Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use

2021 ◽  
Vol 9 (2) ◽  
pp. 145-159
Author(s):  
Charmaine Mangram ◽  
Kathy Liu Sun
Keyword(s):  
Preservice Teachers ◽  
Digital Technology ◽  
Technology Use ◽  
Teacher Educators ◽  
Mathematical Thinking ◽  
Mathematical Practice ◽  
Secondary Mathematics ◽  
Ease Of Use ◽  
Professional Judgment ◽  
Mathematics Methods

The pervasiveness of digital technology creates an imperative for mathematics teacher educators to prepare preservice teachers (PSTs) to select technology to support students’ mathematical development. We report on research conducted on an assignment created for and implemented in secondary mathematics methods courses requiring PSTs to select and evaluate digital mathematics tools. We found that PSTs primarily focused on pedagogical fidelity (ease of use), did not consider mathematical fidelity (accuracy), and at times superficially attended to cognitive fidelity (how well the tool reflects students’ mathematical thinking processes) operationalized as the CCSS for Mathematical Practice and Five Strands of Mathematical Proficiency. We discuss implications for implementing the assignment and suggestions for addressing PSTs’ challenges with identifying the mathematical practices and five strands.

Using the iPad to Develop Preservice Teachers’ Understanding of the Common Core State Standards for Mathematical Practice

2013 ◽  
pp. 370-386
Author(s):  
Mary Grassetti ◽  
Silvy Brookby
Keyword(s):  
Preservice Teachers ◽  
Student Teaching ◽  
Common Core ◽  
Common Core State Standards ◽  
Mathematical Practice ◽  
State Standards ◽  
Habits Of Mind ◽  
Mathematics Methods ◽  
Core State ◽  
The Common

The Standards for Mathematical Practice as delineated in the Common Core State Standards for Mathematics describe the processes, proficiencies, and habits of mind that students are expected to develop through their engagement with mathematics (Dacey & Polly, 2012). The purpose of this chapter is to discuss, anecdotally, how the iPad, a tablet computer designed by Apple ™, can be used to develop preservice teachers’ understanding and implementation of the Standards for Mathematical Practice, most specifically Mathematical Practice Standard 3: Construct viable arguments and critique the reasoning of others. Under examination are the authors’ experiences using the iPad as an observational tool during student teaching and as a teaching tool in their mathematics methods courses. The chapter concludes with suggestions for additional uses of the iPad to support preservice teachers as they work to develop their understanding of the Standards for Mathematical Practice.

Supporting PSTs in Using Appropriate Tools Strategically: A Learning Sequence for Developing Technology Tasks That Support Students' Mathematical Thinking

2017 ◽  
Vol 5 (2) ◽  
pp. 122-157 ◽  
Author(s):  
Milan F. Sherman ◽  
Charity Cayton ◽  
Kayla Chandler
Keyword(s):  
Preservice Teachers ◽  
Mathematics Teachers ◽  
Teacher Educators ◽  
Mathematical Thinking ◽  
Mathematical Tasks ◽  
Learning Sequence ◽  
Mathematics Teacher Educators ◽  
Preservice Mathematics Teachers ◽  
High Level ◽  
Support Students

This article describes an intervention with preservice mathematics teachers intended to address the use of Interactive Geometry Software (IGS) for mathematics instruction. A unit of instruction was developed to support teachers in developing mathematical tasks that use IGS to support students' high-level thinking (Smith & Stein, 1998). Preservice teachers used the IGS Framework (Sherman & Cayton, 2015) to evaluate 3 tasks, to revise a task, and ultimately to design a task using the framework. Results indicate that a majority of preservice teachers in this study were successful in creating a high-level task where IGS was instrumental to the thinking demands, and that the IGS Framework supported them in doing so. The article concludes with suggestions for use by fellow mathematics teacher educators.

Do You See What I See? Formative Assessment of Preservice Teachers’ Noticing of Students’ Mathematical Thinking

2020 ◽  
Vol 8 (3) ◽  
pp. 88-104
Author(s):  
Stephanie Casey ◽  
Joel Amidon
Keyword(s):  
Preservice Teachers ◽  
Formative Assessment ◽  
Mathematics Teacher ◽  
Teacher Educators ◽  
Teaching Practice ◽  
Mathematical Thinking ◽  
Learning Experience ◽  
Design Features ◽  
Professional Noticing ◽  
Mathematics Teacher Educators

Developing expertise in professional noticing of students’ mathematical thinking takes time and meaningful learning experiences. We used the LessonSketch platform to create a learning experience for secondary preservice teachers (PSTs) involving an approximation of teaching practice to formatively assess PSTs’ noticing skills of students’ mathematical thinking. Our study showed that approximations of teaching practice embedded within platforms like LessonSketch can enable mathematics teacher educators (MTEs) to carry out effective formative assessment of PSTs’ professional noticing of students’ mathematical thinking that is meaningful for both PSTs and MTEs. The experience itself as well as its design features and framework used with the assessment can be applied in the work of MTEs who develop teachers’ professional noticing skills of students’ mathematical thinking.

Breaking Conventions to Support Quantitative Reasoning

2014 ◽  
Vol 2 (2) ◽  
pp. 141-157 ◽  
Author(s):  
Kevin C. Moore ◽  
Jason Silverman ◽  
Teo Paoletti ◽  
Kevin LaForest
Keyword(s):  
Preservice Teachers ◽  
Teacher Educators ◽  
Secondary Mathematics ◽  
Quantitative Reasoning ◽  
Central Function ◽  
Reasoning Abilities ◽  
Function Concepts ◽  
Teachers And Students ◽  
Sustained Success

Quantitative reasoning is critical to developing understandings of function that are important for sustained success in mathematics. Unfortunately, preservice teachers often do not receive sufficient quantitative reasoning experiences during their schooling. In this paper, we illustrate consequences of underdeveloped quantitative reasoning abilities against the backdrop of central function concepts. We also illustrate tasks that can perturb preservice teachers' thinking in ways that produce opportunities for quantitative reasoning. By implementing strategically designed tasks, teacher educators can support preservice teachers–and students in general–in advancing their quantitative reasoning abilities and their understanding of secondary mathematics content.

Investigating Secondary Mathematics Preservice Teachers’ Instructional Vision: Learning to Teach Through Pedagogies of Practice

2020 ◽  
pp. 002248712096593
Author(s):  
Fran Arbaugh ◽  
Duane Graysay ◽  
Ben Freeburn ◽  
Nursen Konuk
Keyword(s):  
Preservice Teachers ◽  
Secondary Mathematics ◽  
Methods Course ◽  
Mathematics Methods ◽  
Group Discussions ◽  
Individual Interviews ◽  
Mathematics Methods Course ◽  
Instructional Vision ◽  
Constant Comparative Analysis

The purpose of this study was to investigate changes in a cohort of secondary preservice teachers’ (PSTs) vision of the role of a teacher within the context of a mathematics methods course designed around pedagogies of practice. We analyzed data collected in the first and last 2 weeks of the course, consisting of recordings of small- and whole-group discussions, PSTs’ written work, and individual interviews. We first coded using Munter’s Role of Teacher rubric and identified significant differences between beginning-of-semester data and end-of-semester data. We then conducted three rounds of constant comparative analysis resulting in four themes that describe the changes in visions of role of teacher. Findings indicate that engaging in pedagogies of practice in preservice education has the potential to influence PSTs’ visions of their role as mathematics teachers. This study extends both the literatures on pedagogies of practice and on teachers’ instructional vision.

The Three-Minute-Rehearsal Cycle of Enactment and Investigation: Preservice Secondary Mathematics Teachers Learning to Elicit and Use Evidence of Student Thinking

2019 ◽  
Vol 8 (1) ◽  
pp. 22-48
Author(s):  
Fran Arbaugh ◽  
Duanne Graysay ◽  
Nursen Konuk ◽  
Ben Freeburn
Keyword(s):  
Preservice Teachers ◽  
Mathematics Teachers ◽  
Teacher Educators ◽  
Secondary Mathematics ◽  
Learning Opportunities ◽  
Learning To Teach ◽  
Student Thinking ◽  
National Council ◽  
Design Learning ◽  
The Impact

In the last decade, mathematics teacher educators have begun to design learning opportunities for preservice mathematics teachers using a pedagogies-of-practice perspective. In particular, learning cycles provide a structure for engaging PSTs in learning to teach through the use of representations, approximations, and decompositions of practice (Grossman et al., 2009). In this article, we provide details of one learning cycle designed to support secondary mathematics preservice teachers' learning to elicit and use evidence of student thinking and pose purposeful questions (National Council of Teachers of Mathematics, 2014). Through qualitative analyses conducted on learning reflections, we provide evidence of the impact on engagement of this cycle through the lens of the Framework for Learning to Teach (Hammerness et al., 2005).

Technology Familiarization to Preservice Teachers

2016 ◽  
Vol 45 (2) ◽  
pp. 236-255 ◽  
Author(s):  
Gilbert Kalonde ◽  
Rabab Mousa
Keyword(s):  
Preservice Teachers ◽  
Technology Integration ◽  
Instructional Technology ◽  
Teacher Educators ◽  
Ease Of Use ◽  
Methods Courses ◽  
Different Types ◽  
K 12

The purpose of this study was to investigate factors that influence teacher educators’ technology decisions in methods courses. Research has shown various reasons why teachers use different types of technologies and not able to integrate certain technologies. However, this study focused on the source of teachers’ instructional technology foundations, knowledge, and preparation for teaching. A total of 90 teacher educators were surveyed and stated that content, ease of use, availability, experiences, students’ interest, and obstacles influence decisions on technologies modeled to preservice teachers in the methods courses. This study provides a different perspective on understanding teachers’ dilemma on technology integration in K-12 classrooms. The findings provide information to understand teacher educators’ technology decisions and modeling influence on K-12 teachers’ technology integration in the classroom.

Nurses’ attitudes towards occupational transformation processes brought about by digital care technologies

2020 ◽  
Vol 6 (3) ◽  
pp. 628-634
Author(s):  
Larissa Schlicht ◽  
Johannes Wendsche ◽  
Liliann Lehrke ◽  
Marlen Melzer ◽  
Ulrike Rösler
Keyword(s):  
Digital Technology ◽  
Technology Use ◽  
Knowledge Work ◽  
Ease Of Use ◽  
Technology Appraisal ◽  
Electronic Documentation ◽  
Negative Attitudes ◽  
User Behaviour ◽  
Study Results ◽  
Attitudes Towards Technology

AbstractBackground. Digital technologies increasingly shape today’s world of work. This not only affects sectors such as knowledge work and the automotive industry, but also the care sector. On the one hand, many nurses today use technologies supporting some selected and rather peripheral nursing tasks (e.g., electronic documentation). However, on the other hand, more comprehensive and additionally proximal care-related task devices (e.g., diagnostics via telecare) seem to be used less often. From a psychological perspective, attitudes towards technology are an important antecedent of user behaviour. Therefore, in two studies we aimed to examine if nurses’ attitudes towards four digital technology fields (i.e., electronic documentation ED, ambient assisted living AAL, telecare application and robotics) are differing in relation to the type of task substitution, how technology appraisal and knowledge shape these attitudes, and how attitudes predict user behaviour. Method. We conducted two cross-sectional survey studies with German nurses (Study 1: N = 148, Study 2: N = 252) with well-established scales (i.e., general and work-related positive and negative attitudes towards technologies, ease of use, usability, knowledge, and technology use). Results. We found that it is important to consider positive and negative attitudes towards technology distinctively as intercorrelations were only moderately negative. As expected, we found in both studies that nurses reported stronger positive and less negative attitudes towards technologies assumed to be substituting more specific and peripheral (e.g., ED) than comprehensive and proximal care tasks (e.g., robotics). Moreover, we found that two types of technology appraisal (ease of use and usability) both positively correlated with positive attitudes towards all four technology fields, whereas patterns were more inconsistent and additionally influenced by technology knowledge when predicting negative attitudes. Although inconsistently across both studies and the considered technologies, in general, technology users reported more positive and less negative attitudes than non-users. Conclusion. If technology developers and nursing facility managers want to help nurses successfully adopting new technologies in their work routines, nurses’ technology appraisal and technology attitudes have to be considered already in the pre-development phase. Our study results show that nurses report different attitudes towards the four digital technology fields considered here in relation to the levels and types of task-substitution. More specifically, if core carerelated work-tasks (e.g., direct care) are not substituted, nurses report stronger positive and less negative attitudes towards the supporting technologies and higher user behaviour.

New International Factors of Twenty First Century

2019 ◽  
Vol 3 (11) ◽  
pp. 106
Author(s):  
Saif Nasrat Tawfiq Al - Haramazi
Keyword(s):  
International Relations ◽  
International Organizations ◽  
Digital Technology ◽  
Ease Of Use ◽  
First Century ◽  
International Context ◽  
New Concepts ◽  
Important Input ◽  
Twenty First Century ◽  
International Interaction

There are many non-traditional additions to the influential works in the international or international context, which have expanded and become very large.  Some of them have not entered into this field of international relations. Hence the need to supplement, renew and add new concepts There digital (electronic) factor, has become the key to the hard and soft domination of international units, and an important input in international relations, especially the twenty-first century. We have been able to explore the reality of the international interaction based on (cooperation, competition, conflict). In conclusion, the global system will remain state-based and international organizations. At the same time, it will continue to be born and no states in its interactions with the ease of use of digital technology by individuals on the planet..

Category Theory and Foundations

2018 ◽  
Author(s):  
Michael Ernst
Keyword(s):  
Category Theory ◽  
Mathematical Thinking ◽  
Mathematical Practice ◽  
Foundations Of Mathematics ◽  
Ongoing Debate ◽  
Technical Adequacy ◽  
Theoretical Foundations

In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy. Finally, it calls attention to a neglected feature of the debate, the claim that categorical foundations are more natural and readily useable, and how deeper investigation of that claim could prove fruitful for our understanding of mathematical thinking and mathematical practice.

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