Effects of attitudes and behaviours on learning mathematics with computer tools

This mixed-methods study investigates the effects of student attitudes and behaviours on the outcomes of learning mathematics with computer tools. A computer tool was used to help students develop the mathematical concept of function. In the whole sample (N = 521), student attitudes could account for a 3.4 point difference in test scores between individuals on a 10-point scale. General attitude towards mathematics positively predicted test scores. However, more able students who were well-disposed towards mathematical computer tools achieved lower scores. Self-reported behaviours were unrelated to test scores. Detailed observation of a small number of students (N = 8) revealed that positive attitudes towards mathematics and mathematical computer tools augmented exhibited learning behaviours, and that both a positive attitude to mathematical computer tools and exhibited learning behaviours benefited tool mastery. Although tool mastery and test scores are intimately related, reflective processes appear to mediate this relationship. Promoting learning with mathematical computer tools needs to take several factors into account, including improving student attitudes, raising levels of learning behaviours, and giving sufficient opportunity for constructing new mathematical knowledge within meaningful mathematical discourse.     

A formative analysis of individual differences in the effectiveness of learning objects in secondary school

The purpose of this study was to examine individual differences in the effectiveness of learning objects in secondary school classrooms. Specifically, gender, age, grade, subject area, and computer comfort (self-efficacy) were examined in 850 students. Effectiveness was measured in terms of student attitude (learning, quality, and engagement) and student performance. No gender differences were observed between males and females with respect to student attitudes or performance. Age was significantly correlated with student attitudes and performance, however correlation coefficients were small. Grade 12 students were more positive about learning objects and performed better than grade 9 and 10 students. Science students had significantly more positive attitudes and performed better than mathematics students. Finally, students who were more comfortable about computers, appreciated learning objects more than their less confident peers, however performance was unaffected.     

The impact of a technology-based mathematics after-school program using ALEKS on student's knowledge and behaviors

The effectiveness of using the Assessment and LEarning in Knowledge Spaces (ALEKS) system, an Intelligent Tutoring System for mathematics, as a method of strategic intervention in after-school settings to improve the mathematical skills of struggling students was examined using a randomized experimental design with two groups. As part of a 25-week program, student volunteers were randomly assigned to either a teacher-led classroom or a classroom in which students interacted with ALEKS while teachers were present. Student's math performance, conduct, involvement, and assistance was needed to complete tasks were investigated to determine overall impact of the two programs. Students assigned to the ALEKS classrooms performed at the same level as students taught by expert teachers on the Tennessee Comprehensive Assessment Program (TCAP), which is given annually to all Tennessee students. Furthermore, student's conduct and involvement remained at the same levels in both conditions. However, students in the ALEKS after-school classrooms required significantly less assistance in mathematics from teachers to complete their daily work.     

The WebQuest model effects on mathematics curriculum learning in elementary school students

Since its inception in 1995, the WebQuest instructional model has received substantial attention from educators who have applied it to teaching activities. However, WebQuest has seldom been applied to mathematical teaching. Therefore, exploring curriculum development and learning achievement in mathematical teaching that integrates the WebQuest model is necessary. The objective of this study is to explore using the WebQuest model for teaching the concepts of proportion in elementary school mathematics, and the subsequent effects on student learning achievements. Furthermore, this study endeavors to understand student learning attitudes and learning satisfaction regarding the WebQuest model. This study employed the quasi-experimental research method, and the participants were two sixth-grade classes with 52 students at a Taiwanese elementary school. The experimental group was taught using WebQuest, while the control group was taught by employing the traditional IT-integrated curriculum. The two groups completed a 5-week course on proportion concepts. The study results indicate the following: (a) Regarding learning achievements, students who learned with the WebQuest model demonstrated superior learning performance than students who were taught using the traditional IT-integrated curriculum; (b) no significant difference existed between the learning attitudes of students who were taught using the WebQuest model and those who learned with the traditional IT-integrated curriculum; (c) on the learning-satisfaction survey, the students who learned with the WebQuest model showed high learning satisfaction, selecting between agree and strongly agree for the 6 dimensions, including WebQuest teaching, IT capability, the assistance of mathematics curriculum, collaborative learning, learning reflection, and learning feedback. This indicates that the students were largely satisfied and identified with the task-oriented WebQuest learning curriculum that was designed in this study. Finally, specific recommendations are made based on the results, providing teachers and future researchers with a reference for integrating the WebQuest model in the mathematics field.     

The computer as a Trojan Horse

Abstract This paper reports on a study of boys in an Australian secondary school who were under achieving in school mathematics. The subjects were asked to develop computing software to teach fellow students about aspects of Ancient Egyptian mathematics. The paper reports four example case studies of the experience of the subjects during the course of the intervention. The paper examines the use of computing software development as a vehicle for the incidental learning of mathematical technique and for changes in attitude towards mathematics. Four different mathematical activities are reported in the case studies with a screen-dump of the subjects work included as an illustrative example.     

Comparing marginal effects of Chilean students' economic,social and cultural status on digital versus reading and mathematics performance

This paper provides evidence that helps understand the digital divide in education. It does so by comparing the effect of economic, social and cultural status (ESCS) on the digital skills of Chilean students compared with mathematics and language. This comparison is made using national standardized tests. The marginal effect of a group of variables measuring student ESCS was compared both as a whole and separately using multivariate linear regression analysis. The results show that the marginal effect of ESCS as a whole on students' digital skills was equal to the effect on mathematics and greater than the effect on language. Furthermore, the results show that the parents' level of education was the most relevant factor of ESCS for explaining student performance on the digital test, more so than for mathematics and language. These findings challenge the belief that the Internet would reduce economic, social and cultural inequalities in new generations. Instead, they reveal that the gap among Chilean students tends to perpetuate or widen when comparing performance in mathematics and language with performance in the digital domain. At the same time, by comparing national test results, this paper offers empirical evidence for the existence of a second digital divide in the field of education, a concept which is widely discussed at a theoretical level but with little empirical support to date.     

Evaluation of an adaptive and intelligent educational hypermedia for enhanced individual learning of mathematics: A qualitative study

The purpose of this study is to design a personalized adaptive and intelligent web based tutoring system based on learning style and expert system named UZWEBMAT and to evaluate its effects on 10th grade students’ learning of the unit of probability. In the study, initially, learning objects were prepared in three different ways in relation to three sub-learning areas of Visual–Auditory–Kinesthetic (VAK) learning style for each subject of the probability unit. These were appropriate for secondary school mathematics curricula. Then, they were transferred into the digital environment. Each student’s dominant learning style determines the content to which s/he will be directed since s/he is directed to the content that is appropriate for his/her learning style. The course to be followed by the students within UZWEBMAT and their browsing around the pages are decided by expert system integrated into the system. This expert system sets the situations in which s/he will get solution supports and the course s/he will follow in accordance with the performance of the student. Hereby, each student may follow a different course, and the solution supports s/he will get may also differ highlighting the individual learning. The sample of the study consists of 81 10th grade students and 3 mathematics teachers from two high schools in Trabzon, Turkey. Qualitative data were obtained both from the teachers and students participating in the study in order to answer the research questions about the implementation and evaluation of UZWEBMAT for mathematics teaching in a high school classroom. Obtained data were analyzed using qualitative data analysis methods. According to the results of the present study, positive opinions of students and teachers such as taking into account the individual learning differences and deriving mathematical relations and formulas through exploration became prominent. In addition, there were also other positive opinions of students and teachers such as providing permanent learning and introducing learning responsibility to the students. In this sense, it was concluded that UZWEBMAT is a beneficial instrument for both students and teachers.     

Learning secondary mathematics with technology: Exploring the complex interrelationship between students’ attitudes,engagement, gender and achievement

The aim of this study was to investigate the complex relationship between students’ mathematics confidence, confidence with technology, attitude to learning mathematics with technology, affective engagement and behavioural engagement, achievement, gender and year level. The participants were secondary students from state co-educational schools in Metropolitan Athens, Greece. Gender differences as well as differences between year levels and the resulting clusters of students were investigated by using a MANOVA. It was found that boys expressed more positive views towards mathematics and more positive views towards the use of technology in mathematics, compared to girls. It was also found that high achievement in mathematics was associated with high levels of mathematics confidence, strongly positive levels of affective engagement and behavioural engagement, high confidence in using technology and a strongly positive attitude to learning mathematics with technology. Low levels of mathematics achievement was associated with low levels of mathematics confidence, strongly negative levels of affective engagement and behavioural engagement, low confidence in using technology, and a negative attitude to learning mathematics with technology.     

Computer support for learning mathematics: A learning environment based on recreational learning objects

In this paper, we introduce an electronic collaborative learning environment based on Interactive Instructors of Recreational Mathematics (IIRM), establishing an alternative approach for motivating students towards mathematics. The IIRM are educational software components, specializing in mathematical concepts, presented through recreational mathematics, conceived as interactive, recreation-oriented learning objects, integrated within the environment. We present the architecture of the learning environment which integrates communication services that support the interaction processes of the learning community, through instant messaging, chat rooms, and multi-player math games. Through the environment’s interface of their personal workspace, students have access to several easy-to-use mechanisms that allows them to customize its content, its layout, and its appearance. At internal levels, the functionality of IIRM is enhanced with features supported by the environment infrastructure. We evaluated different aspects of the learning environment in three short, motivation-oriented math courses given to Mexican high-school students. The results indicate that the use of the IIRM-based electronic learning environment, positively affects student attitudes towards mathematics. We believe that this approach has the potential to promote the mathematics learning process, basically on its motivational aspects.     

Development and evaluation of multimedia whiteboard system for improving mathematical problem solving

This study developed a web-based multimedia whiteboard system to help students learning with mathematical problem solving. The purpose is to promote a new online mathematical learning model that students not only use electronic whiteboard to write down their mathematical problem solving solutions but also use voice recording tool to give oral explanations about their thinking behind the solutions. To cultivate students’ critical thinking capability and encourage collaborative peer learning, the new learning model also requests students to criticize others’ solutions and reply to others’ arguments. With the multimedia supporting tools, students can communicate easily with each other about what they think and how they solve mathematical problems. We have conducted an experiment with sixth grade primary school students for evaluation. After the experiment, a questionnaire about students’ attitude toward the multimedia whiteboard system for math learning was then held. The results show that students were satisfied with the use of the multimedia whiteboard system for helping them with learning fractional division. Most students were interested in studying mathematics with the multimedia whiteboard system and thought this tool is particularly useful for doing collaborative learning. After analyzing the recorded solving processes and discussions content of students, we found that the performance of female students was superior to male students in communications and mathematical problem solving. Additionally, students with higher final exam grades had better mathematical abilities for doing critiques, arguments and communications.     

Linear syntax for communicating elementary mathematics

We consider computer aided assessment (CAA) of mathematics in which a student provides an answer in the form of a mathematical expression. A common approach is for CAA system implementors to adopt a linear syntax to allow students to communicate their answer to the machine. In this paper we consider the problems students encounter when mediating between (i) traditional mathematical notation and (ii) the requirements of a strict computer algebra system (CAS) syntax. We compare the linear syntaxes of five commonly used general purpose CAS, and report surprising variety even at the elementary levels.     

The Digital Learning Classroom: Improving English Language Learners’ academic success in mathematics and reading using interactive whiteboard technology

This study presents the findings from the first-year evaluation of the Round Rock Independent School District’s (ISD) Digital Learning Classroom project, an initiative focused on the improvement of English Language Learners’ (ELL) learning using interactive whiteboard (IWB) technology. An objective of the evaluation was to determine the extent IWB technology could foster performance parity in academic achievement between ELL and regular students, that is, reduce the student achievement gap between these two student groups in 3rd and 5th grade mathematics and reading. These grade levels and subjects were the primary focus of the project because students in grades 3 and 5 that do not pass the state’s standardized assessments in mathematics and reading cannot be promoted to the next grade level and therefore, these are “high stakes” tests for students. A second evaluation objective was to determine whether and the extent to which the Digital Learning Classroom could increase ELL students’ academic learning relative to that of ELL students in traditional classrooms (i.e., without IWBs). Using a quasi-experimental design, the results strongly indicate that IWBs can foster performance parity thereby closing the achievement gap between ELL and regular students while increasing ELL student achievement. Pedagogical implications for teachers of ELL students within the context of Digital Learning Classroom project implementation are presented, as well as recommendations for future study of the Digital Learning Classroom in ELL classroom settings.     

Examining Factors That Influence the Effectiveness of Learning Objects in Mathematics Classrooms

Abstract

Learning objects are interactive online tools that support the acquisition of specific concepts. Limited research has been conducted on factors that affect the use of learning objects in K–12 mathematics classrooms. The current study examines the influence of student characteristics (gender, age, computer comfort level, subject comfort level, and mathematics grade), instructional design (structured vs. open ended), and teaching strategy (teacher led vs. student based) on student attitudes toward the use of learning objects and learning performance. Data in the form of surveys and pre- and posttests were collected from 286 middle and secondary school students. Higher computer and subject area comfort ratings were significantly correlated with more positive student attitudes about learning objects. Older students in higher grades learned more than younger students in lower grades after using learning objects. Learning performance was significantly higher for students who used structured (vs. open-ended) learning objects and participated in teacher-led (vs. student-based) lessons. It is speculated that younger students might need more scaffolding when using mathematics-based learning objects.     

The effects of computer-assisted instruction on the achievement,attitudes and retention of fourth grade mathematics students in North Cyprus

The purpose of this study was to examine the effects of the educational software Frizbi Mathematics 4 on 4th grade student's mathematics achievement, retention, attitudes toward mathematics and attitude toward computer assisted learning. Two groups (experimental and control) of students from the state primary school in Gazimagusa, North Cyprus were used in this study. The control group was taught using a lecture-based traditional instruction and experimental group was taught using educational software, namely Frizbi Mathematics 4. The control group consisted of 26 students while the experimental group consisted of 29 students. The groups were compared on achievement of mathematics, retention, and attitude toward mathematics and computer assisted learning. The study included three units, Multiplication of Natural Numbers, Division of Natural Numbers, and Fractions. Scores on achievement tests were collected three times; at the beginning of the study, immediately after the intervention, and 4 months later. The mathematics attitude scale and computer assisted learning attitude scale were administrated only two times; at the beginning of the study and immediately after the completion of the study. A series of ANOVAs for repeated measures revealed significant difference between the groups on the post achievement tests and attitude scales in favor of experimental group. However, statistically significant differences in favor of the treatment group, on the retention tests were attained on the multiplication and division units but not on fractions. The evidence indicates that Frizbi Mathematics 4 for learning and teaching mathematics at the primary school level in North Cyprus is an effective tool.     

数学软件MatLab在《线性代数》教学中的应用研究

《线性代数》是大学数学课程的一个重要组成部分,是大学的一门公共基础课,而且是考研的必考课程之一。如何很好地完成这门课程的教学任务而且学生能学有所用,这是每个大学数学教师面临的主要问题。在教学过程中适当地引入数学软件,不仅可以提高学生的学习兴趣,也可以使学生在以后的学习工作中真正地使用这门课程的一些基本的方法。     

The effects of spatial contiguity within computer-based instruction of group personalized two-step mathematics word problems

This study investigated the effects of the spatial contiguity principle within computer-based instruction (CBI) of group personalized two-step mathematics word problems on the achievement and attitude of 98 sixth-grade predominantly Hispanic students. Students were randomly blocked by ability level based on their pretest scores to a spatially contiguous or non-spatially contiguous version of the CBI. The results revealed students who received the spatially contiguous treatment made significantly greater pretest-to-posttest gains than students who received the non-spatially contiguous treatment. In addition, lower-ability students made significantly greater pretest-to-posttest gains than higher-ability students. Findings from the student attitude survey revealed no significant difference in treatment responses to the two survey factors on CBI Satisfaction and Attitude About Math. Student comments from the open-ended questions on the attitude survey and the focus group interview indicated that the spatially contiguous version of the CBI was more helpful and less confusing than the non-spatially contiguous version.     

A programming approach to mathematics

This article presents an attempt to employ a programming approach to mathematical formalization. Six self-instructional units (120 instructional hours) have been developed for the Open University in Israel. This material was tried on three different types of populations: (a) bright high school students (11th–12th grade, A-level mathematics), (b) mathematics teachers with a programming background, and (c) university students studying mathematics, natural sciences and engineering. The results indicated that the programming approach is complementary to high school and university mathematics. The opportunity to explore, the algorithmic approach to mathematical operations and the visualization of mathematical objects and processes facilitates mathematical understanding and insights. It was most beneficial to the majority of the students who perform on a moderate level of abstraction. The course was less advantageous to those who have a very abstract way of perceiving mathematics or to those who are interested in mathematics only on a technical level. However, the vast majority of students gained new ways of understanding mathematical topics such as functions, curves, probability, game theory, recursive functions, envelopes, tiling, curve fitting, etc. They gained, as well, new strategies of using microcomputers to solve and further explore many mathematical problems which they could not solve before.     

Explanations in Mathematics Classrooms: A Discourse Analysis

Abstract

This article focuses on student explanations as a discourse practice central to mathematics teaching and learning. I discuss classrooms as hybrid discourse spaces and focus on how talk is used to accomplish social action. In doing so, I contrast several different social and sociomathematical norms for explanation and suggest that students’ choices of discourse practices position them within the classroom. Further, I caution educators against assuming that complete and detailed explanations are always best to support student learning. I discuss how explanations that are coconstructed by several students can actually support joint engagement in mathematical work and help peers stay “on the same page” while avoiding hierarchical positioning.