effective in promoting subsequent achievement behaviors. Forty children drawn from two elementary schools and lacking in subtraction skills received training and opportunities to solve subtraction problems. In the context of training, children received effort attribution for prior achievement, attribution for future achievement, or no attribution. Results showed that attribution for prior achievement led to more rapid training progress, greater skill development, higher percepts of self-efficacy, and more accurate self-appraisal of capabilities. In contrast, attribution for future achievement did not influence children's achievement outcomes. The results demonstrate important differences in outcomes as a result of how effort is linked with achievement. Effort attribution may have complex effects including the possibilities that the two forms of attribution differ in: (1) social reinforcement value; and (2) the type of performance feedback they provide to children. A third complexity relates to the idea that effort attribution is most effective with tasks perceived as intermediate in difficulty. The need for future research clarifying how these effects occur is suggested. (Author/RL)

The Proceedings of PME-XI has been published in three separate volumes because of the large total of 161 individual conference papers reported. Volume I contains four plenary papers, all on the subject of "constructivism," and 44 commented papers arranged under 4 themes. Volume II contains 56 papers (39 commented; 17 uncommented) arranged under 9 themes. Volume III contains 53 papers arranged under 17 themes, and 4 Research Agenda Project papers. Due to space limitations, the subject content of these volumes will be represented by listing the 30 themes used to categorize the papers. Volume I: (1) Affective Factors in Mathematics Learning; (2) Algebra in Computer Environments; (3) Algebraic Thinking; (4) Fractions and Rational Numbers; Volume II: (5) Geometry in Computer Environments; (6) In-Service Teacher Training; (7) Mathematical Problem Solving; (8) Metacognition and Problem Solving; (9) Ratio and Proportion; (10) Number and Numeration; (11) Addition and Subtraction; (12) Rationals and Decimals; (13) Integers; Volume III: (14) Cognitive Development; (15) Combinatorics; (16) Computer Environments; (17) Disabilities and the Learning of Mathematics; (18) Gender and Mathematics; (19) Geometry; (20) High School Mathematics; (21) Effect of Text; (22) Socially Shared Problem Solving Approach; (23) Didactic Engineering; (24) Curriculum Projects; (25) Affective Obstacles; (26) Instructional Strategies; (27) Measurement Concepts; (28) Philosophy, Epistemology, Models of Understanding; (29) Pre-Service Teacher Training; (30) Teritary Level. Each volume contains an author index covering all three volumes. (MKR)

Two experiments tested the idea that the means by which children acquire efficacy information can produce different levels of task motivation and self-perception of competence. In Experiment 1, children periodically received either ability attributional feedback, effort feedback, ability plus effort feedback, or no attributional feedback. Although the three feedback conditions did not differ in rate of problem solving, ability feedback alone led to the highest self-efficacy and achievement. In Experiment 2, children pursued either difficult or easier performance goals, and received either direct or comparative attainment information. Difficult goals enhanced rate of problem solving; combining difficult goals with direct information resulted in the highest self-efficacy and skill. Collectively, these results support the idea that self-efficacy is an important variable in understanding students' achievement behavior. (Author/PN)

This experiment tested the hypothesis that the sequence of ability and effort attributional feedback influences children's attributions, self-efficacy, and skillful performance. Children deficient in subtraction skills received training on subtraction operations and solved problems over four sessions. During the problem solving, some children periodically received ability feedback whereas others were given effort feedback. Children in a third condition received ability feedback during the first two sessions and effort feedback during the last two; this sequence was reversed in a fourth condition. Childen who initially received ability feedback developed higher levels of self-efficacy and skill and placed greater emphasis on ability as a cause of task success compared with subjects initially given effort feedback. Future research should explore how students interpret forms of attributional feedback as their skills develop on different types of tasks. (Author)

This study investigates the influence of changes in the wording of simple addition and subtraction problems without affecting their semantic structure on the level of difficulty of those problems for first and second graders and on the nature of their errors. The objective is to contribute to a better understanding of the process of constructing a mental problem representation starting from the verbal text. A quantitative and qualitative analysis of the data produces findings supporting the hypothesis that rewording the problem in such a way that the semantic relations are made more explicit has a facilitating effect on the construction of an appropriate mental representation. (Author)

The paper describes strategies for remediating mathematics difficulties (particularly the process of regrouping or "borrowing" in whole number subtraction) in children. Three interrelated aspects of the process (the meaning of subtraction, understanding of non-standard numerals, and the function of the subtraction algorithm), are considered. The set-subset model for learning subtraction, in which children manipulate concrete objects in an illustration of the part-whole inclusion relationship, is described. The difficulties facing children with reversal problems in dealing with value concepts are noted. The part-total terms is illustrated as one way of teaching the subtraction algorithm, while the comparison model is viewed as an alternative approach. The author suggests that parents and teachers should be wary of computer materials designed for learning disabled children. (CL)

This study sought to determine the effectiveness of self-instructional strategy training on the addition and subtraction problem-solving skills of four upper elementary-level learning-disabled students, and to evaluate maintenance and generalization of the trained skills. Each subject received individual criterion-based training in self-instructional strategies. Training emphasized the student's role as an active collaborator in the learning process, with responsibility for recruiting and applying strategies gradually placed upon the student. Strategies were explicitly and overtly modeled in context. Subjects' scores on one-step word problems in addition and subtraction significantly improved following training. All subjects showed that the skills were generalized across settings and were maintained 3-5 weeks after training. Subjects were more confident of their ability to complete the word problems following training, though they had overestimated their pre-training ability. The four students and their teacher evaluated the self-instructional strategy training positively. Inspection of students' papers collected when probes were administered provided concrete evidence of post-training use of the instructed problem-solving strategy. (JDD)

The experiment reported here investigated how verbalization of subtraction with regrouping operations influenced learning disabled students' self-efficacy and skillful performance, and also explored how effort attributional feedback affected these achievement behaviors. Learning disabled students (N=90) from grades 6 through 8 received training and solved problems over six 45-minute sessions. Some students verbalized aloud while solving problems (continuous verbalization); those in a second condition verbalized only during the first half of training (discontinued verbalization); students in a third condition did not verbalize (no verbalization). All students were periodically monitored and either received effort feedback during the first half of training, effort feedback during the second half of training, or no effort feedback. Continuous verbalization led to higher self-efficacy, and effort feedback promoted these achievement behaviors more than no feedback. Delivering effort feedback during the first half of training enhanced effort attributions. Findings support the notion that private speech can help regulate task performance. References, footnotes, and a data table are appended. (Author/CL)

A study was undertaken of the effects of formal education and conservation of numerousness on addition and subtraction problem types. Thirty-six kindergarten and 36 first-grade subjects randomly selected from one area of a school district were administered measures of conservation, problem-solving success, and modeling ability. Following factor analysis of the instruments, and a regression analysis to ascertain demographic effects, a nested posttest only control group design was analyzed using a covariate MANOVA technique. Both formal schooling and conservation significantly affected the subject's modeling and accuracy scores (p less than .05). Further, transformational addition and take-away subtraction were significantly (p less than .05) more difficult than other problem types. (Author/SD)

This study sought to determine the basis for young children's understanding of fundamental addition and subtraction processes, and to expose any limitations on such arithmetic reasoning. Thirty-six two-year-olds and 36 three-year-olds participated in six experiments which examined children's relational quantity judgments about pairs of arrays in static and transformation conditions. There were two principal conclusions drawn from the investigation. First, the judgments of two-year-olds reflected chance responses on all problems, whereas three-year-olds' judgments indicated an understanding of the fundamental addition and subtraction processes studied. This difference in performance attests to a qualitative difference in the arithmetic knowledge of these two age groups. Second, although three-year-olds manifested an understanding of fundamental addition and subtraction, approximately half of these children based their reasoning exclusively on quantity transformation. Their failure to evaluate the outcome of the quantity transformation in making relational judgments about altered arrays reveals an important limitation on early arithmetic reasoning. (Author/MK).

This set of papers was selected from presentations made at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics because of their pertinence to classroom teachers. The papers concern: (1) "Research and Development Related to Learning about Numerals for Whole Numbers: Implications for Classroom/Resource Room/Clinic" (Ashlock); (2) "Levels of Maturity in Diagnosis and Instruction" (Engelhardt); (3) "Teaching Arithmetic: A Diagnostic Approach" (Hopkins); (4) "Using Manipulative Aids to Model Algorithms in Remedial Situations" (Hynes); (5) "A Theoretical Study of the Organization of Basic Addition Facts for Memorization" (Heddens); (6) "How Do You Get Children to Quit Using Their Fingers to Add and Subtract?" (Rathmell); (7) "But I Have 42 Students in My Class" (Connelly); (8) "Implementing Diagnosis in the Classroom" (Inskeep); and (9) "The Role of Dual Programming in Diagnostic and Prescriptive Mathematics" (Wyer). (MNS)

This study empirically examined the proposition that different item selection procedures contribute to the development of achievement tests that optimally serve different purposes. A test of 110 addition and subtraction problems was given to a sample of 371 first-grade students. Three subsets of 30 items were selected from this 110-item test. The first included those items with the highest classical item discrimination indexes, the second of those best describing the continuum of Rasch item difficulties of the 110-item test, and the third of randomly selected items. The study examined which set of items best reflected student performance on the set of 110 items if the purpose of such testing was the differentiation of students, location of students on an achievement continuum, or generalizing student performance to the domain of 110 items. Primary analyses of the data indicated that the subtests consisting of classically discriminating items and those describing the continuum of Rasch difficulties yielded statistically different results from all other tests for differentiating students or generalizing performance to the domain of items. Secondary analyses indicated that these differences were attributed to the performance of the lower quartiles of students. (Sixteen tables are appended.) (Author)

Based on the traditional Matched Mask Bone Elimination (MMBE) method, this paper presents an improved subtraction method of Brain Computer Tomography Angiography (CTA) images. The method can be divided into two main parts, registration and bone elimination algorithms. Firstly, based on three-dimensional mutual information registration algorithm, this paper adapted sample and compression of gray scales through stastical analysis of the volume data to decrease data account and improve the calculate speed of registration. Then in the bone elimination algorithm, the extraction of bone mask in CT images is implemented by the combination of threshold and refinement of bone mask We proposed a method to optimize the calculation strategies to decrease the cost of calculation. Through the analysis of the experiments on the clinical image data, the developed method proposed in this paper have improved about eight times of computing speed. The operation time of brain CT/CTA images with about two hundred slices has been limited in twenty seconds. And the main arteries can be displayed clearly in three-dimensional space. [ABSTRACT FROM PUBLISHER]

The real time X-ray angiography based on C-arm cone beam system is the workhorse imaging modality for interventional cardiac procedures. These images are two-dimensional (2D) projections of three dimensional (3D) objects along the X-ray direction. The organ of interest (OOI), such as left ventricle (LV) endocardium, in the projection image is superimposed with other anatomical structures and often has low contrast. In this study, a novel approach is proposed to isolate the OOI in projection images by subtracting with a background image, which is generated by numerical projection of 3D tomographic image with OOI masked out. Study based on one patient and one pig image is taken. About two to three-fold increase in the contrast-to-noise ratio (CNR) is achieved for LV endocardium, compared to an unprocessed image. [ABSTRACT FROM PUBLISHER]

Traditional surveillance system needs a lot of manpower to search video for finding the invaders. Therefore, using manpower to search the videos is very unprofitable. Hence, the developments of intelligent surveillance system are very important issue for surveillance system. object segmentation method is most important technique on intelligent surveillance system, because the results of object segmentation can support intelligent surveillance system to detect and monitor Intrusive object. And background subtraction method is very popular of object segmentation. However, background subtraction methods have a problem in initial background extraction when the scene exist slow-speed objects. Because the discrimination between slow-speed objects and background are very difficult. In the paper, we propose a robust initial background extraction algorithm applied to video sequences with a static camera. The algorithm can classify and extract the background effectively. Even in slow-speed objects in the video sequence, the proposed algorithm can extract the initial background by dynamic analysis and maintained the background accurately. [ABSTRACT FROM PUBLISHER]

Functional magnetic resonance imaging (fMRI) was used to investigate brain responses due to arithmetic working memory. Nine healthy young male subjects were given simple addition and subtraction instructions in noise and in quiet. The general linear model (GLM) and random field theory (RFT) were implemented in modelling the activation. The results showed that addition and subtraction evoked bilateral activation in Heschl’s gyrus (HG), superior temporal gyrus (STG), inferior frontal gyrus (IFG), supramarginal gyrus (SG) and precentral gyrus (PCG). The HG, STG, SG and PCG activate higher number of voxels in noise as compared to in quiet for addition and subtraction except for IFG that showed otherwise. The percentage of signal change (PSC) in all areas is higher in quiet as compared to in noise. Surprisingly addition (not subtraction) exhibits stronger activation. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper reports work in progress towards achieving improved simulation tools for ultrasonic Nondestructive Evaluation (NDE) in the power generation industry. Hybrid models are shown to arise as a natural consequence of a modular approach to tackling complex processes, which is attractive in the face of the increasing sophistication of practical ultrasonic inspection. It is argued that although such models are not new to the community, there is an urgent need for developing them to be independent of their constituent methods and that an interface mechanism capable of handling field quantities in the near-field is essential to achieve optimal performance. A domain-linking algorithm capable of stable performance in the near-field is then presented and preliminary Finite Element simulation studies for validating the procedure and demonstrating its capabilities show positive results . [ABSTRACT FROM AUTHOR]

A unified approach to a broad class of number systems is proposed in this paper. This class contains all positive and negative radix systems and other well-known number systems. The proposed approach enables us to develop a single set of algorithms for arithmetic operations and conversion methods between number systems. [ABSTRACT FROM PUBLISHER]