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The aim of this study was to develop, implement, and evaluate an intervention program focusing on developing Grade 5 and 6 students' functional thinking. The innovative aspect lies in addressing simultaneously various aspects of function—input–output, covariation, correspondence, and object— in terms of manipulating tasks that involve functional relationships. The program adopts promising design principles, including an inquiry-based approach, engaging students in embodied dynamic mathematics learning environments, and making connections to real-world situations. A sample of 104 students took part in the program. The results showed a significant improvement in students' performance related to functional thinking between the pre- and post-tests. Grade 5 students' mean value improved from 0.29 to 0.58 and Grade 6 students from 0.37 to 0.60, respectively. Analysis indicated that students with varying performance potential in developing functional thinking are likely to be significantly affected by the program. Regression analysis showed that students' gender as well as mathematics- and functions-related self-concept and interest did not serve as predictive factors of students' gain score magnitude. Students' progression goes along with a significant shift in strategies used. While the dominant strategies in the pre-test relied on recursive and single variation, in the post-test, students moved to covariational and correspondence approaches. The findings indicate that upper primary school students are capable of grappling abstract facets of functions. This underscores the potential effectiveness of targeted interventions that adopt innovative design principles, particularly in light of the limitations of conventional curricula in adequately preparing students to explore functional relationships across diverse contexts. [ABSTRACT FROM AUTHOR]

Aim: This study aimed to investigate the effect of using Wordwall on academic achievement and motivation towards learning mathematics among sixth grade students in the Nablus District. Methodology: this study used the experimental method with a semiexperimental design, and the study was applied to a sample of 46 female students from the sixth grade at Sarra Secondary School for Girls. They were divided equally into two groups: control and experimental. The algebra unit was taught to the students of the experimental group using Wordwall. The researcher used a pre-test to verify the equivalence of the two study groups, a scale to measure students’ motivation towards learning mathematics, a test to measure students’ achievement in the algebra unit, and the training material according to the Wordwall platform. Results: The results revealed that there is a statistically significant difference at the significance level (α=0.05) between the average scores of sixth grade female students in the post-achievement test between the experimental group and the control group in favor of the experimental group. Moreover, there is a statistically significant difference at the significance level (α=0.05) between the average scores of sixth grade female students in the motivation scale towards learning mathematics between the experimental group and the control group in favor of the experimental group. Conclusions: The results of this study showed that there is a positive effect of using the Wordwall platform in developing academic achievement and increasing the motivation of sixth grade students towards learning mathematics. Recommendations: Using the Wordwalll platform in teaching various mathematics subjects for all educational levels, as it has a positive impact on developing academic achievement and increasing students’ motivation to learn mathematics, as well as using the Wordwall platform in teaching other subjects. [ABSTRACT FROM AUTHOR]

The study attempted to ascertain the significant relationship between the level of pupils' learning achievements and the extent of utilization of user-centered word game-based approach in teaching Science and Mathematics among Grade 6 pupils. This study also utilized the descriptive-correlational research and the Statistical tools used in the study were the mean and standard deviation to determine the extent of utilization of user-centered word game-based approach to teaching in Science and Mathematics and frequency and percentage distribution were used to determine the level of pupils' learning achievements. Pearson r was utilized to ascertain significant relationship between the level of pupils' learning achievements and the extent of utilization of user-centered word game-based approach in teaching Science and Mathematics. Findings revealed that teachers "Highly Utilized" the user-centered word gamebased approach in teaching Science and Mathematics and many of the pupil-respondents, that is 81 or 31% out of 160 respondents had an "Outstanding" learning achievements while only 3 or 2% were rated "fairly satisfactory". Further, result suggests that user-centered word game-based approach in teaching Science and Mathematics had "low or slight correlation" to pupils' learning achievements. Hence, the null hypothesis is rejected. Subsequently, it was recommended that in teachers should be inspired to continuously design, develop, and utilize their strategic intervention materials which are responsive to pupils' inclusive and individual learning needs to improve their learning performance. [ABSTRACT FROM AUTHOR]

The relevance of improving arithmetic calculus learning in students is evidenced by its impact on overall academic performance and preparation for higher educational levels. The main objective of this quasi-experimental study, with a mixed approach, was to evaluate the effectiveness of a ludic strategy specifically designed to improve arithmetic calculation performance in sixth grade EGB students at the Isabel Robalino Educational Unit. A sample of 40 students was selected, divided into an experimental group, which participated in ludic activities for 12 weeks, and a control group, which continued with traditional methods. The methods applied included initial diagnostic tests, perception questionnaires for students and teachers, academic performance tests, and in-depth interviews with teachers and administrators, complemented by consultation with a panel of experts in mathematics education. The results showed that the experimental group experienced a significant improvement in their arithmetic calculation skills, in contrast to the control group. In addition, the perceptions of students and teachers were highly positive, highlighting the motivation and interest generated by the play activities, as well as their effectiveness in the understanding and application of mathematical concepts. The implemented ludic strategy proved to be an effective pedagogical tool, not only to improve academic performance, but also to increase students' interest and participation in learning arithmetic calculus. [ABSTRACT FROM AUTHOR]

Copyright of Roca: Revista Científico-Educacional de la Provincia de Granma is the property of Universidad de Granma, Departamento Editorial and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study tests a model that predicts the problem-posing performance of sixth-grade students (independent variable metacognition, mediator variables mathematics and native language course success scores at the end of the year). The research was conducted with the relational model. The results regarding the mediation effect indicated that the mathematics course success scores and the native language course success scores were separately full mediators in the effect metacognition has on problem-posing performance. The results regarding serial mediation effect revealed that the mathematics course success scores and native language course success scores had a full mediating effect on the effect of metacognition on problem-posing performance. [ABSTRACT FROM AUTHOR]

There is a significant body of research that indicates that the use of tablets to learn mathematics in elementary school motivates students to learn. Low mathematical attainment in international benchmarking tests of mathematics in South Africa led the authors to investigate the potential that the mobility of the tablet provided for children to learn how to reason using what Mercer called 'exploratory' talk, a form of dialogical interaction indicative of reasoning. In this article the authors investigate two grade 6 classrooms in two schools where students are learning mathematics using tablets. In this multiple case study, the authors videotaped children during mathematics lessons where they used tablets to solve mathematical problems, and the data were transcribed. Findings indicate that the tablets across both contexts facilitate what Mercer calls exploratory talk, which is indicative of reasoning and, therefore, learning. [ABSTRACT FROM AUTHOR]

Peer tutoring is a learning method that entails student partnerships that pair good students with lower achievers or pupils with comparable achievement for systematic reading and math study times. The main purpose of this study is to determine the problems of selected grade 6 students in mathematics that would help the students enhance their academic performance in the subject. The data gathering will be done by selecting grade 6 students, both female and male, with separate results from the conducted pretest and posttest questionnaires. Other students who do not fall into the category are not included in the collection of information. The only purpose of this study is to achieve its goal, and it won't investigate anything else. After using dependent T test at the scores of the students after pretest and posttest, we got a computed value (T Value) of -5.6803. With a critical value of -2.0195, we can reject the null hypothesis and conclude that peer tutoring can bring a significant difference to the combined result of critical thinking and problemsolving test. The finding suggests that school heads and classroom teachers may use "peer tutoring" as a learning method for helping the learners improve their performance in mathematics. The school and the classroom teachers may use peer tutoring as a learning method that entails student partnerships that pair good students with lower achievers or pupils with comparable achievement for systematic reading and math study times. [ABSTRACT FROM AUTHOR]

In the 21st Century, it has become more difficult for teachers to attract students to the curriculum due to many factors that entertain students. Hence, teachers need to think about teaching methods that indirectly motivate students to learn. Moreover, this need is more felt in mathematics because it requires the constant creation of new cognitive structures. Therefore, one of the effective teaching methods for this demand is teaching with the help of various games. For this purpose, the present study investigated the effect of playbased learning methods on math learning in sixth-grade students. This research is quantitative. The results of this study were collected from experiments on control and experimental groups. The statistical population, at first, all male students in the sixth grade of primary school in the city of Karaj were considered for the academic year 2021-2022. Then, by cluster sampling, it was reduced to one school and finally, randomly, to two classes of 30 people. The control group was trained by the usual method of the teacher's explaining and then solving the book's exercises. The training of the experimental group was done by the simulation game of bank and supermarket space. In this method, students calculated discount percentages during their play and learned lesson points. In the end, the same tests were taken from both control and experimental groups and the average scores of students in both groups were obtained. The mean for the control group was equal to 10.06 and for the experimental group, equal to 15.23. The results of research data showed that the gamebased teaching method has a positive effect on students' math learning compared to teaching by teacher's lecture. [ABSTRACT FROM AUTHOR]

The aim of this research is to examine sixth grade students' skills of solving and posing problems which require using the knowledge of the order of operations to solve. The case study design, one of the qualitative research methods, was adopted in the research. The study group consisted of 44 sixth grade students attending a public secondary school in Eskisehir. Within the scope of the application, the forms including the questions to measure their problem solving and posing skills were directed to the study group. The data were analyzed by thematic analysis method. According to the results obtained, it was found that while most of the students were successful in solving problems which require the knowledge of the order of operations, they were not successful in posing such type of problems. In addition, it was found that students made mistakes in Turkish language grammar and expressions and in using the mathematical language. Students made mathematical terminology mistakes generally in subtraction and division operations. As a result, it is recommended to increase the problem posing and order of operations activities in mathematics lessons. [ABSTRACT FROM AUTHOR]

This study investigated the developmental influence of collaborative games, in the form of game-based worksheets, on the performance and attitudes of sixth-graders in the mathematics classroom. It is posited that games have the potential to enhance learning through positive emotional experiences. Non-digital game-based learning methodologies are accessible in terms of cost effectiveness, providing opportunities for social interactions while learning, and demanding few prerequisite skills. This study investigated the opportunities for learning that non-digital, textbook-based game worksheets could afford mathematics learners. In this case study, a quasi-experimental design was implemented and pre- and post-tests were conducted around an intervention. From a statistical analysis of the test data, using the Mann–Whitney U-test, it was concluded that the intervention on the topics of multiplication and division had a positive impact on the experimental group of this sample. The experimental group was observed while participating in the games and the observation schedule was member-checked. The Game Object Model provided the conceptual framework. The results indicated that learners benefited from the incorporation of the combination of collaboration and games and that their achievement improved. The findings also suggest that the collaborative games positively influenced learners' confidence, skills and understanding in mathematics. [ABSTRACT FROM AUTHOR]

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able groups and to find two-parameter models for the assigned word problem. An independent two-sample t-test was used to determine differences in the difficulty of word problems. Further insight was gained by analyzing pupils' written solutions and complementary task-based interviews. We confirmed the influence of the variables in question on the word problem difficulty and showed that their combined influence manifests itself in further achievement drop and in the change of strategies and errors. We documented multiple ways in which an irrelevant number influences pupils' reasoning. We showed that pupils' insufficient familiarity with decimals may prevail over their apparent ability to mathematize a relational term with natural numbers. This shows the importance of adjusting the word problem difficulty to pupils' knowledge and experience as the effect of a variable does not have to show itself under some circumstances. [ABSTRACT FROM AUTHOR]

The aim of this research was to examine the measurement-based estimation skill levels of middle school 6th grade students and the processes of comparing their estimations with measurements. In this research, the case study design, one of the qualitative research methods, was used. Six students one female and one male student, at low, medium and high mathematics achievement levels from a public middle school in the central districts of Ankara formed the study group. Activities were prepared, which included questions in different categories, both for estimating the length, area and liquid volume of the measurement, and for the proximity of objects to the student. In order to determine the study group, activities were applied to 35 students, and their measurement-based estimation skill levels were examined. While determining the levels, a method called "Evaluation of estimates by percentage of measurements" was used. Before conducting clinical interviews with the study group, the activities were applied to the students, the students were first allowed to make predictions, they were expected to compare their estimations with the possible real measurement without measuring, and then, in some questions, the students were asked to make measurements using tools and compare their estimations with the measurements. As a result, it was observed that the students' estimation skills based on measurement were at a low level. When they were asked to evaluate their estimations without measuring, it was concluded that the students were not successful and they had problems both in the use of measurement tools and in the measurement process while measuring. [ABSTRACT FROM AUTHOR]

This study aimed to determine whether educational games improve mathematics performance in elementary school students. Volunteers were 47 Costa Rican students from a public school, who were assigned to an experimental (EXP: educational games) or a control (CTRL: traditional class) group. Twenty games were created and nine experienced teachers provided expert judge validity assessed by Kendall's concordance coefficient (W). The EXP group completed 20 sessions (8 weeks) of 10-min games and following every game, students provided feedback. Before and after the treatment, students completed an official sixth-grade mathematics test. Two-way mixed ANOVA (assessments: pre-test, post-test by groups: EXP, CTRL) showed a significant main assessment effect. The W for teachers' feedback allowed to use the games indoors, and student's opinion following the games was considered 'very good'. In conclusion, 20 educational games failed to improve mathematics academic performance in sixth-grade students; however, students enjoyed the games and there was a trend to improve performance compared to a CTRL group. [ABSTRACT FROM AUTHOR]

Teaching students to self-regulate enhances their mathematics performance, yet few studies have investigated the long-term differential impact of particular self-regulation strategies specifically for lowachieving students. This quasi-experimental study evaluates the effect of teaching different selfregulation strategies on mathematical problem solving in low-achieving students. The participants were 69 sixth-grade elementary school students randomly assigned to one of three experimental groups (and taught predominantly cognitive, metacognitive or volitional strategies, while verifying intervention fidelity) or a control group for 16 sessions. Mathematical problem-solving skills were evaluated prior to the intervention, upon completion, and two months later. While all three intervention groups obtained significantly better results compared to the control group immediately after the intervention, volitional and metacognitive strategies showed the strongest and most lasting positive effects. We conclude that low-achieving students could benefit from learning self-regulation strategies, particularly when these strategies take into account the affective and motivational dynamics of learning. [ABSTRACT FROM AUTHOR]

Purpose of the study is to investigate the effectiveness of the use of Realistic Mathematics Education (RME) approach on sixth grade students' statistical thinking levels. Mooney's (2002) statistical thinking framework describing four thinking levels across four different statistical thinking processes was used. This study utilized a quasi-experimental pretest-posttest design. In the experimental group, the data handling unit was taught using RME approach whereas in the control group lessons were taught traditionally using a mathematics textbook and direct instruction. A statistical thinking test composed of seven open-ended questions was prepared and applied to both groups as pretest and posttest. The change of students' statistical thinking levels in pretest and posttest were analyzed and compared in both groups as well as between groups. The data analysis showed that the overall growth at Level 4 across statistical thinking processes was higher for the students who were taught using the RME approach than for those taught traditionally. [ABSTRACT FROM AUTHOR]

Explicit instruction is a pedagogical approach in which students are taught step-by-step procedures for solving problems and practice using the procedures. Despite considerable evidence supporting the use of this general approach, relatively little is known about how varying specific design features impact its effectiveness. This preregistered study investigated the impact of two design features, explaining rationales for procedures and practicing in interleaved sequence, on the efficacy of explicit instruction in fraction arithmetic. Participants were 156 sixth to ninth grade children. Children received a brief intervention involving explicit instruction in fraction arithmetic procedures. They were randomly assigned to receive or not receive explanations of rationales for the procedures, and to practice different procedures in either interleaved or blocked sequence. Relative to pretest, accuracy improved on immediate and delayed posttests (Cohen's d = 0.88 and 0.55 respectively). The magnitude of this improvement was not affected by either experimentally-manipulated factor or by both of them together. The results support the use of explicit instruction in fraction arithmetic, but provide no evidence that explaining rationales for procedures, or interleaving practice thereof, increases the effects of such instruction on procedural knowledge. • Children received a fraction arithmetic intervention using explicit instruction. • The intervention improved fraction arithmetic calculation accuracy. • Explaining rationales for procedures did not improve the intervention's effectiveness. • Interleaved practice also did not improve the intervention's effectiveness. • Findings support the use of explicit instruction in fraction arithmetic procedures. [ABSTRACT FROM AUTHOR]

This paper explores how problem solving is approached in two 6th grade mathematics textbooks and national elementary mathematics curriculum in Turkey. The curriculum and textbooks' problem solving approaches are analysed and compared in the light of three approaches of 'teaching for, about and through problem solving'. Four learning objectives from different content areas (e.g. algebra, data processing) from the curriculum are determined and their treatments in the textbooks are specifically analysed. The analysis showed that the curriculum did not have a prescriptive stance on any one of problem solving approaches. Similarly, the textbooks also did not follow any approach faithfully. 'Teaching for problem solving' approach was not employed while 'teaching through problem solving' approach was used for only one learning objective in the textbooks. 'Teaching about problem solving' approach was encountered in terms of only one problem solving heuristic (table drawing). We discuss the implications of these findings and note some further research areas. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a novel approach for collaborative retrospective analysis. One researcher was directly involved in a classroom teaching experiment, adopting an emergent perspective as an interpreter-witness of classroom interactions during a four-week algebra instructional unit with sixth-grade students. The other researcher experienced and analyzed the data in reverse chronological order. We describe how this re-emergent perspective revealed aspects of students' early algebraic reasoning. [ABSTRACT FROM AUTHOR]

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth graders (12-year-olds) use shortcut strategies in solving multidigit addition, subtraction, multiplication, and division problems, to what extent student factors and task instructions affected this frequency of shortcut strategy use, and to what extent the strategies differed in performance. A sample of 648 sixth graders from 23 Dutch primary schools completed a paper-and-pencil task of 12 multidigit arithmetic problems, designed to elicit specific shortcut strategies such as compensation. Based on the students’ written work, strategies were classified into whether a shortcut strategy was used or not. Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies. An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems. Finally, the use of shortcut strategies did not yield higher performance than using standard strategies. All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common. [ABSTRACT FROM AUTHOR]

The purpose of this study is to examine the psychometric properties of an instrument to measure word problem solving skills in mathematics related to speed with 706 sixth grade Chinese and Singaporean students. Rasch measurement models were applied to examine the reliability, unidimensionality, rating scale functioning, item difficulty, and person difficulty. The differential item functioning (DIF) analysis was also performed to examine the differences in item difficulty estimates between Chinese and Singaporean students. Results suggest that the data satisfied the unidimensionality requirements of the Rasch model and that most of the item difficulty measures aligned the person ability distribution. The instrument demonstrated adequate reliability. The fit statistics were within acceptable limits for the vast majority of items, with a few exceptions. The rating scale structure functioned properly although the middle categories had very few observations. Deleting misfitting cases and collapsing middle categories slightly improved the psychometric properties. DIF analysis revealed that four items were more difficult for Chinese students whereas two other items were more difficult for the Singaporean students. Results also indicated that the Chinese participants scored higher than the Singaporean participants for 11 of the 14 items and the Singaporean students scored higher than their Chinese cohorts in the other 3 items. The validation of this instrument has implications for the teaching and learning of mathematical word problems in practice. [ABSTRACT FROM AUTHOR]

This study examined cross-task consistency and longitudinal stability in elementary school students' task interest, success expectancy, and performance from fourth to sixth grade, and their predictive effects on sixth-grade intrinsic value, self-concept, and achievement in mathematics. The results demonstrated consistency in interest, success expectancy, and performance across tasks and stability over time, and these to predict domain-specific motivation and achievement. Virtually no evidence for reciprocal effects was found for task-specific measures, as only previous task performance predicted change in later success expectancy. Cross-lagged effects were observed, however, for predictions of task motivation and performance on domain-specific motivation and achievement, so that success expectancy predicted intrinsic value, interest predicted self-concept, and task performance predicted both self-concept and achievement. Based on the findings, it would seem that students' task-related motivational experiences are associated with their domain-specific beliefs, and that those, in turn, are to some extent manifested in students' task motivation. [ABSTRACT FROM AUTHOR]

The purpose of this study is to determine the misconceptions of 6th-grade secondary school students in terms of part-whole relation in fractions, representation of fractions on the number line, comparison of fractions and operations in fractions. The sample of this study is composed of 104 students who are being educated in 6th-grade of five secondary schools in 2017-2018 teaching year in a province which takes place in the north part of Turkey. Fractional information test, which consists of 5 open-ended questions developed by researchers, was used as data collection tool. The data of the study were analyzed using the content analysis method and in this method frequency/percentage tables were used. By examining the explanations that the students have made, the incorrect answers are divided into categories, and the misconceptions in each question are presented separately. As a result of the study, it has been seen that students have misconceptions in terms of parts-whole relation in fractions, representation of fractions on the number line, comparison of fractions and operations in fractions. [ABSTRACT FROM AUTHOR]

This text presents a qualitative research, which aims to verify the participation in a statistical research of a group of 6th grade students enrolled in a state public school in the city of Guaratinguetá-SP. The data construction work was carried out during three meetings, in which a statistical problem was elaborated, the collection procedures, the data collection, its organization in tables and graphs, and the interpretation of the results. The analyzes indicate that the students already had evidence of notions of proportionality, measures of central tendency, census and sample, which contributed significantly to the development of the study. In addition, the development of the work, as proposed, favored a growing mobilization of statistical concepts by the students. [ABSTRACT FROM AUTHOR]

Background: Students' ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. Most of the related research on unit coordination relies on time-intensive clinical interviews and teaching experiments. In this study, we investigate the work of 93 sixth-grade students on a written assessment containing whole number and fraction contexts using both continuous and discrete quantities, and how this work can be used to assess stages in students' construction and coordination of units. Our investigation is guided by the following general research questions: (1) What forms of written work evidence the construction of and operation on composite units (units made up of other units)? (2) How does the categorization of students based on responses from a written assessment compare to written performance on a set of tasks conveying a continuous whole number multiplicative context? Results: We documented the different ways students represented composite units in their written work. In particular, student written work on tasks that included figurative unit items provided the greatest variety of evidence regarding students' construction of and operation on composite units. However, written evidence from partitioning tasks did not seem as promising for distinguishing student stages. Students' performance on decontextualized bar tasks involving continuous quantities was found to be consistent with students' level of unit coordination based on written work providing evidence for the validity of stage categorizations. Conclusions: Our findings shed light on the affordances and constraints associated with particular stages in unit construction and coordination that a student brings to bear on tasks provided in a formal, written assessment. These findings provide promising evidence for scaling up the assessment of students construction and coordination of units through the use of written assessments instead of time-intensive clinical interviews. [ABSTRACT FROM AUTHOR]

This case study of mathematics instruction using children's literature reports on the experiences 47 elementary preservice teachers had in their mathematics methods course while completing a microteaching assignment. As part of the microteaching assignment, preservice teachers were required to plan and teach mathematics lessons based on children's books that included both mathematics concepts and multicultural aspects. The preservice teachers audio-recorded their lessons, transcribed the audio, and wrote reflective essays to articulate their experiences. At the end of the assignment, the professor and two additional researchers interviewed the preservice teachers about their experiences. Themes that emerged were (a) teaching experiences, (b) teaching performance, and (c) learning purposes and tools for integrating multicultural children's math books. The Learning Purposes and Teaching Strategies for Integrating Multicultural Mathematics Picturebooks Framework was developed to demonstrate the intricate balance needed to ensure mathematics learning happens during instruction with multicultural mathematics picturebooks. [ABSTRACT FROM PUBLISHER]

Educating students for higher-order thinking provides them with tools that turn them into more critical thinkers. This supports them in overcoming life problems that they encounter, as well as becoming an integral part of the society. This students' education is attended to by educational organisations that emphasise the positive consequences of educating students for higher-order thinking, including creative thinking. One way to do that is through educational programmes that educate for higher-order thinking. One such programme is the Cognitive Research Trust (CoRT) thinking programme. The present research intended to examine the effect of the participation of Grade 6 students in a CoRT programme on their creative thinking. Fifty-three students participated in the research; 27 participated in a CoRT programme, while 26 did not participate in such programme. The ANCOVA test showed that the students who participated in the CoRT programme outperformed significantly, in creative thinking, the students who did not. Moreover, the students in the CoRT programme whose achievement scores were between 86 and 100 outperformed significantly the other achievement groups of students. Furthermore, students with reported high ability outperformed significantly the other ability groups of students. The results did not show statistically significant differences in students' creativity attributed to gender. [ABSTRACT FROM AUTHOR]

Ce travail, développé dans le cadre de la théorie des situations didactiques de Guy Brousseau, porte sur revolution des strategies d'élèves de sixième dans le jeu Mankala Récolte Trois. Pour cela, un répertoire de configurations possibles de jeu a été construit dans Vanalyse a priori. Le dispositif experimental est constitué de deux moments de jeu et d'un entretien avec quatre élèves de sixième. Parmi les resultáis, il a été constaté que le dispositif expérimental a permis de renforcer le caractère adidactique des situations de jeu avec le Mankala Récolte Trois et que les differ entes formes d'interaction ont favorisé l'evolution des strategies des élèves le long des parties jouées. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Theory & Practice in Education (JTPE) / Eğitimde Kuram ve Uygulama is the property of Journal of Theory & Practice in Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A growing body of research implicates students’ ability to coordinate multiple levels of numerical units as an important aspect of their mathematical development. In this paper, we consider relationships between the ways students coordinate units with whole numbers (their multiplicative concepts) and the ways students coordinate units with fractions (their fractions schemes). Interviews with 50 sixth-grade students suggest commonality in the number of levels of units-within-units structures that students construct for the two contexts, consistent with Steffe's (2001. The Journal, of Mathematical Behavior , 20 (3), 267) reorganization hypothesis. The results suggest that fractions may be a fertile domain for elementary and middle grades students to continue to develop whole number understandings. [ABSTRACT FROM AUTHOR]

This study investigated sixth-grade middle-level students' geometric spatial development by gender and race within and between control and experimental groups at two middle schools as they participated in an Earth/ Space unit. The control group utilized a regular Earth/ Space curriculum and the experimental group used a National Aeronautics and Space Administration-based curriculum. The quantitative data sources included the Lunar Phases Concept Inventory, Geometric Spatial Assessment, and the Purdue Spatial Visualization- Rotation Test. The results indicated the experimental males and females, and the students of color and white students in the experimental group showed significant gains in their understanding of geometric spatial visualization from pre- to post-implementation. However, for the control group, the significant gains were limited to the males and the white students. The findings reveal that support is needed for males, females, and all racial groups to have the opportunity to develop their spatial reasoning, which in turn, increases students' scientific understanding. [ABSTRACT FROM AUTHOR]

Students' difficulties in mathematics and science may stem from interference of the task's salient irrelevant variables. Here, we focus on a comparison of perimeters task, in which the area is the irrelevant salient variable. In congruent trials (no interference), accuracy is higher and reaction time is shorter than in incongruent trials (area variable interference). A brain-imaging study related to this task indicated that correctly answering the incongruent condition is associated with activation in prefrontal brain regions known for their executive inhibitory control. These findings suggested that intervention aimed at activating inhibitory control mechanisms could improve students' success. In this paper, we explore the effect of an intervention that explicitly warns about the possible interference of the variable area. Eighty-four sixth graders performed the same comparison of perimeters reaction time test, with warning intervention (warning group) or without it (control group). Accuracy in the warning group was significantly higher in incongruent conditions and reaction time was significantly longer in all conditions than in the control group. The results suggest that the explicit warning activates inhibitory control mechanisms and thus helps students overcome the interference. The findings point to the possibility of improving students' problem-solving abilities through simple and focused interventions that explicitly warn them about the trap in the task. Such research-based simple interventions appear to require only teachers' knowledge and awareness and could complement the traditional educational technique of supporting relevant content knowledge. [ABSTRACT FROM AUTHOR]

Communication about prediction is complex in a number of ways. First, language is by nature recursive — language is an indicator of meaning as well as a force that shapes meaning. Second, the same language used to communicate prediction in uncertain environments is used for other purposes. In this article, we describe how the recursive nature of language impacted the choices we made in a cross-sectional longitudinal study aimed at gaining insight into children’s language repertoires relating to conjecture. We then explore some Grade 6 students’ communication about prediction to develop insight into their meaning and meaning-making with prediction language. From this we raise questions about interpreting data from such contexts. Finally, we discuss implications for educators. [ABSTRACT FROM AUTHOR]

Most studies of students' understanding of decimals have been conducted within Western cultural settings. The broad aim of the present research was to gain insight into Chinese Hong Kong grade 6 students' general performance on a variety of decimals tasks. More specifically, the study aimed to explore students' mathematical reasoning for their use of 'rules' and algorithms and to determine whether connections exist between students' conceptual and procedural knowledge when completing decimals tasks. Results indicated that conceptual understanding for rules and procedures were built into the students' knowledge system for most of the items concerned with place value in decimals-ordering decimals, translating fractions into decimals, the representation of place value in decimals, the concept of place value in decimals on number line and the concept of continuous quantity in decimals. However, the students were not able to provide such clear explanations for the use of algorithms for the multiplication and division items. The findings are discussed in the light of Chinese perspectives on procedural and conceptual understanding. [ABSTRACT FROM AUTHOR]

Adescriptive, holistic, multiple-case methodology was applied to examine the nature of participation in discourse of two low- and two high-achieving grade 6 students while solving mathematical tasks in a standards-based classroom. Data collected via classroom observations and student interviews were analyzed through a multiple-cycle coding process that yielded the within-case themes of use of space, meaning-making, and peer and teacher interactions. This student-focused inquiry addressed a methodological gap in the extant empirical literature by employing videorecording as a means of eliciting student awareness and reflection, which notably revealed differences in participation between the two low-achieving students. When considering implications, the results illuminate needed additional classroom norms, issues related to relative differences in students' abilities in heterogeneous groups, benefits of using video-recording as a means of promoting student reflection, and the important role of the teacher in maintaining equitable participation. [ABSTRACT FROM AUTHOR]

We often understand something only after we've had to teach or explain it to someone else. Learning-by-teaching (LBT) systems exploit this phenomenon by playing the role of tutee. BELLA, our sixth-grade mathematics LBT systems, departs from other LTB systems in several ways: (1) It was built not from scratch but by very slightly extending the ontology and knowledge base of an existing large AI system, Cyc. (2) The 'teachable agent'-Elle-begins not with a tabula rasa but rather with an understanding of the domain content which is close to the human student's. (3) Most importantly, Elle never actually learns anything directly from the human tutor! Instead, there is a super-agent (Cyc) which already knows the domain content extremely well. BELLA builds up a mental model of the human student by observing them interact with Elle. It uses that Socratically to decide what Elle's current mental model should be (what concepts and skills Elle should already know, and what sorts of mistakes it should make) so as to best help the user to overcome their current confusions. All changes to the Elle model are made by BELLA, not by the user-the only learning going on is BELLA learning more about the user-but from the user's point of view it often appears as though Elle were attending to them and learning from them. Our main hypothesis is that this may prove to be a particularly powerful and effective illusion to maintain. [ABSTRACT FROM AUTHOR]

Educational research indicates that error reflection, especially reflection on incorrect examples, has a positive effect on knowledge acquisition. The benefit of error reflections might be explained by the extended knowledge of incorrect strategies and concepts (negative knowledge) which fosters the learning of new content. In a field experiment with a pre-post-design we taught fractions to N = 195 6th grade students and compared two conditions that encouraged reflection on either incorrect or correct examples. We found that incorrect examples supported students' negative knowledge more than correct examples. However, regarding the knowledge of fractions, only advanced students could benefit from incorrect examples; students with low prior knowledge learned more from correct examples. Even though negative knowledge showed a partial mediation effect for knowledge acquisition, it did not mediate the effect of error reflections on the acquisition of knowledge of fractions. The implications for school instruction are discussed. [ABSTRACT FROM AUTHOR]

Copyright of Dicle University Journal of Ziya Gokalp Education Faculty / Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi is the property of Dicle University Journal of Ziya Gokalp Education Faculty and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Kirsehir Education Faculty is the property of Journal of Kirsehir Education Faculty and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Pegem Journal of Education & Instruction / Pegem Egitim ve Ögretim is the property of Pegem Journal of Education & Instruction / Pegem Egitim ve Ogretim and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study focuses on quantifying the quality of mathematics teaching in 183 randomly selected sixth grade classrooms: 100 from the North West province of South Africa and 83 from South East Botswana. The teaching quality is measured by coding videotaped lessons for three different components: mathematical proficiency, level of cognitive demand, and observed teacher knowledge. Results suggest that the overall teaching quality is about the same in both regions. Some variation was observed at the level of each component. For example, in the South Africa sample the students engage more in tasks that just involve 'memorization' and less in tasks that involve 'procedures without connections' in comparison with the Botswana students. Teachers in Botswana implement the official curriculum more faithfully than do those in North West. In both countries most of the learners engaged only in low-level tasks (very little activity involved 'procedures with connections') and teachers demonstrated a lack of knowledge about how to integrate mathematical content with effective pedagogical techniques. [ABSTRACT FROM AUTHOR]

Mathematics education research has documented several classroom practices that might influence student self-regulation. We know little, however, about the ways these classroom practices could be structured in real classroom settings. In this exploratory case study, we purposefully selected a sixth-grade mathematics teacher who had participated in a professional development program focussed on NCTM standards and SRL in the mathematics classroom for extensive classroom observation. The purpose was to explore how and to what extend she structured classroom practices to support strategic competence in her students. Four features of classroom practices were found as evidence for how strategic competence was potentially supported in this classroom: (a) allowing autonomy and shared responsibility during the early stages of learning, (b) focusing on student understanding, (c) creating contexts for students to learn about strategic learning and to exercise strategic behaviour, and (d) helping students to personalise strategies by recognising their ideas and strategic behaviours. [ABSTRACT FROM AUTHOR]

This study consisted in the application of questionnaires to 297 sixth-grade students from 13 different elementary schools in Mexico. Pupils were asked to identify the quantity represented by common fractions (e.g., 1/2, 1/4, 1/3, 3/4). Findings suggest that many students are finishing elementary school in Mexico with a very limited understanding of fractions. Some seem not to have developed basic quantitative concepts that would allow them to readily and correctly recognize the quantitative meaning of the most common fractions, including "1/2". We explain the implications of such findings for students' future mathematical development. [ABSTRACT FROM AUTHOR]