Designing Professional Learning Tasks for Mathematics Learning Trajectories

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project

Mathematical Model for Adaptive Technology in E-learning Systems

The emergence of a large number of e-learning platforms and courses does not solve the problem of improving the quality of education. This is primarily due to insufficient implementation or lack of mechanisms for adaptation to the individual parameters of the student. The level of adaptation in modern e-learning systems to the individual characteristics of the student makes the organization of human-computer interaction relevant. As the solution of the problem, a mathematical model of the organization of human-computer interaction was proposed in this work. It is based on the principle of two-level adaptation that determines the choice of the most comfortable module for studying at the first level. The formation of an individual learning path is performed at the second level. The problem of choosing an e-module is solved using a fuzzy logic. The problem of forming a learning path is reduced to the problem of linear programming. The input data are the characteristics of the quality of student activity in the education system. Based on the proposed model the computer technology to support student activities in modular e-learning systems is developed. This technology allows increasing the level of student’s cognitive comfort and optimizing the learning time. The most important benefit of the proposed approach is to increase the average score and increase student satisfaction with learning

Theoretical models of the role of visualisation in learning formal reasoning

Although there is empirical evidence that visualisation tools can help students to learn formal subjects such as logic, and although particular strategies and conceptual difficulties have been identified, it has so far proved difficult to provide a general model of learning in this context that accounts for these findings in a systematic way. In this paper, four attempts at explaining the relative difficulty of formal concepts and the role of visualisation in this learning process are presented. These explanations draw on several existing theories, including Vygotsky's Zone of Proximal Development, Green's Cognitive Dimensions, the Popper-Campbell model of conjectural learning, and cognitive complexity. The paper concludes with a comparison of the utility and applicability of the different models. It is also accompanied by a reflexive commentary[0] (linked to this paper as a hypertext) that examines the ways in which theory has been used within these arguments, and which attempts to relate these uses to the wider context of learning technology research

Putting theory oriented evaluation into practice

Evaluations of gaming simulations and business games as teaching devices are typically end-state driven. This emphasis fails to detect how the simulation being evaluated does or does not bring about its desired consequences. This paper advances the use of a logic model approach which possesses a holistic perspective that aims at including all elements associated with the situation created by a game. The use of the logic model approach is illustrated as applied to Simgame, a board game created for secondary school level business education in six European Union countries

Logic Models....Not Just for Big Foundations Anymore

Logic modeling is popular with large foundations, but has not been embraced by many of the smaller ones. One reason is that foundations with few or no staff fear that producing one is complicated and time consuming. It doesn't have to be. And it can be a crucial tool for small asset foundations looking to make sustained impact.This report offers a case study of how the KDK-Harman Foundation created a logic model laying out its underlying assumptions and theories of change and aligning goals, activities, and intended outcomes and how it incorporated the model into decision-making processes

The Potency Of Metacognitive Learning To Foster Mathematical Logical Thinking

The ability of thinking logically needs to be developed due to the fact that it is an essential basic skill. Logical thinking affects that giving reason must be true, and that a sequence of assumptions is based on the high truth value. Mathematics is a subject that functions to train students to think logically. The understanding of logic will help students to arrange the proof that support through process to finally arrive at a conclusion. Currently, metacognition is viewed as an essential element of learning. It refers to someone knowledge of processes and the result itself or of that connected to the process. Metacognition is needed when student solves the task that needs argumentation and logical understanding. In order to help student to skillful think logically, mathematics learning must be designed as such so that the condition will raise the skill of metacognitive acts. Key words: metacognitive learning, mathematical logical thinkin

Introduction to Iltis: An Interactive, Web-Based System for Teaching Logic

Logic is a foundation for many modern areas of computer science. In artificial intelligence, as a basis of database query languages, as well as in formal software and hardware verification --- modelling scenarios using logical formalisms and inferring new knowledge are important skills for going-to-be computer scientists. The Iltis project aims at providing a web-based, interactive system that supports teaching logical methods. In particular the system shall (a) support to learn to model knowledge and to infer new knowledge using propositional logic, modal logic and first-order logic, and (b) provide immediate feedback and support to students. This article presents a prototypical system that currently supports the above tasks for propositional logic. First impressions on its use in a second year logic course for computer science students are reported

School Leadership Interventions Under the Every Student Succeeds Act: Evidence Review - Updated and Expanded

This RAND analysis offers guidance to states and districts on how they can choose to use the Every Student Succeeds Act to help achieve their school improvement goals by supporting principals and other school leaders

Critical Thinking Skills of Prospective Elementary School Teachers in Integrated Science-Mathematics Lectures

The purpose of this study is to find out the critical thinking skills indicators and aspects of prospective elementary school teachers in mathematics-science integration lectures on electrical circuits and mathematical logic lesson. This research uses random sampling technique in which 30 first semester students were chosen randomly from one of university in Padang region West Sumatera Indonesia. This research uses Research and Development (R & D). The critical thinking skills are seen from processes, observations, and tests. The process of critical thinking skills of prospective elementary school teachers on the average of critical thinking skills indicator is 84% in strategies and tactics, 80% in advanced clarification and 83% in elementary clarification, basic support, and inference. The result of observing the critical thinking skills of prospective elementary school teachers on the average of each lectures is significantly increased to be 81.9%. The results of pre-test and post-test were increased significantly. It is shown from N-gain of 0.7 to be medium category