NCTM Standards Research Articles

Pengaruh Gaya Belajar Terhadap Kemampuan Penalaran Matematis Siswa SD 5 Mejobo

This research aims to examine the influence of learning styles on students' mathematical reasoning abilities at SDN 5 Mejobo. The learning styles studied include three main categories, namely auditory, kinesthetic and visual. Mathematical reasoning abilities are measured through tests that cover various aspects of reasoning such as identifying patterns, making generalizations, and solving mathematical problems logistically. This research uses quantitative methods with a survey approach. The research population was all 6th grade students at SDN 5 Mejobo, totaling 12 students, and the entire population was used as a sample population using saturated sampling techniques. Data was collected through a learning style questionnaire adapted from the VARK model and a mathematical reasoning test that refers to NCTM standards. Data analysis was carried out using regression and correlation analysis techniques with the help of SPSS software. The research results show that learning style does not have a significant influence on students' mathematical reasoning abilities (value 0.030 > 0.05). These findings indicate that individuals' learning style preferences do not determine their mathematical reasoning abilities. Therefore, it is recommended that other factors such as teaching methods, learning motivation, and learning environment be considered in an effort to strengthen students' mathematical reasoning abilities. It is hoped that this research will provide insight into the development of learning strategies that are more efficient and meet student needs.

The Effect of Training Program Based on Instructional Practices According to the (NCTM) Standards on Improving the Pedagogical Knowledge among Mathematics Teachers in Jordan

The current study aims at revealing the effect of a training program based on teaching practices according to NCTM standards in improving the pedagogical knowledge of mathematics teachers. The study followed the semi- experimental method. To achieve the aims of the research, a training program that is based on the standards of NCTM was designed. The program consists of eight packages which are (Establish mathematics goals to focus learning, implement tasks that promote reasoning and problem solving, Use and connect mathematical representations, facilitate meaningful mathematical discourse, pose purposeful questions, build procedural FLuency from conceptual understanding, support productive struggle in learning mathematics, Elicit and use evidence of student thinking). After confirming the validity of the tool, a sample of (20) male and female teachers from Deir Ala Directorate of Education in the academic year 2020-2021.To reveal the effectiveness of the program, a test in pedagogical knowledge was prepared. The test consists of six respects which are identification of mathematics content, the pedagogical knowledge of the mathematical content and knowing students' thinking. The test validity and reliability were checked. The results of the study showed that there were statistically significant differences between measuring averages in the post application of the test. These results were pro- sample in all dimensions and in the total degree. Depending on these results, the study asserted the necessity for the training department in the Jordanian Ministry of Education to benefit from the suggested and used program in the study to focus more on the teaching practices.

Examination of the Interactive Digital Mathematics Games According to NCTM Standards

This study aimed to examine the interactive digital games that are open to access at the secondary education level on the Education Informatics Network [EIN] platform according to NCTM standards. 20 interactive mathematics games that are open to access on the EIN platform have been reached. Accessed games were analysed descriptively with a code book developed by Joung and Byun (2021) based on the NCTM Content and Process Standards. According to the results of the study, it was determined that the majority of the games are focused on the Numbers and Operations. All of the games targeted fifth and sixth graders, and no games were included for probability domain. Geometry has the highest mean scores for content standards while algebra has the lowest. Games related to geometry, measurement, and numbers exhibit a moderate degree of alignment with the underlying content domains, whereas games centered on data and algebra show a relatively weaker correspondence between the content and the contextual aspects of the game. On the other hand, as for the process standards, algebra has the highest mean scores while geometry and numbers have the lowest mean scores. Highest mean scores for process standards belong to problem solving for data, reasoning and proof for measurement, connections for data and algebra, representations and communication for algebra. Among the process standards, reasoning and proof, and communication were represented with the lowest means for all domains. Considering the results it is advisable to revise digital interactive mathematics games to meet the content and process standards.

Augmented reality applications for mathematical creativity: a systematic review

AbstractAugmented reality (AR) applications are often studied in education. However, little literature has systematically reviewed the applications of AR for mathematical creativity. This paper aims to analyze the research trends comprehensively and systematically on 66 articles from 2015 to 2023. Based on the NCTM Principles and Standards guidelines, trends in the application of AR in mathematics education can be analyzed into six themes: equity, mathematics curriculum, mathematics teaching, learning, assessment, and mathematics technology. The results of the study show that (1) AR for mathematical creativity has implications for improving students' cognitive performance; problem-solving process; self-potential; social skills, and self-ability of students; (2) the most dominant features in developing AR applications for mathematical creativity are the Unity3D tool and Vuforia; (3) AR has a positive impact on equity for improving the quality of teaching and learning, supporting the educational curriculum; improve the teaching and learning of mathematics; effective evaluation and technology development in the learning process; (4) AR as a creative learning media; AR helps creative collaboration between students; and able to improve students' creative thinking skills. The results of a systematic review of AR applications for mathematical creativity can help educators and the development of future educational research.

The Compatibility of Developed Mathematics Textbook Content in Saudi Arabia with NCTM Standards: A Critical Review

The Compatibility of Developed Mathematics Textbook Content in Saudi Arabia with NCTM Standards: A Critical Review

Evaluation of Primary School Mathematics Curricula of Northern and Southern Cyprus for NCTM Principles and Standards

Evaluation of Primary School Mathematics Curricula of Northern and Southern Cyprus for NCTM Principles and Standards

Visions of the Possible: Using Drawings to Elicit and Support Visions of Teaching Mathematics

Mathematics Teacher Educators (MTEs) help preservice teachers in transitioning from students to teachers of mathematics. They support PSTs in shifting what they notice and envision to align with the collective vision encoded in the AMTE and NCTM standards. This study analyzes drawings and descriptions completed at the beginning and end of a one-year teacher education program—snapshots depicting optimized visions of teaching and learning mathematics. This study analyzed drawings-and-descriptions by cohort and by participants. The findings suggest that the task can be used as formative assessment to inform supports for specific PSTs such as choosing a cooperating teacher or coursework that challenges problematic beliefs. It can also be used as summative assessment to inform revision of coursework for the next cohort.

Then: Transparency in My Mathematics Classroom

Transparencies were commonplace in the 1980s when the first NCTM Standards were released. This article reflects on how the use of an overhead projector and transparencies helped to enact the Process Standards - and make the real purpose of learning mathematics more transparent to students.

In-Service and Pre-Service Special Education Teachers’ Perception of NCTM Standards: Implications for Professional Development

Special Education teachers face increasing difficulties when teaching students with Mathematical learning disorders. The purpose of this study was to investigate whether special education pre-service and in-service teachers in a university in the Middle East are receiving proper training to deal with students with disabilities in learning mathematics. A 24-item self-developed questionnaire was distributed to a sample of 95 (N=95) special education pre-service and in-service teachers. The analysis of the data revealed that pre-service teachers had not accomplished sufficient competency in any of the NCTM standards that are necessary for providing meaningful and useful learning experiences to their future students. However, the analysis of the data revealed that in-service teachers had sufficient competencies in all NCTM standards. These results help to contribute in informing the design and implementation of teacher education programs. Implications of these findings are further discussed along with recommendations for further development within the teacher education program for special education teachers.

NCTM’s Principles and Standards for Developing Conceptual Understanding in Mathematics

The purpose of this study is to develop understanding of concepts in mathematics through the application of the NCTM's Principles and Standards. This research method is descriptive. The results obtained are understanding concepts in mathematics can be developed through the application of NCTM Principles and Standards consisting of 6 principles, namely: 1. Equity, 2. Curriculum, 3. Teaching, 4. Learning, 5. Assessment, and Technology. Understanding concepts in mathematics that can be developed are: a. defining concepts verbally and in writing, b. Make examples and not examples, c. Using various symbols to present a concept, d. Change the form of representation to various forms, e. Identifying the characteristics of a concept, f. compare various concepts, and g. interpret concepts.

A review of research on affect of elementary prospective teachers in university mathematics content courses 1990–2016

AbstractThe purpose of this study was to review the existing research on affect (beliefs, attitudes, and emotions) of elementary prospective teachers (EPTs) in university mathematics content courses. We use as our time period from publication in the United States of the Curriculum and Evaluation Standards for Schools Mathematics through 2016. A search of a combination of electronic databases and targeted international journals resulted in a total of 11 studies that looked at some aspect of affect with EPTs in all or some part of a university mathematics course over the 27‐year time period. Nine of the 11 studies occurred in the context of a course or courses categorized as involving an alternative pedagogy that was student‐centered. Overall we found that a student‐centered approach to instruction supported changes in EPTs’ affect that align with pedagogical recommendations in reform documents such as the NCTM Standards. However, shifts were sometimes difficult to come by and encountered resistance from EPTs. Implications for course learning experiences are offered and conflicting results between studies suggest directions for future research.

A Guide to Analyzing Mathematics Tasks and Their Implementation in Curriculum Resources

Since the publication of the NCTM Standards in 1989, which was followed by a new generation of curriculum development projects, the field has seen increasing interest in research on curriculum resources, how they are used by teachers and experienced by students, and the outcomes that they produce. Although some studies seek to draw direct lines between particular curriculum materials used and student outcomes, a majority of researchers argue that understanding whether and how teachers are implementing a given written curriculum resource1 with some measure of fidelity is necessary to determining its effects on learning (Stein, Remillard, & Smith, 2007). Over the last 2 decades, research has expanded to consider how teachers interpret, learn from, interact with, and generate curriculum resources. Over a similar timespan, the number and types of curriculum resources available to teachers have also expanded to include print, digital, and blended comprehensive curricula along with a slew of supplemental resources and tools available through the Internet.

The Idea Man: An Interview with Lynn Steen

SummaryAn interview with Lynn Arthur Steen, this article questions this consummate idea man about his childhood, editing MATHEMATICS MAGAZINE with Arthur Seebach, being a member of the St. Olaf Math Department through its period of phenomenal growth, serving as MAA President, being on the front lines of math education—writing and being involved in the conversations about the NCTM Standards and Quantitative Literacy, and also commenting on what he sees as the most important issue facing the MAA today.

Promoting Risk Taking in Mathematics Classrooms: The importance of Creating a Safe Learning Environment

Do the one thing you think you cannot do. Fail at it. Try again. Do better the second time. The only people who never tumble are those who never mount the high wire. This is your moment. Own it.-Oprah WinfreyRisk abounds in our everyday life and workplace. Risk can delight, annoy and engage us. As the above quote suggests people need to be aware of the importance of risk taking. Notions of risk appear in various messages that we encounter such as when receiving forecasts of medical, financial or environmental risks from media research reports and public officials. In such situations, we have to make decisions in the presence of conflicting goals and constraints (Schlottmann & Wilkening, 2011; Shapira, Nattinger, & McHomey, 2001). In recent times, risk taking and risk-aversion has drawn increased attention of educators and researchers for a range of reasons (Anthony & Walshaw, 2007; Fesser, Martignon, Engel & Kuntze, 2010; Martignon & Kurz-Milcke, 2006; Till, 2014). These include recognition of its importance for solving differences and reaching consensus, as well as its central role in thinking and making infonned decisions (Gaissmaier & Gigerenzer, 2008; Galesic & Garcia-Retamero, 2010; Martignon & Krauss, 2009; Schlottmann & Wilkening, 2011). Indeed, to learn and grow people must take risks, but most people will not take risks in an emotionally unsafe environment.Moreover, there has been significant shifts in the way teaching and learning of mathematics is conceptualised internationally. The American policy document, Principles and Standards for School Mathematics states that if students are to learn to construct mathematical arguments and respond to arguments, then creating an environment that fosters these kinds of activities is essential (National Council of Teachers of Mathematics, 2000, p. 18). This reform teaching aligns with vision promoted by NCTM's Professional Teaching Standards (National Governor's Association for Best Practices and Council of Chief State School Officers. 2010) that encourages students to communicate mathematical ideas and nurtures intellectual risk-taking by students. However, reasoning at complex cognitive levels and risk taking through mathematical discourse is not something many students are able to achieve easily without adult mediation (Anthony & Walshaw, 2007; Cobb & McClain, 2004; French, 2009; Hunter, 2010).While there has been ample discussion of students at risk (Clark, 2001; Franco, Sztajn, & Ortigao, 2007; Lubienski, 2007; Winsor, 2007), mathematics education at risk, and nations at risk (Center for the Study of Mathematics Curriculum, 2005; Nasir,, Hand, & Taylor, 2008; Wagner, 2008), risk assessment (Gigerenzer, 2002; Gigerenzer, Gaissmaier, Kurz-Milcke, Schwartz, & Woloshin, 2009; Martignon & Krauss, 2009), there has been limited discussion of students' willingness to take risks in mathematics classrooms where they are asked to solve open-ended tasks (Lubienski, 2007; Sullivan, Mousley, & Zevenbergen, 2006). Individuals who have different perceptions of risk are more or less likely to do well in these environments (Clifford, 1991; Hills, Stroup, & Wilensky, 2005). It follows that learning environments must take into account individual student's and teachers' risk-taking or risk-averse behaviours. There is very little research on students' mind-sets and motivation for risk tolerance in mathematics education. In 2010, for the first time, risk was included in a session of the ICOTS, as a topic for instruction in school in connection with statistics education (Fesser et al., 2010).This paper describes some research-based ideas for promoting risk taking behaviours in a mathematics classroom. It presents interactional pedagogical strategies from a design collaborative research (Sharma et al., 2011) conducted at one secondary school. As part of the learning activities, students critically evaluated statistical investigations undertaken by others (Ministry of Education, 2007). …

Learning Contents of Spatial Thinking in Geometry Curriculum: Through Comparison with NCTM Standards and Common Core State Standard for Mathematics

Learning Contents of Spatial Thinking in Geometry Curriculum: Through Comparison with NCTM Standards and Common Core State Standard for Mathematics

How Common Is the Common Core?

This article identifies major differences between NCTM's Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics, including examples and implications for practice.

Connecting Mathematical Reasoning and Language Arts Skills: The Case of Common Core State Standards

Many relationships exist between language arts and mathematics. These relations become apparent in NCTM's process standards (2000). McIntosh, (1991) emphasized the importance of using various language art skills to enhance mathematics learning. Curriculum standards have potential to show teachers the possible ways and targeted objectives of a content area (Clements et al., 2009). As a result, in this study through content analyses of Common Core State Standards- English Language Arts (CCSS-ELA) we aim to identify potential contribution of the targeted objectives and skills mentioned in ELA standards K-2 to children's mathematical reasoning and practices. Results of the study indicate that language art standards emphasize the importance of using the tools such as communication, multiple representation and understanding in mathematical reasoning.

All hands on deck!

Math by the Month is a regular department of the journal, featuring collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes at least four activities each for grade bands K–2, 3–4, and 5–6. In the current issue, the problems are designed to actively engage your students in a literacy-rich mathematics environment, which is recommended by the NCTM Principles and Standards and the Common Core State Standards in Mathematics.

A NEW AGE IN MATHEMATICS EDUCATION IN THE U.S.: INTERPRETING THE COMMON CORE STATE STANDARDS FOR MATHEMATICS

For the first time ever in its history, the United States has a national version for K-12 mathematics programs, the Com-mon Core State Standards for Mathematics. Since its final version appeared in 2010 in the United States, the Common Core State Standards have started getting much attention from the Korean mathematics and mathematics education communities. Although attempts have been made to translate the original text of the stan-dards, the information such as the paradigm shift that led to the development of the standards, design principles and a comparison with the NCTM Standards would aid understating the standards in the intended way and avoiding unnecessary confusion.

Supporting students’ strategic competence: a case of a sixth-grade mathematics classroom

Mathematics education research has documented several classroom practices that might influence student self-regulation. We know little, however, about the ways these classroom practices could be structured in real classroom settings. In this exploratory case study, we purposefully selected a sixth-grade mathematics teacher who had participated in a professional development program focussed on NCTM standards and SRL in the mathematics classroom for extensive classroom observation. The purpose was to explore how and to what extend she structured classroom practices to support strategic competence in her students. Four features of classroom practices were found as evidence for how strategic competence was potentially supported in this classroom: (a) allowing autonomy and shared responsibility during the early stages of learning, (b) focusing on student understanding, (c) creating contexts for students to learn about strategic learning and to exercise strategic behaviour, and (d) helping students to personalise strategies by recognising their ideas and strategic behaviours.