Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 19

Mathematics Education Related Abstracts

19 The Dilemma of Giving Mathematics Homework from the Perspective of Pre-Service Elementary Teachers

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

Abstract:

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: Mathematics Education, pre-service teachers, attitude, Philippines, homework

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18 Investigation of Preschool Children's Mathematics Concept Acquisition in Terms of Different Variables

Authors: Hilal Karakuş, Berrin Akman

Abstract:

Preschool years are considered as critical years because of shaping the future lives of individuals. All of the knowledge, skills, and concepts are acquired during this period. Also, basis of academic skills is based on this period. As all of the developmental areas are the fastest in that period, the basis of mathematics education should be given in this period, too. Mathematics is seen as a difficult and abstract course by the most people. Therefore, the enjoyable side of mathematics should be presented in a concrete way in this period to avoid any bias of children for mathematics. This study is conducted to examine mathematics concept acquisition of children in terms of different variables. Screening model is used in this study which is carried out in a quantity way. The study group of this research consists of total 300 children, selected from each class randomly in groups of five, who are from public and private preschools in Çankaya, which is district of Ankara, in 2014-2015 academic year and attending children in the nursery classes and preschool institutions are connected to the Ministry of National Education. The study group of the research was determined by stage sampling method. The schools, which formed study group, are chosen by easy sampling method and the children are chosen by simple random method. Research data were collected with Bracken Basic Concept Scale–Revised Form and Child’s Personal Information Form generated by the researcher in order to get information about children and their families. Bracken Basic Concept Scale-Revised Form consists of 11 sub-dimensions (color, letter, number, size, shape, comparison, direction-location, and quantity, individual and social awareness, building- material) and 307 items. Subtests related to the mathematics were used in this research. In the “Child Individual Information Form” there are items containing demographic information as followings: age of children, gender of children, attending preschools educational intuitions for children, school attendance, mother’s and father’s education levels. At the result of the study, while it was found that children’s mathematics skills differ from age, state of attending any preschool educational intuitions , time of attending any preschool educational intuitions, level of education of their mothers and their fathers; it was found that it does not differ by the gender and type of school they attend.

Keywords: Mathematics Education, Preschool Education, preschool period children, mathematics concept acquisitions

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17 Understanding Mathematics Achievements among U. S. Middle School Students: A Bayesian Multilevel Modeling Analysis with Informative Priors

Authors: Jing Yuan, Hongwei Yang

Abstract:

This paper aims to understand U.S. middle school students’ mathematics achievements by examining relevant student and school-level predictors. Through a variance component analysis, the study first identifies evidence supporting the use of multilevel modeling. Then, a multilevel analysis is performed under Bayesian statistical inference where prior information is incorporated into the modeling process. During the analysis, independent variables are entered sequentially in the order of theoretical importance to create a hierarchy of models. By evaluating each model using Bayesian fit indices, a best-fit and most parsimonious model is selected where Bayesian statistical inference is performed for the purpose of result interpretation and discussion. The primary dataset for Bayesian modeling is derived from the Program for International Student Assessment (PISA) in 2012 with a secondary PISA dataset from 2003 analyzed under the traditional ordinary least squares method to provide the information needed to specify informative priors for a subset of the model parameters. The dependent variable is a composite measure of mathematics literacy, calculated from an exploratory factor analysis of all five PISA 2012 mathematics achievement plausible values for which multiple evidences are found supporting data unidimensionality. The independent variables include demographics variables and content-specific variables: mathematics efficacy, teacher-student ratio, proportion of girls in the school, etc. Finally, the entire analysis is performed using the MCMCpack and MCMCglmm packages in R.

Keywords: Mathematics Education, multilevel, Bayesian multilevel modeling, PISA

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16 Effects of Using Interactive Whiteboards at High School Mathematics Classrooms

Authors: Huseyin Demir

Abstract:

This article is the results of a quantitative research about the effects of using interactive whiteboards in high school mathematics classroom. The aim of this article is to investigate the effects of using interactive whiteboards in high school mathematics classrooms. During the article the following questions are answered: 'What can we do with an interactive whiteboard?' and 'Do we really need those properties of the interactive whiteboard?' For the research part of the article, two groups of lessons are executed in Private Demirel College. In the first 6 weeks, the topics are taught on a normal blackboard. Starting from seventh week, we have used interactive whiteboard in the mathematics lessons. At the end of an eight week lectures with interactive whiteboards, a questionnaire is prepared and executed for the students. In the questionnaire 10 questions were asked about the benefits and differences of using the interactive whiteboards in mathematics lessons. By looking at the conclusion of the results of questionnaire and some discussions with the students we found some useful benefits of the usage of interactive whiteboards in mathematics lessons. This article will be helpful for the high school mathematics teachers.

Keywords: Mathematics Education, blackboard, interactive whiteboard, using interactive whiteboard in mathematics lessons

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15 Implementing Lesson Study in Qatari Mathematics Classroom: A Case Study of a New Experience for Teachers through IMPULS-QU Lesson Study Program

Authors: Areej Isam Barham

Abstract:

The implementation of Japanese lesson study approach in the mathematics classroom has been grown worldwide as a model of professional development for teachers. In Qatar, the implementation of IMPULS-QU lesson study program aimed to establish a robust organizational improvement model of professional development for mathematics teachers in Qatar schools. This study describes the implementation of a lesson study model at Al-Markhyia Independent Primary School through different stages; and discusses how the planning process, the research lesson, and the post discussion participates in providing teachers and researchers with a successful research lesson for teacher professional development. The research followed a case study approach in one mathematics classroom. Two teachers and one professional development specialist participated the planning process. One teacher conducted the research lesson study by introducing a problem solving related to the concept of the ‘Mean’ in a mathematics class, 21 students in grade 6 participated in solving the mathematic problem, 11 teachers, 4 professional development specialists, and 4 mathematics professors observed the research lesson. All previous participants except the students participated in a pre and post-lesson discussion within this research. This study followed a qualitative research approach by analyzing the collected data through different stages in the research lesson study. Observation, field notes, and semi-structured interviews conducted to collect data to achieve the research aims. One feature of this lesson study research is that this research describes the implementation for a lesson study as a new experience for one mathematics teacher and 21 students after 3 years of conducting IMPULS-QU project in Al-Markhyia school. The research describes various stages through the implementation of this lesson study model starting from the planning process and ending by the post discussion process. Findings of the study also address the impact of lesson study approach in teaching mathematics for the development of teachers from their point views. Results of the study show the benefits of using lesson study from the point views of participated teachers, theory perceptions about the essential features of lesson study, and their needs for future development. The discussion of the study addresses different features and issues related to the implementation of IMPULS-QU lesson study model in the mathematics classroom. In the light of the study, the research presents recommendations and suggestions for future professional development.

Keywords: Mathematics Education, teacher professional development, lesson study, mathematics teaching experience

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14 Sfard’s Commognitive Framework as a Method of Discourse Analysis in Mathematics

Authors: Dong-Joong Kim, Sangho Choi, Woong Lim

Abstract:

This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.

Keywords: Discourse Analysis, Mathematics Education, commognitive framework, mathematical discourse

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13 The Roles of Teachers in Promoting Self-Regulated Learning

Authors: Mine Cekin

Abstract:

Self-regulated learning (SRL), which can be defined as learning that takes place when an individual is an active controller over his cognition, behavior, and motivation in the learning process, seems to be an essential educational goal. However, it is asserted that students need an assistance to become self-regulated learners. Therefore, teachers appear to play an important role in the introduction of SRL. Even though the importance of SRL has been shown by many researchers, the issue of how teachers can introduce it in a classroom environment needs to be investigated thoroughly. When it comes to mathematics learning particularly, it seems really difficult to associate this area with self-regulated learning because of the fact that it is mainly seen as a domain that is overwhelmingly memorizing written notations. As a result, self-regulated learning in mathematics education and what roles teachers have seem to deserve a significant attention. In this study, the significance of SRL and the roles of teachers in promoting SRL in the field of mathematics education particularly with the help of current literature have been highlighted. Some of the roles of teachers are becoming self-regulated learners themselves, facilitating motivation and collaboration with their colleagues in their schools.

Keywords: Mathematics Education, Motivation, Self-regulated learning, teacher self-regulation

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12 Computational Thinking Based Coding Environment for Coding and Free Semester Mathematics Education in Korea

Authors: Han Hyuk Cho, Hanik Jo

Abstract:

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: Mathematics Education, computational thinking, coding education, TurtleMAL and Turtlecraft

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11 Overcoming Reading Barriers in an Inclusive Mathematics Classroom with Linguistic and Visual Support

Authors: A. Noll, J. Roth, M. Scholz

Abstract:

The importance of written language in a democratic society is non-controversial. Students with physical, learning, cognitive or developmental disabilities often have difficulties in understanding information which is presented in written language only. These students suffer from obstacles in diverse domains. In order to reduce such barriers in educational as well as in out-of-school areas, access to written information must be facilitated. Readability can be enhanced by linguistic simplifications like the application of easy-to-read language. Easy-to-read language shall help people with disabilities to participate socially and politically in society. The authors state, for example, that only short simple words should be used, whereas the occurrence of complex sentences should be avoided. So far, these guidelines were not empirically proved. Another way to reduce reading barriers is the use of visual support, for example, symbols. A symbol conveys, in contrast to a photo, a single idea or concept. Little empirical data about the use of symbols to foster the readability of texts exist. Nevertheless, a positive influence can be assumed, e.g., because of the multimedia principle. It indicates that people learn better from words and pictures than from words alone. A qualitative Interview and Eye-Tracking-Study, which was conducted by the authors, gives cause for the assumption that besides the illustration of single words, the visualization of complete sentences may be helpful. Thus, the effect of photos, which illustrate the content of complete sentences, is also investigated in this study. This leads us to the main research question which was focused on: Does the use of easy-to-read language and/or enriching text with symbols or photos facilitate pupils’ comprehension of learning tasks? The sample consisted of students with learning difficulties (N = 144) and students without SEN (N = 159). The students worked on the tasks, which dealt with introducing fractions, individually. While experimental group 1 received a linguistically simplified version of the tasks, experimental group 2 worked with a variation which was linguistically simplified and furthermore, the keywords of the tasks were visualized by symbols. Experimental group 3 worked on exercises which were simplified by easy-to-read-language and the content of the whole sentences was illustrated by photos. Experimental group 4 received a not simplified version. The participants’ reading ability and their IQ was elevated beforehand to build four comparable groups. There is a significant effect of the different setting on the students’ results F(3,140) = 2,932; p = 0,036*. A post-hoc-analyses with multiple comparisons shows that this significance results from the difference between experimental group 3 and 4. The students in the group easy-to-read language plus photos worked on the exercises significantly more successfully than the students who worked in the group with no simplifications. Further results which refer, among others, to the influence of the students reading ability will be presented at the ICERI 2018.

Keywords: Mathematics Education, Inclusive Education, Special Educational Needs, symbols, easy-to-read language, photos

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10 Incorporating Polya’s Problem Solving Process: A Polytechnic Mathematics Module Case Study

Authors: Pei Chin Lim

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School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved.

Keywords: Mathematics Education, problem solving, metacognition, weak students

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9 Distance Education: Using a Digital Platform to Improve Struggling University Students' Mathematical Skills

Authors: Robert Vanderburg, Nicholas Gibson

Abstract:

Objectives: There has been an increased focus in education students’ mathematics skills in the last two years. Universities have, specifically, had problems teaching students struggling with mathematics. This paper focuses on the ability of a digital platform to significantly improve mathematics skills for struggling students. Methods: 32 students who demonstrated low scores on a mathematics test were selected to take part in a one-month tutorial program using a digital mathematics portal. Students were provided feedback for questions posted on the portal and a fortnightly tutorial session. Results: A pre-test post-test design was analyzed using a one-way analysis of variance (ANOVA). The analysis suggested that students improved skills in algebra, geometry, statistics, probability, ratios, fractions, and probability. Conclusion: Distance university students can improve their mathematics skills using a digital platform.

Keywords: Higher Education, Distance Education, Mathematics Education, Digital Education

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8 Mitigating Self-Regulation Issues in the Online Instruction of Math

Authors: Robert Vanderburg, Nicholas Gibson, Michael Cowling

Abstract:

Mathematics is one of the core subjects taught in the Australian K-12 education system and is considered an important component for future studies in areas such as engineering and technology. In addition to this, Australia has been a world leader in distance education due to the vastness of its geographic landscape. Despite this, research is still needed on distance math instruction. Even though delivery of curriculum has given way to online studies, and there is a resultant push for computer-based (PC, tablet, smartphone) math instruction, much instruction still involves practice problems similar to those original curriculum packs, without the ability for students to self-regulate their learning using the full interactive capabilities of these devices. Given this need, this paper addresses issues students have during online instruction. This study consists of 32 students struggling with mathematics enrolled in a math tutorial conducted in an online setting. The study used a case study design to understand some of the blockades hindering the students’ success. Data was collected by tracking students practice and quizzes, tracking engagement of the site, recording one-on-one tutorials, and collecting data from interviews with the students. Results revealed that when students have cognitively straining tasks in an online instructional setting, the first thing to dissipate was their ability to self-regulate. The results also revealed that instructors could ameliorate the situation and provided useful data on strategies that could be used for designing future online tasks. Specifically, instructors could utilize cognitive dissonance strategies to reduce the cognitive drain of the tasks online. They could segment the instruction process to reduce the cognitive demands of the tasks and provide in-depth self-regulatory training, freeing mental capacity for the mathematics content. Finally, instructors could provide specific scheduling and assignment structure changes to reduce the amount of student centered self-regulatory tasks in the class. These findings will be discussed in more detail and summarized in a framework that can be used for future work.

Keywords: Distance Education, Mathematics Education, Digital Education, Self-regulation

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7 Evaluation of Technology Tools for Mathematics Instruction by Novice Elementary Teachers

Authors: Christopher J. Johnston

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This paper presents the finding of a research study in which novice (first and second year) elementary teachers (grades Kindergarten – six) evaluated various mathematics Virtual Manipulatives, websites, and Applets (tools) for use in mathematics instruction. Participants identified the criteria they used for evaluating these types of resources and provided recommendations for or against five pre-selected tools. During the study, participants participated in three data collection activities: (1) A brief Likert-scale survey which gathered information about their attitudes toward technology use; (2) An identification of criteria for evaluating technology tools; and (3) A review of five pre-selected technology tools in light of their self-identified criteria. Data were analyzed qualitatively using four theoretical categories (codes): Software Features (41%), Mathematics (26%), Learning (22%), and Motivation (11%). These four theoretical categories were then grouped into two broad categories: Content and Instruction (Mathematics and Learning), and Surface Features (Software Features and Motivation). These combined, broad categories suggest novice teachers place roughly the same weight on pedagogical features as they do technological features. Implications for mathematics teacher educators are discussed, and suggestions for future research are provided.

Keywords: Mathematics Education, Technology, novice teachers, virtual manipulatives

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6 Challenges for Competency-Based Learning Design in Primary School Mathematics in Mozambique

Authors: Satoshi Kusaka

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The term ‘competency’ is attracting considerable scholarly attention worldwide with the advance of globalization in the 21st century and with the arrival of a knowledge-based society. In the current world environment, familiarity with varied disciplines is regarded to be vital for personal success. The idea of a competency-based educational system was mooted by the ‘Definition and Selection of Competencies (DeSeCo)’ project that was conducted by the Organization for Economic Cooperation and Development (OECD). Further, attention to this topic is not limited to developed countries; it can also be observed in developing countries. For instance, the importance of a competency-based curriculum was mentioned in the ‘2013 Harmonized Curriculum Framework for the East African Community’, which recommends key competencies that should be developed in primary schools. The introduction of such curricula and the reviews of programs are actively being executed, primarily in the East African Community but also in neighboring nations. Taking Mozambique as a case in point, the present paper examines the conception of ‘competency’ as a target of frontline education in developing countries. It also aims to discover the manner in which the syllabus, textbooks and lessons, among other things, in primary-level math education are developed and to determine the challenges faced in the process. This study employs the perspective of competency-based education design to analyze how the term ‘competency’ is defined in the primary-level math syllabus, how it is reflected in the textbooks, and how the lessons are actually developed. ‘Practical competency’ is mentioned in the syllabus, and the description of the term lays emphasis on learners' ability to interactively apply socio-cultural and technical tools, which is one of the key competencies that are advocated in OECD's ‘Definition and Selection of Competencies’ project. However, most of the content of the textbooks pertains to ‘basic academic ability’, and in actual classroom practice, teachers often impart lessons straight from the textbooks. It is clear that the aptitude of teachers and their classroom routines are greatly dependent on the cultivation of their own ‘practical competency’ as it is defined in the syllabus. In other words, there is great divergence between the ‘syllabus’, which is the intended curriculum, and the content of the ‘textbooks’. In fact, the material in the textbooks should serve as the bridge between the syllabus, which forms the guideline, and the lessons, which represent the ‘implemented curriculum’. Moreover, the results obtained from this investigation reveal that the problem can only be resolved through the cultivation of ‘practical competency’ in teachers, which is currently not sufficient.

Keywords: Mathematics Education, Curriculum, Competency, Mozambique

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5 Implementing Effective Mathematical-Discussion Programme for Mathematical Competences in Primary School Classroom in South Korea

Authors: Saeyoung Lee

Abstract:

As the enthusiasm for education in Korea is too much high, it is well known by others that children in Korea get good scores in Mathematics. However, behind of this good reputation, children in Korea are easy to get lose self-confidence, tend to complaint and rarely participate in the class because of too much competition which leads to lack of competences. In this regard, the main goals of this paper are, by applying the programme based on peer-communication on Mathematics education field, it would like to improve self-managemental competence to make children gain self-confidence, communicative competence to make them deal with complaint and communitive competence to make them participated in the class for the age of 10 children to solve this problem. 14 children the age of 10 in one primary school in Gangnam, Seoul, Korea had participated in the research from March 2018 to October 2018. They were under the programme based on peer-communication during the period. Every Mathematics class maintained the same way. Firstly a problem was given to children. Secondly, children were asked to find many ways to solve the problem as much as they could by themselves. Thirdly all ways to solve the problem by children were posted on the board and three of the children made a group to distinguish the ways from valid to invalid. Lastly, all children made a discuss to find one way which is the most efficient among valid ways. Pre-test was carried out by the questionnaire based on Likert scale before applying the programme. The result of the pre-test was 3.89 for self-managemental competence, 3.91 for communicative competence and 4.19 for communitive competence. Post-test was carried out by the same questionnaire after applying the programme. The result of the post-test was 3.93 for self-managemental competence, 4.23 for communicative competence and 4.20 for communitive competence. That means by applying the programme based on peer-communication on Mathematics education field, the age of 10 children in Korea could improve self-managemental, communicative and communitive competence. Especially it works very well on communicative competence by increasing 0.32 points as it marked. Considering this research, Korean Mathematics education based on competition which leads to lack of competences should be changed to cooperative structure to make students more competent rather than just getting good scores. In conclusion, innovative teaching methods which are focused on improving competences such as the programme based on peer-communication which was applied in this research are strongly required to be studied and widely used.

Keywords: Mathematics Education, Primary education, competences, peer-communication

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4 Use of Mobile Phone Applications in Teaching Precalculus

Authors: Jay-R Hosana Leonidas, Jayson A. Lucilo

Abstract:

The K-12 Curriculum in the Philippines shed light to mathematics education as it recognizes the use of smartphones/mobile phones as appropriate tools necessary in teaching mathematics. However, there were limited pieces of evidence on the use of these devices in teaching and learning process. This descriptive study developed lessons integrating the use of mobile phone applications with basis on low-level competencies of students in precalculus and determined its effects on students’ conceptual understanding, procedural skills, and attitudes towards precalculus. Employing Bring Your Own Device (BYOD) scheme in the study, lessons developed were conducted among Grade 11 Science, Technology, Engineering, and Mathematics (STEM) students at Central Bicol State University of Agriculture for the academic year 2018-2019. This study found that there is a significant difference between the competency levels of students along with conceptual understanding and procedural skills prior to and after the conduct of lessons developed. Also, it disclosed that the use of mobile phone applications had positive effects on students’ attitudes towards precalculus. Thus, the use of mobile phone applications in teaching precalculus can enrich students’ understanding of concepts and procedural skills (solving and graphing skills) and can increase students’ motivation, self-confidence, and enjoyment in dealing with precalculus.

Keywords: Mathematics Education, senior high school, Bring Your Own Device, mobile phone applications

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3 Creative Mathematics – Action Research of a Professional Development Program in an Icelandic Compulsory School

Authors: Osk Dagsdottir

Abstract:

Background—Gait classifying allows clinicians to differentiate gait patterns into clinically important categories that help in clinical decision making. Reliable comparison of gait data between normal and patients requires knowledge of the gait parameters of normal children's specific age group. However, there is still a lack of the gait database for normal children of different ages. Objectives—This study aims to investigate the kinematics of the lower limb joints during gait for normal children in different age groups. Methods—Fifty-three normal children (34 boys, 19 girls) were recruited in this study. All the children were aged between 5 to 16 years old. Age groups were defined as three types: young child aged (5-7), child (8-11), and adolescent (12-16). When a participant agreed to take part in the project, their parents signed a consent form. Vicon® motion capture system was used to collect gait data. Participants were asked to walk at their comfortable speed along a 10-meter walkway. Each participant walked up to 20 trials. Three good trials were analyzed using the Vicon Plug-in-Gait model to obtain parameters of the gait, e.g., walking speed, cadence, stride length, and joint parameters, e.g., joint angle, force, moments, etc. Moreover, each gait cycle was divided into 8 phases. The range of motion (ROM) angle of pelvis, hip, knee, and ankle joints in three planes of both limbs were calculated using an in-house program. Results—The temporal-spatial variables of three age groups of normal children were compared between each other; it was found that there was a significant difference (p < 0.05) between the groups. The step length and walking speed were gradually increasing from young child to adolescent, while cadence was gradually decreasing from young child to adolescent group. The mean and standard deviation (SD) of the step length of young child, child and adolescent groups were 0.502 ± 0.067 m, 0.566 ± 0.061 m and 0.672 ± 0.053 m, respectively. The mean and SD of the cadence of the young child, child and adolescent groups were 140.11±15.79 step/min, 129±11.84 step/min, and a 115.96±6.47 step/min, respectively. Moreover, it was observed that there were significant differences in kinematic parameters, either whole gait cycle or each phase. For example, RoM of knee angle in the sagittal plane in the whole cycle of young child group is (65.03±0.52 deg) larger than child group (63.47±0.47 deg). Conclusion—Our result showed that there are significant differences between each age group in the gait phases and thus children walking performance changes with ages. Therefore, it is important for the clinician to consider the age group when analyzing the patients with lower limb disorders before any clinical treatment.

Keywords: Professional Development, Mathematics Education, action research, creative learning

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2 Why and When to Teach Definitions: Necessary and Unnecessary Discontinuities Resulting from the Definition of Mathematical Concepts

Authors: Josephine Shamash, Stuart Smith

Abstract:

We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.

Keywords: Mathematics Education, Mathematics Teaching, concept image, mathematical definitions

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1 Use of Mobile Phone Applications in Teaching Precalculus

Authors: Jayson A. Lucilo, Jay-R. Hosana Leonidas

Abstract:

The K-12 Curriculum in the Philippines shed light to mathematics education as it recognizes the use of smartphones/mobile phones as appropriate tools necessary in teaching mathematics. However, there were limited pieces of evidence on the use of these devices in teaching and learning process. This descriptive study developed lessons integrating the use of mobile phone applications with basis on low-level competencies of students in Precalculus and determined its effects on students’ conceptual understanding, procedural skills, and attitudes towards Precalculus. Employing Bring Your Own Device (BYOD) scheme in the study, lessons developed were conducted among Grade 11 Science, Technology, Engineering, and Mathematics (STEM) students at Central Bicol State University of Agriculture for the academic year 2018-2019. This study found that there is a significant difference between the competency levels of students along conceptual understanding and procedural skills prior to and after the conduct of lessons developed. Also, it disclosed that the use of mobile phone applications had positive effects on students’ attitudes towards Precalculus. Thus, the use of mobile phone applications in teaching Precalculus can enrich students’ understanding of concepts and procedural skills (solving and graphing skills) and can increase students’ motivation, self-confidence, and enjoyment in dealing with Precalculus.

Keywords: Mathematics Education, senior high school, Bring Your Own Device, mobile phone applications

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