Search results for: mathematics model

Authors: Faiza Abdul Latip

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One of the ultimate goals of any nation is to produce competitive manpower and this includes Philippines. Inclination in the field of Mathematics has a significant role in achieving this goal. However, Mathematics, as considered by most people, is the most difficult subject matter along with its topics to learn. This could be manifested from the low performance of students in national and international assessments. Educators have been widely using learning style models in identifying the way students learn. Moreover, it could be the frontline in knowing the difficulties held by each learner in a particular topic specifically concepts pertaining to fractions. However, as what many educators observed, students show difficulties in doing mathematical tasks and in great degree in dealing with fractions most specifically in the district of Datu Odin Sinsuat, Maguindanao. This study focused on the Datu Odin Sinsuat district grade six pupils’ learning styles along with their achievements and difficulties in learning concepts on fractions. Five hundred thirty-two pupils from ten different public elementary schools of the Datu Odin Sinsuat districts were purposively used as the respondents of the study. A descriptive research using the survey method was employed in this study. Quantitative analysis on the pupils’ learning styles on the Kolb’s Learning Style Inventory (KLSI) and scores on the mathematics diagnostic test on fraction concepts were made using this method. The simple frequency and percentage counts were used to analyze the pupils’ learning styles and their achievements on fractions. To determine the pupils’ difficulties in fractions, the index of difficulty on every item was determined. Lastly, the Kruskal-Wallis Test was used in determining the significant difference in the pupils’ achievements on fractions classified by their learning styles. This test was set at 0.05 level of significance. The minimum H-Value of 7.82 was used to determine the significance of the test. The results revealed that the pupils of Datu Odin Sinsuat districts learn fractions in varied ways as they are of different learning styles. However, their achievements in fractions are low regardless of their learning styles. Difficulties in learning fractions were found most in the area of Estimation, Comparing/Ordering, and Division Interpretation of Fractions. Most of the pupils find it very difficult to use fraction as a measure, compare or arrange series of fractions and use the concept of fraction as a quotient.

Keywords: difficulties in fraction, fraction, Kolb's model, learning styles

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Authors: Han Hyuk Cho, Hanik Jo

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In recent years, coding education has been globally emphasized, and the Free Semester System and coding education were introduced to the public schools from the beginning of 2016 and 2018 respectively in Korea. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this paper aims to design ‘Coding Environment’ and Minecraft-like Turtlecraft in which learners can design and construct mathematical objects through mathematical symbolic expressions. Students can transfer the constructed mathematical objects to the Turtlecraft environment (open-source codingmath website), and also can print them out through 3D printers. Furthermore, we design learnable mathematics and coding curriculum by representing the figurate numbers and patterns in terms of executable expression in the coding context and connecting them to algebraic symbols, which will allow students to experience mathematical patterns and symbolic coding expressions.

Keywords: coding education, computational thinking, mathematics education, TurtleMAL and Turtlecraft

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Authors: Joanne Hardman

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South Africa’s crisis in mathematics attainment is well documented. To meet the need to develop students’ mathematical performance in schools the government has launched various initiatives using computers to impact on mathematical attainment. While it is clear that computers can change pedagogical practices, there is a dearth of qualitative studies indicating exactly how pedagogy is transformed with Information Communication Technologies (ICTs) in a teaching activity. Consequently, this paper addresses the following question: how, along which dimensions in an activity, does pedagogy alter with the use of computer drill and practice software in four disadvantaged grade 6 mathematics classrooms in the Western Cape province of South Africa? The paper draws on Cultural Historical Activity Theory (CHAT) to develop a view of pedagogy as socially situated. Four ideal pedagogical types are identified: Reinforcement pedagogy, which has the reinforcement of specialised knowledge as its object; Collaborative pedagogy, which has the development of metacognitive engagement with specialised knowledge as its object; Directive pedagogy, which has the development of technical task skills as its object, and finally, Defensive pedagogy, which has student regulation as its object. Face-to-face lessons were characterised as predominantly Reinforcement and Collaborative pedagogy and most computer lessons were characterised as mainly either Defensive or Directive.

Keywords: computers, cultural historical activity theory, mathematics, pedagogy

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Authors: Zahra Abdolkarimi, Naser Zourikalatehsamad,

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Up to 40 years ago, after recognition of epilepsy, it was generally believed that these attacks occurred randomly and suddenly. However, thanks to the advance of mathematics and engineering, such attacks can be predicted within a few minutes or hours. In this way, various algorithms for long-term prediction of the time and frequency of the first attack are presented. In this paper, by considering the nonlinear nature of brain signals and dynamic recorded brain signals, ANFIS model is presented to predict the brain signals, since according to physiologic structure of the onset of attacks, more complex neural structures can better model the signal during attacks. Contribution of this work is the co-evolution algorithm for optimization of ANFIS network parameters. Our objective is to predict brain signals based on time series obtained from brain signals of the people suffering from epilepsy using ANFIS. Results reveal that compared to other methods, this method has less sensitivity to uncertainties such as presence of noise and interruption in recorded signals of the brain as well as more accuracy. Long-term prediction capacity of the model illustrates the usage of planted systems for warning medication and preventing brain signals.

Keywords: co-evolution algorithms, brain signals, time series, neural networks, ANFIS model, physiologic structure, time prediction, epilepsy suffering, illustrates model

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Authors: Joel S. Mtebe, Aron Kondoro, Mussa M. Kissaka, Elia Kibga

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Sub-Saharan Africa is described as the second fastest growing mobile phone penetration in the world more than in the United States or the European Union. Mobile phones have been used to provide a lot of opportunities to improve people’s lives in the region such as in banking, marketing, entertainment, and paying various bills such as water, TV, and electricity. However, the potential of using mobile phones to enhance teaching and learning has not been explored. This study presents an experience of developing and delivering SMS quizzes questions that were used to assess mastery of the subject content knowledge of science and mathematics secondary school teachers in Tanzania. The SMS quizzes were used as a follow up support mechanism to 500 teachers who participated in a project to upgrade subject content knowledge of science and mathematics subjects. Quizzes of 10-15 questions were sent to teachers each week for 8 weeks and the results were analyzed using SPSS. The results showed that chemistry and biology had better performance compared to mathematics and physics. Teachers reported some challenges that led to poor performance, invalid answers, and non-responses and they are presented. This research has several practical implications for those who are implementing or planning to use mobile phones for teaching and learning especially in rural secondary schools in sub-Saharan Africa.

Keywords: mobile learning, elearning, educational technolgies, SMS, secondary education, assessment

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Authors: Murray Olowa

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This article examines the studies investigating the Mathematical Knowledge for Teaching (MKT) of secondary preservice teachers in Papua New Guinea based on probabilities. This research was conducted due to the continuous issues faced in the country in both primary and secondary education, like changes in curriculum, emphasis on mathematics and science education, and a decline in mathematics performance. Moreover, the mathematics curriculum doesn’t capture Pedagogical Content Knowledge (PCK) or Subject Matter Knowledge (SMK). The two main domains that have been identified are SMK and PCK, which have been further sub-divided into Common Content Knowledge (CCK), Specialised Content Knowledge (SCK) and Horizon Content Knowledge (HCK), and Knowledge of Content and Students (KCS), Knowledge of Content and Teaching (KCT) and Knowledge of Content and Curriculum (KCC), respectively. The data collected from 15-_year-_ ones and 15-_year-_fours conducted at St Peter Chanel Secondary Teachers College revealed that there is no significant difference in subject matter knowledge between year one and year four since the P-value of 0.22>0.05. However, it was revealed that year fours have higher pedagogical content knowledge than year one since P-value was 0.007<0.05. Finally, the research has proven that year fours have higher MKT than year one. This difference occurred due to final year preservice teachers’ hard work and engagement in mathematics curriculum and teaching practice.

Keywords: mathematical knowledge for teaching, subject matter knowledge, pedagogical content knowledge, Papua New Guinea, preservice teachers, probability

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Authors: Farhaz Amyn Rajabali, Collins Odour

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Mathematics has been there for over 4000 years and has been one of the very first educational topics explored by human civilization. Throughout the years, it has become a complex study and has derived so many other subjects. With advancements in ICT, most of the computation in mathematics is done using powerful computers. In many different countries, the children in primary and secondary schools face difficulties in learning mathematics, and this has many reasons behind it, one being the students don’t engage much with the mathematical concepts hence failing to understand them deeply. The objective of this system is to help the students understand this mathematical concept interactively, which in return will encourage the love for learning and increase thorough understanding of many concepts. Research was conducted among a group of samples and about 50% of respondents replied that they had never used an augmented reality application before. This means that the chances for this system to be accepted in the market are high due to its innovative idea. Around 60% of people did recommend the use of this system to learn mathematics. The study also showed several challenges in an educational system, including but not limited to lack of resources which was chosen by 30% of respondents, the challenge to read from textbooks (34.6%) and how hard it is to visualize concepts (46.2%). The survey question asked what benefits the users see using augmented reality to learn mathematics. The responses that were picked the most were increased student engagement and using real-world examples to understand concepts, both being 65.4% and followed by easy access to learning material at 61.5%, and increased knowledge retention at 50%. This shows that there are plenty of issues with an education system that can be addressed by software applications; now that the newer generation is so enthusiastic about electronic devices, it can actually be used to deliver good knowledge and skills to the upcoming students and mitigate most of the challenges faced currently. The study concludes that the implementation of the system is a best practice for the educational system especially leveraging a new technology that has the ability to attract the attention of many young students and use it to deliver information. It will also give rise to awareness of new technology and on multiple ways it can be implemented. Addressing the educational sector in developing countries using information technology is an imperative task since these kids studying now is the future of the country and will use what they learn and understand during their childhood will help them to make decisions about their lives in the future which will not only affect them personally but also affect the whole society in general.

Keywords: AR, mathematics, system development, augmented reality

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Authors: Melaku Takele Abate, Abbi Lemma Wodajo, Adula Bekele Hunde

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This study aimed at exploring mathematics teachers' reactions, learning, school leaders’ support, and use of the Lesson Study for Transformative Assessment (LSforTA) program ideas in practice. The LSforTA program was new, and therefore, a local and grounded approach was needed to examine teachers’ knowledge and skills acquired using LSforTA. So, a design-based research approach was selected to evaluate and refine the LSforTA approach. The results showed that LSforTA increased teachers' knowledge and use of different levels of mathematics assessment tasks. The program positively affected teachers' practices of transformative assessment and enhanced their knowledge and skills in assessing students in a transformative way. The paper concludes how the LSforTA procedures were adapted in response to this evaluation and provides suggestions for future development and research.

Keywords: classroom assessment, feedback practices, lesson study, mathematics, design-based research

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Authors: Stephen O. Amaraihu

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This research investigated the effect of Computer Based Instruction on Students’ interest, achievement, and retention in Algebra in Abia State College of Education (Technical), Arochukwu. Three research questions and two hypotheses guided the study. Two instruments, Maths Achievement Test (MAT) and Maths Interest Inventory were employed, to test a population of three hundred and sixteen (316) NCE 1 students in algebra. It is expected that this research will lead to the improvement of students’ performance and enhance their interest and retention of basic algebraic concept. It was found that the majority of students in the college are not proficient in the use of ICT as a result of a lack of trained personnel. It was concluded that the state government was not ready to implement the usage of mathematics in Abia State College of Education. The paper recommends, amongst others, the employment of mathematics Lectures with competent skills in ICT and the training of lecturers of mathematics.

Keywords: achievement, computer based instruction, interest, retention

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Authors: Sumeyra Karatas, Veysel Karatas, Reyhan Safak, Gamze Bulut-Ozturk, Ozgul Kartal

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Productive struggle entails a student's cognitive exertion to comprehend mathematical concepts and uncover solutions not immediately apparent. The significance of productive struggle in learning mathematics is accentuated by influential educational theorists, emphasizing its necessity for learning mathematics with understanding. Consequently, supporting productive struggle in learning mathematics is recognized as a high-leverage and effective mathematics teaching practice. In this study, the investigation into the role of productive struggle in learning mathematics led to the development of a comprehensive rubric for productive struggle pedagogy through an exhaustive literature review. The rubric consists of eight primary criteria and 37 sub-criteria, providing a detailed description of teacher actions and pedagogical choices that foster students' productive struggles. These criteria encompass various pedagogical aspects, including task design, tool implementation, allowing time for struggle, posing questions, scaffolding, handling mistakes, acknowledging efforts, and facilitating discussion/feedback. Utilizing this rubric, a team of researchers and teachers designed eight 90-minute lesson plans, employing a productive struggle pedagogy, for a two-week unit on solving systems of linear equations. Simultaneously, another set of eight lesson plans on the same topic, featuring identical content and problems but employing a traditional lecture-and-practice model, was designed by the same team. The objective was to assess the impact of supporting productive struggle on students' mathematics learning, defined by the strands of mathematical proficiency. This quasi-experimental study compares the control group, which received traditional lecture- and practice instruction, with the treatment group, which experienced a productive struggle in pedagogy. Sixty-six 10th and 11th-grade students from two algebra classes, taught by the same teacher at a high school, underwent either the productive struggle pedagogy or lecture-and-practice approach over two-week eight 90-minute class sessions. To measure students' learning, an assessment was created and validated by a team of researchers and teachers. It comprised seven open-response problems assessing the strands of mathematical proficiency: procedural and conceptual understanding, strategic competence, and adaptive reasoning on the topic. The test was administered at the beginning and end of the two weeks as pre-and post-test. Students' solutions underwent scoring using an established rubric, subjected to expert validation and an inter-rater reliability process involving multiple criteria for each problem based on their steps and procedures. An analysis of covariance (ANCOVA) was conducted to examine the differences between the control group, which received traditional pedagogy, and the treatment group, exposed to the productive struggle pedagogy, on the post-test scores while controlling for the pre-test. The results indicated a significant effect of treatment on post-test scores for procedural understanding (F(2, 63) = 10.47, p < .001), strategic competence (F(2, 63) = 9.92, p < .001), adaptive reasoning (F(2, 63) = 10.69, p < .001), and conceptual understanding (F(2, 63) = 10.06, p < .001), controlling for pre-test scores. This demonstrates the positive impact of supporting productive struggle in learning mathematics. In conclusion, the results revealed the significance of the role of productive struggle in learning mathematics. The study further explored the practical application of productive struggle through the development of a comprehensive rubric describing the pedagogy of supporting productive struggle.

Keywords: effective mathematics teaching practice, high school algebra, learning mathematics, productive struggle

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Authors: Edwin Christmann, John Hicks

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This meta-analysis compared the mathematics achievement of students who received either traditional instruction or traditional instruction supplemented with computer-assisted instruction (CAI). From the 27 conclusions, an overall mean effect size of 0.236 was calculated, indicating that, on average, students receiving traditional instruction supplemented with CAI attained higher mathematics achievement than did 59.48 percent of those receiving traditional instruction per se.

Keywords: CAI, science, meta-analysis, traditional

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Authors: Silvia Benvenuti, Alessandra Cardinali

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In recent years, for instance, in relation to the Covid 19 pandemic and the evidence of climate change, it is becoming quite clear that the development of a young kid into an adult citizen requires a solid scientific background. Citizens are required to exert logical thinking and know the methods of science in order to adapt, understand, and develop as persons. Mathematics sits at the core of these required skills: learning the axiomatic method is fundamental to understand how hard sciences work and helps in consolidating logical thinking, which will be useful for the entire life of a student. At the same time, research shows that the axiomatic study of geometry is a problematic topic for students, even for those with interest in mathematics. With this in mind, the main goals of the research work we will describe are: (1) to show whether non-Euclidean geometries can be a tool to allow students to consolidate the knowledge of Euclidean geometries by developing it in a critical way; (2) to promote the understanding of the modern axiomatic method in geometry; (3) to give students a new perspective on mathematics so that they can see it as a creative activity and a widely discussed topic with a historical background. One of the main issues related to the state-of-the-art in this topic is the shortage of experimental studies with students. For this reason, our aim is to show further experimental evidence of the potential benefits of teaching non-Euclidean geometries at high school, based on data collected from a study started in 2005 in the frame of the Italian National Piano Lauree Scientifiche, continued by a teacher training organized in September 2018, perfected in a pilot study that involved 77 high school students during the school years 2018-2019 and 2019-2020. and finally implemented through an experimental study conducted in 2020-21 with 87 high school students. Our study shows that there is potential for further research to challenge current conceptions of the school mathematics curriculum and of the capabilities of high school mathematics students.

Keywords: Non-Euclidean geometries, beliefs about mathematics, questionnaires, modern axiomatic method

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Authors: Entisar A. Elgmati

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Recurrent infant diarrhea is studied using daily data collected in Salvador, Brazil over one year and three months. A logistic regression model is fitted instead of Aalen's additive model using the same covariates that were used in the analysis with the additive model. The model gives reasonably similar results to that using additive regression model. In addition, the problem with the estimated conditional probabilities not being constrained between zero and one in additive model is solved here. Also martingale residuals that have been used to judge the goodness of fit for the additive model are shown to be useful for judging the goodness of fit of the logistic model.

Keywords: additive model, cumulative probabilities, infant diarrhoea, recurrent event

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Authors: Wern Lin Yeo, Choo Kim Tan, Sook Ling Lew

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Mathematics anxiety refers to the feeling of anxious when one having difficulties in solving mathematical problem. Mathematics anxiety is the most common type of anxiety among other types of anxiety which occurs among the students. However, level of anxiety among males and females are different. There were few past study were conducted to determine the relationship of anxiety and gender but there were still did not have an exact results. Hence, the purpose of this study is to determine the relationship of anxiety level between male and female undergraduates at a private university in Malaysia. Convenient sampling method used in this study in which the students were selected based on the grouping assigned by the faculty. There were 214 undergraduates who registered the probability courses had participated in this study. Mathematics Anxiety Rating Scale (MARS) was the instrument used in study which used to determine students’ anxiety level towards probability. Reliability and validity of instrument was done before the major study was conducted. In the major study, students were given briefing about the study conducted. Participation of this study were voluntary. Students were given consent form to determine whether they agree to participate in the study. Duration of two weeks were given for students to complete the given online questionnaire. The data collected will be analyzed using Statistical Package for the Social Sciences (SPSS) to determine the level of anxiety. There were three anxiety level, i.e., low, average and high. Students’ anxiety level were determined based on their scores obtained compared with the mean and standard deviation. If the scores obtained were below mean and standard deviation, the anxiety level was low. If the scores were at below and above the mean and between one standard deviation, the anxiety level was average. If the scores were above the mean and greater than one standard deviation, the anxiety level was high. Results showed that both of the gender were having average anxiety level. Males having high frequency of three anxiety level which were low, average and high anxiety level as compared to females. Hence, the mean values obtained for males (M = 3.62) was higher than females (M = 3.42). In order to be significant of anxiety level among the gender, the p-value should be less than .05. The p-value obtained in this study was .117. However, this value was greater than .05. Thus, there was no significant difference of anxiety level among the gender. In other words, there was no relationship of anxiety level with the gender.

Keywords: anxiety level, gender, mathematics anxiety, probability and statistics

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Authors: Ayoub Kafyulilo, Petra Fisser, Joke Voogt

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This study was conducted to assess the continuation of the use of technology in science and mathematics teaching of the pre-service and in-service teachers who attended the professional development programme. It also assessed professional development, personal, institutional, and technological factors contributing to the continuous use of technology in teaching. The study involved 42 teachers, thirteen pre-service teachers, and twenty-nine in-service teachers. A mixed-method research approach was used to collect data for this study. Findings showed that the continuous use of technology in teaching after the termination of the professional development arrangement was high among the pre-service teachers, and differed for the in-service teachers. The regression model showed that knowledge and skills, access to technology and ease of use were strong predictors (R2 = 55.3%) of the teachers’ continuous use of technology after the professional development arrangement. The professional development factor did not have a direct effect on the continuous use of technology, rather had an influence on personal factors (knowledge and skills). In turn, the personal factors had influence on the institutional factors (access to technology) and technological factors (ease of use), which together had an effect on the teachers’ continuous use of technology in teaching.

Keywords: technology, professional development, teachers, science and mathematics

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Authors: M. Rodionov, N. Sharapova, Z. Dedovets

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The article describes methods of preparation of future teachers that includes the entire diversity of traditional and computer-oriented methodological approaches. The authors reveal how, in the specific educational environment, a teacher can choose the most effective combination of educational technologies based on the nature of the learning task. The key conditions that determine such a choice are that the methodological approach corresponds to the specificity of the problem being solved and that it is also responsive to the individual characteristics of the students. The article refers to the training of students in the proper use of mathematical electronic tools for educational purposes. The preparation of future mathematics teachers should be a step-by-step process, building on specific examples. At the first stage, students optimally solve problems aided by electronic means of teaching. At the second stage, the main emphasis is on modeling lessons. At the third stage, students develop and implement strategies in the study of one of the topics within a school mathematics curriculum. The article also recommended the implementation of this strategy in preparation of future teachers and stated the possible benefits.

Keywords: education, methodological approaches, teacher, secondary school

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Authors: Abubakar Sadiq Mensah, Hassan Usman

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The study compared the effectiveness of Audition, Multiplication, subtraction and Division (AMSD) and Addition, subtraction, Multiplication and Division (ASMD), sequence of teaching these four basic operations in mathematics to primary one pupil’s in Katsina Local Government, Katsina State. The study determined the sequence that was more effective and mostly adopted by teachers of the operations. One hundred (100) teachers and sixty pupils (60) from primary one were used for the study. The pupils were divided into two equal groups. The researcher taught these operations to each group separately for four weeks (4 weeks). Group one was taught using the ASMD sequence, while group two was taught using ASMD sequence. In order to generate the needed data for the study, questionnaires and tests were administered on the samples. Data collected were analyzed and major findings were arrived at: (i) Two primary mathematics text books were used in all the primary schools in the area; (ii) Each of the textbooks contained the ASMD sequence; (iii) 73% of the teachers sampled adopted the ASMD sequence of teaching these operations; and (iv) Group one of the pupils (taught using AMSD sequence) performed significantly better than their counter parts in group two (taught using AMSD sequence). On the basis of this, the researcher concluded that the AMSD sequence was more effective in teaching the operations than the ASMD sequence. Consequently, the researcher concluded that primary schools teachers, authors of primary mathematics textbooks, and curriculum planner should adopt the AMSD sequence of teaching these operations.

Keywords: matematic, high school, four basic operations, effectiveness of teaching

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Authors: Luis Miguel Méndez Díaz

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In this article, a mathematics teaching-learning strategy will be presented, specifically differential calculus in one variable, in a fun and competitive space in which the action on the part of the student is manifested and not only the repetition of information on the part of the teacher. Said action refers to motivating, problematizing, summarizing, and coordinating a game of dominoes whose thematic cards are designed around the basic and main contents of differential calculus. The strategies for teaching this area are diverse and precisely the game of dominoes is one of the most used strategies in the practice of mathematics because it stimulates logical reasoning and mental abilities. The objective on this investigation is to identify the way in which the game of dominoes affects the learning and understanding of fundamentals concepts of differential calculus in one variable through experimentation carried out on students of the first semester of the School of Engineering and Sciences of the Technological Institute of Monterrey Campus Querétaro. Finally, the results of this study will be presented and the use of this strategy in other topics around mathematics will be recommended to facilitate logical and meaningful learning in students.

Keywords: collaborative learning, logical-mathematical intelligence, mathematical games, multiple intelligences

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Authors: Myla Zenaida Cabrillas-Torio, Von Anthony G. Torio

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Homework is defined as an additional task that a student does outside of the school. This added activity is in recognition of the necessity to spend additional time for subjects such as Mathematics. The dilemma comes in the form of the advantages and disadvantages that can be derived from homework. Studies have revealed varying effects to students on academic and non-academic areas. Teachers are at the forefront of the decision towards the giving or not of homework. Pre-service teachers at the elementary level represent the future leaders of the educational system and should be acquainted and involved at the onset of the dilemma. The main objective of this study is to determine the perspective of pre-service elementary teachers towards homework. The anatomy of their belief can be key towards addressing the issue via teacher training. Salient results revealed that the subjects favor the giving homework on the following grounds: it helps add knowledge and confidence. Those who do not favor homework find it as an additional burden. Difficulties in complying with homework are usually associated with lack of references and performance of other household chores. Students usually spend late nights to comply with homework and are unable to perform at the best of their potentials.

Keywords: attitude, homework, pre-service teachers, mathematics education, Philippines

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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Authors: M. Rodionov, Z. Dedovets

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The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.

Keywords: education, teaching of mathematics, proof, deductive reasoning, secondary school

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Authors: Daya Weerasinghe

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Parental expectations often differ to that of their children and the influence and involvement of parents, at home, may affect the student performance in the classroom. This paper presents results from a survey of Asian and European background secondary school mathematics students (N=128) in Melbourne, Australia. Student responses to survey questions were analysed using confirmatory factor analysis, followed by t-tests and ANOVA. The aim of the analysis was to identify similarities and differences in parental expectations in relation to ethnicity, gender, and the year level of the students. The notable findings from the analysis showed no significant difference (at 0.05 level) in parental expectations and student performance, in relation to ethnicity or gender. Conversely, there was a significant difference in both parental expectations and student performance between year 7 and year 12 students. Further, whilst there was a significant difference in parental expectations between year 7 and year 11 students, the students’ performances were not significantly different. The results suggest further research may be needed to understand the parental expectations and student performance between the lower and upper secondary school mathematics students.

Keywords: ethnic background, gender, parental expectations, student performance, year level

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Authors: Jodie Lee, Lorena Chan, Esther Tong

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Hong Kong students face a unique learning environment. Starting from the 2010/2011 school year, The Education Bureau (EDB) of the Government of the Hong Kong Special Administrative Region implemented the fine-tuned Medium of Instruction (MOI) arrangements for secondary schools. Since then, secondary schools in Hong Kong have been given the flexibility to decide the most appropriate MOI arrangements for their schools and under the new academic structure for senior secondary education, particularly on the compulsory part of the mathematics curriculum. In 2019, Hong Kong Diploma of Secondary Education Examination (HKDSE), over 40% of school day candidates attempted the Mathematics Compulsory Part examination in the Chinese version while the rest took the English version. Moreover, only 14.38% of candidates sat for one of the extended Mathematics modules. This results in a serious of intricate issues to students’ learning in post-secondary education programmes. It is worth to note that when students further pursue to an higher education in Hong Kong or even oversea, they may facing substantial difficulties in transiting learning from learning mathematics in their mother tongue in Chinese-medium instruction (CMI) secondary schools to an English-medium learning environment. Some students understood the mathematics concepts were found to fail to fulfill the course requirements at college or university due to their learning experience in secondary study at CMI. They are particularly weak in comprehending the mathematics questions when they are doing their assessment or attempting the test/examination. A government funded project was conducted with the aims of providing integrated learning context and language support to students with a lower level of numeracy and/or with CMI learning experience. By introducing this “integrated concept + language mapping approach”, students can cope with the learning challenges in the compulsory English-medium mathematics and statistics subjects in their tertiary education. Ultimately, in the hope that students can enhance their mathematical ability, analytical skills, and numerical sense for their lifelong learning. The “Concept + Language Mapping “(CLM) approach was adopted and tried out in the bridging courses for students with a lower level of numeracy and/or with CMI learning experiences. At the beginning of each class, a pre-test was conducted, and class time was then devoted to introducing the concepts by CLM approach. For each concept, the key thematic items and their different semantic relations are presented using graphics and animations via the CLM approach. At the end of each class, a post-test was conducted. Quantitative data analysis was performed to study the effect on students’ learning via the CLM approach. Stakeholders' feedbacks were collected to estimate the effectiveness of the CLM approach in facilitating both content and language learning. The results based on both students’ and lecturers’ feedback indicated positive outcomes on adopting the CLM approach to enhance the mathematical ability and analytical skills of CMI students.

Keywords: mathematics, Concept+Language Mapping, level of numeracy, medium of instruction

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Authors: Arturo Tobias Calizon Jr.

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The study investigated the practices in critical reflection being employed in teaching and learning mathematics in public and private schools for students to achieve perspective transformation in psychological, convictional and behavioral dimensions. There were 1,969 senior high school and college student-respondents selected at random from 33 schools. Process reflection is most commonly practiced in both public and private schools. Convictional dimension of perspective transformation is most frequently achieved. There is no significant difference in practices of process reflection between senior high school and college students. However, there is a significant difference in perspective transformation in behavioral dimension achieved by students from public and private schools. Also, there are significant differences in psychological, convictional and behavioral dimensions of perspective transformation achieved by senior high school and college students. There is a high and significant relationship between critical reflection practices and perspective transformation of students. The researcher concludes that there are teaching strategies that facilitate critical thinking, and there are learning activities that alter perspective of students about mathematics as an abstract field. The researcher further concludes that consistent use of appropriate teaching and learning activities could bring about perspective transformation in students with success.

Keywords: critical reflection, perspective transformation, process reflection, convictional dimension, teaching and learning mathematics

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Authors: Endrik Mifta Shaiful, Firman Riyudha

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Acquired Immunodeficiency Syndrome (AIDS) is one of the world's deadliest diseases caused by the Human Immunodeficiency Virus (HIV) that infects white blood cells and cause a decline in the immune system. AIDS quickly became a world epidemic disease that affects almost all countries. Therefore, mathematical modeling approach to the spread of HIV and AIDS is needed to anticipate the spread of HIV and AIDS which are widespread. The purpose of this study is to determine the parameter estimation on mathematical models of HIV transmission and AIDS using cumulative data of people with HIV and AIDS each year in Indonesia. In this model, there are parameters of r ∈ [0,1) which is the effectiveness of the treatment in patients with HIV. If the value of r is close to 1, the number of people with HIV and AIDS will decline toward zero. The estimation results indicate when the value of r is close to unity, there will be a significant decline in HIV patients, whereas in AIDS patients constantly decreases towards zero.

Keywords: HIV, AIDS, parameter estimation, mathematical models

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Diriba Gemechu, Lamessa Abebe

Abstract:

The aim of this study was to examine the effect of cooperative learning method on student’s academic achievement and on the achievement level over a usual method in teaching different topics of mathematics. The study also examines the perceptions of students towards cooperative learning. Cooperative learning is the instructional strategy in which pairs or small groups of students with different levels of ability work together to accomplish a shared goal. The aim of this cooperation is for students to maximize their own and each other learning, with members striving for joint benefit. The teacher’s role changes from wise on the wise to guide on the side. Cooperative learning due to its influential aspects is the most prevalent teaching-learning technique in the modern world. Therefore the study was conducted in order to examine the effect of cooperative learning on the academic achievement of grade 9 students in Mathematics in case of Mettu secondary school. Two sample sections are randomly selected by which one section served randomly as an experimental and the other as a comparison group. Data gathering instruments are achievement tests and questionnaires. A treatment of STAD method of cooperative learning was provided to the experimental group while the usual method is used in the comparison group. The experiment lasted for one semester. To determine the effect of cooperative learning on the student’s academic achievement, the significance of difference between the scores of groups at 0.05 levels was tested by applying t test. The effect size was calculated to see the strength of the treatment. The student’s perceptions about the method were tested by percentiles of the questionnaires. During data analysis, each group was divided into high and low achievers on basis of their previous Mathematics result. Data analysis revealed that both the experimental and comparison groups were almost equal in Mathematics at the beginning of the experiment. The experimental group out scored significantly than comparison group on posttest. Additionally, the comparison of mean posttest scores of high achievers indicates significant difference between the two groups. The same is true for low achiever students of both groups on posttest. Hence, the result of the study indicates the effectiveness of the method for Mathematics topics as compared to usual method of teaching.

Keywords: academic achievement, comparison group, cooperative learning, experimental group

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Authors: M. Fathi, Z. Farhaninejad, M. Shahedi, M. Sadeghi

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Drying is one of the oldest preservation methods for food and agriculture products. Appropriate control of operation can be obtained by modeling. Limitation of continues models for complex boundary condition and non-regular geometries leading to appearance of discrete novel methods such as cellular automata, which provides a platform for obtaining fast predictions by rule-based mathematics. In this research a one D dimensional CA was used for simulating thin layer drying of banana. Banana slices were dried with a convectional air dryer and experimental data were recorded for validating of final model. The model was programmed by MATLAB, run for 70000 iterations and von-Neumann neighborhood. The validation results showed a good accordance between experimental and predicted data (R=0.99). Cellular automata are capable to reproduce the expected pattern of drying and have a powerful potential for solving physical problems with reasonable accuracy and low calculating resources.

Keywords: banana, cellular automata, drying, modeling

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Authors: Shams Alyusof

Abstract:

This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

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Authors: Asrat M.Belachew, Tiago Pereira, Institute of Mathematics, Computer Sciences, Avenida Trabalhador São Carlense, 400, São Carlos, 13566-590, Brazil

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Infectious diseases are among the most prominent threats to human beings. They cause morbidity and mortality to an individual and collapse the social, economic, and political systems of the whole world collectively. Mathematical models are fundamental tools and provide a comprehensive understanding of how infectious diseases spread and designing the control strategy to mitigate infectious diseases from the host population. Modeling the spread of infectious diseases using a compartmental model of inhomogeneous populations is good in terms of complexity. However, in the real world, there is a situation that accounts for heterogeneity, such as ages, locations, and contact patterns of the population which are ignored in a homogeneous setting. In this work, we study how classical an SEIR infectious disease spreading of the compartmental model can be extended by incorporating the mobility of population between heterogeneous cities during an outbreak of infectious disease. We have formulated an SEIR multi-cities epidemic spreading model using a system of 4k ordinary differential equations to describe the disease transmission dynamics in k-cities during the day and night. We have shownthat the model is epidemiologically (i.e., variables have biological interpretation) and mathematically (i.e., a unique bounded solution exists all the time) well-posed. We constructed the next-generation matrix (NGM) for the model and calculated the basic reproduction number R0for SEIR-epidemic spreading model with cities mobility. R0of the disease depends on the spectral radius mobility operator, and it is a threshold between asymptotic stability of the disease-free equilibrium and disease persistence. Using the eigenvalue perturbation theorem, we showed that sending a fraction of the population between cities decreases the reproduction number of diseases in interconnected cities. As a result, disease transmissiondecreases in the population.

Keywords: SEIR-model, mathematical model, city mobility, epidemic spreading

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