Knowledge Of Mathematical Concepts Research Articles

Analisis Penyebab Rendahnya Kemampuan Pemecahan Masalah Calon Guru Matematika Menggunakan APKL, USG, dan Diagram Fishbone

Problem-solving is one of the process standards that has been discussed by NCTM and is very important for prospective mathematics teachers to master. The reality is that prospective mathematics teachers have low problem-solving abilities, so it is necessary to analyze the causes of these low-solving abilities. This research aims to uncover the causes of the low problem-solving abilities of prospective mathematics teachers using PKL, USG, and fishbone diagrams. The research method used is qualitative. The research subjects were students of the Mathematics Education study program, FMIPA, Universitas PGRI Banyuwangi who were prospective mathematics teachers according to the achievements of study program graduates. The main instrument of this research is the researcher. Meanwhile, supporting instruments include tests, open questionnaires, researcher notes, interviews, and documentation. Data analysis was carried out using the APKL, followed by the USG method, and then using the fishbone diagram. The results of the research reveal that the causes of low problem-solving abilities are inadequate procedural abilities in solving mathematical problems, inadequate declarative knowledge or knowledge of mathematical concepts, inadequate representational abilities, biological problems, and inadequate interests. This research provides signs for educators to anticipate the causes of the low problem-solving abilities of prospective mathematics teachers.

How much does using the Mind Mapping learning approach "improve" the grasp of mathematical ideas in junior high school students?

The learning model is a teacher's tool in the form of structured images that are presented to students. The learning model applied aims to improve students' understanding of mathematical concepts. The author determines the purpose of this study. Namely to assess the impact of experiments on the subject's knowledge of mathematical concepts in geometry material. This type of research uses experimental research using a mind mapping learning model with a pre-experimental design, one-group pretest-posttest. Tests were carried out randomly or through cluster sampling on building materials class VII Realschule. The data collection tool that the researchers used for this research was a test designed to test students' understanding of concepts. The researcher interviewed teachers, students, and documents in this data collection method. A hypothesis test was carried out on the data obtained after conducting a sig5% level t-test, normality test, and homogeneity test on statistical data. It was found that students could not understand mathematical concepts (mind mapping). This dramatically influences the results of understanding mathematical concepts. After using this method, students receive higher performance scores than before. Based on the t-test results, we can conclude the difference in the value of learning outcomes before and after applying the author's teaching method.

PENGARUHaPENERAPAN MODELvPEMBELAJARANdPROBLEMqBASED LEARNINGrTERHADAPdPEMAHAMANxKONSEPtMATEMATISo PESERTAkDIDIKzKELASiXIiMIPA SMA NEGERI 1 PAINAN

Mathematicskconceptual understanding ability is oneloffabilities thattmust be mastered by students. However, students' understanding of mathematical concepts is not optimal yet. The PBL model can be used to enhance students' knowledge of mathematical concepts. Thekgoal of this researchk is to find out whetherdmathematics conceptual understandingf ability of studentspwho learn with PBL modell is betterk thanq mathematics conceptual understanding ability of students that learning by directj learning. According to the study's findings, it was discovered that the ability of students who studied with PBL was better than those who applied the direct learning model. Keywords – Mathematics Conceptual Understanding, PBL , Direct Learning

A prospect of developing epistemology of moral intuitions by analogy with mathematical knowledge

In the first part, this article deals with the idea of supporting Moral Intuitionism by drawing an analogy with conceptual mathematical knowledge. The analysis shows that arguments of pro and contra to the above idea are rather aimed toward assumptions and expectations of moral epistemologists; the arguments miss the essence of mathematical conceptual thinking. The image of mathematical thinking exemplified in the epistemological discussion is probably afflicted by implicit biases. The second part of the article applies a very tentative model of mathematical thinking to several cases, or thought experiments, that have been bothering analytical philosophers, practical philosophers, and moral epistemologists. As a result, one can find that the considered thought experiments look very undefined even from a point of view of an imaginary applied mathematician.

The Roles of Gestural and Symbolic Schematizations in Inhibition as a Component of Executive Functions.

The role of gestural schematization in enhancing thinking processes has been the subject of a large body of works. In this process, contextually unimportant or irrelevant information related to a concept (or a system of concepts) is deleted or ignored, while relevant spatial information is maintained. This process is a special type of inhibition, which is one of the key components of executive functions. In this short paper, it is suggested that gestural schematization is a special type of symbolic schematization, a much more general process through which irrelevant information related to features of a concept (or a system of concepts) is suppressed, while relevant information (spatial and non-spatial) is maintained. Through symbolic schematization, abstract structural similarity between two concepts or between two systems of concepts can be discovered. In this way, an individual's knowledge about the first situation can be generalized to the second situation. Symbolic schematization is the basis of abstraction, knowledge generalization, and knowledge development. This is particularly the case with abstract mathematical thinking. This proposal offers a picture of cognitive mechanisms through which knowledge of abstract mathematical concepts is created and developed in the mind.

Implikasi Pengalaman Etnomatematika dan Gender Terhadap Pemahaman Konsep Bilangan Siswa

This research is causal-quantitative research that aims to find out and examine the implications/influence of ethnomathematical experiences, namely things that have been experienced by students related to mathematics who was born based on the culture and value system of an ethnic group; and differences in characteristics on the understanding of the students’ number concept. is a trait used as the basis for identifying differences between men and women in terms of socio-cultural conditions, values ​​and behavior, mentality, and so on. The research was carried out in the even semester of the 2020/2021 academic year at SMP Negeri 3 Kendari. The results show that the experience of ethnomathematics has a significant effect on understanding the concept of numbers by 0.302. Meanwhile, differences in characteristics have no effect on students' understanding of the concept of numbers at SMP Negeri 3 Kendari. This result explains that if students' ethnomathematical experience increases by one unit, then students' knowledge of mathematical concepts will increase by 0.302 units. Ethnomathematics experience can be used to design mathematics learning in an ethnomathematical context based on local wisdom in the classroom. Teachers can consider using ethnomathematical contexts based on students' experiences with traditional games they know and have played to create a condition for learning mathematics that is fun and easier to understand because it is close to students' daily lives and contains cultural values ​​that can shape students' character.

Cognitive predictors of children’s arithmetic principle understanding

The understanding of arithmetic principles (APs) is an important component of our conceptual mathematical knowledge, but we have limited knowledge about how children acquire APs. The current study examined this issue through a longitudinal study with 273 Chinese fourth graders. These children were assessed on various cognitive capacities (e.g., verbal and visuospatial working memory, processing speed, inhibition skill, numerical magnitude representation) in Grade 4 as well as on their AP understanding using multifaceted assessment and their arithmetic competence in Grade 5. Results from structural equation modeling suggested that verbal memory and inhibition skill directly predicted AP understanding, which in turn predicted arithmetic competence. Visuospatial working memory predicted AP understanding through numerical magnitude representation. The findings allow researchers to better account for the individual differences in AP understanding.

EXPLORING LEGITIMATE PERIPHERAL PARTICIPATION OF STUDENTS IN A COLLEGE MATHEMATICS COURSE

Students, by just listening to and being observant of mathematical procedures to gain conceptual knowledge in mathematics, do not often lead valuable performance. Students need to participate. Learning is initiated and enhanced via continuing legitimate participation in a community of practice. Hence, this study explores students' legitimate peripheral participation in a college mathematics course, explicitly to describe the (1) activities students do to refine practice, (2) barriers students face to advance to full participation, and (3) participation support structures that allow students' legitimate peripheral participation. This study used qualitative-exploratory research design via the qualitative tool—reflective journal—comprising second-year teacher education students (N = 42) from a state university in Bulacan, Philippines, taking the Logic and Set Theory course as study participants, obtained purposively. Data were analyzed through thematic coding. This study showed that the activities of students that refine their practice could be thematized as individual engagement or collaborative involvement. Students faced both intrinsic and extrinsic barriers in progressing to full participation. The participation support structures facilitating students' legitimate peripheral participation were the manifestation of a welcoming environment that offered students additional practice activities to work into supplemented with constructive feedback, joined with the convenience of peer groups where they could go when needed. Inspirational life quotes, fascinating lessons that stir interest, and closed knowledge gaps equally enable student participation. A legitimate peripheral participation activity cycle may still arise when faced with difficulties as participants gradually try to work independently. A friendship-based collaborative group is suggested for Filipino learners.

STUDENTS' LEARNING DIFFICULTIES IN PROBLEM SOLVING ABILITY IN FACE-TO-FACE LEARNING LIMITED ELEMENTARY SCHOOL

Face-to-face learning activities in the current conditions found that there are still students who have difficulty in solving the problem in the topic of shapes. This can be seen from the fact that the success of students in problem solving is still low because students think mathematics is difficult as mathematics is abstract and uses symbols or language. In this study, the researchers wanted to find out more about the types of student learning difficulties in solving questions about shapes and the factors that cause student learning difficulties. This research was conducted using case study research. Collecting data was done to determine students' learning difficulties by using the methods of tests, observations, interviews, and documentation as complementary data in the hope of explaining the types and factors of learning difficulties in problem solving abilities. The results showed that the students had weakness in numeracy, weakness in knowledge, weakness in mathematical language, and visual perception. This is due to the lack of understanding of students' knowledge of mathematical concepts and arithmetic operations, as well as students' lack of accuracy. The factors that cause students to have learning difficulties are giving students negative responses to mathematics lessons, low student motivation, lack of guidance and assistance from family members, and limited time for face-to-face learning.

Teachers’ perceptions about collaboration as a strategy to address key concepts in mathematics

Background: The aim of the study is to investigate teachers’ perceptions about peer collaborative work in designing lessons as a team helped them to identify threshold concepts in the teaching and learning of foundation phase mathematics in Motheo District of Education.Methods: A qualitative approach, with a case study design, was used to combine data from observation and focus group discussions, interviews and group task sheets.Classroom observation was conducted during a workshop conducted by a subject advisor from the Motheo District of Education in collaboration with the researcher. Teachers were purposively selected from seven schools in the Motheo District of Education based on cluster sampling as a way of reviving their professional development through acquisition of mathematical teaching skills involving innovative approaches to teaching and learning of early childhood mathematics. Seven mathematics teachers, one from each school, were interviewed during the workshop.Results: Underpinned by a collaborative theory, the findings of the study revealed that peer collaboration in mathematics teaching was key to helping them (participant teachers) identify threshold concepts in mathematics that they had initially found difficult as individual teachers. This assisted them in teaching the subject effectively at the foundation phase level. The study, furthermore, established that collaboration by mathematics teachers was necessary in order to overcome the paucity of global mathematics teaching skills for early childhood mathematics, to foster learners’ knowledge of mathematical concepts and to stimulate their interest in the subject.Conclusion: It is recommended that more structured collaborative work amongst teachers in general should be encouraged to enable teachers overcome the problem of content gap in their area of specialisation.

Dialogical interactions mediated by technology in mathematics education

This paper discusses the results of a research[1] that integrates Digital Interactive Storytelling (DIST), competence-oriented mathematical activities, and argumentation called DIST-M. The general aim is to support a reflective knowledge of mathematical concepts by implementing a digital educational device based on collaborative and dialogical activities proposed by researchers. Within a dialogical dimension of interactions (Bakhtin, 1981), argumentative practice is considered a social activity, where the acquisition and elaboration of new knowledge take place within a social space with multiple interlocutors in a dynamic process. The participants are engaged in constructing and negotiating mathematical meanings within a specific context. This dialogical approach to argumentation tends to create an authentic argumentative culture that is a system of implicit and explicit rules where the exchanges and interactions among participants require a joint elaboration of new meanings, within a given mathematical context, through a dialogical exchange. Learning and development result from a dialogical negotiation process during which new knowledge is developed and those already possessed are re-organized and systematized (Bakhtin, 1981; Vygotskij, 1978). In the current pandemic circumstances, technologies are the main tools to uphold the educational processes. Despite the fact that the DIST-M was implemented and tested before the Covid-19 era, its epistemic bases of dialogism mediated by technology could significantly keep alive the dialogic interaction in educational settings that have been heavily affected by the social distancing and promote mathematical thinking. The articles focus on the United Nations Sustainable Development Goal n. 4,” Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all.”
 
 [1] The research is funded by the Italian Ministry of Education, University and Research under the National Project “Digital Interactive Storytelling in Mathematics: a competence-based social approach”, PRIN 2015, Prot. 20155NPRA5.

Conceptual Knowledge and Its Importance in Teaching Mathematics

Purpose: This study highlights the importance of teaching conceptual knowledge alongside procedural knowledge in mathematics. It examines the effects of a lack of conceptual knowledge on students’ responses to mathematics teaching from the perspectives of researchers and educators. Approach/Methodology/Design: This study draws on interviews with 30 secondary school mathematics teachers from Erbil in the Kurdistan region of Iraq on conceptual knowledge in mathematics. The study focuses on three main areas: mathematics teachers’ perspectives on teaching conceptual knowledge, the conditions needed to teach conceptual knowledge, and the obstacles that they face in teaching conceptual knowledge. Findings: A thematic analysis of the interviews revealed that mathematics teachers believed that conceptual knowledge is as important as procedural knowledge. In addition, they believed that achieving a balance between conceptual and procedural understanding and emphasizing the connections between them are necessary for understanding real mathematics. Practical Implications: Many mathematics teachers tend to use traditional teaching methods that focus on procedure and neglect conceptual mathematics. The results of this study would offer insights into the difficulties associated with mathematics teaching. Moreover, it would have practical implications for curriculum planning, emphasizing the balance of both conceptual and procedural knowledge. Originality/value: The study focuses on mathematics teachers’ perspectives on teaching mathematics conceptually, the conditions needed to teach conceptually, and the obstacles that they face in teaching mathematics conceptually.

Mathematics’ Conceptual Knowledge of for Form Four Daily School Students in District of PetalingUtama, Selangor

This study aimed to examine the level of students' conceptual knowledge on mathematics. In addition, the difference between conceptual knowledge based on gender and program was also studied. Measurement of knowledge is based on the Conceptual Knowledge Test (CKT). A total of 350 respondents were selected from five daily secondary schools in PetalingUtama, Selangor as a sample of the study. The data were analyzed using descriptive analysis to find out the level of variables measured. In order to identify the main effects and interactions between gender and program variables, inference analysis is a two-way ANOVA test performed for conceptual knowledge dimensions. The findings showed no interaction effects between gender for conceptual knowledge of mathematics (p <.05), but it showed a significant effect on the program (p> .05). In conclusion, mathematical knowledge is very important at the upper secondary level as a high level of mathematical thinking is required to ensure excellent in mathematical achievement.This is essentially as a long time learning system and methods as well as the imitation approach and dependent on the examinations orientation has long been a measure of student achievement. The implication of this study is that basic conceptual knowledge of students' mathematics needs to be enhanced to realize Malaysia's aspiration to be in the top third place in international assessments such as TIMSS and PISA.

Commognitive Analysis Of Students' Errors In Solving High Order Thinking Skills Problems

This study aims to describe the commognitive analysis of students' errors in solving High order thinking skills problems. The problem of this study is that students have difficulty of solving mathematical problems because students do not build their own knowledge of mathematical concepts but tend to memorize concepts so that when students solve math problems students often make mistakes and do not find solutions to solve these problems. Students also taught themselves that math is difficult. This type of research is a qualitative description. The research subjects were three grade X students of Senior High school 1 Pamekasan. The instruments used in this study were mathematical problem seets and semi-structured interviews. The results showed that students experienced faults in 1) word use (mistake writting mathematical symbol and not consisstent in writting naming. the factors are hasty, inaccurate, not understanding the questions, incomplete writing is known, and asked, not understanding the material.); 2) Visual mediator (mistakes in drawing or illustrating the problem. Student is not using visual mediators, some students use visual mediators but are still wrong and use it,); 3) Narrative (not writing the formula but writing the results directly. Student mistakes also occur because students do not know the strategy that will be used to solve them, while the students' mistakes made at this stage are: students are wrong in writing the formula definition sine and wrong for not writing the formula.); 4) Routine (inaccurate in arithmetic operations so that the final answer is wrong. The mistakes of some students in general in doing routine are the students doing wrong calculations, wrong in substituting values or numbers that are known in the formula.). With this research, teachers can find out where the difficulties and misconceptions of students are in doing it so that it becomes new learning for students to improve learning outcomes and minimize errors.

Between confidence and procedural flexibility in calculus

Greater flexibility with procedures is known to be associated with greater conceptual knowledge of mathematics and vice versa. In parallel, a student’s emotional relationship to mathematics – i.e. their ‘affect’ – is known to influence how they learn and perform in mathematics. For example, a confident student may engage more fully with mathematics, thereby improving their knowledge and skill acquisition and performance. What remains to be understood is the relationship between a student’s affect and their procedural flexibility. The results of this study indicate a positive, albeit moderate, correlation between a student’s confidence and their flexibility with calculus procedures. This reveals a potential avenue to improved mathematical understanding and performance: the symbiosis between confidence and flexible procedural knowledge.

A matemática vai à escola: concepções, saberes, práticas e formação do professor dos anos iniciais do ensino fundamental

O trabalho apresenta resultados e discussões sobre uma proposta desenvolvida no âmbito do curso superior de Matemática Licenciatura do Instituto Federal Catarinense – IFC Campus Concórdia em 2019, considerando ações pregressas entre os anos de 2016 e 2017. Objetivou integrar ações de ensino, pesquisa e extensão na dimensão da Alfabetização Matemática, justificadas por uma problemática e hipóteses levantadas por licenciandos quando do curso da disciplina de estágio, acerca de saberes e formação de professores dos anos iniciais do ensino fundamental. As diferentes frentes postas em prática na proposta foram desenvolvidas nos espaços do campus do IFC e em escolas do município de Concórdia/SC. Dentre as atividades desencadeadas se destacam: estudo da sistematização curricular das turmas assistidas; observação de aulas; planejamentos de ensino; intervenções nas escolas e; questionários aplicados aos professores das turmas. A pauta metodológica do estudo esteve ancorada em uma perspectiva qualitativa de pesquisa, tendo sido considerados os dados empíricos frente às observações e interações vivenciadas, análise documental, além da coleta e tratamento de informações sob a ótica da Análise Textual Discursiva. Diferentes resultados acompanharam o desfecho do estudo, incluindo, especialmente, o conhecimento sobre as práticas metodológicas, o déficit na formação inicial com relação aos conhecimentos conceituais em Matemática e o papel da formação continuada para as condutas educativas dos professores polivalentes.

Tablet assessment in primary education: Are there performance differences between TIMSS' paper‐and‐pencil test and tablet test among Dutch grade‐four students?

AbstractOver the last two decades, the educational use of digital devices, including digital assessments, has become a regular feature of teaching in primary education in the Netherlands. However, researchers have not reached a consensus about the so‐called “mode effect,” which refers to the possible impact of using computer‐based tests (CBT) instead of paper‐and‐pencil‐based tests (PBT) to assess student performance. Some researchers suggest that the occurrence of a mode effect might be related to the type of device used, the subject being assessed and the characteristics of both the test and the students taking the test. The international TIMSS 2019 Equivalence Study offered the opportunity to explore possible performance differences between a PBT and a tablet assessment in mathematics and science among Dutch primary school students. In the spring of 2017, the TIMSS PBT and tablet test were administered to 532 grade‐four Dutch students. Item response theory was used to explore potential mode effects. This exploration revealed no significant differences in the student ability scales between the paper and the tablet tests for mathematics and science. Also, no systematic mode effects were found for the items with high reading demand. A marginal difference was found for girls outperforming boys on the TIMSS tablet test, although no gender differences in achievement were found for the PBT. Practitioner NotesPrevious knowledge about this topic Many studies have investigated the test mode differences between CBT and PBT, but their results are divergent and inconclusive. Factor familiarity with the test device has an important impact on test performance. The difference between reading on paper or on a tablet is an important factor. Many studies demonstrate that when reading on a screen, text comprehension is perceived to be more difficult. What this paper contributes This equivalence study shows that CBT is highly comparable to PBT, indicating that both test modes are suitable for testing the conceptual knowledge of mathematics and science and are comparable for assessing TIMSS in the Netherlands. When assessed on a tablet, Dutch grade‐four girls slightly outperform boys in mathematics. Implications for practice and/or policy Within the Netherlands, the tablet test could be a good alternative to the traditional PBT. Digital testing enables investigations on the differences between boys and girls in terms of response behaviour, such as response time by analysing the log files of the assessment.

Mismatch of the South African Foundation Phase Curriculum Demands and Learners’ Current Knowledge

Against the background of the low mathematical performance of South African learners in international panel studies, there is an urgent need to improve mathematical education. In particular, the curriculum and its structure raise questions. It is logical that the prescribed curricula should align with learners’ developmental trajectories. Given the hierarchical structure of mathematics, the curricular requirements should pay attention to learners’ current knowledge of mathematical concepts. The aim of this study was to compare the curricular requirements as defined by the CAPS with the conceptual current knowledge of South African learners. South African Grade 1 learners (N = 602) were assessed on a test of numeracy concepts, based on a theoretically informed and empirically validated model of developing mathematical proficiency. The content of the CAPS for Grade 1 was aligned to the model levels by two experts (Cohen’s κ = .753, p < 0.001). Results show that the curricular requirements go far beyond the current knowledge required to engage with these new concepts of the vast majority of South African Grade 1 learners. The mismatch may to some extent be responsible for the unsatisfactory results in international comparison studies. These results show that the intended curriculum is beyond the grasp of most South African Grade 1 learners. These children are unlikely to develop new arithmetic concepts based on their lack of required foundation knowledge. We therefore argue that the intended curriculum for Grade 1 should focus more on counting skills, ordinal relations between numbers and—most importantly—set-based number representations and part–part–whole relations.

Upotreba problema Abul-Vefe za podsticanje metodičkog znanja budućih nastavnika matematike

Solving Abu'l-Wafa's problem could be a powerful tool for building and fostering pedagogical content knowledge of prospective mathematics teachers. The goal of this case study is to examine if this episode in the history of mathematics would foster the subject content knowledge and pedagogical content knowledge of a group of prospective mathematics teachers. Abu'l-Wafa's problem was presented to five prospective mathematics teachers in the Mathematics Teaching Methodology Course. They had to find out at what point of learning geometry and how to engage pupils to solve this problem, taking into account the question of procedural and conceptual knowledge in mathematics as well as the important question of the role of proof and argumentation in mathematics classes. Our case study showed that an integration of the history of mathematics in education may be particularly relevant for supporting and improving the pedagogical content knowledge of prospective mathematics teachers.

Junior high school students’ mathematical creative thinking ability based on gender differences in plane and solid geometry subjects

Mathematical creative thinking is the ability of students to find solving ways that are unusual, unique, and have never been found by others. The development of the concept of mathematical creative thinking can make students despair and give up, so that another ability is needed so that they are able to survive and turn their difficulties to be opportunities for themselves to advance. This study aims to determine the mathematical creative thinking ability of class VIII junior high school students in one of the junior high schools in Bandung Barat on the subject to construct plane and solid geometry based on gender differences. The samples are 4 students consisting of two men and two women. Besides that, the discussion of mathematical creative thinking skills for junior high school students is viewed from gender differences, between male and female students in terms of their creative thinking abilities. The instrument of this research is a test of the ability to think creatively and interview. This study is a descriptive qualitative research that aims to describe the ability of creative thinking mathematically in solving problems of plane and solid geometry. The results show that the ability difference between male and female students is that the female students have much better mathematical creative thinking. In addition to gender factors, other factors can also influence the achievement of creative thinking skills; namely, students and teachers’ readiness to learn, students’ basic abilities and knowledge of mathematical concepts. Male students are more detailed in explaining the shape of each space given to the problem.