Visualizing Student's Difficulties in Learning Calculus

AbstractVisualization is well recognized as a powerful problem representation process for solving mathematical problems. Van Garderen and Montague (2003) emphasizes that good problem solvers generally construct a representation of the problem to facilitate understanding. The purpose of this study was to investigate student's performance in solving Calculus problems and further analysed student's difficulties in solving the problems. It is clear from the protocol analyses that some students require special treatment such as further tutorial session in correcting their misconception. Also students need to monitor their steps in problem solving or deriving problem solution. Much attention should be directed to fostering student's ability to plan for problem solution. If this is not done, the students are likely to become progressively more confused and in the long run they may not survive in their mathematics problem solving experiences

An examination of effects of online scaffolding on students' online behavior and reaction

Many researchers emphasize the effectiveness of online interaction with scaffolding in enhancing learning and performance. However, little is known about the students' behavior and reaction toward participation in online interaction, and whether scaffoldings have any effects on students' behavior or not. This study utilized times series data to investigate how students' usage of offered instructional tools in an online interaction could change their behavior as well as considered reaction. The results obtained by weekly observations confirmed that there were noticeable changes on students' behavior and reaction within scaffolding time with a same drop in both weeks 7, and 10. Such changes seemed to be associated with differences in times they spent for using the instructional tools. Students' opinion about the usefulness of online scaffolding was consistent and aligned with their online behavior

Assessing thinking skills: a case of problem-based learning in learning of algebra among Malaysian form four students

The teaching and learning of mathematics is a complex and dynamic process involving interaction between previously acquired levels of understanding and conceptualization of mathematical knowledge which consists of mathematical concepts and skills of problem solving in a student centered learning environment. The objective of the study was to examine the effectiveness of PBL in teaching algebra among Form Four students. PBL is a teaching strategy which simultaneously develops higher-order thinking (HOT), disciplinary knowledge bases and practical skills by placing students in an active role as problem solvers confronted with ill-structured problems that mirror real-world problems. The results suggest that the experimental group following the PBL approach performed significantly better than the control group following the traditional approach in the overall performance in algebra, lower-order thinking questions and also higher-order thinking questions. Therefore, PBL is a powerful tool in teaching abstract and intricate concepts of mathematics like algebra

Cognitive and Affect Outcomes of Group Learning among Secondary Learners in Bangladesh

AbstractGroup learning (GL) is well recognized as a successful pedagogy in mathematics education. The purpose of this research study was to compare the effects of GL and conventional learning on 2-aspect: cognitive outcome ‘mathematics achievement’ and affect outcome ‘attitudes toward mathematics’ among secondary learners in Bangladesh. Quasi-experimental design was administered for the experiment with 168 full-time students into 2-group: an experimental (EG) group (n=84) and a control (CG) group (n=84). EG was exposed to GL treatment while CG was taught using conventional learning method for the duration of 15-week. Data were collected using students’ mathematics achievement test and attitudes toward mathematics questionnaire. Both EG and CG were compared using independent-sample t-test. It was found that GL had significant effect on mathematics achievement [t (166)=34.25, p<0.05] and attitudes toward mathematics [t (166)=49.72, p<0.05]. The MANOVA with repeated measure was employed to determine the main and interaction effect of GL on test-time and achievement. The multivariate tests indicated a significant main effect of time, Wilks’ Lambda=0.065, F (1, 166)=2373.307, p=0.000, η2=0.935; a significant interaction effect of GL by time, Wilks’ Lambda=0.310, F (1, 166)=369.802, p=0.000, η2=0.690. These findings suggest that GL is more effective than conventional learning in mathematics teaching. As such GL can be effectively incorporated to improve students’ mathematics performance in secondary schools in Bangladesh

Visual Representations in Mathematical Word Problem Solving Among Form Four Students in Malacca

AbstractLearning how to solve mathematical problems has been a long withstanding difficulty faced by students and has been given constant focus in mathematical development. Successful problem solvers spend more time analyzing a problem and they will find all the alternatives related to the situation. Therefore many educators (Cai, 2003, National Council of Teachers of Mathematics, 2000; Smith, 1991) agreed that teaching mathematics through problem solving hold great promise. Furthermore, according to the Malaysian Curriculum Development Centre (2003), one of the important objectives in teaching mathematics is to develop student's mathematical problem solving skills. Mathematical problems are not simply computational tasks type but are problems which also require appropriate selection of strategies and decisions that lead to logical solutions. Word problem solving is one of the important components of mathematics problem solving which incorporate real-life problems and applications. However, many researches revealed that students express great difficulties in handling a word or story problem. This study examined the use of visual representations which posed great difficulties in most mathematical tasks. Secondary students were given the 15Mathematical Processing Instrument (MPI) adapted from Hegarty and Kozhevnikov (1999). This study examined 381 students from eight secondary schools in three different districts in Malacca. Results indicated that less than two percent of the problems were solved using pictorial representation and most of the students preferred to used schematics solutions

Why Teach Mathematical Problem Solving

Problem solving is a basic skill needed by today's learners. Guided by recent research III mathematical problem solving, the changing professional standards, new workplace demands, technological changes and recent changes in learning theories, educators are to include integrated learning environments which encourage learners to use this higher order thinking skills, specifically problem solving skills. Teaching mathematical problem solving should take an approach of teaching in context where students are learning mathematics while solving realistic problems. Both holistic and componential opportunity modelings are approaches that have been emphasized in higher learning

Instructional efficiency of mathematical learning using Geometer's Sketchpad and graphing calculator: technology tools versus traditional chalk and talk

In this study, two technological tools in teaching and learning mathematics namely Geometer’s Sketchpad and graphing calculator were investigated. The purpose of this research was to compare instructional efficiency of utilizing Geometer’s Sketchpad and graphing calculator versus traditional approach for a secondary level topic ‘Quadratic Function’. A total of 134 students aged 16-17 years participated in this study. The students were randomly assigned to three groups and undergo three different treatments. Four phases were conducted: 1)Introduction to Software, 2) Induction to Quadratic Functions, 3) Integrated teaching and learning using Software, 4) Testing using Achievement Test and the Paas Mental Effort Rating Scale. The data were analyzed using ANOVA and post-hoc analyses. The findings from this study showed that there is no significant difference in performance between the technology-assisted instruction as compared to conventional chalk and talk instruction. However findings indicated that students in the geometer sketchpad group and the graphing calculator group performed better than students in traditional group in their procedural knowledge. Using Paas Mental Effort Rating Scale (2004) however indicated that instructional efficiency of using graphing calculator condition is significantly efficient [F (2, 131) = 9.888; p = 0.000< 0.05] compared to the geometer sketchpad and conventional chalk and talk condition. Graphing calculator condition thus far imposed relative low mental effort with high performance. Geometer sketchpad condition imposed high mental effort with low performance. Hence the use of technology within short period of time induce high mental effort in solving traditional assessment questions thus affects performance. This findings provide empirical evidence and confirmed earlier studies about the advantages of using graphic calculator as facilitative tool for improving students’ performance and provide explanation for the benefit of graphic calculator as a tool of learning from the cognitive load theory. However the use Geometer Sketchpad as facilitative technological tools has yet to be explored

Mathematical learning attributes impacting students' performance in Sarawak

The purpose of the study is to examine the mathematics learning attributes in mathematics classroom at the secondary school level in Malaysia. Students’ responses related to mathematics learning attributes were sought. A survey was conducted using a set of questionnaire (62 items) among rural secondary school students in the state of Sarawak, Malaysia. Four hundred and fifteen responses were collected. Self-reported students’ achievement in school based assessment was used as the measurement of mathematics performance which later was collapsed into categorical variables. Logistics Regressions was used to examine the significant predictors contributed to mathematics performance. The study indicates Learning Styles and Teaching Practices are predictors of students’ higher achievement in mathematics while other learning attributes are in place. This finding concurred with other studies which stressed the importance of teaching strategies and practices in mathematics learning class. Mathematics teacher must adapt their teaching technique according to their students’ learning style preferences and beliefs on mathematics to improve learning. This study will contribute to rural school educational research. The findings in this study would expand the current body of knowledge and data about the importance of learning attributes in pedagogical context. The study provides valuable information to teachers and school administrative to create effective learning program matching the needs of the students

Relationship between mathematical thinking, mathematics anxiety and mathematics attitudes among university students

This study investigates the relationships between mathematics anxiety, attitudes toward mathematics and mathematical thinking among university students. A 60-item questionnaire included mathematical thinking rating scale, mathematics anxiety rating scale and mathematics attitudes rating scale completed by 203 university students from the Faculty of Science, Engineering, Food Science, and Human Ecology in one of the public university in Malaysia. The correlation analysis was used to establish relationship between mathematical thinking, mathematics attitude, and mathematics anxiety and independent t-test was used to investigate differences between the two gender groups and two race groups on their mathematics anxiety, attitudes toward mathematics and mathematical thinking. The results indicated that a significant high positive correlation exists between mathematical thinking and mathematics attitude (r=.856, p<0.05). Also there was negative moderate correlation between mathematical thinking and mathematics anxiety (r=.-576, p<0.05). There was also negative correlation between mathematics anxiety and mathematics attitude (r=.509, p<0.05). In conclusion, these findings indicated that level of mathematics anxiety is related to mathematical thinking and mathematics attitude. On the other hand, students' backgrounds in terms of their majors have no effect on the three constructs

UTILIZATION OF INFORMATION AND COMMUNICATION TECHNOLOGIES IN MATHEMATICS LEARNING

Attention to integrate technology in teaching and learning has provided a major transformation in the landscape of education. Therefore, many innovations in teaching and learning have been technology-driven. The study attempted to examine what is engineering students’ perception regarding the use of Information and Communication Technologies (ICT) in mathematics learning as well as investigate their opinion about how ICT can be integrated to improve teaching and learning processes. The subjects were Iranian engineering students from two universities. The finding showed they are fully aware of importance of ICT in teaching and learning mathematics. Whilst, they were feeling comfortable and confident with technology, they do not have more experience of using technology in mathematics classes before. The findings supported the other studies, which indicated the potentials of ICT to facilitate students’ learning, improve teaching, and enhance institutional administration as established in the literature.Keywords: Technology, Mathematics Learning, Facebook, Attitude Toward ICT DOI: http://dx.doi.org/10.22342/jme.5.2.1498.138-14