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How We Think: A Theory of Goal-Oriented Decision Making and its Educational Applications
Abstract and Figures
Teachers try to help their students learn. But why do they make the particular teaching choices they do? What resources do they draw upon? What accounts for the success or failure of their efforts? In How We Think, esteemed scholar and mathematician, Alan H. Schoenfeld, proposes a groundbreaking theory and model for how we think and act in the classroom and beyond. Based on thirty years of research on problem solving and teaching, Schoenfeld provides compelling evidence for a concrete approach that describes how teachers, and individuals more generally, navigate their way through in-the-moment decision-making in well-practiced domains. Applying his theoretical model to detailed representations and analyses of teachers at work as well as of professionals outside education, Schoenfeld argues that understanding and recognizing the goal-oriented patterns of our day to day decisions can help identify what makes effective or ineffective behavior in the classroom and beyond.
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... A widely accepted definition of a mathematical problem is one where the procedure for solving the task is unknown to the solver, the number of solutions is uncertain, and the task requires critical thinking [40]. This definition underscores the significance of fostering problem-solving abilities in students. ...
... The studies indicate that contextual learning strategies significantly enhance students' conceptual understanding in trigonometry [23]. Furthermore, as part of the CMMI, research emphasizes that effective mathematics instruction should actively engage students in problem-solving, reasoning, and the construction of mathematical knowledge [40]. This approach not only fosters a deeper understanding of mathematical concepts but also equips students with essential skills for applying mathematics in real-world situations. ...
... This finding indicates that the Contextual Mathematical Modeling instructional practice is notably important for the improvement of student`s problem solving abilities compared to the traditional instructional approach in learning trigonometry. This result aligns with previous research findings that reveal the CMMI approach significantly enhances students' trigonometric problem-solving performance [40]. Effective mathematics instruction also fosters students' problem-solving abilities [3]. ...
Trigonometry is a crucial topic in high school mathematics that significantly influences students' understanding and problem-solving skills. However, many students face challenges in this area after traditional instructional approaches. By employing a context-based mathematical modeling instructional approach, educators can make trigonometry lessons more meaningful and relevant to students' lives, effectively connecting the academic content to their real-world experiences and contexts. This study aimed to investigate the impact of context-based mathematical modeling instructional approach on secondary school students’ conceptual understanding and problem-solving skills in trigonometry. A quasi-experimental non-equivalent pretest, posttest control group design involving 97 Grade 10 students from two separate schools in Bahir Dar City, Ethiopia was employed. The students’ conceptual understanding and problem-solving skills were assessed before and after the intervention using a trigonometric concept test and problem-solving tasks developed by the researchers and field experts. The collected data were analyzed using independent, paired sample t-tests and analysis of covariance (ANCOVA). The findings indicated that the treatment group, which participated in the context-based mathematical modeling instructional approach, showed significant improvements in understanding and solving real-life trigonometric concepts and problems compared to the control group. This contextualized approach, supported by effective teacher training and the strategic use of readily available materials significantly enhanced students' conceptual understanding of trigonometry, problem-solving skills, and their ability to apply these concepts to real-world situations. These results suggest that accessible resources, combined with effective instructional delivery, are essential factors in improving mathematics learning outcomes.
... We adopted two theoretical perspectives to study the core practice of prospective teacher learning of task modification: Schoenfeld's resources-orientations-goals (ROG) model of teacher decision-making (Schoenfeld, 2010); and inquiry-based teaching principles in mathematics education as a conceptual tool to support prospective mathematics teachers' reasoning (Artigue & Blomhøj, 2013;Dorier & Maass, 2020). ...
... Depending on a mathematical task's characteristics, students either perform a routine procedure or their thinking is stimulated, as they must search for connections between mathematical concepts and properties when faced with non-routine problems (Artigue & Blomhøj, 2013;Stein & Smith, 2011). Therefore, modifying tasks to enhance students' mathematical thinking can be regarded as a mathematics professional teaching problem (Schoenfeld, 2010(Schoenfeld, , 2011. We adapted the ROGframework (Schoenfeld, 2010) to understand prospective secondary mathematics teachers' decisionmaking as they modified mathematical tasks using a set of inquiry-based teaching principles. ...
... Therefore, modifying tasks to enhance students' mathematical thinking can be regarded as a mathematics professional teaching problem (Schoenfeld, 2010(Schoenfeld, , 2011. We adapted the ROGframework (Schoenfeld, 2010) to understand prospective secondary mathematics teachers' decisionmaking as they modified mathematical tasks using a set of inquiry-based teaching principles. Our assumption was that we could describe and explain the prospective mathematics teachers' decisionmaking during task-modification to achieve specific learning objectives by examining the relationships between their knowledge, orientations, and goals. ...
The objective of this study was to investigate how prospective secondary mathematics teachers apply inquiry-based teaching principles to modify tasks that support students' engagement in specific mathematical practices. The research employed the theory of goal-oriented decision-making to describe and explain the use of inquiry-based teaching principles as a conceptual tool by these prospective teachers. The study involved two cohorts, comprising 43 prospective teachers (20 in one cohort and 23 in the other) enrolled in a Secondary Education Teaching program. Data were collected from written reports documenting the implementation of two professional tasks, where participants modified textbook assignments to promote exploratory teaching. An inductive analysis was conducted in two phases. The findings revealed that prospective teachers consistently applied inquiry-based teaching principles when they set specific mathematical practices as student learning objectives, such as analyzing particular cases, identifying patterns and relationships, and formulating conjectures and generalizations. However, when these mathematical practices were not established as learning objectives, teachers struggled to apply inquiry-based teaching principles consistently during task modification. These results suggest that inquiry-based teaching principles are an effective conceptual tool for prospective teachers' instructional reasoning. Nonetheless, for consistent application, it is crucial to establish a coherent network of logical connections between the conceptual tool and the intended learning objectives.
... Resolución de problemas: Los estudiantes deben ser capaces de identificar y plantear problemas, así como encontrar soluciones a partir del uso de estrategias lengua y literatura. La resolución de problemas implica la habilidad de descomponer una situación compleja en partes manejables y buscar patrones o relaciones lengua y literatura que conduzcan a una solución (Schoenfeld, 2011). ...
... Mejora del rendimiento académico: La enseñanza de habilidades críticas en lengua y literatura se ha asociado con una mejora en el rendimiento académico, ya que los estudiantes que dominan el pensamiento crítico tienden a entender más profundamente los conceptos y a retener el conocimiento a largo plazo. Investigaciones demuestran que los estudiantes que desarrollan habilidades de razonamiento crítico son capaces de resolver problemas literarios más complejos y aplicar el conocimiento a nuevas situaciones (Schoenfeld, 2011). ...
El Aprendizaje Basado en Problemas (ABP) es una metodología educativa que fomenta el desarrollo del pensamiento crítico y el razonamiento en los estudiantes, siendo particularmente eficaz en la enseñanza de lengua y literatura. Este trabajo analiza la relación entre el ABP y el desarrollo del pensamiento literario crítico en estudiantes de educación básica. Se exploran los beneficios del ABP, como la mejora del desempeño académico y la motivación estudiantil, así como los desafíos en su implementación, como la formación docente y la evaluación. Además, se examinan teorías pedagógicas que sustentan el ABP, incluyendo el constructivismo y el aprendizaje colaborativo. Se concluye que el ABP, pese a sus retos, es una herramienta valiosa para transformar la enseñanza de la lengua y literatura, promoviendo habilidades esenciales para la resolución de problemas complejos en la vida real.
... This paper focuses on the first two strands of mathematical proficiency identified by the National Research Council (2001)-conceptual understanding and productive disposition-while acknowledging the importance of the other three strands: strategic competence, adaptive reasoning, and procedural fluency. Schoenfeld (2010) introduces the notion of orientation, which includes beliefs, values, dispositions, and biases that fundamentally shape people's behaviors in well-practiced domains such as teaching and learning. Building on this work, Huang (2023) elaborates on the construct of orientations with respect to understanding in mathematics, defining it as "the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematics learning" (p. ...
Many instructors observe that students often rely on memorization in introductory college mathematics. However, existing literature on effective teaching strategies does not fully address the need to cultivate both conceptual understanding and deeper orientations towards understanding in students' learning. This study presents a case analysis of calculus lectures delivered by an experienced instructor at an R1 institution, revealing significant opportunities for enhancing conceptual learning and promoting stronger orientations towards understanding among students. The analysis identified four key strategies employed by the instructor: 1) framing instructional activities as a pursuit of understanding; 2) examining underlying meanings while connecting students' intuition; 3) providing motivations, justifications, and multiple perspectives; and 4) creating cognitively challenging tasks and encouraging students to embrace discomfort in learning. These simple, practical strategies do not impose significant demands on instructors yet hold great potential for helping more students approach mathematics through deep understanding.
... Misalnya, dalam bidang optimasi, turunan fungsi dua peubah digunakan untuk mencari titik ekstrem dan menentukan titik maksimum atau minimum dari fungsi (Nocedal & Wright, 2020). Penelitian lainnya menunjukkan bahwa teknik visualisasi dalam kalkulus multivariat dapat membantu siswa dan mahasiswa untuk memahami konsep-konsep abstrak seperti gradien dan titik ekstrem, yang dapat meningkatkan efektivitas pembelajaran matematika (Schoenfeld, 2021). Selain itu, dalam bidang teknik, turunan fungsi dua peubah digunakan untuk menganalisis respons sistem terhadap perubahan variabel yang berhubungan dengan suhu, tekanan, atau waktu (Boulton & Harrison, 2019). ...
This study aims to analyze the derivatives of a two-variable function and visualize the results in the form of a 3D graph using Python. Derivatives of two-variable functions are essential in multivariate analysis, such as optimization and surface analysis. The study uses Visual Studio Code as the Integrated Development Environment (IDE) to develop and run Python code, utilizing libraries such as NumPy, SymPy, and Matplotlib for mathematical computations and visualization. The first step involves programming partial derivatives of a two-variable function using SymPy. Subsequently, the derivative results are visualized in 3D using Matplotlib to illustrate the surface and gradient of the function. The goal of this research is to provide a deeper understanding of the application of derivatives in two-variable functions and the benefits of visualization in analyzing these derivative results. The findings are expected to contribute to the fields of mathematics education and numerical computation applications.
... Im Theoriebeitrag von Herbst et al. (2016) werden Entscheidungen von Lehrpersonen als Produkte der Art und Weise betrachtet, wie Individuen persönliche Ressourcen nutzen, um Anforderungen ihrer institutionellen Positionen und Normen der von ihnen wahrgenommenen Aktivitäten zu verhandeln. Die Autoren beziehen sich u. a. auf die Theory of goal-oriented decision making von Schoenfeld (2011). ...
Zusammenfassung
In unserem Beitrag stellen wir erste empirische Ergebnisse aus unserem Forschungsprojekt „Professionalisierung von Lehrpersonen der Fächer Mathematik und Englisch“ (ProME) vor. Wir untersuchen die Frage, wie Lehrpersonen zu ihren alltäglichen Handlungsentscheidungen kommen und welche Rolle (organisationale, gesellschaftliche und fachbezogene) Normen in diesen Entscheidungsprozessen spielen. Als Erhebungs- und Auswertungsmethode dienen das episodische Interview und die Dokumentarische Methode. Metatheoretische Grundlage ist eine (Neu‑)Fassung des Entscheidungsbegriffs: Entscheidungen werden an die Definition des Orientierungsrahmens im weiteren Sinne der Praxeologischen Wissenssoziologie nach Bohnsack angebunden und mit Bezugnahme auf Luhmann als mit Kontingenzreduktion verbundene Reaktionen auf Erwartungen verstanden. In den empirischen Analysen dieses Beitrags fokussieren wir auf eine Englisch- und zwei Mathematiklehrpersonen und zeigen, wie diese in Entscheidungsprozessen routinisiert Habitus-Norm-Spannungen bearbeiten, was uns einen Zugang zum Orientierungsrahmen im weiteren Sinne eröffnet. Davon unterscheiden lassen sich nicht-routinisierten Entscheidungen, in welchen wir ein Potenzial für Transformationen des Habitus sehen.
... Studies on classroom activity based on teachers' knowledge help explain the teacher's actions in terms of tools available to them, specifically their knowledge (Schoenfeld, 2010). This study explores, based on the paradigm of networking theories (Prediger et al., 2008), the case of a secondary-level teacher who teaches TT. ...
In this article, we analyse a lesson on Thales’s theorem in a Chilean secondary school classroom through the combination of two theories: Mathematics Teachers’ Specialised Knowledge (ThMTSK) and Mathematical Working Spaces (ThMWS). Both theories, first separately and then in relation to one another, are used to analyse two tasks proposed by the teacher in the classroom following a cross-methodology for networking of theories. Through a single case study research design, a content analysis of the transcript of the video recording of the lesson was conducted. The joint analysis of this lesson allows us to better understand the mathematical work taking place in the classroom. In particular, the results show the scope of each model and their complementarity through the detection of meeting points and blind spots, through the role of proof, representations, and the change between geometrical and numerical work in teaching Thales’s theorem. This allows for a deeper understanding of a teacher’s practice and teaching. Ultimately, relationships between the theoretical elements of both theories are established to show their complementarity. We conclude that networking between theories can contribute to the development of these theories by raising questions that involve examining their foundations and assumptions in greater depth.
... In this vein, the relationship among investigated topics stresses the importance of adopting a holistic approach. Accordingly, we propose a revisited version of the six steps of the rational decision-making model (Schoenfeld, 2010) to allow managers to fully grasp and exploit the interconnectedness between AI, KM processes and decision-making by providing structured guidelines on how AI can effectively support the decision-making process by enhancing KM practices: ...
Purpose
This paper aims to provide empirical evidence on adopting artificial intelligence (AI), including generative AI, in knowledge management (KM) processes and its impact on organisational decision-making. Specifically, the study addresses three key research questions: RQ1: How is (generative) AI adopted within KM processes in organisations? RQ2: What factors influence the adoption of AI in these processes, either facilitating or inhibiting it? RQ3: How does AI adoption in KM processes affect organisational decision-making?
Design/methodology/approach
An explorative investigation has been conducted through semi-structured interviews with KM and AI experts from a worldwide sample of 52 mostly private, large and for-profit organisations. Interviews have been analysed through a mixed thematic analysis.
Findings
The study provides an original framework in which the three investigated concepts are interconnected according to a dual relationship: linear and retroactive and 20 factors affecting AI adoption within KM processes.
Practical implications
The provided model guides managers in improving their organisational decision-making through AI adoption in KM processes. Moreover, according to the rational decision-making model, the authors propose a six-step systematic procedure for managers.
Originality/value
To the best of the authors’ knowledge, this is the first study that simultaneously addresses AI, KM and decision-making and provides an integrated framework showing the relationships between them, allowing organisations to better and practically understand how to ameliorate their decision-making through AI adoption in KM processes.
El Aprendizaje Basado en Problemas (ABP) es una metodología educativa que fomenta el desarrollo del pensamiento crítico y el razonamiento en los estudiantes, siendo particularmente eficaz en la enseñanza de lengua y literatura. Este trabajo analiza la relación entre el ABP y el desarrollo del pensamiento literario crítico en estudiantes de educación básica. Se exploran los beneficios del ABP, como la mejora del desempeño académico y la motivación estudiantil, así como los desafíos en su implementación, como la formación docente y la evaluación. Además, se examinan teorías pedagógicas que sustentan el ABP, incluyendo el constructivismo y el aprendizaje colaborativo. Se concluye que el ABP, pese a sus retos, es una herramienta valiosa para transformar la enseñanza de la Lengua y Literatura, promoviendo habilidades esenciales para la resolución de problemas complejos en la vida real.
This "Research Commentary" explores the roles of theoretical and empirical work in the development of productive lines of research. It elaborates on 3 main points. First, the dialectic between theory and empirical practice is highly productive for both: Theory is enriched by close attention to data, and one's understanding of empirical issues is deepened when one attends closely to theory. Second, an effective mechanism for making systematic progress is to focus on cases at the edge of one's (and the field's) collective theoretical understanding. Third, close observations of empirical phenomena often raise issues that have theoretical import and that give rise to new lines of work. These 3 points, and implications, are illustrated with examples from my research.
Results from the third national mathematics assessment indicate that the decline in performance of 17 year olds between 1973 and 1978 has leveled out over the last four years, and 13 year olds' performance improved significantly between 1978 and 1982. However, most gains were on lower-order skills. (MNS)
