Mathematics Standards Research Articles

Teaching argument writing in math class: challenges and solutions to improve the performance of 4th and 5th graders with disabilities.

Incorporating argument writing as a learning activity has been found to increase students' mathematics performance. However, teachers report receiving little to no preservice or inservice preparation to use writing to support students' learning. This is especially concerning for special education teachers who provide highly specialized mathematics instruction (i.e., Tier 3) to students with mathematics disabilities (MLD). The purpose of this study was to examine the effectiveness of teachers providing content-focused open-ended questioning strategies, which included both argument writing and foundational fraction content, using Practice-Based Professional Development (PBPD) and Self-Regulated Strategy Development (SRSD) for implementing a writing-to-learn strategy called FACT-R2C2. We report the relative number of higher-order mathematical content questions that teachers asked during instruction, from among three different-level question types: Level 1: yes/no questions focused on the mathematics content; Level 2: one-word responses focused on the mathematics content; and Level 3: higher-order open-ended responses centered around four mathematical practices from the Common Core State Standards for Mathematics. Within a well-controlled single-case multiple-baseline design, seven special education teachers were randomly assigned to each PBPD + FACT-R2C2 intervention tier. Results indicated that: (1) teachers' relative use of Level 3 questions increased following the introduction of the FACT intervention; (2) this increase was apart from the professional development training that the teachers had initially received; and (3) students' writing quality improved to some extent with the increase in teachers' relative use of Level 3 questions. Implications and future directions are discussed.

데이터 리터러시 관점에서 초등 수학과 성취기준 및 교과서 문제의 비구조성(ill-structured) 비교분석

Objectives The purposes of this study were to analyze the achievement standards of elementary mathematics and curriculum in each country from the perspective of data literacy, compare and analyze the problem of ill-structured in math textbooks, and present the direction of future curriculum and textbook development.
 Methods To analyze the elementary mathematics curriculum standards in Korea, the United States, Japan, and India from a data literacy perspective, components of data literacy was selected and analyzed with a focus on whether the standards in each country's curriculum reflect the content of the components. After categorizing the standards, to analyze the cognitive level of the standards, the level of the standards is compared by the mathematics cognitive domain, which is an indicator for the development of the TIMSS 2019 assessment, and the problems ill-structured of in each country are examined in terms of realism, complexity, and openness.
 Results Compared to other countries, Korea did not deal with various aspects of data literacy in the curriculum standards, and showed a low proportion in the cognitive domain that requires high-dimensional thinking. The problems of ill-structured in textbook were practical in that it mimics the real situation and provides descriptions and information about the situation, but complexity and openness were relatively not revealed, confirming the need to develop meaningful textbook problems for learners in the future.
 Conclusions In the curriculum, it is necessary to emphasize various aspects and high-dimensional thinking on the perspectives and components of data literacy and to be guided in connection with ‘data ethics’. Mathematics textbooks should be able to utilize high-dimensional thinking skills through ill-structured status and aspects of practicality, complexity, and openness need to be systematically presented. Pre-service teachers and teachers also suggested that the development of training and programs to foster data literacy capabilities, cultivate background knowledge on ill-structured status, and support teaching and learning design be conducted as follow-up studies.

Life Tasks as a Means of Studying New Material When Teaching Geometry in Secondary School

The article reveals the role of life tasks in teaching geometry in high school. The teaching of mathematics in a general education school, in addition to equipping students with certain knowledge, skills and abilities necessary to prepare them for life activities in the conditions of modern production, also pursues the goal of achieving such a level of their mathematical development that they need to study other school subjects at a high level, to continue their education in higher education. And also, for the formation of key and subject competencies in mathematics. The article deals with life tasks as a means of learning new material when teaching geometry in high school. Examples from the production industry are given. And also, the article presents the requirements and goals of studying mathematics, geometry in high school. The content of the textbooks proposed by the Ministry of Education, respectively, for general education and subject state standards in mathematics, contains many examples related to life tasks. The above conclusions define the main problem of the study: to study the role and place of tasks with vital content in revealing the content-applied significance of the school geometry course and in solving general educational problems facing the school. Develop a methodology for teaching problem solving. In the school teaching of geometry, the connection of the studied material with life, with practice, is often not yet rationally realized. Students have poorly developed skills and abilities to apply the acquired knowledge in practice. The goals and requirements of education standards for student-centered learning, i. e. to connect the teaching of mathematics, geometry with life, the passion for studying the basics of production, to form the key and subject competencies of students.

Factors influencing teachers’ grading standards in mathematics

ABSTRACT National assessments can be used to explore the strictness of teachers in grading students by comparing student grades to their scores on standardised tests. Several factors influence teacher-given grades, including student gender, school type, geographical regions, and socioeconomic status. In this paper, we used data from the Italian institute INVALSI, responsible for the organisation of national mathematics assessments, to investigate how these factors influence teachers’ grading standards. We considered a sample of 36,589 Grade 13 Italian students from 2,062 classes at 990 high schools. The relationships between the variables were analysed using hierarchical linear modelling. The findings reveal that teacher-given grades are related to student-level variables (e.g. gender, socioeconomic status, and score on the INVALSI test) and school-level variables (e.g. school type and location). When the difference between teacher-assigned grades and scores on the INVALSI test was considered, only student gender, school type, and location accounted for the gap in student achievements. Therefore, student socioeconomic status has a lower influence on their performance on the INVALSI test, suggesting that using standardised assessments might improve equity in assessment.

Transcendental and mathematical infinity in Kant's first antinomy

ABSTRACT Kant's first antinomy uses a notion of infinity that is tied to the concept of (finitary) successive synthesis. It is commonly objected that (i) this notion is inadequate by modern mathematical standards, and that (ii) it is unable to establish the stark ontological assumption required for the thesis that an infinite series cannot exist. In this paper, I argue that Kant's notion of infinity is adequate for the set-up and the purpose of the antinomy. Regarding (i), I show that contrary to appearance, the Critique can even accommodate a modern notion of infinity without consequences for the antinomy; and regarding (ii), that the ‘ontological’ consequence indeed follows once its covertly epistemic character is adequately understood.

Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Place Value, Rounding, and Expanded Notation

This study investigated the effects of a place value intervention with third–grade students with learning disabilities. The intervention added content to a research–based intervention using the concrete–representational–abstract (CRA) sequence. The added content reflected current mathematics standards for third grade. Students’ place value understanding was measured using probes in which students had to identify the value of each digit within a three–digit number, round three–digit numbers to the nearest 10 or 100, and write three equations showing an expanded form of a three–digit number. A single–case, multiple–probe–across–students design showed a functional relation between CRA and completion of items requiring place value understanding. Students completed a generalization task by estimating the sum of a given equation.

The Development of Mathematical Model Consciousness in Junior Secondary Students: A Lesson Study of the Instruction of Congruent Triangles

The Compulsory Education Course Standards for Mathematics 2022 have highlighted the educational objectives of junior secondary mathematics by emphasizing the development of mathematical competence and practical learning. Model consciousness, as one of the fundamental mathematical competencies to be developed at the junior secondary level, can facilitate students’ comprehension of the universal application of mathematics. Teachers of mathematics in junior high school should construct effective classroom activities based on the cognitive qualities of their students in order to enhance their mathematical model consciousness and comprehension of the substance of mathematics knowledge. This paper is a lesson study of the education of Congruent Triangles, and its purpose is to investigate strategies for fostering mathematical model consciousness among junior high school pupils.

Technology as a tool for assisting students with special educational needs to learn and like mathematics and science: a literature review

Students with Special Educational Needs are encouraged to achieve high academic standards in Mathematics and Science education to better understand the natural world, develop life skills, and achieve career success. In this regard, digital technology assists students with disabilities in achieving Mathematics and Science literacy. This article presents a systematic literature review on the role of technology in Science education for students with Special Education Needs. An extensive search in academic databases yielded 24 journal articles from 2006 to 2022. These 24 empirical studies’ were reviewed through electronic databases, including Scopus, ERIC, Google Scholar, and Science Direct. The findings demonstrate that using assistive technology in Mathematics and Science education had a major positive impact on students’ motivation, attitude, and academic performance. Positive learning outcomes probably depend on how digital technology is used, specifically the capabilities of each unique technological implementation. For evidence-based research designs in digitally supported learning environments for students with Special Education Needs, digital technology and its affordances are recommended, among other quality indicators.

Multi-attribute group decision-making problem of medical consumption products based on extended TODIM-VIKOR approach with Fermatean fuzzy information measure

The fundamental goal of this research is to develop a MAGDM (Multi-Attribute Group Decision Making) problem of Medical Consumption Products. We propose TODIM–VIKOR approach in this paper, which combines the TODIM (an acronym in Portuguese for Interactive and Multi-criteria Decision-Making) and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) procedures under Fermatean fuzzy information. A new Fermatean fuzzy scoring function is presented for dealing with comparison problems. In addition, we introduce a novel entropy measure for assessing the degree of fuzziness associated with an FFS. We also offer a Jensen–Shannon divergence measure for the Fermatean Fuzzy set that can be used to compare the discrimination information of two FFSs. This suggested measure meets all mathematical standards for being considered a measure. We introduced entropy and divergence measures to determine the objective weight in the TODIM–VIKOR approach. Meanwhile, to deal with multiple attribute group decision-making, a new decision procedure based on the suggested Entropy and Jensen–Shannon divergence measure was proposed in a Fermatean Fuzzy environment. In this article, TODIM has in view to find out the overall dominance degree, and VIKOR is to determine the compromise solution. Finally, we manage a supplier selection problem to verify the performance of the suggested Fermatean fuzzy TODIM–VIKOR method by comparing the ranking solution to the rankings of existing methodologies. We investigate the reliability and effectiveness of our proposed methodology.

Preparing Secondary Mathematics Preservice Teachers for Rural Schools in Colombia

AbstractThis article describes a qualitative research case study that aimed to explore the complexity levels and types of mathematical thinking and national mathematics standards that a group of preservice teachers (PSTs) used to write mathematics word problems for secondary school students. The context was a teacher preparation course at a public university located in a rural region in Colombia, South America. The collected data included PSTs’ community reports, audio recordings of small-group discussions, and mathematics word problems. The data analysis process encompassed inductively created codebooks, several rounds of coding, and the inter-rater technique. The findings of the study demonstrated that most word problems written by the PSTs aligned with a few national mathematics standards and different potential levels of mathematical thinking. However, there was a disconnect between these levels of mathematical complexity and the types of funds of knowledge identified. The article ends by sharing implications for mathematics teacher education and suggestions for future research.

The keymath-3 essential resource program: mathematics achievement of students served in resource settings

Special Education teachers serve students who are struggling in mathematics and continue to fall further behind each year. Educators are faced with the challenge of selecting the most effective program for assessing and teaching mathematics that will promote mathematics achievement for students who are served in resource settings. The KeyMath-3 Essential Resources (KeyMath-3 ER) is a mathematics program aligned with National Council of Teachers of Mathematics standards, which incorporates research-based practices for teaching mathematics to students with disabilities. This study utilized the KeyMath-3 ER program as an intervention with five second-grade students with various disabilities receiving their mathematics instruction in a resource setting. The results demonstrated the potential usefulness of KeyMath-3 ER as an effective program for students in a resource setting. The one outlier was a student with autism who did not show significant progress demonstrating a need for further research to assess the effectiveness of using this program with like students.

Kemampuan Penalaran dan Komunikasi Matematis Berdasarkan Kemampuan Awal Mahasiswa Melalui E-Learning Berbantuan Program Maple

Mathematical reasoning and communication skills were added by NCTM and PISA as process standards in mathematics learning that received special attention. The population in this study were all students of Mathematics Education, Pasundan University. The sample in this study was two classes, namely semester 3. The research design used was One-Group-Pretest-Postest. The conclusions of this study include (1) the mathematical reasoning and communication abilities of prospective teacher students after receiving learning with e-learning assisted by the Maple Program are better than before receiving learning; (2) The mathematical reasoning ability of the superior group > moderate group > the low group significantly; (3) The increase in students' mathematical reasoning abilities is in the medium category. The increase in mathematical reasoning ability of the superior group > moderate group > the low group, only not significant; (4) The mathematical communication ability of the superior group > moderate group, it's justnot significant. The superior group > significant assessor group, and the moderate group > significant assessor group; (5) The improvement of students' mathematical communication skills are in a low category. Improved mathematical communication skills of the superior group > moderate group, and the superior group > the low group significantly. Medium group > low group, only not significant.

Examining the scenarios created by pre-service teachers regarding misconceptions that may occur in the teaching process

In this research, pre-service mathematics teachers were asked to prepare scenarios about what possible misconceptions might be in the classroom teaching process and how a solution strategy could be used based on the cognitive conflict approach in order to overcome these misconceptions. Based on these scenarios, it is aimed to determine what type of possible misconceptions may be related to which content standards. This research was conducted using an integrative mixed method design, which allows qualitative and quantitative methods to be used together or sequentially. The study group of the research consists of 60 primary school pre-service mathematics teachers who have successfully completed the "Misconceptions in Mathematics Teaching" and "Teaching Practice" courses. The data of this research consists of misconception scenarios created by pre-service teachers and a semi-structured interview form. In the analysis of the scenarios, correspondence analysis was used to evaluate the relationship between misconception types and content standards. Considering the research results based on misconception types, it was seen that the most common misconception type was overgeneralization, whereas the misconception type in the wrong translation did not emerge. When the research results are examined in the context of content standards of mathematics, it is seen that the misconceptions mostly belong to the subjects of numbers and operations.

Mathematics Content in Early Childhood Classroom Libraries: Alignment with Common Core Mathematics Standards

Mathematics Content in Early Childhood Classroom Libraries: Alignment with Common Core Mathematics Standards

Neural-Network-Based Terminal Sliding Mode Control of Space Robot Actuated by Control Moment Gyros

This paper studies the trajectory tracking control of a space robot system (SRS) in the presence of the lumped uncertainties with no prior knowledge of their upper bound. Although some related control methods have been proposed, most of them have either not been applied to SRSs or lack rigorous stability proof. Therefore, it is still a challenge to achieve high accuracy and rigorous theoretical proof for tracking control of SRSs. This paper proposes a new integrated neural network- based control scheme for the trajectory tracking of a SRS actuated by control moment gyros (CMGs). A new adaptive non-singular terminal sliding mode (ANTSM) control method is developed based on an improved radial basis function neural network (RBFNN). In the control method, a new weight update law is proposed to learn the upper bound of the lumped uncertainties. With the advantages of RBFNN and ANTSM, the controller has high control accuracy, fast learning speed and finite-time convergence. Different from most on-ground robotic manipulator controllers, a kinematic controller with position and attitude control laws is also designed for the satellite platform to remain stable. The stability of the closed-loop system is proved by the Lyapunov method with a high mathematical standard. Comparative simulation results demonstrate the effectiveness of the proposed control scheme with preferable performance and robustness.

Bhutanese Pre-service Teachers’ Self-Efficacy Beliefs towards Teaching Secondary Mathematics

Prospective teachers’ self-efficacy beliefs determine the success of teaching and learning in their future professional practices. Teachers with high self-efficacy are believed to have more confidence and success in teaching as compared to those teachers with low self-efficacy. Thus, this study aimed at examining the Bhutanese pre-service teachers’ self-efficacy beliefs towards teaching secondary mathematics. The study employed a survey design within the positivist methodological framework. The study consisted of 81 pre-service teachers who responded to the secondary mathematics teachers’ self-efficacy beliefs questionnaire (SMTSEBQ), an abridged version of several past instruments. This instrument assessed their perceived self-efficacy in terms of process standards of school mathematics. Findings of the study revealed that the Bhutanese pre-service teachers generally perceived their self-efficacy beliefs towards teaching mathematics somewhat positively. Comparison of the pre-service teachers’ mean scores on the five SMTSEBQ scales in terms of gender revealed that there was a statistically significant difference for problem-solving and reasoning-proof scales. In regard to programme level, there was a statistically significant difference in their self-efficacy beliefs on the four scales, except for the communication scale. The study is distinctive because it is the first study investigating into the pre-service teachers’ self-efficacy beliefs towards teaching secondary mathematics in Bhutanese context.

Examining US elementary students’ strategies for comparing fractions after the adoption of the common core state standards for mathematics

Choosing appropriate strategies and implementing them correctly to solve problems are essential parts of mathematical reasoning. In this study, we examined 214 US fourth graders’ strategy choice and implementation when solving a fraction ordering task amenable to multiple strategies. The students used 12 distinct fraction comparison strategies. Of these, the rectangle model, butterfly, circle model, and common denominator strategies were used most frequently. Overall, visual strategies were more common than symbolic or verbal strategies, perhaps reflecting the emphasis on visual models in the US Common Core State Standards for Mathematics and textbooks. Students experienced a range of difficulties in implementing their chosen strategies. Only 28 % solved the focal problem correctly, and only 22 % provided both correct fraction order and correct justifications. The implications of students’ strategy choice and implementation for teachers, teacher educators, and researchers are discussed.

IS READING COMPREHENSION ASSOCIATED WITH MATHEMATICS SKILLS: A META-ANALYSIS RESEARCH

The literature on the association between reading comprehension and mathematics skills is complicated and conflicting. This study seeks to illuminate the nature of the association between mathematics skills and reading comprehension by incorporating potential moderators, namely components of mathematics skills, domains of content standards in mathematics, age, language status, and developmental issues. The dataset for this study included 49 studies with 91 correlation coefficients representing 37.654 participants. The findings obtained in this study showed that reading comprehension had a significantly strong effect on students’ mathematics skills. This association was moderated by components of mathematics skills, domains of content standards in mathematics, age, language status, and developmental issues. Moderation analyses revealed that problem-solving was the strongest moderator of the association between reading comprehension and mathematics skills, whereas spatial skills were the weakest moderator of this relationship. Based on domains of content standards in mathematics, geometry was the weakest moderator of the association between mathematics skills and reading comprehension. Moreover, the effects of reading comprehension on students’ mathematics skills significantly differed in favor of elementary students, students with learning disabilities, and second language learners. Therefore, this research can shed light on the literature by synthesizing the effects of reading comprehension on students’ mathematics skills.

Connection Quality Prediction and Nonlinear Control of Power Grid Communication Wireless Network

Learn about effective and uncontrolled gambling on wireless networks. Firstly, according to the control purpose, considering the reliability requirement of microgrid for network communication, the characteristics of wireless sensor network communication quality of service in microgrid, the influence of wireless connection reliability, and the mathematical standard of wireless communication are determined. Then, according to the estimation of the occurrence time of wireless communication link reliability, the reliability of wireless sensor network communication link in a smart grid is improved based on a fuzzy nonlinear control algorithm. Finally, the security and reliability of the control system described in this paper are measured by simulation. The experimental results show that the reliability of the wireless communication estimation time estimation algorithm and the power control algorithm based on fuzzy control can estimate the reliability, shortsightedness, and accuracy of good connections in real time. By adjusting the output power of the node, the connection quality and reliability can be controlled stably.

Language Demands Tool: Attuning Prospective Teachers’ Vision to the Role of Language in Mathematics Education

Mathematics standards and practices highlight the vital role that language plays in mathematics education. However, there remains a common misconception that mathematics is somehow language-free or less linguistically demanding than other content areas. This qualitative study describes an intervention implemented in six elementary mathematics methods courses. The intervention was designed to attune prospective teachers’ noticing to the language modalities and supports in mathematics teaching and learning. The intervention began with an observation tool that prospective teachers completed in their field placement classrooms. This article classifies prospective teachers’ noticings and explicates how these noticing became a pedagogical catalyst for further learning and discussion in subsequent mathematics methods classes.