scholarly journals Instrumental Genesis of a Learning Trajectory: The Case of Pedro’s Professional Noticing

2021 ◽  
Vol 23 (7) ◽  
pp. 91-119
Author(s):  
Gloria Sánchez-Matamoros ◽  
Mar Moreno ◽  
Julia Valls
Keyword(s):  
Learning Trajectory ◽  
Instrumental Genesis ◽  
Professional Noticing

Shifting Roles in Continuous Advising Sessions

Relay Journal ◽  
2019 ◽  
pp. 69-72
Author(s):  
Huw Davies ◽  
Robert Stevenson ◽  
Isra Wongsarnpigoon
Keyword(s):  
Learning Process ◽  
Transformational Learning ◽  
Learning Trajectory ◽  
Learner Readiness ◽  
Linguistic Support ◽  
Reflective Dialogue ◽  
Open Mind ◽  
To Receive

It is common for learning advisors to receive a request such as conversation practice or simple linguistic support in our institution simply because learners find them accessible and friendly. Although this may not be the usual role of a learning advisor, it can be the beginning of a long-lasting reflective dialogue. Learning advisors are aware that the learners’ initial interest is not necessarily an opportunity for reflection on their learning process. Nevertheless, they also acknowledge the fact that learner readiness for reflection varies depending on the learner. Thus, while advisors appear to be “conversation partners” at first, they endeavor to create reflective dialogues by incorporating advising strategies in each session. As the learning trajectory that the learner follows is not always straightforward, keeping an open mind and engaging in each advising session is crucial. The following stories depict the importance of openness to learners’ needs and maintaining continuous advising sessions in order to generate transformational learning.

Preservice Teachers’ Professional Noticing When Viewing Standard and 360 Video

2020 ◽  
pp. 002248712093954
Author(s):  
Karl W. Kosko ◽  
Richard E. Ferdig ◽  
Maryam Zolfaghari
Keyword(s):  
Teacher Education ◽  
Preservice Teachers ◽  
Virtual Reality ◽  
Future Research ◽  
Teacher Noticing ◽  
Professional Noticing ◽  
Novel Technology

Use of video as a representation of practice in teacher education is commonplace. The current study explored the use of a new format (360 video) in the context of preservice teachers’ professional noticing. Findings suggest that preservice teachers viewing 360 videos attended to more student actions than their peers viewing standard video. In addition, using a virtual reality headset to view the 360 videos led to different patterns in where preservice teachers looked in the recorded classroom, and to increased specificity of mathematics content from the scenario. Thus, findings and results support the use of 360 video in teacher education to facilitate teacher noticing. However, future research is needed to further explore this novel technology.

scholarly journals Designing Tasks for a Dynamic Online Environment: Applying Research into Students’ Difficulties with Linear Equations

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 557
Author(s):  
Morten Elkjær ◽  
Uffe Thomas Jankvist
Keyword(s):  
Design Theory ◽  
Teaching And Learning ◽  
Linear Equations ◽  
Task Design ◽  
Tree Structure ◽  
Learning Trajectory ◽  
Variation Theory ◽  
Online Environment ◽  
School Students ◽  
Personalised Learning

Despite almost half a century of research into students’ difficulties with solving linear equations, these difficulties persist in everyday mathematics classes around the world. Furthermore, the difficulties reported decades ago are the same ones that persist today. With the immense number of dynamic online environments for mathematics teaching and learning that are emerging today, we are presented with a perhaps unique opportunity to do something about this. This study sets out to apply the research on lower secondary school students’ difficulties with equation solving, in order to eventually inform students’ personalised learning through a specific task design in a particular dynamic online environment (matematikfessor.dk). In doing so, task design theory is applied, particularly variation theory. The final design we present consists of eleven general equation types—ten types of arithmetical equations and one type of algebraic equation—and a broad range of variations of these, embedded in a potential learning-trajectory-tree structure. Besides establishing this tree structure, the main theoretical contribution of the study and the task design we present is the detailed treatment of the category of arithmetical equations, which also involves a new distinction between simplified and non-simplified arithmetical equations.

A Proposed Instructional Theory for Integer Addition and Subtraction

2012 ◽  
Vol 43 (4) ◽  
pp. 428-464 ◽  
Author(s):  
Michelle Stephan ◽  
Didem Akyuz
Keyword(s):  
Number Line ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Realistic Mathematics Education ◽  
Instructional Theory ◽  
Education Theory ◽  
Addition And Subtraction ◽  
Support Students ◽  
Grade Classroom ◽  
Viable Model

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional sequence, which was based on a financial context, was designed using the Realistic Mathematics Education theory. Additionally, an empty, vertical number line (VNL) is posited as a potentially viable model to support students' organizing their addition and subtraction strategies. Particular emphasis is placed on the mathematical practices that were established in this setting. These practices indicate that students can successfully draw on their experiences with assets, debts, and net worths to create meaning for integer addition and subtraction.

Book Review: Multiple Perspectives of Teacher Noticing: An Emerging Area of Research

2015 ◽  
Vol 46 (3) ◽  
pp. 371-376
Author(s):  
Edna O. Schack ◽  
Molly H. Fisher ◽  
Jonathan N. Thomas
Keyword(s):  
Teacher Education ◽  
Education Research ◽  
Mathematics Teacher ◽  
American Education ◽  
Research Association ◽  
Multiple Perspectives ◽  
Teacher Noticing ◽  
Professional Noticing ◽  
Education Award

“Noticing matters” (p. 223). Through these words in the concluding chapter, Alan Schoenfeld succinctly captures the theme of this seminal book, Mathematics Teacher Noticing: Seeing Through Teachers' Eyes. The book received the American Education Research Association 2013 Exemplary Research in Teaching and Teacher Education Award. It addresses a variety of meanings and interpretations of teacher noticing from Dewey's earlier work of inner and outer attention to more specific variations such as that of professional noticing, as defined by Jacobs, Lamb, and Philipp. Chapter contributors have provided the foundation and framing of teacher noticing as a construct for studying and improving teaching.

scholarly journals Statistical modeling processes through the lens of instrumental genesis

2021 ◽  
Author(s):  
Marianne van Dijke-Droogers ◽  
Paul Drijvers ◽  
Arthur Bakker
Keyword(s):  
Mathematics Education ◽  
Statistical Modeling ◽  
Conceptual Understanding ◽  
Digital Technology ◽  
Statistics Education ◽  
Modeling Processes ◽  
Digital Environment ◽  
Instrumental Genesis ◽  
Digital Tool ◽  
Conceptual Shift

AbstractDigital technology is indispensable for doing and learning statistics. When technology is used in mathematics education, the learning of concepts and the development of techniques for using a digital tool are known to intertwine. So far, this intertwinement of techniques and conceptual understanding, known as instrumental genesis, has received little attention in research on technology-supported statistics education. This study focuses on instrumental genesis for statistical modeling, investigating students’ modeling processes in a digital environment called TinkerPlots. In particular, we analyzed how emerging techniques and conceptual understanding intertwined in the instrumentation schemes that 28 students (aged 14–15) develop. We identified six common instrumentation schemes and observed a two-directional intertwining of emerging techniques and conceptual understanding. Techniques for using TinkerPlots helped students to reveal context-independent patterns that fostered a conceptual shift from a model of to a model for. Vice versa, students’ conceptual understanding led to the exploration of more sophisticated digital techniques. We recommend researchers, educators, designers, and teachers involved in statistics education using digital technology to attentively consider this two-directional intertwined relationship.

Sign in / Sign up

Export Citation Format

Share Document