Modeling, Symbolizing, and Tool Use in Statistical Data Analysis

In recent years there has been an increased focus on the need for teachers to develop learning communities where all students have opportunities to engage in interactive discourse. However, there are few studies that focus on student perceptions and accounts of mathematical reasoning in classrooms with interactive mathematical talk as a focus of reform. A framework of teacher actions to develop classroom and mathematical practices was developed from classroom observations. Photo-elicitation interviews were used to investigate student perception and accounts of mathematical explanations and reasoning. The professional development programme, shifts in the teacher actions, and subsequent shifts in student perception and their recall of their own and peers’ mathematical reasoning over a school year are highlighted. Developing interactive dialogue in the classroom took considerable time and attention. Facilitating change to the way students both participated and understood their obligations required constant, ongoing attention to both the classroom and mathematical practices.

An ongoing debate in education has centered on the concept of domain-general reasoning practices and whether such a position can explain how student learning in one discipline can influence their practices in another. For example, student learning in science impacts their learning in mathematics. Based on a model highlighting a significant relationship between reasoning practices used across science and mathematics, this study explored the lasting impact of learning science through the Science Writing Heuristics (SWH) approach on inductive and deductive reasoning in mathematics as well as deductive reasoning in science. Utilizing fourth-grade student data and follow-up data collected over three subsequent years, we applied the generalized DINA (deterministic inputs, noisy “and” gate) and linear regression models for analysis. The findings provide evidence of the immeote utilization of inductive reasoning in mathematics and a delayed advantage of deductive reasoning in both mathematics and science. These results support the implementation of argument-based approaches, like the SWH approach, on student development and utilization of domain-general reasoning. The findings of this study highlight the need for further research on the development of such reasoning resources when students are immersed in epistemically rich learning environments as proposed by national curricula. Additionally, further investigation is needed to determine whether these reasoning skills are applied across different disciplines, regardless of context.

This study focuses on weaving drafts as the core research subject, exploring their application value in the pattern arrangement principles of plane composition and instructional design. The research samples were selected from the Tie-ups in Straight Twill, Crepe, and Dice Weaves in The Weaver’s Book of 8-Shaft Patterns. A total of 55 samples were collected and analyzed. Threading draft and Treadling were used as structural references to examine the correspondence between the visual composition of weaving drafts and the arrangement in graphic design. The research methodology consists of two aspects. From the perspective of plane composition, seventeen compositional principles were applied to analyze pattern characteristics, including symmetry, rotation, displacement, translation, and black–white inversion. From the perspective of instructional design, this study investigates how weaving drafts can be transformed into teaching content for plane composition, constructing a framework for pattern analysis and teaching that can be applied in basic design courses. The results indicate that weaving drafts not only possess clear structural logic in weaving construction but also exhibit a high degree of visual order and formal aesthetics. Among the compositional principles, black–white inversion, translation, reflection, and rotation are the most frequently observed, demonstrating regularity, symmetry, and variation in pattern generation. Furthermore, weaving drafts can serve as concrete and systematic visual teaching materials in plane composition. Through the correspondence among Tie-ups, Threadling draft, and Treadling, students are able to better understand the relationship between abstract compositional principles and actual patterns, thereby enhancing their compositional ability and formal interpretation in graphic design.

We use a utility model to illustrate that, firstly, selecting an assessment method involves context-dependent compromises, and secondly, that assessment is not a measurement problem but an instructional design problem, comprising educational, implementation and resource aspects. In the model, assessment characteristics are differently weighted depending on the purpose and context of the assessment. Of the characteristics in the model, we focus on reliability, validity and educational impact and argue that they are not inherent qualities of any instrument. Reliability depends not on structuring or standardisation but on sampling. Key issues concerning validity are authenticity and integration of competencies. Assessment in medical education addresses complex competencies and thus requires quantitative and qualitative information from different sources as well as professional judgement. Adequate sampling across judges, instruments and contexts can ensure both validity and reliability. Despite recognition that assessment drives learning, this relationship has been little researched, possibly because of its strong context dependence. When assessment should stimulate learning and requires adequate sampling, in authentic contexts, of the performance of complex competencies that cannot be broken down into simple parts, we need to make a shift from individual methods to an integral programme, intertwined with the education programme. Therefore, we need an instructional design perspective. Programmatic instructional design hinges on a careful description and motivation of choices, whose effectiveness should be measured against the intended outcomes. We should not evaluate individual methods, but provide evidence of the utility of the assessment programme as a whole.

Mathematical computation and reasoning are the core of mathematics teaching and learning. It is important for students to put on their thinking caps instead of merely memorizing facts and figures. This study was conducted to investigate mathematical reasoning and mental computation proficiencies among primary school students in Malaysia. This outcome would depict students' ability, whether the reasoning is logical or merely applying formulas without making sense of it. Utilizing a descriptive correlational design, a total of 213 primary school students comprising Primary 5 and Primary 6 participated in the study. The findings of the study show both Primary 5 and Primary 6 students have a moderately high level of mental computation proficiency with scores of 15.36 and 22.9 respectively (from a maximum score of 30). On the other hand, students obtained a low-level proficiency in the mathematical reasoning test with scores of 14.83 (SD = 6.76) and 18.74 (SD = 6.45) for primary 5 students and primary 6 students respectively from a maximum score of 70. How well do current exams grades reflect the student's proficiency in mathematical reasoning? The outcome indicates that the school grades do not guarantee the ability to solve complex, mathematical problems, thus does not reflect their ability in mathematical reasoning and mental computational.

This research will be conducted at Yapim Pandan Private High School. Population is all data that concerns us in a scope and time that we determine. The purpose of this study was to determine the effect of the problem-solving learning approach on students' mathematical reasoning and communication skills on SPLDV material. Where the hypothesis of this study is that there is a significant effect of the problem-solving learning approach on students' mathematical reasoning and communication skills in SPLDV material in class X SMA Swasta Yapim Pandan. To achieve this goal, researchers first conducted a pre-test with the aim of knowing the initial ability of the experimental class (X IPA 1) and the control class (X IPA 2). The results showed that the design of the learning model that had been designed was good to use. By looking at the tcount value, it is concluded that there is a significant effect of the problem solving learning approach on students' mathematical reasoning and communication skills on SPLDV material in Class X SMA Swasta Yapim Pandan T.P 2019/2020. These results indicate that learning mathematics using a problem- solving learning approach is better than the conventional learning model on students' mathematical reasoning and communication skills on SPLDV material in Class X SMA Swasta Yapim Pandan T.P 2019/2020.

Purpose This study aims to examine the relationship between concrescent conversation environment (CCE), psychological safety and team effectiveness. Although CCE has been known to influence team outcomes, little is known about how it influences them. Integrating the social constructionist and social psychology perspectives, this study argues that CCE ignites a climate of psychological safety resulting in “joint-action” necessary for positive team outcomes. Design/methodology/approach Survey data were collected from 301 team members from US firms operating in different industries. Data were analyzed using SmartPLS. Findings The study establishes CCE as an antecedent to psychological safety and demonstrates that psychological safety mediates the relationship between CCE and team effectiveness. Research limitations/implications This is one of the initial studies to show how verbal behaviors socially construct team dynamics in the shape of psychological safety to influence team outcomes. In doing so, the authors advance the theory pertaining to the role of social exchanges in team processes and outcomes. Practical implications The results provide insights on how managers can improve team outcomes by influencing the conversational environment of the team to elicit feelings of psychological safety. The results also suggest that managers must focus on relational outcomes as well, along with performance outcomes. Originality/value From a social constructionist perspective, team development is built upon the verbal behaviors of the members as they pursue tasks. However, the extant group dynamics literature undervalues conversations’ role in team processes and outcomes. This is the first study that examines the link between a team's conversational environment, psychological safety and team outcomes.

The purpose of this study was to determine the effect of numerical intelligence on students' mathematical reasoning abilities, to determine the effect of interest in learning on students' mathematical reasoning abilities, to determine the influence of numerical intelligence and interest in learning on students' mathematical reasoning abilities. The method used in this study is quantitative with a correlation approach. The sample in this study were students of SMPN 13 Pesawaran class VIII who were randomly selected as many as 28 students. The instruments in this study were test and non-test instruments. The test instrument was used to measure students' numerical intelligence and mathematical reasoning in the form of 5 questions. The non-test instrument was used to measure students' interest in learning which consisted of 24 statements adopted from the research of Bagas Saputro (2017). Data were analyzed using simple correlation and multiple correlation. The results showed that; 1) There is no significant relationship between interest in learning and students' mathematical reasoning; 2) there is a significant relationship between numerical intelligence and students' mathematical reasoning; 3) there is a simultaneous relationship between interest in learning mathematics and numerical intelligence on mathematical reasoning, with a contribution of 68.4%.Keywords: Numerical intelligence, interest in learning, mathematical reasoning ability

The purpose of this chapter is to illustrate how Generative Artificial Intelligence (AI) can be leveraged to support high school students' mathematical reasoning through writing. Specifically, this chapter provides background information related to difficulties high school students with disabilities may experience in mathematics and writing and highlights how AI could be leveraged to address such challenges. In this chapter, we also describe an iterative process our research team used to develop a usable AI browser plugin to facilitate the argument and mathematics learning of high school students with learning challenges and report the preliminary results of studies we conducted to evaluate initial usability and efficacy of an intervention utilizing the AI plugin on students' mathematical reasoning and argumentative mathematical writing. We also discuss implications for practice for teachers, teacher educators, and instructional designers and present recommendations for future research in this area.

With most academic instructional design and technology (IDT) degree programs located within education units in higher education, teacher education is a focal point for research on the classroom teacher as instructional designer and implementer of technology in K-12. Further, teacher education serves as a locus for modelling and testing theory-based teaching practice arising from the discipline. This review examines the historical foundations and recent scholarship in teacher education from an instructional design and technology perspective in US and international contexts, providing a lens to the issues of theory versus practice and evolving research paradigms. Research areas reviewed include teacher thinking and planning, novice versus expert teacher differences, the use of systematic instructional design in classroom practices, and the teacher as designer of instructional materials. Changing research approaches and constructivist philosophies have widened the understanding of teacher instructional planning and action from earlier process–product causation to a more complex, situated view of practice. From an examination of the uneasy relationship between the two disciplines, prospects for future cooperation and research are explored in terms of theory building, impacts on training, debates on the nature of design practice, and potential for shaping educational reform efforts.

This study aims to determine the relationship between the skill of weaving various types of rattan woven motifs with the ability of mathematical logical thinking of students in schools around the Galmantro Rattan Tourism Village of Cirebon Regency. The method used is a quantitative research method with a One-Shot Case Study research design. Data collection techniques used in the form of observation, tests, and questionnaires. The results of this study are (1) during the training, the respondents felt interested in knowing how to weave and the types of woven motifs for rattan crafts because in reality the respondents had never tried directly to weave rattan woven motifs; (2) based on the correlation coefficient test between weaving skills and the mathematical logical thinking test the t and t_table test values are 7.711 more than 2.045, so that the two variables have a significant relationship with the relationship level of 0.599 in the medium category. Keywords: weaving skills, woven motifs, mathematical logical thinking

The purpose of this study is to describe and generate interaction model of learning through Elip – Marc activity via TPS cooperative learning in order to improve student’s mathematical reasoning who have valid, practical and effective criteria. “Elip - Marc” is an acronym of eliciting, inserting, pressing, maintening, reflecting and confirming, an activity in the learning process have aim to improve student’s mathematical reasoning. So there are three types product are developed, namely: (1) The interaction learning model, as a conceptual framework and a reference in developing the supporting device. (2) The learning device, for carrying out teaching methods and to measure the practicality and effectiveness of the interaction model and (3) The research instrument to assess the quality of the model and the device. All products are Elip-Marc activity oriented and supported by worksheet with RAT (Reasonable Answer Test) format. All products are declared valid as constructs and content by expert validator. Practicality and effectiveness criteria of the product conducted in even cemester at 2014-2015 by implementation interaction model on eight grade students of ‘SMP Negeri 3 Kepanjen” Malang East Java, Indonesia on the material “Problem solving about three dimension spaces”. By Analysis of the teacher’s Elip-Marc activity and the response of student’s in the learning process obtained conclusions that interaction model is practical and effective, so can improve student’s mathematical reasoning as the intervention results in desired outcomes. So, If (1) the teacher is pleased to be patient and persistent engage students in the learning process through Elip-Marc activities, (2) and supported by the task of “word problems” challenging (3) and motivated by the question that digging (Prompting Questions) and guided (Probing Question), (4) and provide students the necessary scaffolding, (5) and provide space whorksheet adequate workplace, (5) and following the RAT steps, students were motivated to improve mathematical reasoning. However, the authors suggest that the results of this study can be adapted to the other materials in mathematics learning, and hope a lot of teacher willing to implement this model interaction.

This JiM project set out to research the current state of understanding of mathematical justification by both Singapore secondary school students and Mathematics teachers across the different content strands in the Singapore secondary Mathematics curriculum. This timely and relevant project was started to complement the current goal of the Ministry of Education (MOE) on fostering reasoning in the learning of Mathematics in schools. While MOE focuses on the reasoning process, our study examined the outcomes of this reasoning process. For many years, mathematical reasoning and communication have been two key process skills in the Singapore Mathematics Framework under the Processes component. Thus, mathematical reasoning and justification are essential components of any mathematical activity that students should be familiar with. Yet from our personal communications with secondary school mathematics teachers between 2013 and 2016 and evidence from GCE O and N Level examiners' reports, we obtained the impression that many students, as well as mathematics teachers, struggled to navigate mathematical justification successfully. Mathematics teachers seemed to point students' difficulties in justification to several student-related factors. Other than those factors, we, however, speculated that there might be other potential obstacles, which contribute to students' poor performance in justification tasks. Therefore, this JiM project was undertaken to explore the quality of written justifications constructed by secondary school students and their mathematics teachers, with the aim of proposing a professional development (PD) programme that would allow the teachers to better engage their students in mathematical reasoning and justification more effectively, thereby improving the quality of written justifications provided by their students.

The purpose of this qualitative case study is to examine the use of TPACK and Twitter in an graduate level online course. The overarching research question is, “How is social media, in particular, Twitter, being used in an online graduate course?” This study uses the technological pedagogical content knowledge (TPACK) framework to provide a common language for describing the use of Twitter from an instructional design and research perspective. Data collection included (a) conversational and interactive dialogue between the researchers that included the instructional designer/course instructor, (b) the archived online course, and (c) the class Tweets (from Twitter) identified with class hashtags. Through collaborative autoethnography, the researchers (a) analyzed the instructional designer’s (also course instructor) practices, contextualizing TPACK principles for the design of the online course learning objectives and Twitter activities, and (b) engaged in an in-depth analysis of students’ tweets. Major themes identified are (a) TPACK framework explicitly supported online course design using Twitter, (b) facilitated fluency for technology integration, (c) promoted consciousness and reflection, (d) enhanced transfer of knowledge, and (e) heightened presences (cognitive, social, and teaching). One primary implication is that using TPACK for instructional design can create a common vocabulary and understanding for educators, instructional designers, and researchers.

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsM. Cathleen GardillAsha K. Jitendra is an assistant professor in the Special Education Program at Lehigh University. M. Cathleen Gardill is a research assistant in the Special Education Program at Lehigh University.