scholarly journals Building on student mathematical thinking in whole-class discourse: exploring teachers’ in-the-moment decision-making, interpretation, and underlying conceptions

2021 ◽  
Author(s):  
Chris Kooloos ◽  
Helma Oolbekkink-Marchand ◽  
Saskia van Boven ◽  
Rainer Kaenders ◽  
Gert Heckman
Keyword(s):  
Decision Making ◽  
Mathematics Teachers ◽  
Teaching Practice ◽  
Mathematical Thinking ◽  
Student Understanding ◽  
Student Thinking ◽  
Solution Methods ◽  
Whole Class ◽  
The Moment ◽  
Class Discourse

AbstractOften, mathematics teachers do not incorporate whole-class discourse of students’ various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students’ thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students’ various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers’ in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers’ decision-making was shaped by the teachers’ own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals.

Would you Make the Right Decision? – Decision Making Biases in Economy - Related Dilemmas

2018 ◽  
Vol 9 (1) ◽  
pp. 59-66
Author(s):  
Zsuzsanna Gödör ◽  
Georgina Szabó
Keyword(s):  
Decision Making ◽  
Online Survey ◽  
Framing Effect ◽  
Economic Knowledge ◽  
Bank Account ◽  
Financial Decisions ◽  
Hungarian Population ◽  
The Moment ◽  
The Right ◽  
Decision Making Biases

Abstract As they say, money can’t buy happiness. However, the lack of it can make people’s lives much harder. From the moment we open our first bank account, we have to make lots of financial decisions in our life. Should I save some money or should I spend it? Is it a good idea to ask for a loan? How to invest my money? When we make such decisions, unfortunately we sometimes make mistakes, too. In this study, we selected seven common decision making biases - anchoring and adjustment, overconfidence, high optimism, the law of small numbers, framing effect, disposition effect and gambler’s fallacy – and tested them on the Hungarian population via an online survey. In the focus of our study was the question whether the presence of economic knowledge helps people make better decisions? The decision making biases found in literature mostly appeared in the sample as well. It proves that people do apply them when making decisions and in certain cases this could result in serious and costly errors. That’s why it would be absolutely important for people to learn about them, thus increasing their awareness and attention when making decisions. Furthermore, in our research we did find some connection between decisions and the knowledge of economics, people with some knowledge of economics opted for the better solution in bigger proportion

Equitable Teaching and the Core Practice Movement: Preservice Teachers’ Professional Reasoning

2020 ◽  
Vol 122 (11) ◽  
pp. 1-40
Author(s):  
Britnie Delinger Kane
Keyword(s):  
Teacher Education ◽  
Preservice Teachers ◽  
Student Teacher ◽  
Teacher Educators ◽  
Design Research ◽  
Teaching Practice ◽  
Student Thinking ◽  
The Core ◽  
Collaborative Analysis ◽  
Core Practice

Background/Context The Core Practice movement continues to gain momentum in teacher education research. Yet critics highlight that equitable teaching cannot be reduced to a set of “core” practices, arguing that such a reduction risks representing teaching as technical work that will be neither culturally responsive nor sustaining. Instead, they argue that preservice teachers need opportunities to develop professional reasoning that takes the specific strengths and needs of students, communities, and subject matter into account. Purpose This analysis takes up the question of how and whether pedagogies of investigation and enactment can support preservice teachers’ development of the professional reasoning that equitable teaching requires. It conceptualizes two types of professional reasoning: interpretive, in which reasoners decide how to frame instructional problems and make subsequent efforts to solve them, and prescriptive, in which reasoners solve an instructional problem as given. Research Design This work is a qualitative, multiple case study, based on design research in which preservice teachers participated in three different cycles of investigation and enactment, which were designed around a teaching practice central to equitable teaching: making student thinking visible. Preservice teachers attended to students’ thinking in the context of the collaborative analysis of students’ writing and also through designed simulations of student-teacher writing conferences. Findings/Results Preservice teachers’ collaborative analysis of students’ writing supported prescriptive professional reasoning about disciplinary ideas in ELA and writing instruction (i.e., How do seventh graders use hyperbole? How is hyperbole related to the Six Traits of Writing?), while the simulation of a writing conference supported preservice teachers to reason interpretively about how to balance the need to support students’ affective commitment to writing with their desire to teach academic concepts about writing. Conclusions/Recommendations This analysis highlights an important heuristic for the design of pedagogies in teacher education: Teacher educators need to attend to preservice teachers’ opportunities for both interpretive and prescriptive reasoning. Both are essential for teachers, but only interpretive reasoning will support teachers to teach in ways that are both intellectually rigorous and equitable. The article further describes how and why a tempting assumption—that opportunities to role-play student-teacher interactions will support preservice teachers to reason interpretively, while non-interactive work will not—is incomplete and avoidable.

Efficient Treatment of Gyroscopic Bodies in the Recursive Solution of Multibody Dynamics Equations

2008 ◽  
Vol 3 (4) ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Center Of Mass ◽  
Solution Process ◽  
Body System ◽  
Efficient Treatment ◽  
Composite Body ◽  
Recursive Solution ◽  
System A ◽  
Principal Axes ◽  
Solution Methods ◽  
The Moment

This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an N-body system. The bodies of interest include the reaction wheels in satellites, wheels on a car, and flywheels in machines. More specifically, these bodies have diagonal inertia tensors. They spin about one of its principal axes, with the moment of inertia along the transverse axes identical. Their center of mass lies on the spin axis. Current recursive solution methods treat these bodies identically as any other body in the system. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the order(N−m) where m is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.

scholarly journals The Decision-Making Process and the Construction of Online Sociality through the Digital Storytelling Methodology

Electronics ◽  
2021 ◽  
Vol 10 (20) ◽  
pp. 2465
Author(s):  
Pierpaolo Limone ◽  
Giusi Antonia Toto ◽  
Barbara Cafarelli
Keyword(s):  
Decision Making ◽  
Online Teaching ◽  
Digital Storytelling ◽  
Teaching Practice ◽  
Social Consequences ◽  
Teaching Methodology ◽  
Self Assessment ◽  
Emotional Involvement ◽  
Choice Phase ◽  
Group Thinking

Digital storytelling (DST) is a teaching methodology (and tool) that is very widespread in different types of training: formal and informal, professional, and for adults. Presently, education is evolving and moving towards digital storytelling, starting from the models of Lambert and Olher. Today, although DST is usually used in the training that students receive for narrative learning, experimentation on the psychological and social consequences of this online teaching practice is still scarce. The literature acknowledges the widespread use of DST online, from psychology to communication and from marketing to training, providing Lambert’s and Olher’s models as references. Thus, the purpose of experimentation in this subject has been to try to mix these two models by selecting the phases of the model that focus most on creativity and narrative writing. The purpose of this study is to illustrate the experimentation conducted in the initial training of teachers to monitor the processes of negotiating content, making decisions and building a group atmosphere through the use of a narrative technique in an educational context. The sample was offered comprehension activities on narrative categories, creativity and autobiographical writing. The process in the group choice phase (negotiation) of the story was monitored through a questionnaire that includes three scales (the Melbourne Decision Making Questionnaire, Organisational Attitude, and Negotiations Self-Assessment Inventory). The study concluded that the standardised planning of activities that, to a greater degree of depth, promote participation and emotional involvement allows the creation of strong group thinking and affects the decision-making and negotiation processes of the activities being carried out by the participants.

scholarly journals The Effect of Problem Solving Course on Pre-Service Teachers’ Beliefs about Problem Solving in School Mathematics and Themselves as Problem Solvers

2018 ◽  
Vol 12 (2) ◽  
pp. 141-159
Author(s):  
Ljerka Jukić Matić
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Teaching Practice ◽  
School Mathematics ◽  
Small Scale ◽  
Heuristic Strategies ◽  
Teachers Beliefs ◽  
Before And After ◽  
Problem Solvers ◽  
Positive Effect

Problem solving in schools begins with mathematics teachers. The degree to which mathematics teachers are prepared to teach for, about and through problem solving influences on their implementation of problem solving in school. We conducted a small scale study where we examined the effect of implementation of heuristic strategies and Polya’s steps in mathematics method course. We assessed pre-service teachers’ knowledge and attitudes about them as problem solvers before and after the course. Moreover we assessed their beliefs of problem solving in school mathematics. Those beliefs were assessed in two occasions: right after the course and after finished teaching practice. Although students’ knowledge on problem solving was improved, the results of students’ beliefs show that it is important that pre-service teachers, and consequently in-service teachers, are constantly reminded on the positive effect of constructivist and inquiry-based approach on teaching mathematics.

scholarly journals VALIDATION OF MATHEMATICS TEACHING PRACTICE INSTRUMENTS AMONG SECONDARY SCHOOL MATHEMATICS TEACHERS: EXPLORATORY FACTOR ANALYSIS (EFA)

2020 ◽  
Vol 5 (36) ◽  
pp. 56-69
Author(s):  
Norkumalasari Othman ◽  
Nor Hasnida Che Md Ghazali ◽  
Mohd Nazir Md Zabit
Keyword(s):  
Factor Analysis ◽  
Secondary School ◽  
Mathematics Teachers ◽  
Mathematics Teaching ◽  
Teaching Practice ◽  
School Mathematics ◽  
Chi Square ◽  
Secondary School Mathematics ◽  
Bartlett Test ◽  
Value Measure

This study aims to review the instruments of mathematics teaching practice among secondary school mathematics teachers. A total of 100 mathematics teachers were involved as respondents in this study. The data were analyzed descriptively by access to Alpha Cronbach's reliability and EFA analysis using SPSS software. The results of the analysis show that the Alpha Cronbach value is 0.934 which is more than 0.60. Results from the exploration factor analysis show four factors with Eigenvalues greater than 1.0. The KMO value (Kaiser-Meyer-Olkin) 0.867 > 0.6 indicates the items in the variable of attitude towards math are sufficient for inter-correlation. While the Bartlett Test was significant (Chi-Square 1521.621, p <0.05), an anti-image value (Measure of Sampling Adequacy, MSA) for items correlation exceeded 0.6. However, there are three items that need to be removed because the values obtained are less than 0.60, which were the items G11, G14, and G18. The value of the total variance explained by these three factors was 62.76 percent. Therefore, the overall findings indicate that the items for mathematics teaching practice instruments can measure and answer the study objectives.

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