Learning Functions of Two Variables Based on Mathematical Thinking Approach

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Hamidreza Kashefi ◽  
Zaleha Ismail ◽  
Yudariah Mohammad Yusof
Keyword(s):  
Prior Knowledge ◽  
Mathematical Thinking ◽  
Algebraic Manipulation ◽  
Advanced Mathematics ◽  
Face To Face ◽  
Functions Of Two Variables ◽  
Learning Functions ◽  
Multivariable Calculus ◽  
Mathematical Experience ◽  
Support Students

Multivariable function is one of the most important concepts in the learning of advanced mathematics. We had implemented a teaching approach to support students in the learning of two-variable functions by promoting mathematical thinking in face-to-face Multivariable Calculus classroom. This study investigates the obstacles and difficulties faced by students in the learning of two-variable functions based on the mathematical thinking approach. The findings indicated that students displayed various difficulties in finding the range and sketching the graph of two-variable functions. The students’ difficulties and obstacles such as poor mastery of algebraic manipulation, poor grasp of prior knowledge or lack of it, idiosyncrasy attributed from previous mathematical experience, and restricted mental images of two-variable functions could be classified as difficulties with techniques, concepts, and studying mathematics. Based on students’ responses, the difficulties were considered mainly conceptual in nature and few were related to techniques and studying mathematics.

Designing a Blended Learning Model to Support Mathematical Thinking in Multivariable Calculus

2012 ◽  
pp. 221-239 ◽  
Author(s):  
Hamidreza Kashefi ◽  
Zaleha Ismail ◽  
Yudariah Mohammad Yusof
Keyword(s):  
Blended Learning ◽  
Undergraduate Students ◽  
Teaching And Learning ◽  
Mathematical Thinking ◽  
Learning Difficulties ◽  
Learning Model ◽  
Face To Face ◽  
Multivariable Calculus ◽  
Learning Instruction ◽  
Support Students

Multivariable Calculus is one of the most difficult courses for undergraduate students. Researchers at Universiti Teknologi Malaysia (UTM) endeavor to support students in the learning of Multivariable Calculus by promoting mathematical thinking in a face-to-face classroom. This study attempts to identify not only learning difficulties in Multivariable Calculus through mathematical thinking approach but also the ways and means of improving these difficulties based on students and lecturers recommendations. The main purpose of this study is to establish a model of teaching and learning based on these findings for designing a blended learning instruction of Multivariable Calculus course through mathematical thinking approach. It first attempts to identify the theoretical reasons for selecting blended learning to promote mathematical thinking in Multivariable Calculus. Then, it exemplifies a teaching and learning model to support students’ mathematical thinking in Multivariable Calculus through blended learning instruction.

Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets

2013 ◽  
pp. 228-233
Author(s):  
Ayhan Kursat Erbas ◽  
Sarah Ledford ◽  
Chandra Hawley Orrill ◽  
Drew Polly
Keyword(s):  
Middle School ◽  
Common Core State Standards ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
State Standards ◽  
Educational Technologies ◽  
Core State ◽  
Geometric Patterns ◽  
The Common ◽  
Support Students

As teachers prepare to teach the Common Core State Standards for Mathematics (CCSSM), students’ exploration of patterns and relationships between numbers has gained more importance. Specifically, students’ conceptual understanding of numerical patterns is critical in middle school, as it lays a groundwork for fostering mathematical thinking at all levels. Educational technologies can enhance student’s explorations of patterns by providing opportunities to represent patterns, test conjectures, and make generalizations. In this chapter, the authors illustrate how spreadsheets can support students’ explorations of both arithmetic and geometric patterns in the middle grades.

Defending either a personal or an assigned standpoint

2018 ◽  
Vol 7 (1) ◽  
pp. 72-100
Author(s):  
Timo Salminen ◽  
Miika Marttunen
Keyword(s):  
Secondary School ◽  
Role Play ◽  
Female Students ◽  
Male Students ◽  
School Students ◽  
Face To Face ◽  
Personal Opinion ◽  
Upper Secondary ◽  
Support Students

Abstract This study clarifies whether a specific type of role play supports upper secondary school students’ collaborative argumentation. Data consist of 12 dyadic face-to-face and 12 chat debates. Data analysis focused on the quality of students’ argumentation. Comparisons were made between students who defended standpoints at variance with their personal opinions on the topics, between the two study modes and topics, and by gender. When the students defended a standpoint differing from their personal opinion, the male students engaged in counterargumentation more often than the female students. When, in turn, the students defended their personal standpoint, they produced both counterargumentative and non-argumentative speech turns equally often, and their arguments were more poorly elaborated than when they defended an assigned standpoint. The study suggests that role play in which both counterargumentation and students’ personal standpoints on an issue are taken into account is a viable means to support students’ high quality argumentation.

scholarly journals Implementation of Facebook study groups as supplements for learning management systems in adult ODL environments

2012 ◽  
Vol 7 (1) ◽  
pp. 1-11
Author(s):  
Ishan Sudeera Abeywardena ◽  
Tham Choy Yoong
Keyword(s):  
Undergraduate Students ◽  
Learning Experience ◽  
Participation Rate ◽  
Pilot Project ◽  
Study Groups ◽  
Online Tool ◽  
Postgraduate Students ◽  
Face To Face ◽  
Learning Management ◽  
Support Students

As an open and distance learning (ODL) institution, Wawasan Open University (WOU) employs a blended approach for delivering courses to its undergraduate and postgraduate students, who are entirely adult learners. In this approach, the use of a learning management system (LMS) is absolutely crucial for student support as well as the enhancement of the whole learning experience to compensate for the lack of face-to-face interaction between the students and the academics. WawasanLearn, the open source, Moodle-based LMS system used by WOU, is a comprehensive online tool that enables students and academics to effectively interact in a virtual environment. However, analysis of data from several semesters shows that the rate of student interaction on WawasanLearn is low with respect to the sharing of knowledge. In order to qualitatively and quantitatively identify the factors contributing to the student participation rate in WawasanLearn, a survey was conducted among the undergraduate students studying in various disciplines including science and technology, business administration, liberal studies, education, languages and communication. Feedback regarding the manner of support students expect from WawasanLearn was gathered from close to 550 students throughout Malaysia. Another purpose of the survey was to identify whether and why students are drawn to participate more frequently in social networking platforms such as Facebook (facebook.com). As a result of the findings of the survey, a pilot project was implemented to study the use of Facebook groups as study groups for supplementing WawasanLearn. These study groups were run in parallel to WawasanLearn for seven course modules over two consecutive semesters. This paper discusses the findings of this pilot project with respect to the implementation of Facebook groups as supplements to the LMS in an adult ODL environment.

scholarly journals Enhancing the student experience with the use of a dedicated subject website

2019 ◽  
Vol 17 (2) ◽  
pp. 39
Author(s):  
Rachel Hilliam ◽  
Gaynor Arrowsmith
Keyword(s):  
Social Media ◽  
Peer Support ◽  
Student Experience ◽  
Community Of Learners ◽  
Online Forums ◽  
Face To Face ◽  
Online Spaces ◽  
Effective Assessment ◽  
Assessment Strategies ◽  
Support Students

It is crucial not only to support students at all stages of their student journey, but also to create a space where they can benefit from peer support and interact with the wider mathematics and statistics (M&S) community. In a society awash with social media, it is possible to create online spaces that complement and enhance existing communities available in traditional face-to-face courses, or to provide such an environment for students who learn at a distance. The School of Mathematics and Statistics at The Open University (OU) has recently consolidated existing resources into a website resulting in an active and vibrant community of learners. The site contains resources, which students access at appropriate points in their student journey through M&S modules and qualifications. These resources are complemented by a number of dedicated and well-used online forums. In particular, a forum providing course choice information. Discussions in the forum have ultimately led to improvements in the structure of M&S qualifications, influencing the content of new modules, more effective assessment strategies, and better ways of supporting students. It is a true community of learners, where everyone - students, academics and educational advisors - all contribute, learn from each other, and shape the student experience.

scholarly journals Enacting Number Talks in a Simulated Classroom Environment: What Do Preservice Teachers Notice About Students?

2021 ◽  
Vol 4 (4) ◽  
pp. 772-795
Author(s):  
Dawn M. Woods
Keyword(s):  
Preservice Teachers ◽  
Classroom Environment ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
Learning Cycle ◽  
Missed Opportunities ◽  
Human In The Loop ◽  
Mathematical Discussions ◽  
Support Students ◽  
Number Talks

Number talks are short mathematical discussions offering sensemaking opportunities for students. Aside from bolstering students’ mathematical learning, this instructional routine may also support preservice teachers (PSTs) in investigating how to facilitate discussion-focused instruction. In this study, PSTs engage in a learning cycle to explore, plan and rehearse two separate number talks during human-in-the-loop simulations, and then reflect on these experiences. During the first simulation, PSTs focus on understanding the routine’s components while positioning avatar-students as sensemakers as they elicit their participation. In the second simulation, PSTs build their instructional skills as they record representations of students’ mathematical thinking, probe students’ thinking in order to make mathematics visible, as well as notice missed opportunities to support students’ mathematical reasoning during reflections of their experiences. Implications of this study suggest that simulations, when embedded within a cycle of enactment and reflection, support PSTs in developing professional noticing skills.

scholarly journals Why and how to support students in team assignments

2016 ◽  
Vol 8 ◽  
Author(s):  
Judith Stevenson
Keyword(s):  
Student Experience ◽  
Formal Training ◽  
Face To Face ◽  
Virtual Teamwork ◽  
Team Projects ◽  
University Courses ◽  
Workplace Environments ◽  
Teamwork Skills ◽  
College Setting ◽  
Support Students

Once employed, our graduates will be judged on their ability to be effective team players. In some professions, people’s safety and even survival may depend on good teamwork. Yet teamwork assignments in university courses are not generally a popular option. Team projects are often viewed as a difficult and frustrating requirement, by students and faculty alike. Few instructors receive any formal training on how to create effective team assignments or on ways to educate their students about strategies for success in their team activities. In this session, we discuss ways to educate students about the value of team experiences in their courses, so that they are motivated to improve their teamwork skills. We examine the dynamics of both face-to-face and virtual teamwork, in workplace environments and in a college setting, so as to understand the underlying reasons for the challenges inherent in team activities. Then finally we explore some techniques that instructors can use to design and deliver team assignments that support a positive student experience.  

scholarly journals Which Prior Mathematical Knowledge Is Necessary for Study Success in the University Study Entrance Phase? Results on a New Model of Knowledge Levels Based on a Reanalysis of Data from Existing Studies

2020 ◽  
Vol 6 (3) ◽  
pp. 375-403 ◽  
Author(s):  
Stefanie Rach ◽  
Stefan Ufer
Keyword(s):  
Prior Knowledge ◽  
Mathematical Knowledge ◽  
Mathematics Teacher Education ◽  
Advanced Mathematics ◽  
Formal Representation ◽  
Study Success ◽  
Mathematics Courses ◽  
First Semester ◽  
Four Levels ◽  
Different Levels

Abstract The transition from school to tertiary mathematics courses, which involve advanced mathematics, is a challenge for many students. Prior research has established the central role of prior mathematical knowledge for successfully dealing with challenges in learning processes during the study entrance phase. However, beyond knowing that more prior knowledge is beneficial for study success, especially passing courses, it is not yet known how a level of prior knowledge can be characterized that is sufficient for a successful start into a mathematics program. The aim of this contribution is to specify the appropriate level of mathematical knowledge that predicts study success in the first semester. Based on theoretical analysis of the demands in tertiary mathematics courses, we develop a mathematical test with 17 items in the domain of Analysis. Thereby, we focus on different levels of conceptual understanding by linking between different (in)formal representation formats and different levels of mathematical argumentations. The empirical results are based on a re-analysis of five studies in which in sum 1553 students of bachelor mathematics and mathematics teacher education programs deal with some of these items in each case. By identifying four levels of knowledge, we indicate that linking multiple representations is an important skill at the study entrance phase. With these levels of knowledge, it might be possible to identify students at risk of failing. So, the findings could contribute to more precise study advice and support before and while studying advanced mathematics at university.

scholarly journals EVEKTIFITAS MEDIA PEMBELAJARAN DARING EDMODO DALAM PERKULIAHAN PENDIDIKAN AGAMA ISLAM PADA MASA PANDEMI COVID-19

2020 ◽  
Vol 4 (2A) ◽  
pp. 77-82
Author(s):  
MINTEN AYU LARASATI
Keyword(s):  
Online Learning ◽  
Learning Outcomes ◽  
Learning Process ◽  
Qualitative Case Study ◽  
Student Discipline ◽  
Face To Face ◽  
Learning Functions ◽  
Course Material ◽  
The Media

The Covid-19 outbreak has greatly affected the learning process, because of lecturescannot be implemented in the form of face-to-face lectures. One way to getachieving learning outcomes is to use the system learning mediaonline. Online learning functions as a link between lecturers and studentswith an internet network that can be accessed anytime and anywhere. MediaOnline learning used is Edmodo, a learning platformbased on social networks. The purpose of this research is to analyze the effectiveness of the mediaedmodo in the PAI lecture on semseter 1 students, mix class at the UniversitySumbawa technology. This type of research is a qualitative case study, a methoddata collection used is documentation, interviews and observations.The results of the study concluded that the Covid-19 pandemic changed shapePAI learning becomes online, the media used is edmodo. Edmodo is ratedeffective for carrying out the learning process because, the course material can be accepted,studied and reviewed, assignment collection is simpler, easier and can be scoredaccepted directly, improve student discipline and consistency, easy andnice. Interaction and communication during online learning becomes easier anddirected with the features provided by Edmodo so that the objectives and CPMK PAI canwell earned.

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.

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