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Many studies showed that teachers and prospective teachers have difficulty solving percentage problems. This research is a qualitative descriptive study that aims to investigate the prospective teachers’ strategies in solving problems on the topic of percentages. A total of 250 students majoring in Mathematics Education and Primary Education at IAIN Syekh Nurjati and IAIN Pekalongan were purposively selected to participate in this study. The results showed that only less than half of the participants (40.1%) could give the correct answer. Qualitative data on the strategies used by prospective teachers on the percent question show that (1) teacher candidates ignore the importance of the % symbol and consider the % symbol only as a unit of measurement, (2) teacher candidates ignore the essential role of the reference quantity in the percent question, (3 ) teacher candidates are not used to solving percent problems related to determining initial values before discounts and assume that any percent problem can be solved using multiplication or division.

This study aims to improve learning outcomes, motivation, and students' social skills by applying student teams' achievement division cooperative learning models through PhET simulation media. The method used in this study is quantitative. The research used is Quasi-Experimental. Instruments were used in the form of problems, questionnaires and, observation sheets. The results of the study data analysis prove that the average posttest of the experiment class obtained a score of 77.81, while the control class was 71.82, so that the results obtained in the experimental class were>75 or above from the KKM score that has been determined. Furthermore, the analysis of student motivation data proved an increase where the pretest score showed 60.5 and for the posttest results increased by a score of 66.56 and for the results of social skills learners showed an increase in each meeting in each indicator, which showed an excellent category. The conclusions in this study prove that the student teams achievement division cooperative learning model through PhET simulation media can improve learners' learning outcomes, motivation, and social skills

Utilizing a quantitative approach in research with descriptive-correlational design and through a survey and test instruments, this study determined the attitudes of Grade 12 students of selected senior high schools in Nueva Vizcaya toward religion and the level of their knowledge about the basic tenets, historical contexts, and core teachings of the eight (Judaism, Christianity, Islam, Hinduism, Buddhism, Taoism, Confucianism and Shintoism) world major religions. Findings showed that the Grade 12 students had positive and favorable attitudes toward religion. However, the students generally lacked full knowledge or mastery of the basic tenets, historical contexts and core teachings of the eight world major religions. Finally, the study found out that the attitudes of students toward religion did not affect or influence students’ academic performance in the Introduction to World Religions and Belief Systems subject.

Higher-order thinking skills is an ability that all vocational high school students should have because vocational high school graduates are required to have the good soft skill and hard skill. The reality was their HOTS ability was low, as stated by several explanations from researchers and strengthened by the observation in vocational high school. This research aimed to find the students' learning activity through blended learning of Student Teams Achievement Division (STAD) model and jigsaw model, and their influence on the HOTS. This research was quantitative research using the quasi-experiment method of nonequivalent control group design with research subjects of 50 students that were chosen using simple random sampling. The data was collected using test instruments in multiple choices and descriptions and non-test tool in the form of observation sheets. The data then were analyzed with t-test sample independent test. The results showed that the usage of STAD and jigsaw blended learning made students more active and energized in following the learning activities. The direct learning model made students inactive and not excited during learning activities. Also, the blended learning of STAD and jigsaw had significant influence compared to the direct learning model on higher-order thinking skills.

This article is an extension of a recent article published in The American Economist (Asarta et al., 2021) and presents the second report of basic findings from the 2020 online administration of the sixth national quinquennial survey on teaching and assessment methods in economics. Consistent with the results from the first report, we find that “chalk and talk” remains the staple method of instruction across the entire undergraduate economics curriculum. Lessons, activities, and references that address diversity, inclusion, or gender issues are almost never used in intermediate theory, statistics and econometrics, and other upper-division field courses. There has been notable growth in the use of cooperative learning/small-group assignments, as well as in instructor-led and “student(s) with student(s)” discussions over the past 25 years. Overall, however, there have been minimal changes in teaching methods over time. JEL Classifications: A20, A22

The purpose of this study is to investigate the effectiveness of non-digital game-based learning approach by assessing the students’ achievement score differences of the pre-test with the post-test on the topic of multiplication and division with indices. A paired sample t-test was used to investigate whether there is a significant difference in the students’ achievements after implementing the non-digital game-based learning intervention. A total of 35 students from two Year 9 classes in one of the secondary schools in Brunei Darussalam were involved in the study. Another aim of this study is also to investigate on the students’ perspectives on using non-digital game-based learning approach in their learning process. This was analysed through the questionnaire and interviews. The results showed that the integration of non-digital game-based learning in the mathematics lesson did have a positive effect on the students’ achievement scores. More than half of the students believed that the game has helped them to improve their skills.

The objective of the present study was to access the “comparison of different middle school physical education programs of kashmir division”. The paper endeavors to examine the Adoption of Physical educations program in different schools of Kashmir. The data was collected from various schools of Jammu and Kashmir state. A Standard questionnaire was followed and the collected data was analyzed. During the present study it was concluded that during the females were more interested in physical education than that of males. It is pertinent to mention here that in all the schools the students were more eagerly taking part in physical educational programs.

The study aimed to assess the research capability of public secondary school teachers in the Division of Zambales and utilized a descriptive research design with a questionnaire as the main instrument in gathering data from seven hundred (700) teacher-respondents who were randomly selected. The researcher found out that the respondent is a married female Teacher-I in her early adulthood, with 21-25 hours of teaching load, baccalaureate degree holder had no research conducted and published but had attended a school-based seminar on research with knowledge on basic computer applications. The respondents were assessed "moderately capable" of writing a research proposal and writing a research report. There is significant differences in civil status, academic rank, specialization, number of seminars attended, number of research published, and the level of computer literacy towards writing research proposal while the significant difference in age, specialization, number of seminars attended number of research published, and the level of computer literacy towards writing a research report. There is a slight or weak relationship between the number of research conducted and the research capability and a negligible relationship between the number of seminars attended and the research capability as to writing a research proposal and writing a research report.

Cell division is an abstract material for middle school students in which learning resources and supporting learning media are compulsory to use. This research and development aimed at developing learning supplement book of mitotic cell material for IX graders which eases them to identify cell division, particularly in mitotic phase. This study was developed based on ADDIE model which comprised of four stages (i.e. Analysis, Design, Development, Implementation, and Evaluation). The validation test was conducted by teaching and learning material experts. The two stage tests were conducted in small and large trial groups. The qualitative and quantitative data gained were analyzed using percentage. The results showed that the percentage values were 86.2% (very feasible) for teaching material, 99.4% (very feasible) for learning material. The small-scale trial gained 87.8% (very feasible), meanwhile the large-scale test gained 88.3% (very feasible). In conclusion, the mitotic learning supplement book of cell division material for junior high school can be used as teaching material in classroom learning activities.

The background of this research is that generally students understand the concept of multiplication and division of integers by memorizing. Basically, the memorization method will be appropriate if you memorize it, you know and understand what you have memorized. So that students do not just memorize alone. However, students really understand what they have memorized, and the teacher in providing material on multiplication and division of integers is only glued to the textbook but does not use other solutions that are easier for students to understand. To improve students' understanding of the operations of multiplication and division of integers, learning uses an Open-Ended approach that designs a solution and answer in the operation of multiplication and division of integers with more than one solution and answer. The main objective of this research is to find out how big the Open-Ended learning approach is in improving the understanding of fifth grade students of Al Ankabut SDIT Al Fahmi on the operations of multiplication and division of integers. In this study, the researcher conducted classroom action research with six students as research subjects who were selected based on their ability level, consisting of six students, namely two students with low abilities, two students with moderate abilities, and two students with high abilities. The process of collecting data was done through tests, observations, interviews and field notes. The action was carried out four times, namely Action (1) was learning about all the elements in multiplication using Open-Ended learning through a structural approach. Action (2) is learning about integer multiplication operations with the application of Open-Ended learning through a structural approach. Action (3) is learning about all the elements in the division using Open-Ended learning through a structural approach. Action (4) is learning about the operation of dividing integers by applying Open-Ended learning through a structural approach. The results show that learning with an Open-Ended approach can improve the understanding of fifth grade students at Al Ankabut SDIT Al Fahmi Palu in the operations of multiplication and division of integers.

This paper discusses how 5th-grade students understand quotative fractions division or smaller fractions divided by greater fractions in specific. A context-based mathematics task, making posters, was developed and implemented in two Realistic Mathematics Education (RME)-based lessons involving 6 students and 28 students. The analysis of students’ group discussion and works on the task reveal that the students initially experienced difficulties in determining how many posters can be made using 1/2 of one paper if one poster requires 3/4 of a paper. To support students’ understanding, a task, which carefully sequences fractions division content and utilizes contexts that can be easily modeled, is required.

Fostering conceptual understanding in mathematics classrooms is an important goal in mathematics education. To support this goal, we need to be able to diagnose and assess the extent to which students have conceptual understanding. In this study we employed a problem-posing task and a problem-solving task in order to diagnose and assess preservice teachers’ mathematical understanding of fraction division. The results of the study show that although over 99% of the preservice teachers could correctly perform fraction division, they were much less likely to exhibit conceptual understanding of fraction division either through a problem-solving task involving graphical representation or through a problem-posing task. However, engaging in problem posing appears to more likely than making a graphical representation to elicit preservice teachers’ conceptual understanding. Moreover, a conceptual cue about the meaning of fraction division appears to greatly increase the likelihood that preservice teachers will exhibit conceptual understanding of fraction division in their posed problems and generate conceptually based diagrams of fraction division. The findings highlight the usefulness of problem-posing tasks for diagnosing and assessing preservice teachers’ mathematical understanding.

This study is a qualitative research which was conducted in order to reveal the instructional explanations of class teachers and primary school mathematics teachers working in state schools about division. A semi-structured interview form with three open-ended questions about division, prepared for this purpose, was examined by the experts. The semi-structured interview form inluded three questions asking the teachers to solve the long division operations of 3385: 13 = ?, 1238: 12 =? and 102102: 12 =? using the mathematical table of digits with a descriptive language as if they were telling the primary school students the solutions. While the first two questions were suitable with the 5th grade learning outcomes, the third question was suitable with a high level learning outcome. The main purpose of asking the 3rd question was to evaluate the instructional explanation of the teachers in a problem of different difficulty. The study group consisted of 34 teachers, 16 of whom were primary school mathematics teachers and 18 of whom were class teachers, working at central primary schools in a province located in Eastern Anatolia region of Turkey. The content analysis of the data showed that not all of the teachers could interpret the operation of division regarding the concept of digit accurately, and their division was result and reasoning oriented. However, it was found that few teachers made generalizations in a similar way. It was also seen that teachers who were at problem-solving level according to Kinach’s (2002b) comprehension level framework could not make sense of the logic underlying the division. In addition, the reason why zero (0) was moved to the quotient and when the divisor sought in remaining number should be completed by the teachers could not be clarified because they did not know the logic of the division.

Fraction division is one of the most difficult subjects in elementary school. Not only elementary students but many prospective teachers don’t understand the fraction division concept yet—most of them using a keep-change-flip algorithm to solve fraction division problems. A study using rectangle representation was conducted by us to prospective teachers. This study aims to see whether this rectangle representation will make prospective teachers understand or not. To do so, we made a mixed-method study with 80 prospective teachers as participants. The results show that 53,75% of prospective teachers use the keep-change-flip algorithm without understanding the concept of fraction division, and just 15% of prospective teachers understand fraction division. We assume that most prospective teachers still can’t imagine how fraction division works in a real-life context. They remember what they used to do to finish the fraction division problem that their teacher has introduced in primary school. Based on the results, we conclude that the study with rectangle representation still needs an improvement, whether the teacher’s explanation or the rectangle media.

This study investigated relations between the distribution of practice problems in textbooks and students’ learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal arithmetic problems were present across the 3 series: Addition and subtraction more often involved 2 decimals than a whole number and a decimal, but the opposite was true for multiplication and division. We expected children’s learning of decimal arithmetic to reflect these distributional biases. In Studies 2, 3, and 4, we tested the prediction that children would have more difficulty solving types of problems that appeared less frequently in textbooks, regardless of the intrinsic complexity of solving the problems. We analyzed students’ performance on decimal arithmetic from an experiment conducted in a different lab 35 years ago (Study 2), from a contemporary large-scale web-based learning platform (Study 3), and from a recent controlled experiment conducted in our own lab (Study 4). Despite many differences among the 3 studies, performance in all 3 was in accord with the predictions. These findings suggest that the distributions of practice problems in math textbooks may influence what children do and do not learn. Usefulness of analyzing textbook problem distributions as well as educational implications of the current findings are discussed. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

Community service is carried out by the Pamulang University lecturer team in Pamulang sub-district, South Tangerang city in an effort to increase understanding of mathematical concepts with the target of elementary school students. The activities carried out are divided into 3 stages, the first stage: first giving a pre-test to students to find out the students' initial abilities, the second stage providing mentoring and training in understanding mathematical counting concepts with the help of mathematical teaching aids, and the third stage conducting evaluations with how to give a test (post-test) to determine the results of the treatment in the second stage. The visual aids used in this activity are the nomographic aids, the visual aids weighing the car props. Each of these props provides an understanding of the mathematical counting concepts in the operations of addition, subtraction, multiplication and division. From the results of the post-test conducted an increase in students' understanding of the concepts of mathematical operations in the form of operations of addition, subtraction, multiplication and division after being given understanding with the help of mathematical teaching aids.

The problem in this research is the low social studies learning outcomes. The purpose of this study was to improve the social studies learning outcomes of the fourth grade students of SDN 006 Sencano Jaya, by applying the Student Teams Achievement Division (STAD) type of cooperative learning model. The hypothesis in this study is that if the cooperative learning model (STAD) is applied, it can improve the social studies learning outcomes of students of SDN 006 Sencano Jaya class. The results showed that the teacher activity in the first cycle of the first meeting showed an average of 70.83%, in the first cycle of the second meeting an average of 83.33%. In the second cycle, the first meeting was 87.50%, in the second cycle the second meeting had an average of 95.83%. Teacher activity in this study increased. Student activity in the first cycle of the first meeting with an average of 58.33% in the first cycle of the second meeting was 70.83%, in the second cycle of the first meeting an average of 75.00% in the second cycle of the second meeting with an average of 91.66%. Student activity in this study also increased. The initial data of social studies learning results showed that only 11 students completed with a percentage of 40.74% who did not complete 16 people or 59.25% of students who obtained a basic score above the minimum completeness criteria standard (KKM). In the UH I who completed 15 people or the percentage of 55.55% who did not complete 12 people with a percentage of 44.41%. At UH II, 24 people or 88.88% who did not complete were only 3 students or with a percentage of 11.11%. Social studies learning outcomes in this study are increasing, so with the application of the Cooperative learning model type Students Teams Achievement Division (STAD).

This research scrutinizes how Student Team Achievement Division facilitates and affects students in reading comprehension. A pre-experimental design was applied in this research, and it was conducted in six meetings; by giving pretest, four treatments, and posttest. It involved thirty six of the tenth grade students of secondary school at Lubuklinggau, South Sumatera, in Indonesia who attended reading comprehension class. The data were collected by using reading test that was given twice for students; pre-test and post-test were given before and after treatments. The finding of this research disclosed that the students’ average in pretest was 60.00 and in posttest their average score were increased to be 75.00. Based on the result of the paired t-test calculation, it was found that t-obtained 8.196 was higher than t-table 1.684 as the critical value. It meant that the alternative hypothesis (Ha) was accepted. In other words, the use of Student Team Achievement Division was significantly effective to facilitate and affect the students in reading comprehension.

Este artículo reporta una experiencia en la que se estudió el aporte de las tareas realistas inspiradas en la Educación Matemática Realista a la comprensión del residuo en la división aritmética en población infantil. Las participantes fueron tres estudiantes de la escuela primaria (6 a 10 años de edad) quienes resolvieron una tarea de división con residuo en un contexto realista. Las participantes fueron entrevistadas en un espacio por fuera del ambiente escolar y se les aportó manipulativos como apoyo a la solución y como herramienta para hacer visible las estrategias usadas en el modelado. Los principales hallazgos revelan que las tareas matemáticas realistas tienen el potencial para promover la exploración, construcción e implementación de algoritmos espontáneos en los estudiantes, parecen solucionar el problema de la interpretación del residuo en la división aritmética y promueven el modelado y la matematización dando acceso a una matemática mucho más formal.

Mathematics is considered as a difficult subject for some students, leading to a decrease in students’ interest and motivation in understanding mathematical concept. In the process of classroom teaching and learning, mathematics that seems complicated and makes a bad impression for some students is an obstacle for them in solving daily mathematical problems. To deal with this obstacle, a media innovation in mathematics teaching and learning is deemed necessary as a bridge for students to understand the abstract concepts of mathematical objects through the manipulation of real objects. This paper aims to present how to create and use the media of Medan Perkalian dan Pembagian Bilangan Bulat for elementary school students. This media are quite appropriate as a learning medium used to help students understand the concept of multiplication and division, especially for grade II of elementary school students. Using this medium, students are not only capable to deal with multiplication and the division of integers but also easily understand the concept of multiplication and integers division.

Using lesson study, a team of educators teaches a carefully designed unit on division with remainders to a class of third-grade students.

This research aims to improve the ability to calculate the multiplication of grade III-C students in MIN Yogyakarta II. This research uses class action research methods including planning, implementation, observation, and reflection activities. easy to understand mathematics. The right media choices can be a bridge to the difficulty of primary school students in understanding this lesson. learning activities should be able to provide students with a real experience. Students are actively conducting explorations, experiments, testing, discussions or other activities that emphasize students being active in learning by utilizing the surrounding environment. The results showed that Students can see and feel directly in observing, converting the form of multiplication into a form of division, solving everyday problems involving multiplication and converting the multiplication form into a form of division.

The aim of this paper is to clarify the spatial characteristics of work‐units comprising advanced school buildings in Sweden based on the learning activities of pupils and students. The results of this study are as follows. A work‐unit is composed of seven to nine types of rooms and two types of partitions. Work‐units include four types of learning of the same content together, and three types of learning in small groups or by individuals. The rooms in a work‐unit are separated by doors and removable partitions. This enables students to set the spaces for learning by themselves, by opening/closing the doors or rearranging the partitions. In higher grades, students can be provided the opportunity to choose their own spaces and content for learning.

This paper discusses the use of Realistic Mathematics Education (RME) as an alternative approach to enhance Indonesian 5th-grade students’ ability in multiplication and division. It presents the analysis of Indonesian 5th-grade students’ difficulties in applying stacking method for multiplication and division. Furthermore, it describes a mathematics teaching learning practice to stimulate students constructing their strategies, mathematical models and number sense in solving mathematical problems that involve multiplication and division. The teaching learning practice aims to apply RME for helping students develop their multiplication and division ability.Findings shows that stacking methods for multiplication and division are difficult for the students. The main students’ problem in multiplication and division stacking methods is in reapplying the steps of the methods. The steps taken to improve the learning process by implementing RME are: (1) analyze in detail the difficulties of students in multiplication and division stacking methods, (2) provide contexts of mathematical problems that can stimulate students to think mathematically, (3) hold a class mathematics congress, and (4) conduct a test to measure students’ achievement. Based on the students’ achievement, there has been several improvements. After RME, there were more students whose grades passed the Minimum Mastery Criteria. Moreover, there was a student who got 100. Then, the average test was higher. Meanwhile, there were only 3 children whose grades were 0. Thus, the application of RME has helped the 5th-grade students to improve their ability in multiplication and division.

One of the subjects that requires planting concepts from an early age is mathematics. At school age, especially grade 3 students, the student's age has reached 9 to 10 years. Students at that age, among others, are happy with activity exercises and are happy with activities in the form of competitions. Based on this, learning should be packaged in the form of activities. At the elementary level, one of the materials that is the problem for students is multiplication and division. This material is basic in mathematics but it is often found that there are junior high school students who do not know the results of multiplication under 10. Jarimatika is a method for teaching addition, subtraction, multiplication and division to students, especially at the elementary level. Jarimatika is an abbreviation of finger and arithmetic. As the name implies, the media in this method are the fingers. Based on this community service activity, it can be concluded that the students are enthusiastic and happy with the teaching of multiplication and division with Jarimatika. In addition, students are motivated to answer questions from the teacher.

We examined the type of errors on multiplication and division computation problems of 326 rising fifth graders enrolled in four elementary schools in Northern Portugal. We further examined whether there was a difference in the number of errors across age and whether there was an association between students' performance on number knowledge and multiplication and division computation problems. Error analysis of students' responses indicated that miscalculation and no attempt to solve the problem were the two most frequent error types. We found that older students made more errors compared to younger students. We argue that knowledge of individual student error types is critical to making sound instructional decisions. Based on the results of the present study, we discuss implications for future research and classroom practice., This research was sponsored by a research award to the second author from the Fulbright U.S. Scholar Program.

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students’ understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers’ understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers.

Mathematics is becoming increasingly specialized, divided into a vast and growing number of subfields. While this division of cognitive labor has important benefits, it also has a significant drawb...

Mathematics instruction for students with intellectual disabilities and autism is important. However, it is imperative for researchers and practitioners to focus on the maintenance of mathematical concepts and not just acquisition for these students. Through a single-case multiple probe across participants study, researchers explored an intervention package consisting of a manipulative-based instructional sequence involving virtual manipulatives and then representations (i.e., drawings; referred to as the virtual-representational instructional sequence), explicit instruction, the system of least prompts, overlearning, and support fading to support students with intellectual disability and autism to acquire and maintain multiplication or division skills. The three middle school students who completed the entire intervention acquired and maintained their targeted mathematics skill—in multiplication or division. The results have implications for use of intervention packages to teach foundational mathematics skills to students with developmental disabilities.

This paper describes a research that took place in a University in Rio Grande do Sul, with the aim at verifying levels of comprehension on Complex Numbers in Engineering scholars. The choice of that specific content is justified since complex numbers are the knowledge foundation for the analysis of alternating current circuits, practiced in Engineering courses. In a specific way, this investigation sought to identify and analyze errors committed by the scholars in basic mathematical operations, as addition, subtraction, multiplication and division with complex numbers. The research had a qualitative nature, being characterized as a multiple and holistic case study, whose instrument was a mixed questionnaire and whose analysis method used was Error Analysis. It is concluded that only a few scholars understand basic concepts and are able to operate with complex numbers. That was verified mainly and almost exclusively when considering addition and subtraction operations though. Even academics who had studied complex numbers in previous courses found it difficult to solve multiplication and division operations, and most have not solved these operations. Therefore, seeking to assist engineering professors and academics, a learning object is being created with the purpose of filling these learning gaps. That material aims to provide prior knowledge for the analysis of alternating current circuits and, thus, to help qualifying the processes of teaching and learning in Engineering., Este artigo apresenta um trabalho de pesquisa que se propôs a verificar o nível de compreensão sobre números complexos em acadêmicos de Engenharia de uma Instituição de Ensino Superior do Rio Grande do Sul. Justifica-se a escolha do conteúdo matemático uma vez que números complexos configuram um conhecimento base para a análise de circuitos elétricos em corrente alternada, praticada em cursos de Engenharia. Em específico, esta investigação buscou identificar e analisar os erros cometidos pelos acadêmicos em operações de matemática básica, como adição, subtração, multiplicação e divisão com números complexos. De cunho qualitativo, a pesquisa caracteriza-se como um estudo de caso múltiplo e holístico, cujos dados, produzidos por um questionário misto, foram analisados a partir de proposições da Análise de Erros. Conclui-se que são poucos os acadêmicos que compreendem conceitos e operações básicas com números complexos, tendo sido constatado certo domínio apenas nas operações de adição e subtração. Mesmo havendo, entre os acadêmicos, participantes que estudaram números complexos no Ensino Superior, a maioria deles apresentou dificuldades ou não resolveu as operações de multiplicação e divisão. Diante disso, em busca de auxiliar acadêmicos de Engenharia e seus professores, está sendo criado um objeto de aprendizagem como recurso de apoio para recuperar as lacunas de conhecimento em números complexos. Esse material tem enfoque na análise de circuitos elétricos em corrente alternada, colaborando para qualificar os processos de ensino e de aprendizagem em Engenharia.

The aim of this study was to reveal 5th class middle school students’ determination skills on the truth value of mathematical propositions about multiplication and division. These skills were evalu...

Mathematical learning can never be separated from the arithmetic operations of addition, subtraction, multiplication and division operations. Arithmetic operations that are still widely complained of by junior high school students or equivalent are multiplication arithmetic operations. This study aims to determine the location of students' difficulties in multiplication operations. The analysis technique in this article uses quantitative methods with descriptive and inferential statistical techniques. The subjects of this study were 25 junior high students in Lampung Province. Difficulties faced by students is that it is difficult to understand the intentions of the questions which reach 40%, these difficulties which trigger other difficulties arise. These difficulties include unit multiplication operations, tens, hundreds to thousands. Researchers collected data using a Google form web-based interactive service questionnaire by giving a test in the form of 10 story questions and a column of reasons for difficulty while working on the questions. The questions given refer to the level of difficulty, the validity of the questions with the Product Moment correlation technique for each item and the reliability that reaches 0.707 using the Cronbach Alpha method. Obtained 55% of junior high school students or equivalent difficulty when working on the problem. Keywords: M ultiplication, Junior high school , S tudent difficulties .

Our middle school mathematics department used lesson study to investigate how to introduce fractions division to our sixth-grade students. We highlight our learnings during the Study and Plan phases, describe our observations during the lesson, and provide tips for educators interested in using lesson study to study their own content.

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

Students show deficient understanding on fraction division and supporting that understanding remains a challenge for mathematics educators. This article aims to describe primary students’ understanding of partitive fraction division (PFD) and explore ways to support their understanding through the use of sequenced fractions and context-related graphical representations. In a design-research study, forty-four primary students were involved in three cycles of teaching experiments. Students’ works, transcript of recorded classroom discussion, and field notes were retrospectively analyzed to examine the hypothetical learning trajectories. There are three main findings drawn from the teaching experiments. Firstly, context of the tasks, the context-related graphical representations, and the sequence of fractions used do support students’ understanding of PFD. Secondly, the understanding of non-unit rate problems did not support the students’ understanding of unit rate problems. Lastly, the students were incapable of determining symbolic representations from unit rate problems and linking the problems to fraction division problems. The last two results imply to rethink unit rate as part of a partitive division with fractions. Drawing upon the findings, four alternative ways are offered to support students’ understanding of PFD, i.e., the lesson could be starting from partitive whole number division to develop the notion of fair-sharing, strengthening the concept of unit in fraction and partitioning, choosing specific contexts with more relation to the graphical representations, and sequencing the fractions used, from a simple to advanced form.

In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to de...

The present study aims to examine the pedagogical effectiveness of a Chinese mathematical dialogue-based intelligent tutoring system used for teaching mathematics. The mathematical unit ‘multiplica...

The purpose of this study was to examine the effectiveness of video-based mathematics instruction for seven middle school students with specific learning disability (SLD), using an augmented reality-based training package. The dependent variable was the percentage of steps students performed correctly to solve each type of mathematics problem. The independent variable was the augmented reality video-based intervention, which used video to model the individual steps for solving four types of multistep mathematics problems: (a) addition and subtraction of integers, (b) multiplication and division of integers, (c) using ratio reasoning to convert measurement units, and (d) using multiplication and division to calculate rate of change. Results indicated a functional relation between the video-based mathematics intervention and the percentage of steps completed correctly for each type of problem. All seven participants showed significant gains immediately after receiving the intervention and maintained improved problem-solving skills in at least three out of the four problem categories.

This study aims to explore the students’ mathematical understanding in integer division operation through the context of archipelago traditional cakes in class VII. This research is related to the Indonesian Realistic Mathematics Approach (PMRI) as a learning approach used. The methodology used in this study is Design Research consisting of three stages: preliminary design, experimental design, and retrospective analysis. The study was conducted on VII grade students of Palembang 1 Junior High School. The learning path (Hypothetical Learning Trajectory) in design research plays an important role as a research design and instrument. The Hypothetical Learning Trajectory (HLT) was developed together with a series of activities using the context of archipelago traditional cakes such as: omelette roll, bakpia, milk pie, etc. The medium used in this study was the Students’ Activity Sheet. The results of this study indicate that exploration using the context of traditional archipelago cakes can help students understanding in multiplication and division of integers. The conclusion of this study is the use of archipelago traditional cakes as starting point in mathematics learning in integer division operation material helps the students to explore their understanding in solving mathematics problems.