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In the research conducted, the relationship between teaching complexity and children's mathematical thinking was investigated in 4 "reform" classes and 1 conventional elementary class (7-8 years). Forty lessons were analyzed for the type of teaching and children's mathematical thinking revealed during class discussion. The results indicate increased complexity in teaching and level of children's thinking was highly related to the kinds of interaction that distinguished three class cultures. These findings complete a previously proposed theoretical framework that integrates teaching and learning by detailing acts of teaching in relation to complexity of children's thinking. (Contains 1 footnote and 2 figures.) [For complete proceedings, see ED500860.]

To date, we know little about the exact role of different communication modes on opinion formation and the complexity of thinking. Psychological research (Schweiger et al. 1986) found that while contestatory communication formats (e.g. devil´s advocacy) produce higher validity recommendation than consensual formats, the latter lead to higher decision acceptance and procedural satisfaction. In a recent study, Erisen/Redlawsk/Erisen (2018) found that exposure to congruent information increases the integrative complexity of opposing thoughts. This population-based survey experiment compares the effects of different communication modes – “contestatory” vs “appreciative inquiry” vs “free communication” – and two control conditions - information-only and Placebo - on opinion formation (polarization, depolarization, opinion stability), argument quality (breadth and depth of argument) and procedural satisfaction in the context of the Covid-19 crisis (with a focus on the prioritization of health vs freedom).

The purpose of this paper is to highlight how systems thinking contributes to decision making in uncertain contexts that are characteristic of service systems. Based on the assumption that service systems face complex conditions, the paper posits that systems thinking may support the understanding of key issues in the management of service systems. 

Noticing students' mathematical thinking is recognized as a key element of effective instruction, but novice teachers do not naturally attend to and make sense of student thinking. We describe a design experiment in which prospective teachers were engaged in analysis of minimally edited classroom video in order to support their ability to notice important student mathematical thinking within the complexity of classroom instruction. We discuss evidence of prospective teachers' learning in five iterations of the intervention, including the extent to which they developed a focus on students' mathematics, changes in the ways they discussed that mathematics, and the extent to which they focused on instances of student mathematics that had potential to be capitalized on to support student learning. Aspects of the intervention that seemed to support teachers' noticing are discussed, as well as future directions for the work. [For the complete proceedings, see ED583989.]

Noticing students' mathematical thinking is recognized as a key element of effective instruction, but novice teachers do not naturally attend to and make sense of student thinking. We describe a design experiment in which prospective teachers were engaged in analysis of minimally edited classroom video in order to support their ability to notice important student mathematical thinking within the complexity of classroom instruction. We discuss evidence of prospective teachers' learning in five iterations of the intervention, including the extent to which they developed a focus on students' mathematics, changes in the ways they discussed that mathematics, and the extent to which they focused on instances of student mathematics that had potential to be capitalized on to support student learning. Aspects of the intervention that seemed to support teachers' noticing are discussed, as well as future directions for the work. [For the complete proceedings, see ED583989.]

Noticing students' mathematical thinking is recognized as a key element of effective instruction, but novice teachers do not naturally attend to and make sense of student thinking. We describe a design experiment in which prospective teachers were engaged in analysis of minimally edited classroom video in order to support their ability to notice important student mathematical thinking within the complexity of classroom instruction. We discuss evidence of prospective teachers' learning in five iterations of the intervention, including the extent to which they developed a focus on students' mathematics, changes in the ways they discussed that mathematics, and the extent to which they focused on instances of student mathematics that had potential to be capitalized on to support student learning. Aspects of the intervention that seemed to support teachers' noticing are discussed, as well as future directions for the work. [For the complete proceedings, see ED583989.]

This paper aims at showing a new methodology to assess student learning in virtual spaces supported by Information and Communications Technology-ICT. The methodology is based on the Conceptual Pedagogy Theory, and is supported both on knowledge instruments (KI) and intelectual operations (IO). KI are made up of teaching materials embedded in the virtual environment. The student carries out IO in his/her virtual formation process based on KI. Both instruments of knowledge and intellectual operations can be mathematically modelled by using functions of increasing complexity order. These functions represent the student's learning change. This paper's main contribution is to show that these functions let the student go from a concrete thinking to a formal one in his/her virtual learning process. The research showed that 47% of the students moved from a concrete thinking level to the formal thinking level.

Change, not stability, is the constant in today's world. Massive amounts of information flow around our global system in milliseconds, breaking down the borders of nation states and shifting the balance of power among old and new players. Widely separated and disparate places around our globe communicate across electronic networks in real time, reducing the effects of distance and time. Military thinkers, politicians, scientists, and corporate executives are all looking for ways to understand the dynamics of global change and to prepare for the 21st century. Many are looking to the new science of complexity for answers. The science of complexity, however, does not yield answers, at least not in the sense that we have typically sought to describe our world and predict its events since the beginning of the Scientific Revolution. What it does yield is a new way of thinking about the world.

To date, we know little about the exact role of different communication modes on opinion formation and the complexity of thinking. Psychological research (Schweiger et al. 1986) found that while contestatory communication formats (e.g. devil´s advocacy) produce higher validity recommendation than consensual formats, the latter lead to higher decision acceptance and procedural satisfaction. In a recent study, Erisen/Redlawsk/Erisen (2018) found that exposure to congruent information increases the integrative complexity of opposing thoughts. This population-based survey experiment compares the effects of different communication modes - „contestatory“ vs „appreciative inquiry“ vs „free communication“ – and two control conditions - information-only and Placebo - on opinion formation (polarization, depolarization, opinion stability), argument quality (breadth and depth of argument), ambivalence and procedural satisfaction in the context of the Covid-19 crisis (with a focus on the prioritization of health vs freedom).

To date, we know little about the exact role of different communication modes on opinion formation and the complexity of thinking. Psychological research (Schweiger et al. 1986) found that while contestatory communication formats (e.g. devil´s advocacy) produce higher validity recommendation than consensual formats, the latter lead to higher decision acceptance and procedural satisfaction. In a recent study, Erisen/Redlawsk/Erisen (2018) found that exposure to congruent information increases the integrative complexity of opposing thoughts. This population-based survey experiment compares the effects of different communication modes - „contestatory“ vs „appreciative inquiry“ vs „free communication“ – and two control conditions - information-only and Placebo - on opinion formation (polarization, depolarization, opinion stability), argument quality (breadth and depth of argument), ambivalence and procedural satisfaction in the context of the Covid-19 crisis (with a focus on the prioritization of health vs freedom).

To date, we know little about the exact role of different communication modes on opinion formation and the complexity of thinking. Psychological research (Schweiger et al. 1986) found that while contestatory communication formats (e.g. devil´s advocacy) produce higher validity recommendation than consensual formats, the latter lead to higher decision acceptance and procedural satisfaction. In a recent study, Erisen/Redlawsk/Erisen (2018) found that exposure to congruent information increases the integrative complexity of opposing thoughts. This population-based survey experiment compares the effects of different communication modes - „contestatory“ vs „appreciative inquiry“ vs „free communication“ – and two control conditions - information-only and Placebo - on opinion formation (polarization, depolarization, opinion stability), argument quality (breadth and depth of argument), ambivalence and procedural satisfaction in the context of the Covid-19 crisis (with a focus on the prioritization of health vs freedom).

This monograph examines the question is Clausewitz' theoretical concept of center of gravity the antithesis of a systems approach to warfare. The nature of conflict has changed since the age of Clausewitz, and a theoretical concept designed to explain war in the Napoleonic era may not be applicable to warfare in the present and future. The monograph examines the theoretical origins of the concept in the context of Clausewitz' time. It examines the string of reasoning that may have led Clausewitz to his postulations on the concept of center of gravity, and why an almost literal translation from Clausewitz' era until the present continues to perpetuate the linear nature of the concept. Modem systems theory rich with applicability to warfare in the information age is contrasted against the linear based Clausewitzian concept. The monograph explains the role of the concept relative to systems shock and reveals how operational planners contuse the issue by mixing concepts creating a doctrinal soup of terms centered around the linear based concept of center of gravity. The monograph concludes with recommendations that if accepted would actually develop concepts that reflect how U.S. forces fight. It would incorporate a new systems based concept of center of gravity as an inductive process; conditions that operational planners and systems thinkers seek to induce into a rival system causing System Shock. This would be counter to the deductive concept currently used and would foster a common understanding among joint forces where none currently exists.

This monograph examines the question is Clausewitz' theoretical concept of center of gravity the antithesis of a systems approach to warfare. The nature of conflict has changed since the age of Clausewitz, and a theoretical concept designed to explain war in the Napoleonic era may not be applicable to warfare in the present and future. The monograph examines the theoretical origins of the concept in the context of Clausewitz' time. It examines the string of reasoning that may have led Clausewitz to his postulations on the concept of center of gravity, and why an almost literal translation from Clausewitz' era until the present continues to perpetuate the linear nature of the concept. Modem systems theory rich with applicability to warfare in the information age is contrasted against the linear based Clausewitzian concept. The monograph explains the role of the concept relative to systems shock and reveals how operational planners contuse the issue by mixing concepts creating a doctrinal soup of terms centered around the linear based concept of center of gravity. The monograph concludes with recommendations that if accepted would actually develop concepts that reflect how U.S. forces fight. It would incorporate a new systems based concept of center of gravity as an inductive process; conditions that operational planners and systems thinkers seek to induce into a rival system causing System Shock. This would be counter to the deductive concept currently used and would foster a common understanding among joint forces where none currently exists.