Software Tools Used in Math Refresher Courses at the University of Alcalá, Spain

We describe our experience of using the following mathematical tools: an e-learning platform (Moodle), several components of the WIRIS software suite for mathematics education (the formula editor, WIRIS CAS, and WIRIS-Quizzes), the dynamical geometry package GeoGebra, the computational knowledge engine Wolfram Alpha, and the mathematics software system SAGE. Our aim in this chapter is two-fold: on the one hand, we report the use of these tools in Math refresher courses. On the other, we provide sufficient information about them for readers to decide on the usefulness of these tools in their own particular context (maybe different from that of a refresher course). More specifically, for each tool we give a general description, some comments on its use in Math refresher courses, and a list of (general) advantages and drawbacks.

Interactive Web-Based Tools for Learning Mathematics

There is an abundance of Web-based resources designed for mathematics teachers and learners at every level. Some of these are static, while others are interactive or dynamic, giving mathematics learners opportunities to develop visualization skills, explore mathematical concepts, and obtain solutions to self-selected problems. Research into the efficacy of online mathematics demonstrations and interactive resources is lacking, but it is clear that not all online resources are equal from a pedagogical viewpoint. In this chapter, a number of popular and relevant websites for collegiate mathematics and collegiate preservice teacher education are examined. They are reviewed and investigated in terms of their interactivity, dynamic capabilities, pedagogical strengths and weaknesses, the practices they employ, and their potential to enhance mathematical learning both inside and outside of the collegiate classroom. Culled from these reviews is a working definition of “best practices”: condensing difficult mathematical concepts into representations and models that clarify ideas with minimal words, thereby enabling a typical student to grasp, quickly and easily, the underlying mathematics.

Online Communities of Practice as Vehicles for Teacher Professional Development

The affordances offered by modern Internet technologies provide new opportunities for the pre-service and in-service training of teachers, making it possible to overcome the restrictions of shrinking resources and geographical locations and to offer high quality learning experiences to geographically dispersed teachers. The focus of this chapter is the question of how information and communication tools made available online could be effectively exploited to build and study network-based services with the aim of fostering online communities that promote teacher learning and development. The chapter presents an overview of the main experiences gained from a study which investigated the forms of collaboration and shared knowledge building undertaken by a multinational group of teachers participating in EarlyStatistics, an online professional development in statistics education targeting European elementary and middle school mathematics teachers. Findings from the study provide insights into the factors that may facilitate or hinder the successful implementation of an online community of teaching practitioners.

Implementation of Learning Outcomes in Mathematics for Non-Mathematics Major by Using E-Learning

Learning outcomes are considered to be a key tool for student-centered teaching and learning. They can be successfully implemented in teaching and learning mathematics on higher educational level and together with appropriate level of technology enhanced learning can provide the framework for successful learning process even for students that have not been primarily interested in mathematics. The aim is to present the case study of implementation of learning outcomes and e-learning in several mathematical courses at the Faculty of Organization and Informatics of the University of Zagreb. First of all, there are examples of mathematical courses in the first year since the first study year is crucial for retaining students. Further, there are mathematical courses taught at higher years of undergraduate study and the first year of graduate study. Again, educational process is appropriately supported by ICT and executed through blended e-learning, as well as the use of social software.

Best Practices for Hybrid Mathematics Courses

This chapter is designed for the mathematics teacher, experienced or not, who is interested in incorporating Web-based content and activities into her face-to-face (F2F) classroom (i.e. creating “blended” or “hybrid” classes). It is not a “technical manual” nor is it meant to be exhaustive; rather, the intent is that of describing, colleague to colleague, things that work in an online environment. I will discuss, as if we are sitting in the teacher’s lounge with a laptop in front of us, how I use Web-based content in my mathematics instruction and how my students benefit from it in their mathematics learning. I will attempt to present some specific examples for clarity; be aware that these are just guides for you and not strict demarcations. For ease of discussion I will choose common tools / programs (e.g. Microsoft Word, GoogleDocs, Adobe Acrobat, etc.) and for cost effectiveness I will choose Open Source items whenever possible.

My Equations Are the Same as Yours!

In this chapter we explain how computer aided assessment (CAA) can automatically assess an answer that consists of a system of equations. In particular, we will use a computer algebra system (CAS) and Buchberger’s Algorithm to establish when two systems of equations are the “same.”

Mathematics Education

This chapter is concerned with the integration of research in mathematics education and e-learning. Its main aim is to provide a perspective on the teaching/learning opportunities offered by e-learning platforms in a blended learning setting, as experienced at the Universities of Salerno and of Piemonte Orientale. Two types of teaching actions have been set above all: a) tailored units of learning, which have required the design/implementation of a huge pool of learning objects, according to domain-specific guidelines from mathematics education research and to various educational parameters from e-learning research; b) cooperative or individual teacher-driven learning activities together with various practice for self or peer assessment, which have been designed according both to e-learning and mathematics pedagogies based on the active role of the learner, the interaction with tutors and peers, and the importance of critical thinking and communication skills. Finally some feedback from students is reported, and some opportunities for future research are outlined.

Screencasting for Mathematics Online Learning

This chapter presents a case study of technology integration to support student learning in a first year operations research course at a dual delivery mode university. The course is taken by on-campus and distance students at the same time. It is shown how both groups are treated the same in this course in terms of provision of course material, access to the course learning management system, and to screencasts of live classes and additional explanations. The only difference between the two groups is the on-campus students’ ability to attend live face-to-face classes and to interact with the lecturer. The chapter demonstrates how screencasting is used effectively in online learning. Its objective is to share good practice of technology enhanced learning.

A Blended Learning Approach in Mathematics

In this chapter we present our work aimed at interweaving e-learning and face-to-face learning in Calculus courses for undergraduate engineering students. This type of blended learning (BL) contains the best properties of e-learning and face-to-face learning and helps overcome many obstacles in traditional teaching. We use our approach in order to improve students’ conceptual understanding of theorems. We describe online assignments specifically designed to help students better understand the meaning of a theorem. These assignments are given to students in addition to traditional lectures and tutorials with the objective that they can learn to learn on their own. Students “discover” the theorem and study it independently, by using a “bank” of examples and a lot of theoretical exercises we supply. The assignments are built in such a way that students receive feedback and instructions in response to their Web-based activity.

A Model for Asynchronous Discussions in a Mathematics Content Course

In this chapter a model is outlined for using asynchronous online discussions in a mathematics content course for preservice elementary teachers. The model integrates conversational discussion threads as a component of a traditional, face-to-face course. This successful approach is based on elements of the variation theory of learning, and derives from a comprehensive dissertation study examining its effectiveness.