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This article discusses the methods of solving and explaining problems related to the elements of combinatory that are newly introduced into the elementary mathematics curriculum and the teaching methods need to be studied. Solving such problems allows students their knowledge of the problem itself. The decision-making process requires the search for several different solutions. In addition, training aimed at solving combinatorial issues will help develop the quality of thinking, such as variability. Calculation is always carried out according to some properties of objects and is directly related to the activity of classification of objects.

This case study explores the utility of Expectancy Value Theory (EVT) as a framework for studying elementary teachers’ beliefs and motivations with respect to reformed mathematics instruction. A model for coding and evaluating qualitative data using EVT is proposed and illustrated using interviews with three primary school teachers in an urban school district in the United States. Results from the study indicate that anticipated costs associated with reform instruction, including not covering required content and not meeting district benchmarks, function as strong inhibitors to reform, even among teachers who value reform instruction, who exhibit a strong sense of self-efficacy, and who believe in their students’ capacities to succeed with reform-oriented instruction.

It has been shown that the emotional state of students plays an important role towards learning; for instance, engaged concentration is positively correlated with learning. This paper proposes Inductive Control (IC) for educational games. Unlike conventional approaches that only modify the game level, the proposed technique also induces emotions in the player for supporting the learning process. This paper explores a fuzzy system that analyzes the players’ performance and their emotional state for controlling the level and aesthetic content of an educational video game. The emotional state of the player is recognized through voice analysis. A total of 40 subjects played a video game designed to practice basic math skills; for each trial, a student plays twice in a row the same game but each time the game was controlled by one of the two approaches—Dynamic Difficulty Adjustment (DDA) and IC, the playing order was assigned randomly. Results show that when the proposed approach is used the participants changed faster from unpleasant–low to pleasant or high emotions. These experiments demonstrate that the inductive control technique improves the learning effectiveness through detection and stimulation of positive emotions.

This paper presents a research carried out in the Amazon, specifically in the state of Para, Brazil, where the implementation of workshops in the field of elementary mathematics presented to teachers from Pedagogy degree. To develop such a proposal, the workshop is centered on two main issues: Discussion on triggering vectors of some topics in arithmetic and geometry that are part of the content taught to students from the first to the fifth year; questionnaire on which methods of these topics are taught to students or whether teachers choose only one method for each topic and/or whether they use new (active?) methodologies learned during graduation. The results and the speeches indicate that traditional methods are widely used. On the other hand, teachers who participated in the workshops are strongly willing to change their strategies in teaching elementary mathematics to children.

In this paper, we consider several ways to solve problems of high complexity that occur in the school course of mathematics, test tasks of mathematical literacy, and Olympic problems. Problem solving is the most productive form of learning mathematics, and this process should be a necessary component of all extracurricular activities conducted in mathematics. Mathematical Olympic problems, as a rule,will help to a large extent to learn, to find independent nonstandard methods of solving problems. The main goal of solving problems of high complexity plays a special role in the development of students. Helps them learn the material more strongly and consciously. The ability to analyze a given situation, compare data and search for data, determine the hidden properties of this case, synthesize useful information for solving problems, and form the necessary skills not only for solving problems. The high school program considered solving equations that are not defined using Euclid's rules for catching ordinary multipliers,classifying complex expressions by the properties of Prime numbers, and solving economic problems

The focus in this paper is on the analysis of student-centered discourse through applying a discourse analysis tool that I developed to analyze data from an elementary mathematics classroom. The purpose of the analysis tool is to understand the impact of the complex learning system on the emerging classroom discourse. The minimum conditions for complexity created an invitational space for students that allowed interactions and meaningful exchanges to flourish through exploration of mathematical concepts and collective participation in classroom discourse. The analytic lens provides the teacher with a tool to understand more clearly the dynamics of meaningful exchanges identified as sharing, building, exploring and blocking. Keywords: Classroom discourse; mathematics education; complexity

These notes are from lectures given in 2015 at University College Cork. They aim to explain the most concrete and fundamental aspects of algebra, in particular the algebra of the integers and of polynomial functions of a single variable, grounded by proofs using mathematical induction. It is impossible to learn mathematics by reading a book like you would read a novel; you have to work through exercises and calculate out examples. You should try all of the problems. More importantly, since the purpose of this class is to give you a deeper feeling for elementary mathematics, rather than rushing into advanced mathematics, you should reflect about how the simple ideas in this book reshape your vision of algebra. Consider how you can use your new perspective on elementary mathematics to help you some day guide other students, especially children, with surer footing than the teachers who guided you.

The purpose of this study is to investigate the effect of manipulative (concrete learning materials) in teaching elementary mathematics. The study employed a pretest posttest quasi experimental design. The study was conducted in two grade 3 sections of San Agustin Elementary School in the school year 2016-2017. The experimental group was taught mathematics using the manipulative while the control group was taught mathematics using the conventional method. Data were collected and analyzed from both the experimental and control groups using T-test, Paired T-test, and standard deviation. As a result of the research, the pretest and posttest scores of experiment and control groups were found to differ significantly in favor of posttest in both groups. There was a significant mean gain difference in the pupils’ pretest and posttest scores in mathematics exposed to manipulative and conventional method. Generally, the use of manipulative in teaching mathematics is more effective than the use of conventional method.

The ability to notice students’ mathematical thinking is key to better understanding student learning and effective teaching. Our professional development program utilized a Child Study Assignment ...

Previous research has assumed that all types of semantic knowledge are similarly affected by aging. We investigate whether knowledge of vocabulary and math concepts show comparable lifetime change. A sample of 252 participants aged 17-91 completed two multiple-choice tasks that examined knowledge of infrequent word meanings and knowledge of basic math concepts. Up to age 64, vocabulary scores improved, whereas math scores remained stable. After that age, vocabulary scores remained stable, while math scores declined. We suggest that the fact that the learning and use of infrequent vocabulary are incidental, incremental, and contextual contributes to maintenance of word knowledge into old age. In contrast, learning of basic math concepts occurs relatively early in life in an intentional manner, and both learning and use of these concepts involve constrained contexts. Thus, the nature of the acquisition and use of semantic knowledge across the lifespan affects its fate in old age.

Researchers often develop instruments using correctness scores (and a variety of theories and techniques, such as Item Response Theory) for validation and scoring. Less frequently, observations of ...

Results from an experiment in Fall 2013 of 902 incoming students at this university are reported. In this experiment, after students were given a basic math assessment to ensure they had the necessary math skills to take a principles of economics course, they were randomly allocated to a treatment or control group to test whether there was a significant impact of test format, calculator use, and calculator type on students’ scores. The interaction of calculator use/type and test format was also tested. The results from this experiment suggest that each treatment had a significant positive impact on students’ assessment scores, with much variation depending on the type of question asked and the level of performance. JEL Classifications: A22, C23

To support continuous professional development model in the teaching and learning of mathematics, many districts and schools have begun hiring elementary mathematics coaches and/or specialists (MCSs). However, limited large-scale empirical research exists that determines how the use of MCSs affect student learning and achievement. Kristin E. Harbour and Evthokia Stephanie Saclarides begin to fill in this gap by using data from the National Assessment of Educational Progress to explore the relationship between the presence and responsibilities of elementary MCSs and 4th-grade student achievement in mathematics. Based on their findings, they share practical implications for districts and administrators to consider.

PurposeThis study aims to explore how the theories of professional capital and decisional capital can be extended to introduce “professional mathematics capital” and “decisional mathematics capital”.Design/methodology/approachProfessional development (PD) efforts in one school district in elementary mathematics education are described to illustrate these extensions and to contemplate ways to enhance teacher learning of mathematics pedagogy.FindingsBoth theoretical extensions provided useful frameworks for conceptualizing mathematics PD. Preliminary evidence suggests that participants demonstrated the emergence of professional and decisional mathematics capital.Research limitations/implicationsWhile there were observed and reported changes to teacher practice, further research is needed to explore the implications of these theoretical extensions on student learning.Originality/valueThis study serves to enhance the literature related to PD and teachers' mathematical content knowledge. The theoretical extensions of professional and decisional mathematics capital are a novel and promising concept that allows for a unique approach to be laid out for those designing PD in mathematics.

Several teaching moves have been suggested to support young children’s simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using...

Multimedia programs having a number of elements like Texts, spoken words, sound & music, graphics, animations and still pictures provide different stimuli in their presentations. Art is the field of education that provides a platform for rigorous investigation, representation, expression, and reflection of both scholastic content and the art form itself. The integration of art with other subjects of school curriculum can open new pathways of learning for students, particularly for those who are at risk and have special needs. Vedic Mathematics is an approach to resolve the crisis in education especially in the field of mathematics. It is not simply a collection of new computational techniques; rather, it provides an entirely different approach to mathematical computation based on pattern recognition. It has been shown that the system is applicable to up-to-date aspects of mathematics both at an elementary level as well as in more sophisticated fields. The present paper deals with the development of multimedia packages using techniques of art and Vedic aphorisms on some selected common topics of curriculum of UK and Indian elementary mathematics and the effectiveness of multimedia packages for the development of mathematical skills. The study was conducted using quasi experimental design for research in both the countries. The quantitative analysis of data revealed that the multimedia packages developed by using techniques of art and Vedic Aphorisms have significantly improved the mathematical skills of UK elementary school students.

The purpose of this study was to investigate how pre-service elementary mathematics teachers explain three primitive terms: point, line, and plane. A qualitative exploratory case study design was conducted with 61 participants. The data collected by an open-ended questionnaire was analyzed through the content analysis technique by utilizing NVivo software. The findings showed that pre-service mathematics teachers tended to use signs related to both characteristics and the essence of the terms. This can be due to the fact that terms tried to be explained are the primitive terms and that the explanations given by Euclid about these terms are not easy to understand. In some explanations, more than one sign was used to make the definition more understandable. However, although the signs used for explaining the term seem to constitute its definition, these signs cannot always literally represent this term and cannot be used in place of that term.

This study aims to develop an acquisition-oriented STEM activity that primary school teachers can implement in the classroom. The design-based teaching activity developed and implemented within this study is intended to be presented as an example of an activity suitable for STEM education focused on mathematics lessons. The activity was developed in line with the design process indicators within the K-12 engineering education framework. The steps of this framework are (1) problem and background, (2) plan and implementation, and (3) testing and evaluation. The activity particularly targets elementary school students produce an engineering design product using simple and low-cost materials. The four criteria presented to the students in this process were (1) apartments receiving light, (2) being earthquake resistant, (3) being economical and (4) aesthetics and marketing. Throughout the design process, the criterion that students had the most difficulty was observed as the sun exposure of the flats. Also, most of the students focused more on the aesthetic criterion than other criteria, and they emphasized this criterion most in the marketing process of their products.

Can a school or district improve student achievement simply by switching to a higher‐quality textbook or curriculum? We conducted the first multi‐textbook, multi‐state effort to estimate textbook efficacy following widespread adoption of the Common Core State Standards (CCSS) and associated changes in the textbook market. Pooling textbook adoption and student test score data across six geographically and demographically diverse U.S. states, we found little evidence of differences in average achievement gains for schools using different math textbooks. We found some evidence of greater variation in achievement gains among schools using pre‐CCSS editions, which may have been more varied in their content than post‐CCSS editions because they were written for a broader set of standards. We also found greater variation among schools that had more exposure to a given text. However, these differences were small. Despite considerable interest and attention to textbooks as a low‐cost, “silver bullet” intervention for improving student outcomes, we conclude that the adoption of a new textbook or set of curriculum materials, on its own, is unlikely to achieve this goal.

The aim of this study was to identify the kinematic parameters in track start swimming, and the relationships between these kinematic parameters among Jordanian Female Team. To achieve these six elite female’s swimmers from the Jordanian Female Team participated in this study performed the track start (age 19 ± 0.6 years; height 166 ± 2 cm; mass 61± 2kg; training age 6.5±0.58 y). Subjects were filmed above water at 60 Hz by one digital video camera (Nikon, D3400) and (sports Cam, 1080p, H.264) for under water. The video data were analysis performed with Kinovea analysis program. This study involved (8) kinematic parameters: the achievement time (s), time to 15 m (s), flight time (s), take-off angle (°), entry angle (°); Entry CoM velocity (m/s), take of CoM velocity (m/s). According to the results obtained in this research, we can conclude that there is (5) variables were less than the results achieved in the previous studies, which constituted (62.5) % of the variables of this study. In order to the results also showed a statistically significant correlation between the achievement time and the take-off angle, entry angle, Entry CoM velocity, take of CoM velocity (m/s), and the maximum depth of the body under water. The researchers recommend creating a kinematic file for each swimming. هدفت هذه الدراسة التعرف إلى قيم بعض المتغيرات الكينماتيكية لمرحلة البدء بإسلوب المضمار لدى سباحات المنتخب الوطني في سباحة الصدر (50م)، كذلك العلاقة بين هذه المتغيرات. ولتحقيق ذلك استخدم الباحثان المنهج الوصفي على عينة تكونت من (6) سباحات في المنتخب الاردني للسباحة (العمر 19± 0.6 عام، الطول 166± 2 سم، الكتلة 61± 2 كغم، سنوات الخبرة 6.5± 0.58 عام. وللحصول على بيانات الدراسة تم تصوير عينة الدراسة في المسبح الاولمبي في مدينة الحسين للشباب باستخدام كامرتين فيديو أحدهما 60صورة/ث، والاخرى 30صورة/ث. حيث تم استخدام برنامج (Kinovea) لتحليل الفيديو الخاص بعينة الدراسة، بالإضافة لبرنامج الرزم الإحصائي (spss) لمعالجة البيانات إحصائياً. وتناولت الدراسة بعض المتغيرات الكينماتيكية لمرحلة البدء في سباحة الصدر منها: زمن الانجاز، زمن (15) م، زمن مرحلة الطيران، زاوية الاقلاع ودخول الماء. وأظهرت نتائج الدراسة أن تكنيك عينة الدراسة في مرحلة البدء يشوبه بعض الاخطاء حيث كان هناك (5) متغيرات كينماتيكية ليست ضمن النتائج المتحققة في الدراسات السابقة، كذلك أظهرت النتائج وجود علاقة ارتباط دالة احصائياً بين زمن الإنجاز وزاوية دخول الماء، سرعة الانطلاق، سرعة دخول الماء وأقصى عمق للجسم تحت الماء. ويوصي الباحثان بضرورة أنشاء ملف كينماتيكي لكل سباحة.

Too few mathematics teachers have the expertise to apply baseline assessment for differentiated learning in mathematics classes. This empirical study was conducted in a focus group of sixty learners and three teachers in a grade four mathematics class. It proved that teachers of mathematics in elementary grades could profitably learn to conduct baseline assessments; developing activities to benchmark learners’ abilities and learning needs. The exploratory research design was utilized to set up the general sample and the focus group, and mixed research methods; qualitative and quantitative instruments to collect data and analyzing data. The records of scores obtained by learners from the assessment activities and the interviews with teachers were the main sources of data. Data analysis followed quantitative procedures and presented in figures and categorized them in frequency distribution tables. Findings highlighted that learners can reach their optimal levels in learning mathematics in a free and flexible environment. This paper concludes that the lack of knowledge about how to conduct baseline and its value is one of the attributes of the high failure rate of children in the middle class. This article recommends the consideration of baseline assessment to be an essential aspect of a continuous professional development program for mathematics teachers. https://doi.org/10.26803/ijlter.19.8.18

The study aimed to determine the extent of associations of physics, mathematics, and between physics and mathematics based on the results of the 2007, 2011, and 2015 Trends in Mathematics and Science Survey achievement tests. Utilizing educational data mining and correlational data analysis (significance set at α = 0.05), this study’s findings revealed that there was a significant positive correlation between elementary physics and secondary physics (r = 0.821, ρ = 0.045), between elementary mathematics and secondary mathematics (r = 0.914, ρ = 0.011), between elementary physics and elementary mathematics (r = 0.914, ρ = 0.011), and between secondary physics and secondary mathematics (r = 0.891, ρ = 0.017). With these findings, the study concluded that physics and mathematics in elementary and high school are significantly associated that physics is not significantly associated with previous-level mathematics and that advanced courses in physics and mathematics are not associated with the secondary counterparts. Furthermore, implications toward physics education in the Philippines are formulated.

Purpose: This study aims to investigate students' problem-solving abilities and responses during involving metacognitive strategy in learning. Methodology: This study used one group pre-test post-test design. The participants of this study were thirty-one first semester students of the Department of Mathematics Education, Universitas Muhammadiyah Surakarta. All participants have been enrolled in elementary mathematics courses. The data were collected by using tests and questionnaires. Before the first lesson has begun, students were given a pre-test to solve three contextual problems. Furthermore, the learning is carried out by integrating the metacognitive strategy for one and a half months. At the end of the lesson, the students were provided a post-test that consists of two contextual problems. Results: The result of the t-test showed that t-value = -7.937 < t-table = -2.0423. It can be concluded that there were significant differences between pre-test and post-test. Performance of the student's problem-solving abilities has increased after involving metacognitive strategy in learning with an average score of 73.5, compared to the pre-test with an average score of 47.9. Besides, students provide a positive response while engaging a metacognitive strategy in learning. Applications/Originality/Value: Involving metacognitive strategy in learning can enhance student's problem-solving abilities effectively.

Professional noticing of children’s mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169–202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children’s mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics teachers’ (PTs’) responses to a pedagogical activity designed to engage them in an approximation (Grossman et al. in Teach Coll Rec 111(9): 2055–2100, 2009) of professional noticing of children’s mathematical thinking in the moment of teaching, with a focus on developing responses which extend the student’s thinking. PTs were provided two different examples of student work and a series of questions designed to elicit information about their ability to professionally notice student work. We present data and analysis of 73 PTs’ abilities to engage in the individual skills associated with noticing as well as their abilities to use the skills cohesively in concert. Our results demonstrate the type of representation used determined PTs’ success in all three facets of noticing, with a particular effect on interpreting. Further, our focus on a specific type of response move, along with the introduction of a scaffold for that response move, made a difference in PTs’ ability to successfully respond to student work when compared to a prior study with the same PTs (Tyminski et al. 2014). We unpack these results along with suggestions for pedagogical practice as well as directions for future research.

In this study, teacher candidates were asked to evaluate activities designed with the use of the history of mathematics (HoM) as a tool in terms of the obstacles to the use of the HoM. A total of 12 activities which used the HoM as a tool were utilized in the study. The study group consisted of 40 teacher candidates who were first-year students in an elementary mathematics education program. The activities were used within the HoM course. The presentation and implementation of all activities took six weeks. Then, 40 teacher candidates completed written opinion forms, and 10 of them got interviewed. As the collected data were analyzed, teacher candidates’ perceptions about whether each obstacle to the use of the HoM could emerge were identified. Afterwards, two different researchers examined the reasons underlying the identified perceptions.The findings showed that the activities used in this study could be used in mathematics classes and similar activities may stop the emergence of philosophical, student-related, stylistic and instructional preparation obstacles. . In the future, longer-term studies may be conducted with mathematics teachers and secondary school students with the activities used in this study. In this way, stronger evidence may be obtained about the effectiveness of using such activities in the instructional process.

Penelitian ini bertujuan mendeskripsikan analisis kebutuhan terhadap tes hasil belajar Matematika berkarakteristik HOTS (higher-order thinking skills) atau keterampilan berpikir tingkat tinggi berbentuk pilihan ganda untuk siswa kelas V di kota Singaraja, Kabupaten Buleleng, Provinsi Bali. Penelitian ini dilakukan pada beberapa Sekolah Dasar (SD) di kota Singaraja. Populasi penelitian adalah semua guru Matematika Sekolah Dasar di Kota Singaraja. Sampel yang digunakan adalah sampel purposif, yakni peneliti menentukan responden dari sekolah-sekolah yang dipilih berdasarkan beberapa karakteristik. Beberapa karakteristik yang dimaksud, yakni (a) sekolah dalam kota dan luar kota, (b) sekolah favorit dan non favorit, (c)) sekolah negeri dan swasta, dan (d) sekolah umum dan muslim. Sampel yang diperoleh berjumlah 7 (tujuh) SD. Metode pengumpulan data yang digunakan adalah kuesioner. Kuesioner pada penelitian ini menghasilkan data kuantitatif dan kualitatif. Data kuantitatif berupa data nominal dari respon “ya” dan “tidak”, sedangkan data kualitatif berupa komentar berdasarkan respon “ya” atau “tidak” yang diberikan. Hal ini dilakukan peneliti agar dapat menarik simpulan yang lebih kuat dan lengkap. Teknik analisis data kuantitatif menggunakan statistik deskriptif, sedangkan teknik analisis data kualitatif menggunakan analisis deskriptif. Berdasarkan hasil penelitian dapat disimpulkan bahwa guru memerlukan tes hasil belajar Matematika SD berkarakteristik HOTS. Hasil penelitian ini digunakan untuk mengembangkan tes hasil belajar Matematika berkarakteristik HOTS berbetuk pilihan ganda.

This paper explores peer interactions in an elementary mathematics classroom (ages 9–10) where the teacher intentionally shared authority with her students and supported them in learning to share authority with one another. Authors examine how students shifted between shared, concentrated, and contested social and intellectual authority relations in partner and small group work during a three-week unit on place value. Findings show that (a) students were able to share both social and intellectual authority, and did so often; (b) the distribution of social authority was more dynamic than that of intellectual authority; and (c) when groups shifted into shared intellectual authority, shifts were usually preceded by a student making some aspect of the collaborative task public. We connect these findings to research on authority in mathematics classrooms that serve racially and linguistically minoritized students and offer directions for future work.

Mathematics teacher educators can use video clips of children solving mathematics problems to help teacher candidates attend to nuanced aspects of teaching and learning mathematics. However, the pr...

In this paper, we comprehensively consider the problems that depend on the parameter. The necessary and sufficient conditions for the existence of a unique solution of equations and systems of equations that depend on the parameter are investigated. Finding solutions to equations and systems of equations that depend on parameters is one of the most difficult areas of elementary mathematics. To solve them, you need to find ways that require special logical thinking, which must satisfy some additional conditions, for example, to determine a single solution, a solution in a set of all possible values of unknowns, cases when all the solutions of one system are solutions of another, and so on. One of these cases is the use of invariant properties. The article uses various examples of using invariant properties of transformations to consider methods and techniques for solving equations and systems of equations that depend on a single parameter. As a result, due to the presence of invariant properties of transformations, we see that the desired solution is found quickly and easily.

Demonstrating knowledge of content requires teachers to display extensive knowledge of the critical concepts in the discipline. This study was set up to provide a research-based landscape of the content knowledge level of elementary mathematics teachers viewed in the local district of Ayungon in the Division of Negros Oriental, Philippines. Survey and correlational methods of research were used in the study involving 95 non-randomly selected teachers. Results revealed that the content knowledge level of the teachers was approaching proficiency. The teachers’ educational attainment, number of training attended, and the number of years in teaching mathematics were not significantly related to their content knowledge level. It was concluded that teaching experience and professional development in the form of pursuing graduate studies and attending training did not have bearing with the content knowledge level possessed by the teachers. However, the teachers were inferred as resourceful and committed to teaching mathematics despite their weaknesses in the content knowledge to share with their learners. Hence, enhancement training in all areas in mathematics is to be provided to elementary mathematics teachers by implementing the training design developed by the researchers. The ultimate goal is to develop further the content knowledge, mastery, and skills of the teachers to achieve the highest proficiency level in mathematics. Keywords: Content knowledge, proficiency level, enhancement training design

This study aimed to identify the errors of PGSD students on simple algebra assignments on Basic Concept of Elementary Mathematics Subject at STAHN Mpu Kuturan Singaraja. The subjects of this study were Semester II PGSD students of STAHN Mpu Kuturan Singaraja in the academic year 2019/2020 as many as 11 people. Errors in mathematics in this study were divided into factual errors, procedural errors, and conceptual errors. This type of research was a quantitative descriptive study. The data collection method used was a test. The test instrument used was a concept understanding test to be able to find students' errors. A total of 20 items in the test were validated by two experts with the Lawshe’s CVR technique. The results showed that (1) the general error rate of PGSD study program students on Simple Algebra assignment on Basic Concept of Elementary Mathematics Subject was 30.26% in the low error category, (2) there was the highest error of 43% (error category moderate) and lowest 16% (very low error category), 3) factual errors ranged from 10% - 20% (very low category), 4) procedural errors ranged from 7% - 53% (very low category to medium category), and 5) conceptual errors ranged from 35% - 65% (low to high categories).