scholarly journals Doing, Teaching, Learning and Thinking About Mathematics – On Becoming a Transformative Teacher

2018 ◽  
Vol 7 (1) ◽  
pp. 11-24
Author(s):  
Binod Prasad Pant
Keyword(s):  
Mathematics Teacher ◽  
Mathematics Teaching ◽  
Teaching Mathematics ◽  
Algorithmic Problem ◽  
Academic Problems ◽  
Mathematical Concepts ◽  
Teaching Career ◽  
Beliefs And Practices ◽  
Mathematical Problems ◽  
Teaching Learning

I solved many mathematical problems till today - countless academic problems inside the classroom, and a few pragmatic problems outside. At the beginning of my teaching career, I spent significant time convincing my students that mathematics teaching is an algorithmic problem solving of routine mathematical items to get the correct answers. Afterwards, I slowly took a shift from doing mathematics to teaching mathematics, identifying lots of tricks, tips and techniques. I spent more than a decade to train myself with better techniques to become a better mathematics teacher seeking better achievements of students in written tests. Later on, I engaged myself as a math learner and sought the significance of the methods I employed to teach the mathematical concepts, relation, and logics. I am now at the crossroads of searching better alternatives that help students learn mathematics in a meaningful way. I frequently ask myself why I am teaching mathematics. What does a good mathematics teacher mean? What we do is largely guided by what we believe. Questioning on the widely accepted assumptions, examining the deep-rooted beliefs for the positive shift, and highlighting the epiphanies of my professional life could be very essential on becoming a transformative teacher. In this paper, I portray my narratives as a student and as a mathematics teacher to explain my shift towards becoming a transformative teacher. Through my verisimilitude narratives, I invite readers to examine their beliefs and practices on teaching mathematics, and envisage for better alternatives being aware of their limitations and contexts.

scholarly journals The Use of Realistic Mathematics Education (RME) to Help Indonesian 5th-Grade Students to Learn Multiplication and Division

2020 ◽  
Vol 10 (1) ◽  
pp. 41-53
Author(s):  
Nanang Setiadi
Keyword(s):  
Mathematics Education ◽  
Learning Process ◽  
Mathematics Teaching ◽  
Realistic Mathematics Education ◽  
Realistic Mathematics ◽  
Alternative Approach ◽  
Mathematical Problems ◽  
Teaching Learning ◽  
Mastery Criteria ◽  
5Th Grade

Abstract                                                              This paper discusses the use of Realistic Mathematics Education (RME) as an alternative approach to enhance Indonesian 5th-grade students’ ability in multiplication and division. It presents the analysis of Indonesian 5th-grade students’ difficulties in applying stacking method for multiplication and division. Furthermore, it describes a mathematics teaching learning practice to stimulate students constructing their strategies, mathematical models and number sense in solving mathematical problems that involve multiplication and division. The teaching learning practice aims to apply RME for helping students develop their multiplication and division ability.Findings shows that stacking methods for multiplication and division are difficult for the students. The main students’ problem in multiplication and division stacking methods is in reapplying the steps of the methods. The steps taken to improve the learning process by implementing RME are: (1) analyze in detail the difficulties of students in multiplication and division stacking methods, (2) provide contexts of mathematical problems that can stimulate students to think mathematically, (3) hold a class mathematics congress, and (4) conduct a test to measure students’ achievement.            Based on the students’ achievement, there has been several improvements. After RME, there were more students whose grades passed the Minimum Mastery Criteria. Moreover, there was a student who got 100. Then, the average test was higher. Meanwhile, there were only 3 children whose grades were 0. Thus, the application of RME has helped the 5th-grade students to improve their ability in multiplication and division.         

scholarly journals Students’ approaches while solving a non-typical geometrical problem

2020 ◽  
Vol 12 ◽  
pp. 197-210
Author(s):  
Bożena Maj-Tatsis ◽  
Marta Pytlak
Keyword(s):  
Mathematics Education ◽  
Mathematics Teacher ◽  
Mathematics Classroom ◽  
Prior Experience ◽  
Age Groups ◽  
Mathematical Concepts ◽  
Geometrical Problem ◽  
Solution Methods ◽  
Mathematical Problems ◽  
The Relationship

In the paper we present the results of two teaching episodes, which took place in two middle school classes with 13- and 14-year-old students. The students in both classes were asked to solve the same geometrical problem;then a discussion followed, in which they had to justify their solutions. In both cases the students had no prior experience in solving non-typical mathematical problems. Additionally, the students were asked to justify theiranswers, which is not a common characteristic of a ‘typical’ mathematics classroom at that level. The problem was chosen from a wider study, in which twenty classes from twenty different schools were analysed. One of theaims of the present study was to analyse the skills that require a deeper understanding of mathematical concepts and properties. Particularly, we aimed to investigate students’ different solution methods and justifications duringproblem solving. The results show considerable differences among the two classes, not only concerning the depth of investigating (which was expected due to the different age groups), but also concerning the relationship betweenachievement (as assessed by the mathematics teacher) and success in solving the problem. These results demonstrate the need for re-directing mathematics education from a pure algorithmic to a deeper thinking approach.

How and wherer can a Mathematics Teacher Utilize his 33 Years of Teaching Experience? A Math Teacher about Teaching Mathematics-Excerpt from 33 Years of Teaching Experience

2019 ◽  
pp. 467-472
Author(s):  
Ildikó-Anna Pomuczné Nagy
Keyword(s):  
High School ◽  
Mathematics Education ◽  
Teacher Training ◽  
Problem Solving ◽  
Mathematics Teacher ◽  
Teaching Experience ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Years Of Teaching Experience ◽  
Textbook Writing

This paper shows how a mathematics teacher can utilize his teaching experience. I have been working as a mathematics and physics teacher in Hungary for 33 years. I have taught at various levels of the education system: at elementary school, high school, teacher training college, and in teacher training too, but at most time of my job I taught at high school. I am currently working on the series of a new mathematics textbook for 10 to 14-year-old students. It is based on the traditions of the Hungarian mathematics education, but using the opportunities offered by the 21st century, it also includes modern sample tasks that fit into the curriculum, for example Geogebra files, written by me. I would like to share how I use my teaching experience in textbook writing and how I focus primarily on the didactic aspects of teaching mathematics. I pursue my PhD research in the topic of problem-solving thinking, so I study the mathematical thinking of my students studying in different school types. In my lecture, I analyse different tasks by focusing on mathematical methodological aspects. For example I will tell that I believe it is advantageous to introduce mathematical definitions with examples which are astonishing for students in order to draw attention to maths as much as possible. I will give examples of how I build my experience into the textbook in order to make the system of mathematical concepts optimal for pupils. I would like it if give you an insight into a segment the current Hungarian mathematics education, the current teaching of problem-solving thinking and the different ways of students’ thinking.

Thinking in Action and Beyond

2018 ◽  
Author(s):  
Terezinha Nunes
Keyword(s):  
Hard Of Hearing ◽  
Inverse Relation ◽  
Teaching Approaches ◽  
Multiplicative Reasoning ◽  
Mathematical Concepts ◽  
Logical Organization ◽  
The World ◽  
Mathematical Problems ◽  
Addition And Subtraction ◽  
Learning By Imitation

Before children learn to use language, they learn about the world in action and by imitation. This learning provides the basis for language acquisition. Learning by imitation and thinking in action continue to be significant throughout life. Mathematical concepts are grounded in children’s schemas of action, which are action patterns that represent a logical organization that can be applied to different objects. This chapter describes some of the conditions that allow deaf or hard-of-hearing (DHH) children to learn by imitation and use schemas of action successfully to solve mathematical problems. Three examples of concepts that can be taught by observation and thinking in action are presented: the inverse relation between addition and subtraction, the concepts necessary for learning to write numbers, and multiplicative reasoning. There is sufficient knowledge for the use of teaching approaches that can prevent DHH children from falling behind before they start school.

Problem solving with the Sneetches

2016 ◽  
Vol 23 (5) ◽  
pp. 282-283
Author(s):  
James Russo ◽  
Toby Russo
Keyword(s):  
Problem Solving ◽  
Multiple Solutions ◽  
Mathematical Concepts ◽  
Mathematical Problems

Math by the Month features collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes four activities each for grade bands K–2, 3–4, and 5–6. In this issue, teachers read the classic Dr. Seuss book The Sneetches and other stories with their class and get students to engage with these associated mathematical problems. The problems, many of which are open-ended or contain multiple solutions or solution pathways, cover a range of mathematical concepts.

Assimilation of the concept of numeric expression in teaching primary school mathematics

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Ivanka Georgieva ◽  
◽  
◽  
Keyword(s):  
Primary School ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Primary School Mathematics ◽  
Mathematical Problems

The concept of numeric expression is a basic one in teaching mathematics. It is introduced and assimilated in primary school. This concept is a component of many other concepts and problems in school course of mathematics. That is why discussing and analyzing the process of understanding and assimilating the notion of numeric expression is of great importance both to the teachers and pupils. The present study focuses on some key activities and groups of problems aiming at mastering pupils’ abilities to solve various mathematical problems, to overcome some difficulties and prevent from making mistakes in finding the ways of solving different problems and doing so to enrich their knowledge in mathematics.

scholarly journals Project Based Learning (PBL) as a Promising Challenge of Teaching Mathematics

1970 ◽  
pp. 379-409
Author(s):  
Miri Hilai
Keyword(s):  
Cognitive Abilities ◽  
Self Regulation ◽  
Project Based Learning ◽  
Teaching Mathematics ◽  
Mathematical Skills ◽  
The Past ◽  
Innovative Learning ◽  
Different Populations ◽  
Individualized Teaching ◽  
Teaching Learning

Mathematics has always presented a challenge, both for teachers and for pupils, all around the world. Teachers of mathematics of all time periods are interested in having their pupils master the mathematical skills and love math. They deliberate on ways of teaching-learning, because of the tremendous gaps in their pupils’ cognitive abilities and their non-uniform abilities to pay attention and to concentrate. It appears that the main solution in the frontal mathematics lessons is offered to the average pupils, but the main goal is to provide a solution for the entire classroom population. Over the years I have searched for different ways beyond frontal and individualized teaching, so that I could provide a solution for populations with different needs in the mathematics lessons. My search for alternative ways derived also from the need to promote the achievements and to boost the motivation, interest, curiosity, and enjoyment in the learning of mathematics. Contemporary research indicates that there is practical innovative learning which is active and involving; it is called project-based learning (PBL). PBL provides a solution for the improvement of the performances in mathematics, for the motivation of the pupils, and for the inspiration of interest and curiosity in and enjoyment from this field of knowledge. From my experience as a teacher in the past and from the reports of my students in the Gordon Academic College for Education in the PBL course, in such teaching a solution is provided for the different populations in the class. The pupils are engaged in learning in practical and realistic projects that are relevant to their lives. They are more active and autonomous, work cooperatively, and develop patterns of behaviour of independence in learning, self-orientation, and self-regulation. These skills and patterns of behaviour are important to their lives as adults and cultivate the six functions of the learner that are derived from the curriculum in Israel: sensory-motor, self-direction in learning and in its management, intrapersonal and interpersonal, cognitive and meta-cognitive.

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.

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