Mathematical Content Research Articles

高中数学教师对苏教版新教材数学建模内容使用情况的调查研究

高中数学教师对苏教版新教材数学建模内容使用情况的调查研究

The Alignment of P–3 Math Instruction

Preschool through third grade (P–3) alignment is regularly named as a key aspect of early childhood education and the transition to formal schooling. However, little is known about P–3 alignment in practice. Using data from 265 observations of math instruction in preschool, kindergarten, first-, and third-grade classrooms in New York City public schools, we explore P–3 instructional alignment as it would be experienced sequentially, over time and across grades, by students. We examine the continuity of developmentally appropriate instructional environments and high-quality pedagogical practices, as well as the progression of P–3 mathematics content coverage. We find notable discontinuities in instructional environments and some pedagogical practices, particularly across preschool and kindergarten. We also find both progression and repetition in math content coverage. Results suggest that, on some dimensions, kindergarten may be poorly aligned with both preschool and the early elementary grades.

An Empirical Study on Improving Mathematics Application Skills of Engineering Students Using MATLAB Tools

Abstract This paper discusses the implementation and application of MATLAB tools in the teaching of engineering majors so as to improve the quality of education and students’ mathematical application ability. Using the programming and GUI graphical interface design functions of MATLAB, the method of establishing the graphical user interface of the mathematical experiment module closely links the experimental content with the practical teaching of mathematical modeling. With the help of the operation functions provided by the system, we can set the experiment parameters and design the experiment interface ourselves to deepen our intuitive understanding of the mathematical content learned. After the pilot teaching in the mechanism major of University Z, 22 individuals failed to reach course objective 1, and 40 individuals were unable to reach course objective 2. The number of individuals passing the three lab reports increased continuously, from 40 to 57 in Class 1 and from 34 to 56 in Class 2. The math scores in the three exams improved significantly, and the distribution of the scores went from concentrating on scores below 60 to focusing on scores between 70–89. As a result, the teaching method for MATLAB tools application was effective.

Mathematical modelling in the discourses of the KOM and PISA frameworks and teacher interviews

ABSTRACT Mathematical modelling is emphasised in curricula worldwide. Since 2006, mathematical modelling has been considered a fundamental process in the mathematics subject in Norwegian upper secondary schools. This study aimed to identify tensions in the approaches to mathematical modelling expressed in teacher interviews (N = 4) and framework discourses (KOM and PISA) by four characteristics of communication (word use, routines, visual mediators and endorsed narratives). The tensions identified encompassed students’ abilities to make choices and decisions during modelling activities and connection to specific mathematical content or real-life situations. Teachers also questioned the relevance of mathematical modelling, even though the main reason for the implementation of mathematical modelling in education is to make school mathematics relevant for everyday life.

Preparedness of Students for Self-regulated Learning of Mathematics

This work aims to examine the relationship between general self-regulated learning abilities and students' general intellectual abilities, mathematical learning abilities, and academic achievement. A study was conducted with a sample of eighth-grade students (N=325). The research employed a survey and descriptive method, and the instruments used included a test of general intellectual abilities, a test of self-regulated learning abilities, a test to measure mathematical learning abilities, and a standardized math knowledge test. Based on the obtained results, we indicate those factors with high or moderately high correlations. Among the results obtained, there is a high correlation between general intellectual abilities and general self-regulated learning abilities (subtests for interpreting graphs and interpreting geographic maps). The results show a high correlation between the total score on the self-regulated learning abilities test and math achievement. A moderately high correlation was achieved between the test of general intellectual abilities and self-regulated learning abilities (subtests for finding necessary information, exploring new material, and the index of developed abilities and techniques for self-regulated learning). On the math learning ability test, various abilities are differentiated, including formalization of mathematical content, spatial abilities, imagination, flexibility, and critical thinking. Based on the research results, it is considered significant to investigate the effects of different innovative teaching systems and teaching methods on students' self-regulated learning abilities and mathematical learning abilities.

Mathematical Problem Solving Ability Judging from the Percentile Intelligence of Class IV Students in the Problem Based Learning Model with Ethnomathematics Nuances

The problem encountered in class IV at SD 2 Medini was that mathematics learning was still teacher-centred, yet to be linked to the experiences of the students themselves. Knowledge still needs to use media examples from the surrounding environment that are real and based on local culture. This research aims to determine students' problem-solving abilities in mathematics content through learning outcomes and students' intelligence percentages in ethnomathematics nuanced learning. The study was carried out using a mixed method with a sequential explanatory design (sequence of evidence). The sequential explanatory model is a combined research method that combines quantitative and qualitative research methods sequentially, where the first stage of research is carried out using quantitative methods and the second stage is carried out using qualitative methods. The results of the study on the application of the Problem-Based Learning model with nuances of ethnomathematics are effective on mathematical problem-solving abilities. This shows that the Problem-Based Learning model is able to improve student learning outcomes through the results of the T-test carried out in the experimental class and control class where the practical class applies nuanced learning ethnomathematics was able to increase learning outcomes by up to 34% and was supported by an N-gain test score of 0.75 with high criteria and a very effective effectiveness rating, while the control class was only at 0.57 with medium criteria and a less effective effectiveness level. Keywords: Problem Solving Ability, Intelligence Percentile, and Problem Based Learning, ethnomathematics.

PLANNING OF MANIPULATIVE MATERIALS IN THE CONTEXT OF LESSON STUDY IN CONTINUOUS TEACHER TRAINING FOR INCLUSIVE MATHEMATICAL LITERACY

With the goal of exploring aspects of planning based on Lesson Study methodology to fit into the stages of developing, aligning, or adapting, and applying manipulative materials for inclusive mathematical literacy, we offer a continuous training for teachers. We propose a workflow that provides, at each stage of planning, theoretical foundations related to the curricula and the specific subjects of mathematics, as well as practical guidelines for the moments of planning and adaptation of manipulative materials with the help of a specialist in special education. From the results, we report on the work developed by two groups, respectively dealing with the concepts of fractions and number construction, targeting Early Years and Early Childhood Education students. We understand that the workflow provided participating teachers with autonomy and confidence, culminating in the elaboration, alignment, and adaptation of potentially inclusive manipulative materials that were used by the entire class, a characteristic we consider essential in materials with this focus. Teachers were provided with new knowledge about mathematical content, curriculum, and ways of approaching the classroom that can lead to improvements in teaching and learning in their future professional practice.

Impacts of non-locality and memory kernel of fractional derivative, awareness and treatment strategies on HIV/AIDS prevalence

We propose a Liouville–Caputo non-linear fractional order α(0<α≤1) epidemic model to understand the transmission dynamics of infectious diseases, like HIV/AIDS, and explore the presence of memory kernel of fractional derivative for the precautionary measure against the transmission of disease to control HIV/AIDS prevalence. A proper sex education, which depends on number of HIV and AIDS, to unaware susceptible as well as fear of infection among these aware susceptible are employed here. Treatment compartment is incorporated to treat the symptomatic HIV and AIDS infected individuals.Using the Banach fixed point theorem, we first ensure the positivity, existence and uniqueness of solution, and biologically feasible region. Next after defining the basic reproduction number (R0), its uses on stability (local and global) and direction of bifurcation are manifested here. A quantitative assessment is conducted onR0and then we explore the sensitive parameter/s, which control the HIV/AIDS prevalence.Numerical experiment is conducted based on the Adams–Bashforth–Moulton predictor corrector method to obtain the approximate solution of the proposed model. Impacts of disease transmission rate, awareness, psychological fear of infection and treatment strategies on the HIV/AIDS prevalence are analysed based on non-linear dynamical tools, like, time series, phase diagram and spectra analysis. An effort is made to see how the order and kernel of the fractional derivative play a crucial role on the dynamics of the system and in the precautionary measure against the transmission of disease during transition as well as post-transition phases. We employ intervention strategies for controlling the spread as well as possibility of eradicating the HIV/AIDS prevalence. It is seen that the reduction ofαis comparable to awareness, psychological fear of infection and treatment strategies to control disease. Finally, it is shown that the use of fractional derivative in disease transmission dynamics is one of the most efficient applied mathematics content compatible with the natural characteristics of human memory.

Learning Management System Satisfaction and Problem-Solving Skills in Mathematics of Grade 11 Students

Almost all schools needed to adapt and sign up for a learning management system (LMS), which will help them manage students' outputs, provide learning materials, and communicate in a virtual classroom. Numerous studies also showed that the problem-solving skills of students are declining. This study was conducted to determine if there was a domain in LMS satisfaction that significantly influenced the problem-solving skills in Mathematics of Grade 11 students. It also determined the level of LMS satisfaction and the level of problem-solving skills and if there was a significant relationship between the two variables. The researcher has utilized a descriptive correlation non-experimental method in quantitative research in a sample of 102 respondents using stratified random sampling. An adapted and researcher-made questionnaire was given to the respondents. In addition, mean, Pearson-r, and linear regression were the statistical tools employed. Results showed that the level of LMS satisfaction and the problem-solving skills of the students were very high and always evident. Two variables had a significant moderate correlation, and communication quality and overall satisfaction significantly influenced their problem-solving skills. Students believe that LMS gives them accurate and complete mathematics content which allows them to perform well in solving problems in Mathematics. Teachers should continuously help students in using LMS for them to maintain their high problem-solving skills.

Didactic Analysis of Junior High School Students Mathematical Literacy Skill on Space and Shape

It is important for learners to have mathematical literacy skills because it can help learners utilize mathematics in real life, solve problems, assess whether the results obtained make sense, and analyze situations and make conclusions. In the Program for International Students Assessment (PISA), there are four mathematics contents: Space and Shape, Change and Relationship, Quantity, and Uncertainly and Data. The purpose of this study is to identify the learning obstacles experienced by students in the Space and Shape content. This study used a qualitative approach using dedactical design research. With 16 learners, this research was conducted at SMP PST Guppi Samata class IX. The instruments used in data collection are tests and non-tests. The test material consists of questions about mathematical literacy skills level 3, 4, and 6 using flat-sided space building material. The non-test instruments used in collecting data are observation and documentation. Based on the research results, students experience learning difficulties in space and shape content which causes them to be less able to evaluate solutions that have been interpreted. The percentage shows that out of 16 students in class IX, 10% of them have high math ability, 60% have medium math ability, and 30% have low math ability. Efforts can be made to start with the habituation of providing basic calculations so that students can answer test questions correctly. After that, motivation can be given and encourage students to be enthusiastic in understanding the concept of critical thinking in applying the context of the problem to real objects.

Lesson plays as an approach to learning to teach proving

We suggest that writing lesson plays can be a valuable approach in learning to teach proving in teacher education. A lesson play is an imagined discussion between a teacher and some students about a particular mathematical content, written verbatim. In this paper, we investigate novice teachers’ opportunities to work on teaching practices related to proving by generic examples through writing lesson plays. We analyse lesson plays written by 14 novice teachers, and our analysis reveals that several teaching practices are involved. Some of the teaching practices are related to teaching mathematics in general, some are more specifically related to teaching of proving, and some of the practices are particular to teaching of proving by generic examples.

Drama-Based Pedagogy: Ways of Engaging in Mathematics Learning

Mathematics education program always falls under public criticism because of being unable to produce desirable outcomes. From the beginning of formal mathematics education programs in Nepal, mathematics teaching-learning activities have been dominated by the informing and pouring pedagogy for preparing final examinations. Mathematics curricula, contents and pedagogical activities have not bridged the gap between official (formal) mathematics and the learners' lifeworld practices that support creating the mathematical 'Othering'. Likewise, mathematics education programs become unclaimed entity at the crossroads in which no one is willing to take sole responsibility and ownership of the programs but orienting to blame others. Such a blaming culture restrains engaged teaching-learning activities. Against this backdrop, this argumentative paper argues for incorporating the DBP in the mathematics classroom to create an engaged teaching-learning environment. We have metaphorically captured the five significant theoretical features of DBP as/for contextual learning, academic enhancement, reflective practice, agentic development and social wellbeing. Finally, we have briefly described the implications of DBP in mathematics classrooms.

A Textbook Problem-Solving Student Becomes Transformative Contextualized Mathematics Teacher: Journey of Learning and Teaching

This reflective paper portrays my personal-lived experiences via autoethnography (as a method of inquiry); Ethnodrama and narrative (as representational methods); and transformative learning theory (as a theoretical referent). Emphasis on textbook, realization, and obligation were/are the characteristics regarding my transformative journey from a textbook problem-solving mathematics student to being a contextualized mathematics teacher. As a student, the lure of scoring marks led me towards the path of solving as many textbook problems (as possible) with the only goal to perform well in examination. While on the verge of entering the teaching profession; reflecting back to school days, made me think about the question: “Do I desire to give my prospective students (mathematics education) in the same contexts or in the same manner that I experienced during my school days?” Immediately, each time both my heart and mind used to answer, “Not really, No!” This sense of realization led me to the obligation of approaching my two years of Fellowship journey as a mathematics fellow that primarily emphasized linking mathematical contents with the local surroundings (of the learners). This study is beneficial for educators who aim to bring necessary reform regarding educational practices (particularly, in mathematics), so as to provide the outlook (to the learners) that ‘Mathematics is everywhere around the surroundings'.

Tikaram and Chandrakala Dhananjaya: A collaborative couple in mathematics from Nepal

Within the history of mathematics and mathematics education in Nepal, Tikaram and Chandrakala Dhananjaya are relatively well-known figures for their two books Śiśubodha Taraṅgiṇī and Līlāvatī. This is despite there being almost no archival or manuscript materials offering a window into their lives: we have no letters, notebooks, diaries, or school records. Rather than focusing on either individual in isolation, in this article we present an argument for considering the Dhananjayas as an analytically indivisible collaborative couple in mathematics. Of the two aforementioned books, one is attributed to Chandrakala and the other to Tikaram; but in fact, both are translations of the same Sanskrit source text, Līlāvatī, into Nepali. By comparing the mathematical contents of these two works, which were published within a few years of each other, we explore what it means to be an author or translator of a mathematical text and propose different models of spousal collaboration which could plausibly have been adopted by the Dhananjayas. In the absence of documentary evidence, the impossibility of delineating each individual’s contributions removes the temptation to focus exclusively on apportioning credit. Instead, we offer the alternative perspective of considering what labour must have been undertaken to bring their books to publication.

싱가포르 중학교 수학교과서에서의 빅 아이디어 접근 구현 사례 연구

Big Ideas approach is gaining attention as a design and implementation perspective for curriculum that intends connected and coherent mathematics learning. This study conducted quantitative and qualitative analysis on horizontal connections between mathematical content in middle school mathematics textbooks of Singapore where Big Ideas approach was applied. The quantitative analysis revealed the strength of horizontal connections within strands and within topics by Big Ideas. Among the eight Big Ideas in Singapore mathematics curriculum, “diagrams” and “notations” aided generally high level of horizontal connections, while “functions,” “invariance,” and “models” promoted generally lower level. The qualitative analysis distinguished between process-oriented and concept-oriented Big Ideas. Horizontal connections by process-oriented Big Ideas were further classified into “connections by conventional mathematical practices” and “connections through non-routine mathematical reasoning”, while horizontal connections by concept-oriented Big Ideas were classified as “deductive connections based on definitions” and “inductive connections based on awareness of structure”. Results are discussed and implications for the implementation of Big Ideas approach in the 2022 revised mathematics curriculum are suggested.

From Diophantian Equations to Matrix Equations (III) - Other Diophantian Quadratic Equations and Diophantian Equations of Higher Degree

In this paper, we propose to continue the steps started in the first two papers with the same generic title and symbolically denoted by (I) and (II), namely, the presentation of ways of achieving a systemic vision on a certain mathematical notional content, a vision that to motivate and mobilize the activity of those who teach in the classroom, thus facilitating both the teaching and the assimilation of notions, concepts, scientific theories approached by the educational disciplines that present phenomena and processes from nature. Thus, we will continue in the same systemic approach, solving some Diophantine equations of higher degree, more precisely some generalizations of the Pythagorean equation and some quadratic Diophantine equations, in the set of natural numbers, then of the whole numbers, in order to "submerge" a such an equation in a ring of matrices and try to find as many matrix solutions as possible. In this way we will solve 12 large classes of Diophantine quadratic or higher order equations. For attentive readers interested in these matters, at the end of the paper we will propose 6 open problems. The solution of each of these open problems represents, in fact, a vast research activity and that can open the way to solving such more complicated Diophantine and / or matrix equations.

Implementing the flipped classroom model in mathematics class teaching

The aim with this research was to examine how the implementation of the flipped classroom model (FCM) impacted the quality and durability of 4th grade students’ knowledge in the field of measuring and measures when compared to traditional teaching (TT). The research was conducted in Serbia on a sample of 135 students, divided into 3 groups. The 3 groups were a control group (C) which was taught mathematics content using the TT model, an experimental group 1 (E1) which was taught using the FCM, while the students in experimental group 2 (E2) were taught using the FCM – the teacher also provided them with feedback regarding their work and made recommendations for their further development. The results show that the students from the E2 group surpassed those from the C and E1 groups regarding the quality and durability of their knowledge in the field of measuring and measures. There was a statistically significant difference in the knowledge of students in this field at the lower cognitive level among all the groups, while the statistically significant difference at the higher cognitive level was seen between the C and the E2 and between the E1 and the E2 groups.

English to Arabic Machine Translation of Mathematical Documents

This paper is about the development of a machine translation system tailored specifically for LATEX mathematical documents. The system focuses on translating English LATEX mathematical documents into Arabic LATEX, catering to the growing demand for multilingual accessibility in scientific and mathematical literature. With the vast proliferation of LATEX mathematical documents the need for an efficient and accurate translation system has become increasingly essential. This paper addresses the necessity for a robust translation tool that enables seamless communication and comprehension of complex mathematical content across language barriers. The proposed system leverages a Transformer model as the core of the translation system, ensuring enhanced accuracy and fluency in the translated Arabic LATEX documents. Furthermore, the integration of RyDArab, an Arabic mathematical TEX extension, along with a rule-based translator for Arabic mathematical expressions, contributes to the precise rendering of complex mathematical symbols and equations in the translated output. The paper discusses the architecture, methodology, of the developed system, highlighting its efficacy in bridging the language gap in the domain of mathematical documentation.

The Construction of Definitions Through Padovan’s Combinatorial Model: An Investigation With Didactic Engineering in an Initial Education Course for Mathematics Teachers

Background: Given the oversight of specific topics in the history of mathematics books, this research was motivated by the extensive coverage of the Fibonacci sequence. In addition, the existence of the Padovan sequence, which is considered a Fibonacci cousin, stands out. Objectives: Investigating the Padovan sequence, building its definition through a combinatorial model using manipulative materials based on the theory of didactical situations in the initial mathematics teacher education course context. Design: The research methodological design follows didactic engineering, and a didactic teaching situation is created to investigate the Padovan sequence. Thus, manipulative material was developed to facilitate the teaching process and the construction of the sequence definition. Settings and participants: The interventions were done in the mathematics degree course of a higher education institution in Fortaleza. Five students enrolled in the component of History of Mathematics participated in the study. Data collection and analysis: Data were collected during classes, recorded through photos and audio recordings, based on didactic engineering and the theory of didactical situations. Results: The most relevant result of this study is constructing the definition of the Padovan sequence through the manipulative material. Conclusions: We concluded that the research allowed an investigation of the Padovan sequence, enabling the visualisation of its terms and their integration with other mathematical contents, contributing to teaching these numbers.

Resources for planning and teaching mathematics: a Swedish upper-secondary school case study

ABSTRACT This study investigates resource use by upper-secondary mathematics teachers in the context of collaborative planning. A thematic content analysis is conducted on audio-recorded teacher discussions in order to find out what resources are used by the teachers, how they are used, and for what reasons. The findings show that although teachers use a variety of resources to support their instructional enactment as well as instructional design, there is a difference in how they use different resources to support different planning practices. For instructional design, curriculum resources provide support for the mathematical content, while social resources, self-generated documents, and cognitive resources provide support for the design of instructional activities. Authority is given by teachers to curriculum resources, but conflicts of authority emerge in discussions, when teachers’ abilities to exert their agency are not supported by curriculum resources. We discuss the findings in relation to authority and resource use, as well as for established conceptualizations of resources. The findings bear practical implications for the design of curriculum resources.