Using Tools to Make Sense of Right Triangles

2018 ◽  
Vol 23 (4) ◽  
pp. 226-230
Author(s):  
Terri L. Kurz ◽  
Mi Yeon Lee
Keyword(s):  
Conceptual Understanding ◽  
Three Dimensional ◽  
Mathematical Understanding ◽  
Sense Making ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Ideas

Sometimes, teaching mathematics with a focus on conceptual understanding can be challenging. With the advent of standards and principles (CCSSI 2010; NCTM 2014) an emphasis has been placed on using tools for deeper mathematical understanding and learning with understanding. Specifically, there has been a movement to include opportunities for learners to engage in sense-making activities when exploring mathematical concepts (Schoenfeld 1992). Tools can be used to support sense making and the development of mathematical ideas, and numerous tools can support learning in geometry (e.g., geoboards, pattern blocks, three-dimensional shapes, and linking cubes). We focus on AngLegs®, which are linking rods that are becoming more common in the classroom.

Promoting Mathematical Connections Using Three-Dimensional Manipulatives

2017 ◽  
Vol 22 (8) ◽  
pp. 488-492
Author(s):  
Farshid Safi ◽  
Siddhi Desai
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Three Dimensional ◽  
Mathematical Understanding ◽  
Success For All ◽  
Sense Making ◽  
Problem Solving Skills ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Mathematical Success

Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of representations should continually develop in complexity and scope. “[Students] will need to be able to convert flexibly among these representations. Much of the power of mathematics comes from being able to view and operate on objects from different perspectives” (NCTM 2000, p. 361). In fact, when students represent, discuss, and make connections among different mathematical ideas by using different methods, they engage in deeper sense making and improve their problem-solving skills while refining their mathematical understanding (Fuson, Kalchman, and Bransford 2005; Lesh, Post, and Behr 1987).

Geometric Patterns for Exponents

1992 ◽  
Vol 85 (9) ◽  
pp. 746-749
Author(s):  
Frances M. Thompson
Keyword(s):  
Visual Stimuli ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Geometric Models ◽  
Mathematical Ideas ◽  
Geometric Patterns

NCTM's Professional Standards for Teaching Mathematics suggests that “tasks that require students to reason and to communicate mathematically are more likely to promote their ability to solve problems and to make connections” with other mathematical ideas (1991, 24). Yet too frequently our classroom introductions to mathematics concepts and theorems demand little reasoning from students, leaving them unconvinced or with minimal understanding. Concrete, visual, or geometric models are seldom offered as aids, particularly when studying new numerical relations (Suydam 1984, 27; Bennett 1989, 130), even though many people depend heavily on visual stimuli for their learning, The challenge to the teacher is to select appropriate tasks and materials that will stimulate students to visualize and think about new mathematical concepts, thereby allowing them to develop their own understanding.

The number line in the junior high school

1966 ◽  
Vol 13 (7) ◽  
pp. 553-555
Author(s):  
Ronald E. Hursh
Keyword(s):  
High School ◽  
Junior High School ◽  
Subject Matter ◽  
Junior High ◽  
Number Line ◽  
Teaching Mathematics ◽  
New Materials ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Substantial Problem

There has never been a more interesting time to be teaching mathematics. The new programs are rich in subject matter and are a challenge to students and teachers a like. We are building mathematical concepts in addition to drilling on fundamentals in the same amount of time which previously had been used for drilling alone. This presents a substantial problem to which, I am sorry to say, I do not have the total solution. My concern is with being able to teach all of the mathematics desired in the time that is available. There is one device of instruction in the new materials that I believe has great potential in conveying mathematical ideas quickly and accurately. This device is the number line.

scholarly journals An analysis of student error in answer to the skills of conceptual understanding test

2020 ◽  
Vol 6 (1) ◽  
pp. 78-86
Author(s):  
Aas Muhaiminah ◽  
Abas Hidayat
Keyword(s):  
Data Analysis ◽  
Conceptual Understanding ◽  
Basic Science ◽  
Mathematical Understanding ◽  
Mathematical Concepts ◽  
School Year ◽  
The World ◽  
Tenth Grade ◽  
Student Error ◽  
Level Of Understanding

Mathematics is the basic science of all sciences or the first step in learning other sciences, one of which is in education. In the world of education, especially the Indonesian state mathematics subjects ranked lowest in the TIMSS or PISA survey, it is suspected that one reason is the lack of understanding of students' concepts in mathematics. The purpose of this study was: to determine the level of understanding of students' mathematical concepts. This research is a test of the problem in accordance with the indicators in the ability to understand the concept. The population of this study is the tenth grade students at SMAN 1 Cilimus 2018/2019 school year. The sample of this study is class X IPS 5. Based on data analysis it can be concluded that: the ability of students' mathematical understanding is still lacking especially in class X IPS 5.

The Use of the Concrete-representational-abstract (CRA) Sequence to Improve Mathematical Outcomes for Elementary Students with Emotional Behavioral Disorders

2021 ◽  
Author(s):  
Margaret M Flores ◽  
Vanessa M Hinton
Keyword(s):  
Elementary Students ◽  
Behavioral Disorders ◽  
Conceptual Understanding ◽  
Mathematical Thinking ◽  
Emotional Behavioral Disorders ◽  
Teaching Mathematics ◽  
Teaching Sequence ◽  
Positive Effects ◽  
Students With Ebd

The concrete-representational-abstract (CRA) sequence is an explicit methodology for teaching mathematics that has been shown to have positive effects for students with EBD. This teaching sequence fosters conceptual understanding and mathematical thinking. This article describes how a teacher used explicit CRA instruction with two elementary students with EBD. Its aims are to describe and provide rationale for CRA instruction. We will describe lesson activities, methods, materials, and procedures. Finally, we will offer suggestions for implementation.

A Role for Technology in Mathematics Education

1996 ◽  
Vol 178 (2) ◽  
pp. 15-32 ◽  
Author(s):  
Albert A. Cuoco ◽  
E. Paul Goldenberg
Keyword(s):  
Mathematics Education ◽  
Curriculum Change ◽  
Mathematics Curriculum ◽  
New Technology ◽  
Habits Of Mind ◽  
Mathematical Research ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematics Educators

New technology poses challenges to mathematics educators. How should the mathematics curriculum change to best make use of this new technology? Often computers are used badly, as a sort of electronic flash card, which does not make good use of the capabilities of either the computer or the learner. However, computers can be used to help students develop mathematical habits of mind and construct mathematical ides. The mathematics curriculum must be restructured to include activities that allow students to experiment and build models to help explain mathematical ideas and concepts. Technology can be used most effectively to help students gather data, and test, modify, and reject or accept conjectures as they think about these mathematical concepts and experience mathematical research.

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 INTEGRASI TEKNOLOGI DIGITAL DALAM PEMBELAJARAN DI ERA INDUSTRI 4.0

2018 ◽  
Vol 16 (1) ◽  
pp. 42-54 ◽  
Author(s):  
Susilahudin Putrawangsa ◽  
Uswatun Hasanah
Keyword(s):  
Mathematics Education ◽  
Learning Environment ◽  
Conceptual Understanding ◽  
Basic Principle ◽  
Digital Technology ◽  
Technology In Education ◽  
Mathematical Concepts ◽  
Mathematical Skills ◽  
Alternative Learning ◽  
Development Of Students

The recent study intends to describe the roles and the principles of integrating digital technology in education at the 4th Industrial Era. The integrartion is studied from mathematics education perspective. It is concluded that the basic principle of integrating digital technology in mathematics education is that the technology does not diminish students’ conceptual understanding or replace students’ intuitions in doing mathematics. Conversely, the technology is utilized to boost students’ conceptual understanding and maximize the development of students’ intuition in doing mathematics. It is identified that there are three didactical functions of digital technology in mathematics education, such as: (1) Technology for doing mathematics,  that is the technology is incorporated as alternative learning media in doing mathematical activities; (2) Technology for practicing skills, that is the technology is utilized as a learning environment to master particular mathematical skills; (3) Technology for developing conceptual understanding, that is the technology is integrated as a learning environment to develop students’ conceptual understanding of specific mathematical concepts. This last didactical function is the most expected of integrating digital technology in mathematics education.

scholarly journals Analisis kendala pemahaman bahasa untuk mengembangkan kemampuan bernalar matematika siswa

2021 ◽  
Vol 9 (2) ◽  
pp. 61
Author(s):  
Anis Hidayati MS ◽  
Alex Haris Fauzi
Keyword(s):  
Qualitative Research ◽  
Mathematical Reasoning ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Descriptive Approach

Understanding of language is closely related to mathematical reasoning, because language has function as a means of communication to convey ideas or ideas to others. Submission of mathematical ideas delivered by students will show how far the level of student understading of the mathematical concepts they have. This research is a qualitative research with a descriptive approach which aims to describe the obstacles faced by students when using language on mathematical reasoning. Data obtained from observations, interviews, questionnaires, and documentations. Based on the results of the analysis conducted, it can be seen that constraints faced by students when using language on mathematical reasoning are feelings of shame and inferiority, difficulty understanding the sentence, and lack of vocabulary students have.

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