Making Sense of Number

2021 ◽  
Author(s):  
Annette Hilton ◽  
Geoff Hilton
Keyword(s):  
Conceptual Framework ◽  
Real World ◽  
Number Sense ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Making Sense ◽  
Experience Teaching ◽  
Numeracy Skills

Making Sense of Number is a concise introduction to personal and professional numeracy skills, helping readers to become more mathematically competent. It includes relevant content to assist pre-service teachers to improve numeracy for the classroom or to prepare for LANTITE, as well as support for practising teachers to develop their understanding and skills in numeracy. Making Sense of Number focuses on number sense as a conceptual framework for understanding mathematics, covering foundational areas of mathematics that often cause concern such as multiplication, fractions, ratio, rate and scale. The authors use real-world examples to explain mathematical concepts in an accessible and engaging way. Written by authors with over 30 years' experience teaching mathematics at primary, secondary and tertiary levels, Making Sense of Number is an essential guide for both pre-service teachers and those looking to improve their understanding of numeracy.

Teaching and Learning of Mathematics in Lower Primary in Schools in Ghana

2021 ◽  
pp. 136-154
Author(s):  
Frank Quansah
Keyword(s):  
Problem Solving ◽  
Human Activity ◽  
Teaching And Learning ◽  
Qualitative Approach ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Making Sense ◽  
The World ◽  
Problem Solving Strategies ◽  
Research Questions

Mathematics is a fundamental human activity – a way of making sense of the world. Children possess a natural curiosity and interest in mathematics and come to school with an understanding of mathematical concepts and problem-solving strategies that they have discovered through explorations of the world around them. The purpose of this study is to find out how mathematics is being taught and learnt among primary one pupils in basic schools in Ghana. A qualitative approach was employed to provide answers to the research questions raised. It was found that teachers employed variety of procedures for teaching mathematics. However, there were some problems encountered in the teaching and learning of mathematics.

“Is There Lead in My Water?”: Employing a Culturally Compelling Instructional Perspective to Teach for Change

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Fenice B. Boyd ◽  
Monica L. Ridgeway ◽  
Tiffany M. Nyachae
Keyword(s):  
Conceptual Framework ◽  
Real World ◽  
Instructional Practice ◽  
Instructional Delivery ◽  
Learning Opportunities ◽  
Content Area ◽  
Illustrative Case ◽  
Water Crisis ◽  
Alternative Learning ◽  
Instructional Perspective

AbstractIn this paper we build a conceptual framework to argue for culturally compelling instruction that leads to teaching for change. Culturally compelling instruction calls for a substantive shift in how teachers view their students, communities, and what the perspective might mean for students’ future when they have access to alternative learning opportunities. The framework encourages teachers to take a stance and assume responsibility and ownership for their own decisions about the curriculum and instructional delivery. Most prominent is to acquire a depth of understanding of their students’ identities and needs. To represent our vision for culturally compelling instruction we use the lead poisoned water crisis in Flint, Michigan, USA as an illustrative case. Our work provides an example of how a real-world circumstance such as Flint’s may be integrated into content area subjects to frame a culturally compelling instructional practice.

scholarly journals Making sense of international variations in lesson study and lesson study-like practices

2018 ◽  
Vol 7 (3) ◽  
pp. 201-216 ◽  
Author(s):  
Brahm Norwich
Keyword(s):  
Conceptual Framework ◽  
Professional Learning ◽  
Lesson Study ◽  
Learning Approaches ◽  
Content Type ◽  
Group Problem Solving ◽  
Making Sense ◽  
Learning Practices ◽  
Learning Development ◽  
Definition Of

Purpose The purpose of this paper is to examine variations within lesson study (LS) practices and their connections with related traditions: teacher research/enquiry approaches, professional development models, professional learning communities and group problem-solving approaches. Questions are addressed about the relationships between different professional learning approaches in terms of definitions and frameworks. Design/methodology/approach Academic databases and website sources were searched in a purposive way to identify 20 practices associated with these traditions for comparative analysis. Findings A conceptual framework consisting of eight dimensions was constructed to account for the variations within and between these professional learning traditions: for instance, about the settings in which the practices take place, the purposes of the practices and the specific procedures involved. By illustrating how specific practices fitted within this framework it is concluded that the variations within the LS tradition are wide enough to make it difficult to identify a set of necessary and sufficient features of LS to distinguish LS practices from the other non-LS professional learning practices. Reasons are also given for considering whether a polythetic type of definition of professional learning/development practices might be constructed. Research limitations/implications The possibility for a more systematic review of professional learning approaches for the construction of a conceptual framework is discussed. Practical implications Ways in which this kind of conceptualisation can be useful in promoting clarity about professional learning practices and in developing these practices are discussed. Originality/value The originality of this paper lies in the construction of a conceptual framework to analyse similarities and differences within and between various professional learning traditions.

scholarly journals Digital Representations of Mathematical Objects in the Context of Various Forms of Representation of Mathematical Knowledge

2020 ◽  
pp. 58-86
Author(s):  
Semjon F. Adlaj ◽  
◽  
Sergey N. Pozdniakov ◽  
Keyword(s):  
Comparative Analysis ◽  
Digital Media ◽  
Mathematical Knowledge ◽  
Information Environment ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Objects ◽  
Computer Tools ◽  
Digital Representations ◽  
The Impact

This article is devoted to a comparative analysis of the results of the ReMath project (Representing Mathematics with digital media), devoted to the study of digital representations of mathematical concepts. The theoretical provisions and conclusions of this project will be analyzed based on the theory of the information environment [1], developed with the participation of one of the authors of this article. The analysis performed in this work partially coincides with the conclusions of the ReMath project, but uses a different research basis, based mainly on the work of Russian scientists. It is of interest to analyze the work of the ReMath project from the conceptual positions set forth in this monograph and to establish links between concepts and differences in understanding the impact of computer tools (artifacts) on the process of teaching mathematics. At the same time, the authors dispute the interpretation of some issues in Vygotsky’s works by foreign researchers and give their views on the types and functions of digital artifacts in teaching mathematics.

scholarly journals Pedagogical conditions for implementing value and sense direction of training mathematics at higher school

2020 ◽  
pp. 80-92
Author(s):  
Larisa V. Zhuk
Keyword(s):  
Creative Thinking ◽  
Educational Process ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Search Activity ◽  
Mathematical Concepts ◽  
Teaching Aids ◽  
Semantic Orientation ◽  
Cognitive Information ◽  
The University

The article actualizes the issue of updating the content, methods and means of teaching mathematics at the university within the sociocultural paradigm. A significant contradiction characterizing the crisis situation in the field of higher mathematical education is the mismatch between the traditional organization of the educational process and the powerful developing potential of mathematical disciplines. Being overloaded with a lot of information, altogether with its insufficiently developed anthropological, cultural-like and communicative components, mathematical education hinders the mental development of the learner’s personality in relation to such important qualities as search activity, creativity, and creative thinking. The solution to this problem can be the transformation of the cognitive-information model of learning, the introduction of pedagogical technologies that actualize the sociocultural aspect of mathematical education. The aim of the study is to develop methodological foundations for the implementation of the value-semantic orientation of teaching mathematics at the university, expressed in providing a set of pedagogical conditions related to the selection of content, determination of teaching aids and methods, ways of organizing the interaction of students and a teacher, in which students intelligently master mathematical concepts, and freely operate with them. The didactic conditions for the implementation of the value-semantic orientation of teaching mathematics at the university are: the transformation of mathematical content, expressed in learning from sociocultural experience; the psychodidactic approach, focused on building the students’ self-motivation; the use of teaching methods that provide cognitive and emotional empathy (educational mathematical discourse), the activization of productive mental activity (technology of problematic dialogue); inclusion of non-standard, creative tasks, training cases. Providing these conditions will allow to realize the humanitarian potential of mathematics, to reveal the social, practical and personal significance of the subject matter.

scholarly journals Challenges and Opportunities: Experiences of Mathematics Lecturers Engaged in Emergency Remote Teaching during the COVID-19 Pandemic

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2303
Author(s):  
Eabhnat Ní Fhloinn ◽  
Olivia Fitzmaurice
Keyword(s):  
Working Conditions ◽  
Online Teaching ◽  
Online Survey ◽  
Prior Experience ◽  
Teaching Mathematics ◽  
Experience Teaching ◽  
Challenges And Opportunities ◽  
Teaching Of Mathematics ◽  
Nature Of Mathematics ◽  
The Impact

In this paper, we consider the experiences of mathematics lecturers in higher education and how they moved to emergency remote teaching during the initial university closures due to the COVID-19 pandemic. An online survey was conducted in May–June 2020 which received 257 replies from respondents based in 29 countries. We report on the particular challenges mathematics lecturers perceive there to be around teaching mathematics remotely, as well as any advantages or disadvantages of teaching mathematics online that they report. Over 90% of respondents had little or no prior experience teaching mathematics online, and, initially, 72% found it stressful and 88% thought it time-consuming. 88% felt there was a difference between teaching mathematics in this way compared with other disciplines. Four main types of challenges were associated with emergency remote teaching of mathematics: technical challenges; student challenges; teaching challenges; and the nature of mathematics. Respondents identified flexibility as the main advantage of online teaching, with lack of interaction featuring strongly as a disadvantage. We also consider respondents’ personal circumstances during this time, in terms of working conditions and caring responsibilities and conclude by summarizing the impact they perceive this experience may have upon their future teaching. Forty-six percent% of respondents self-identified as having caring responsibilities, and 61% felt the experience would affect their future teaching.

The role and significance of computer animation in school algebra of complex numbers

2021 ◽  
pp. 22-27
Author(s):  
S. V. Larin
Keyword(s):  
Computer Animation ◽  
Research Work ◽  
Complex Numbers ◽  
Teaching Mathematics ◽  
Research Approach ◽  
Mathematical Concepts ◽  
Teaching Aids ◽  
Tenth Grade ◽  
Relevant Topic ◽  
Approach To Teaching

The article discusses computer technologies in teaching mathematics, which is relevant in the light of the digitalization of education. The role and importance of computer animation in algebra lessons in the study of complex numbers in the tenth grade in accordance with the current school textbooks are presented. Animation drawings can be used as demonstration drawings when studying the relevant topic, as a tool for testing knowledge, they provide an opportunity for experimentation, support the research style of developing learning. The use of animated drawings effectively replenishes the arsenal of teaching aids for a practicing mathematics teacher. This allows you to eliminate unnecessarily burdensome computational difficulties, to visualize mathematical concepts and statements, turning some of them into obviously correct ones, to facilitate the teacher's work in compiling tasks of the same type with different data. The management of the student's educational and research work on the manufacture of animation-geometric models of objects and phenomena contributes to the successful assimilation of knowledge by students, stimulates an experimental research approach to teaching.

Integrated Experiences

2015 ◽  
pp. 278-295
Author(s):  
Carol Carruthers ◽  
Dragana Martinovic ◽  
Kyle Pearce
Keyword(s):  
Young Adults ◽  
Statistical Analysis ◽  
Mathematics Education ◽  
Conceptual Framework ◽  
Knowledge Bases ◽  
Successful Implementation ◽  
Community Of Learners ◽  
Mathematical Concepts ◽  
Education Environment ◽  
K 12

This chapter discusses the integrated experiences of a group of instructors who are using tablets to teach mathematics to adolescents and young adults. iPad technology offers learners in different educational streams and with different knowledge bases an environment that fosters the growth of a community of learners engaged in mathematical concepts and processes. The authors present an in-depth examination of the design of a tablet-based mathematics education environment and provide a statistical analysis to highlight the full richness of their classroom-based experiments. The results are presented using the five foundational aspects of a conceptual framework for the successful implementation of technology in a K-12 environment.

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