scholarly journals Immersive teacher training experience on the methodology of problem posing and solving in Mathematics

2019 ◽  
Author(s):  
Francesco Floris ◽  
Alice Barana ◽  
Anna Brancaccio ◽  
Alberto Conte ◽  
Cecilia Fissore ◽  
...  
Keyword(s):  
Teacher Training ◽  
Teaching And Learning ◽  
Problem Posing ◽  
Ministry Of Education ◽  
Training Experience ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Mathematical Exploration ◽  
New Methodologies ◽  
The Individual

In an Italian and European context, one of the fundamental skills in Mathematics is the ability to solve problems in everyday situations, often linked to everyday life. For this reason, the problem posing and solving methodology plays a fundamental role in the process of teaching and learning Mathematics. This paper presents the results of the immersive experience "Mathematical Exploration with Problem Posing and Solving", included in the teacher training activities proposed by the national PP&S - Problem Posing & Solving - Project of the Italian Ministry of Education, which aims at enhancing the teaching and learning of Mathematics by using new methodologies and technologies. In particular, the focus will be on the work and considerations of the 50 teachers who took part in the project, from both primary and secondary school. They were guided through the individual step-by-step creation of a contextualized problem, following a process guided through stimulus-based questions. This immersive experience brought about the production of valid problems and was full of very  stimulating teachers' considerations on the various phases of the problem posing and solving.

scholarly journals Análisis de materiales didácticos digitales para guiar y/o apoyar el proceso de enseñanza - aprendizaje de las matemáticas

2018 ◽  
pp. 72 ◽  
Author(s):  
Dorinda Mato-Vázquez ◽  
Mª Montserrat Castro-Rodríguez ◽  
Camino Pereiro González
Keyword(s):  
Canary Islands ◽  
Teaching And Learning ◽  
Ad Hoc ◽  
Digital Technologies ◽  
Online Resources ◽  
Autonomous Community ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
The Individual ◽  
Media Channels

Digital technologies have brought about a revolution in all areas of life: technological, business, communicative, cultural, and even in knowledge and entertainment. In the educational landscape it also has its reflection and the methodologies and resources have been redrawn, in terms of different media, channels, languages, narratives, etc. These changes, substantive and profound, affect all the society simultaneously, but other agents as educational administrations and the publishing sector is also involved. In this research we analyze a sample of institutional portals and commercial platforms that offer digital didactic resources in the area of mathematics in the Autonomous Community of Galicia. We focus on the type of materials, the pedagogical model that underlies them, the differences between commercial and institutional platforms, their use, impact on teaching and learning mathematics in the classroom, etc. The instrument used was a questionnaire designed ad hoc and validated and administered to 13 commercial platforms; both those produced commercially by publishing companies and those of an institutional nature generated by the regional administrations of the Canary Islands, Galicia and Valencia. The results indicate that, although the range of online offer of didactic materials for mathematics is wide and with varied formats, they have pedagogical shortcomings that do not favor active methodologies or a true integration of other alternatives that promote the development of open, flexible educational projects that facilitate the attention to the individual and collective diversity of each person, as well as the participation, interactivity / connectivity of the educational community, since most reproduce the format of the printed textbook by adding some online resources.

Mathematical Insight: Changing Perspective

2003 ◽  
Vol 96 (4) ◽  
pp. 238-242
Author(s):  
Cliff W. Sloyer
Keyword(s):  
Teaching And Learning ◽  
Higher Order ◽  
Approaches To Teaching ◽  
One Dimensional ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Mathematical Exploration ◽  
Problems And Solutions ◽  
Big Picture

Many great ideas in mathematics have resulted from examining problems and solutions from different perspectives or directions, but one-dimensional thinking in solving a problem is all too familiar. A number of approaches to teaching and learning mathematics, especially those involving algorithms of some form, lend themselves to a reinforcement of one direction in solving problems. Mathematical insight gained by changing perspective is occasionally suggested in specific problems, but the “big picture” of mathematical exploration, conjecture, and proof requires a deeper commitment to this process. This article focuses on problems that can benefit from a change in perspective by looking forward and backward. In particular, the transition from basic mathematical manipulations to higher-order levels of reasoning requires an awareness of such processes.

scholarly journals Problematizing teaching and learning mathematics as “given” in STEM education

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Yeping Li ◽  
Alan H. Schoenfeld
Keyword(s):  
Mathematics Education ◽  
Stem Education ◽  
Teaching And Learning ◽  
Science Technology ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Alternative Approach ◽  
And Mathematics ◽  
Scientific Engineering

AbstractMathematics is fundamental for many professions, especially science, technology, and engineering. Yet, mathematics is often perceived as difficult and many students leave disciplines in science, technology, engineering, and mathematics (STEM) as a result, closing doors to scientific, engineering, and technological careers. In this editorial, we argue that how mathematics is traditionally viewed as “given” or “fixed” for students’ expected acquisition alienates many students and needs to be problematized. We propose an alternative approach to changes in mathematics education and show how the alternative also applies to STEM education.

Teaching and Learning Mathematics

1987 ◽  
Vol 71 (458) ◽  
pp. 314
Author(s):  
Paul Ernest ◽  
Peter G. Dean
Keyword(s):  
Teaching And Learning ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

scholarly journals A Study of Errors and Misconceptions in the Learning of Addition and Subtraction of Directed Numbers in Grade 8

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude
Keyword(s):  
Conceptual Understanding ◽  
Teaching And Learning ◽  
Study Data ◽  
Negative Numbers ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Logical Errors ◽  
Grade 8

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.

Mogućnosti primene istraživački zasnovane nastave (IN) u početnom matematičkom obrazovanju

2021 ◽  
Author(s):  
Dragana Glogovac ◽  
◽  
Marina Milošević ◽  
Bojan Lazić ◽  
Keyword(s):  
Teaching And Learning ◽  
Teaching Practice ◽  
Teaching Mathematics ◽  
Teaching Process ◽  
Inquiry Based Learning ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Key Competencies ◽  
Insight Into

Modern primary education, especially mathematics, requires constant innovation of teaching practice in order to modernize, rationalize, and efficiently the teaching process. Teaching mathematics should be experienced as a process that promotes learning with understanding, stimulates motivation, active learning, research, critical thinking, analysis, problem solving, drawing conclusions, exchange of experiences. The tendency to improve the quality of mathematics education has resulted in many studies pointing to the benefits of research-based mathematics (IN) teaching, known as inquiry-based learning (IBL), recognized as an essential way of organizing the teaching process to develop key competencies, abilities and skills in 21st century. Тhe aim of this paper is to see, based on a comprehensive theoretical analysis and the results of previous research. The created model of teaching mathematics based on research represents a useful framework for improving the quality of the process of teaching and learning mathematics, and empowers teachers in its application and affirmation, gaining insight into the way of organizing research learning.

scholarly journals Student teachers’ perceptions of democracy in the mathematics classroom: Freedom, equality and dialogue

Pythagoras ◽  
2012 ◽  
Vol 33 (2) ◽  
Author(s):  
Wajeeh Daher
Keyword(s):  
Teacher Education ◽  
Student Teachers ◽  
Teaching And Learning ◽  
Mathematics Classroom ◽  
Mathematics Teacher Education ◽  
Comparison Method ◽  
Teachers Perceptions ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Two Stages

This article studies student teachers’ perceptions of the pedagogic and didactic aspects of teaching and learning mathematics in a democratic classroom. It is concerned primarily with issues of democracy in the mathematics classroom, specifically freedom, equality and dialogue. The research was conducted in two mathematics teacher education classes, where students were in their third year of study to major in mathematics. To find these students’ perceptions of democracy in the mathematics classroom the first two stages of the constant comparison method were followed to arrive at categories of democratic and undemocratic acts. The participants in the research emphasised that instructors should refrain from giving some students more time or opportunities to express themselves or act in the mathematics classroom than other students, because this would make them feel unequal and possibly make them unwilling to participate further in the mathematics classroom. The participants also emphasised that instructors should not exert their power to stop the flow of students’ actions in the mathematics classroom, because this would trouble them and make them lose control of their actions. Further, the participants mentioned that instructors would do better to connect to students’ ways of doing mathematics, especially of defining mathematical terms, so that students appreciate the correct ways of doing mathematics and defining its terms.

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