運用「範例(worked-out example)」在國小數學問題解決的教學實驗研究

Prior research has shown that game‐based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in‐game progress positively predicts their later performance. Using data from 253 seventh‐graders (12–13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between students' progress within DragonBox and their algebraic knowledge and general mathematics achievement, (b) the moderating effects of students' prior performance on these relations and (c) the potential factors associated with students' in‐game progress. Among students with higher prior algebraic knowledge, higher in‐game progress was related to higher algebraic knowledge after the intervention. Higher in‐game progress was also associated with higher end‐of‐year mathematics achievement, and this association was stronger among students with lower prior mathematics achievement. Students' demographic characteristics, prior knowledge and prior achievement did not significantly predict in‐game progress beyond the number of intervention sessions students completed. These findings advance research on how , for whom and in what contexts game‐based interventions, such as DragonBox, support mathematical learning and have implications for practice using game‐based technologies to supplement instruction. Practitioner notes What is already known about this topic DragonBox 12+ may support students' understanding of algebra but the findings are mixed. Students who solve more problems within math games tend to show higher performance after gameplay. Students' engagement with mathematics is often related to their prior math performance. What this paper adds For students with higher prior algebraic knowledge, solving more problems in DragonBox 12+ is related to higher algebraic performance after gameplay. Students who make more in‐game progress also have higher mathematics achievement, especially for students with lower prior achievement. Students who spend more time playing DragonBox 12+ make more in‐game progress; their demographic, prior knowledge and prior achievement are not related to in‐game progress. Implications for practice and/or policy DragonBox 12+ can be beneficial as a supplement to algebra instruction for students with some understanding of algebra. DragonBox 12+ can engage students with mathematics across achievement levels. Dedicating time and encouraging students to play DragonBox 12+ may help them make more in‐game progress, and in turn, support math learning.

Abstract: The purpose of this research was to determine the effect of learning models on mathematics achievement viewed from student attitude toward mathematics. The learning models compared were Team Assisted Individualization (TAI) based Assessment for Learning (AfL), TAI, and conventional learning model. The research was quasi experimental. The population of this research was all students of grade VIII State Junior High School of the District Karanganyar, academic year 2013/2014. The samples in this research were SMPN 1 Tasikmadu, SMPN 2 Jaten, and SMPN 2 Colomadu taken by stratified cluster random sampling. Instruments used to collect data were mathematics achievement instrument test and questionnaires students toward mathematics instrument. Data analysis technique used hypothesis test with two-way analysis of variance with unbalanced cells. From the results of the analysis, can be concluded that: 1) the learning achievement in mathematics of the students who were learning mathematics with cooperative learning model TAI Based AfL were better than the ones who were learning mathematics with cooperative learning model TAI and conventional learning model, however the students who were learning mathematics with cooperative learning model TAI were better than the ones who were learning mathematics with conventional learning model, 2) the learning achievement in mathematics of the students with the high attitude toward mathematics were better than the ones with the medium and low attitude toward mathematics, however the students with the medium attitude toward mathematics were better than the ones with the low attitude toward mathematics, 3) in the cooperative learning model TAI Based AfL, the learning achievement in mathematics of the students with ones who have the high attitude toward mathematics were better than the students with the low attitude toward mathematics, and students with the medium attitude toward mathematics were as good as the ones who have low attitude toward mathematics as well. In the cooperative learning model TAI and conventional learning model, the students with the high, medium, and low attitude toward mathematics had the same achievement in learning mathematics, 4) in the students with the high attitude toward mathematics, the learning achievement of the students who were learning mathematics with ones who have cooperative learning model TAI Based AfL were better than the students were learning mathematics with cooperative learning model TAI, the students who were learning mathematics with cooperative learning model TAI had the same achievement in learning mathematics with conventional learning model, and the students who were learning mathematics with cooperative learning model TAI Based AfL had the same achievement in learning mathematics with cooperative learning model TAI. The students with the medium and low attitude toward mathematics had the same achievement in learning mathematics among the ones who were given the cooperative learning model TAI Based AfL, TAI, and conventional learning model. Keywords: Team Assisted Individualization (TAI), Assessment for learning (AfL), students attitude toward mathematics, achievement learning mathematics.

This research identifies important features of mathematics learning from the accounts of early school leavers. These students were enrolled in a Youth Reconnected Program at a Technical and Further Education [TAFE] college. Specifically, it examines the relationship between their experiences of mathematics learning in two different social contexts, the program and secondary school classrooms, the discourses and associated discursive practices of these two contexts, and the forms of identities of participation that are constructed in them. Drawing on a social theory of learning and critical discourse theory, the research identifies the processes by which membership in communities of learning is achieved and identities discursively constructed. It draws on the accounts of forty-three early school leavers and six staff members located in a Youth Reconnected Program, a program designed to re-engage early school leavers in education and or training, about their prior experiences of secondary school and their current experiences of TAFE. From these accounts, the thesis seeks to explicate their experiences of learning mathematics in both contexts and to consider the implications of different student experiences of learning for mathematics education. Critical discourse analysis provides the means for applying this framework to examine the discourses, discursive practices, identities, and forms of participation constructed in the accounts. It views the accounts as constituted by their social context. It shows how the language of the accounts works to construct particular versions of reality and how relations of power construct particular identities. It allows a richer qualitative exploration of the reported practices of mathematics classrooms with particular regard to linking the theoretical and practical concerns of this study. It makes transparent the relations between the social (including relations of power and domination), discourse, and discursive practice, thus enabling a more in-depth reading of the participants‘ accounts. Discourses about two different experiences of mathematics learning were identified—one about mathematics learning in the Youth Reconnected Program (TAFE) and the other about mathematics learning in secondary schools. The discourses and their associated discursive practices—differing application of instructional style, communication and interaction, source of authority, pace of instruction, grouping of students and assessment— were found to contribute significantly to the construction of particular student identities and forms of participation. Student experiences emphasised the importance of four characteristics for membership in a community of learners—mutual engagement, joint enterprise, shared repertoire and access. These characteristics and practices were shown to contribute substantially to the construction of identities of participation in mathematics learning for most of the students who participated in this study. There was strong evidence to indicate that small class sizes impacted significantly on student engagement and participation in learning. A crucial factor here rests with the role of the teachers and tutors and how, given the opportunities for reduced class size, they implement, sustain and maintain interactions with the students for effective teaching and learning to occur. If in this context, consistent interactions are provided that also includes clear and explicit explanations, discussion, and negotiation, students are more likely to maintain their interest and actively participate in mathematics learning. This study‘s significance is twofold. It lies in the critical importance of the issue it addresses—student participation in mathematics learning—and the articulation of a social theory of learning with critical discourse theory to enable a different and more effective understanding of the significance of discourses, identities and communities of participation in mathematics learning. Although the study cannot claim generalisability across other populations of learners or across all mathematics and TAFE classrooms because of the small select sample of early school leavers drawn upon, by highlighting these accounts of students‘ learning experiences in some mathematics classrooms and the TAFE program, and their associated experiences of them, it draws attention to a different perspective on mathematics learning. In this alternative framing, learning as a social process is contingent on access to the discourse of mathematics learning and the discursive practices that support learning, participation, and membership in a community of mathematics learners. An attention to the social processes of mathematics learning infers a significant role for mathematics teachers in enabling student access to certain discourses and communities of learning. Such a role is often neglected in current contexts of accountability that specify a focus on achieving syllabus outcomes.

Learning mathematical concepts and procedures typically requires extended cognitive effort, presenting a challenge for many children. People can make tracing actions with the index finger, as well as mimic another's movements, with little or no conscious effort. From the perspective of cognitive load theory, such biologically primary actions may facilitate learning biologically secondary concepts and skills requiring extensive cognitive effort, such as mathematics. The present study investigated effects on learning processes and outcomes of students mimicking a teacher's tracing actions from the perspective of an evolutionarily informed cognitive load theory. One hundred and thirteen Grade Two children learned about number lines, either observing a teacher tracing out elements of worked examples with her index finger, or mimicking the teacher's tracing actions with their own index finger. In accord with hypotheses, results indicated enhanced performance due to mimicking on cognitive load, motivation, and post‐test performance. Directions for future research are discussed.

This article discusses a three-step method that was used in a college calculus course. The three-step method was developed to help students understand the course material and transition to be more independent learners. In addition, the method helped students to transfer concepts from short-term to long-term memory while lowering cognitive load. The three-step method is based off of the theory of worked examples, which falls under cognitive science and cognitive load theory. The article describes cognitive load theory, worked examples, and how worked examples are connected to the three-step method. The quantitative results of the research study show that, on average, participants performed significantly better than non-participants in the course and performed better on the final exam. The article ends with a discussion of the results of the study and why the three-step method helped students in the class.

This research aims to know the effect of Inquiry learning mode toward students’ mathematic achievement, the effect of students’ cognitive style toward students’ mathematic achievement the interaction effect between learning mode and students’ cognitive style toward students’ mathematic achievement at student grade VIII (Eight) SMP Negeri 6 Kerinci discrit academic year 2015/2016. The resarch conducted by using quasy experimental design research method follows nonequivalent control group design version by implementing factorial design 2 × 2. The population of the research are students of SMP Negeri 6 Kerinci discrit grade VIII odd term academic year 2015/2016. The study sample consisted of two class of experimental and one control class. Data is collected using two kinds of instruments namely instruments Group Embedded Figures Test (GEFT) to measure students' cognitive styles and mathematics achievement test students in essay form. Statistical test used is using ANOVA two paths to see the effect of the learning model and the effect of cognitive style on achievement as well as the interaction between the mathematical model of learning and cognitive styles of students towards mathematics student achievement. Further trials using t-test to see differences in student achievement based on students' cognitive styles. Result data analysis and statistical testing show that inquiry learning mode take effect toward Mathematic achievement, students’ cognitive style take effect toward Mathematic achievement, There is no interaction between learning mode and students’ cognitive style toward students’ Mathematic. Based on the results of this study it is suggested to the teachers, particularly the mathematics teacher that the implementation of the inquiry learning model can be developed as an innovation in teaching and learning process.

The aim of this research was to find out the influence of learning model implementation toward student’s achievement in mathematics. This research was using quasi-experimental research. The population of the research was all of 7th grade students in Karanganyar. Sample was taken using stratified cluster random sampling technique. The data collection has been conducted based on students’ mathematics achievement test. The results from the data analysis showed that the learning mathematics by using Numbered Head Together (NHT) learning model with scientific approach improved student’s achievement in mathematics rather than direct learning model particularly in learning object of quadrilateral. Implementation of NHT learning model with scientific approach could be used by the teachers in teaching and learning, particularly in learning object of quadrilateral.

The fading worked example has emerged from cognitive load theory as an effective strategy for lowering cognitive load in the novice phase of skill acquisition and has been shown to be effective in mathematics, engineering and psychology. This theoretical paper proposes the application of the fading worked example strategy to programming education.

This study aims to know effectiveness of Google Classroom using worked example's strategy in learning angles. This research is quantitative research using pre-experimental design in the form of one-shot case study. There are 29 students of Junior High School at Yogyakarta who have studied angles using google classroom with worked example strategy, were tested to measure student achievement in order to know effectiveness of learning angles using google classroom with worked example strategy. The result is Google Classroom using worked example strategy effectively used for learning angles in terms of student achievement.

This study titled as The Effect of Disposition on Student Mathematics Learning Achievement in Medan State 28 Junior High School. In this study, disposition is an independent variable and achievement in mathematics learning is a dependent variable. Mathematical disposition is a change of student’s tendency in assuming and behaving toward mathematics, also their act when learning mathematics. For example, when students can solve non-routine problems, their behavior and assumption of mathematics as a student become more positive. The more mathematical concepts understood, the more students convinced that mathematics can be mastered. Based on theory, there are many factors that influence student's achievement in mathematics learning. In this study, researcher only took disposition factor. This research took place at Medan State 28 Junior High School which located at Karya Bersama St. No. 17 Medan Johor. The method of this study is a quantitative method with all of VIII class students which amount to 273 students and divided into 8 (eight) study groups. The data obtained by giving a questionnaire consisting of 19 statements. The data then analyzed by using simple linear regression analysis. The data analysis was performed by using SPSS 21 software for Windows. From the results of this study, it can be concluded that there is an effect of disposition on students' achievement in mathematics learning or in other words, students' achievements in mathematics learning are influenced by the disposition attitudes that students have in mathematics learning. The influence occurs in the disposition of achievement in mathematics learning is positive, that is equal to 6.6%.Keywords: Disposition, Mathematics Learning Achievement.

The objectives of this research were: 1) to develop an instructional model to foster learning motivation and learning achievement based on self-efficacy and social cognitive development theories for lower primary students, and 2) to evaluate the effectiveness of the developed model by implementing it in class. A pilot study was conducted to test the feasibility of the developed model before implementing it to a purposively selected sample of 11 Primary 2 students. The study employed a single group time-series design involving one group of participants and several observations or assessments pertaining to the participants’ mathematics learning before and after the treatment. The participants were taught using the developed procedures over 20 lessons. Their motivation to learn mathematics was measured using Young Children’s Academic Intrinsic Motivation Inventory which had been modified with permission from the author and publisher. Classroom observations and structured interviews were conducted to provide more insights into the participants’ learning behaviour. Their mathematics achievement was measured using the scores obtained on tests following the completion of each lesson unit. The findings of this study were as follow: a)The developed model had seven components as follow: 1) Cordiality: Teacher models warmth, respect, and caring attitude. 2) Collection: Teacher uses a variety of material/tool or opening presentation method to start the lesson. 3) Clarity: Teacher demonstrates to students the steps and procedure involved in solving the task by doing worked examples. 4) Coordination: Teacher provides students with initial tasks that are certain to bring success to the students and provide them practice in applying the procedure. 5) Challenge: Provide options of tasks for students to choose that gives them optimal challenge. 6) Confirmation: Record students’ results in individual file for evaluation of progress, and not compared with other students’ results. 7) Communication: Communicate faith in the students’ ability. Praise them for their effort. Challenge them to do their best. Based on those 7 components, the instructional procedure for use in the classroom is as follow: Teacher creates a positive environment throughout the lesson by i) maintaining a positive ambience where students feel encouraged, accepted and unafraid to try, and ii) communicating faith in the students’ ability and praising their effort and response. The lesson is taught in steps: 1) interest stimulation, 2) clear coordination, 3) individualized challenge, and ends with progress check. b)Results of this study show that the research participants’ motivation in learning mathematics was significantly higher (p≤.05) after the treatment. There was an improvement in their mathematics achievement where the participants achieved test scores higher than the set minimum criteria of 80 percent.

There is an increasing use of and rapid advancements in technologies in education. In particular, there is a take-up of advanced calculators (graphing calculators and calculators with computer algebra system [CAS]) in senior secondary high-stakes examinations. Each year, tens of thousands of students in Australia, Singapore, and other regions, use advanced calculators in mathematics examinations that directly affect their entry into tertiary education. Thus, it was pertinent to investigate the ways in which students use these technologies when learning mathematics, and the factors that influenced them. This study was built upon a bricolage of theories from various fields such as mathematics education, educational technology, learning theories, learning styles, and gender studies. From a review of the literature in the different fields, it was hypothesised that factors such as students’ gender, beliefs about and attitudes toward mathematics and technology, approaches to studying mathematics, and learning preferences, influence their ways of using technology. A mixed methods research design was used, consisting of two parts: a quantitative large scale online survey of 964 Singaporean and 176 Victorian senior secondary mathematics students, and a qualitative small scale study of nine students in a Singaporean school. There were several main results found in this study: (i) How students interact with advanced calculators was influenced by their beliefs about and attitudes toward mathematics and their approaches to studying mathematics. Students’ ways of knowing and learning mathematics best explained their ways of interacting with the calculator. (ii) Students' learning preferences were situated, and the use of advanced calculators was associated with visual and kinesthetic modes and a preference to work cooperatively. (iii) There were regional differences (in favour of Victorian students) in how students use the advanced calculators and their attitudes toward calculators. (iv) There were gender differences (in favour of males) in students' attitudes toward mathematics and advanced calculators, and how they used the calculators. Although there were more student factors with gender differences in the Singaporean than the Victorian data, the effect sizes were larger in the Victorian sample. The findings have implications for mathematics teaching practice, in that deep understanding, intrinsic interest, beliefs about the creative, inter-connectedness and contextual aspects of mathematics are associated with using calculators as a partner and collaborator for learning. Additionally, students tend to employ visual and kinaesthetic modes when learning how to use the calculators. Students were also found to have a preference for working on the calculator cooperatively with friends. Therefore, teachers can employ methods such as encouraging students to try out the calculator keys and to work cooperatively in groups when learning how to use the calculators. Another significant contribution of this study was in the use of Facebook to recruit participants. More research can be done on the participation and response rates associated with this recruitment method. Further research can also be conducted to translate the implications of the study into practical classroom strategies and to investigate longitudinally the dynamic interplay between these factors and students’ interactions with the advanced calculators.

Students with low prior numeracy achievement in border areas often struggle with basic numeracy skills. This study developed Electronic Worksheets for Students (EWS), designed around traditional games, to improve numeracy among junior high school students in the Indonesia–Timor Leste Border Area (ITLBA). We employed a research-and-development approach guided by Tessmer’s formative evaluation model and a quasi-experimental pretest–posttest design (N = 56) to evaluate learning effects. The 4-week intervention consisted of a digital EWS delivered as a flipbook to participating classes. Primary outcomes included EWS validity, readability, and practicality, as well as students’ numeracy scores, and normalized gain (N-gain). Data were analyzed using paired t-tests and effect-size estimates (Cohen’s d and Hedges’ g) with 95% confidence intervals to quantify magnitude and precision of observed changes. Results indicate that the EWS satisfied validity, practicality, and readability criteria and produced substantial, statistically significant improvements in numeracy performance over baseline assessments across the intervention. At the TTS site (n = 30), for example, mean numeracy scores increased by 17.50 points (SD = 5.32), 95% CI [15.51, 19.49], t(29) = 18.01, p < .001; corresponding effect sizes were very large (Cohen’s d = 3.34, 95% CI 2.33–4.33; Hedges’ g = 3.29, 95% CI 2.37–4.19). The evidence from TTS is illustrative of the overall pattern observed. In conclusion, the traditional game–based digital EWS represents a valid, practical, and effective means for improving numeracy among students with low prior achievement in the ITLBA. Further research should address broader implementation and scalability, and should investigate potential longer-term effects across similar contexts and school systems.Game, Border Area.

Maximizing math achievement: Strategies from the science of learning.

This study aimed at determining the effect of reform-based-instructional method learning styles on students’ achievement and retention in mathematics. A sample size of 119 students was randomly selected. The quasi-experimental design comprising pre-test, post-test, and randomized control group were employed. The Collin Rose learning styles identification and Mathematics instrument were used for data collection. Data collected were analyzed using mean, standard deviation and analysis of covariance. Results revealed that students taught Mathematics with reform-based instructional method performed better than students taught the same mathematics content with the traditional method. Also, students' achievement in mathematics was influenced by the students' leaning styles. For effective teaching and learning in Mathematics, there should be reforms in the instructional processes, taking into consideration the influence of the students' learning styles in particular.