Connecting Research to Teaching: When Visualization Is a Barrier to Mathematical Understanding

2002 ◽  
Vol 95 (9) ◽  
pp. 714-717
Author(s):  
Leslie Aspinwall ◽  
Kenneth L. Shaw
Keyword(s):  
Mathematics Teachers ◽  
Mathematics Learning ◽  
Mathematical Understanding ◽  
Mathematical Representation ◽  
National Council ◽  
Mathematical Task ◽  
Mathematical Concepts ◽  
Mathematical Objects ◽  
Graphic Representations ◽  
Ways Of Thinking

AS MATHEMATICS TEACHERS, OUR INTUITION TELLS us that students benefit from being able to understand a variety of representations for mathematical concepts and being able to select and apply a representation that is suited to a particular mathematical task. Students develop mathematical power as they learn to operate on mathematical objects and to translate from one mathematical representation to another when necessary. For example, graphic representations convey mathematical information visually, whereas expressions represented symbolically may be easier to manipulate, analyze, or transform. The National Council of Teachers of Mathematics (NCTM) reinforces our intuition: “Different representations support different ways of thinking about and manipulating mathematical objects. An object can be better understood when viewed through multiple lenses” (NCTM 2000, p. 360). Notwithstanding our intuition and experience with students' representations, we teachers tend to think that students' graphic and visual abilities are always an advantage in mathematics learning. Indeed, we accept on pedagogical faith that students' conceptual understandings are enhanced whenever they use visualization.

Connecting Research to Teaching: Visual and Analytic Thinking in Calculus

2009 ◽  
Vol 103 (2) ◽  
pp. 140-145
Author(s):  
Erhan Selcuk Haciomeroglu ◽  
Leslie Aspinwall ◽  
Norma C. Presmeg
Keyword(s):  
Mathematics Education ◽  
Multiple Representations ◽  
Reform Movement ◽  
National Council ◽  
Analytic Thinking ◽  
Mathematical Concepts ◽  
Mathematical Objects ◽  
Ways Of Thinking ◽  
Calculus Reform

A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts (Aspinwall and Shaw 2002). The National Council of Teachers of Mathematics, for instance, claims that “different representations support different ways of thinking about and manipulating mathematical objects” (NCTM 2000, p. 360). A recommendation conveyed in the ongoing calculus reform movement is that students should use multiple representations and make connections among them so that they can develop deeper and more robust understanding of the concepts.

scholarly journals Mathematics learning forum: Role of ICT in the construction of pre-service teachers’ content knowledge schema

2003 ◽  
Vol 19 (2) ◽  
Author(s):  
Mohan Chinnappan
Keyword(s):  
Teacher Knowledge ◽  
Content Knowledge ◽  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Mathematics Learning ◽  
Knowledge Bases ◽  
National Council ◽  
Pedagogical Content ◽  
Recent Interest

Recent interest in the topic of knowledge bases for teachers of mathematics has led to a sustained analysis of how teacher knowledge influences interactions with their students. The results of this body of research have focused on identifying and describing the growth of mathematics teachers’ content and pedagogical content knowledge. In particular, it has been argued that there is a need to examine how mathematics teachers who are new to the classroom construct and structure their knowledge base (National Council of Teachers of Mathematics, 2000). Here I examine this issue by exploring the role of an online mathematics learning forum in creating an environment within which a group of prospective teachers exchanged views about a topic on arithmetic. The online forum was established via WebCT. The results suggest that WebCT provided a convenient and non-threatening medium in which to generate descriptions about mathematics teachers’ knowledge and understanding.

scholarly journals PENGEMBANGAN KURIKULUM MATEMATIKA UNTUK MENINGKATKAN KEMAMPUAN SISWA DALAM PENALARAN DAN PEMECAHAN MASALAH

2019 ◽  
Vol 1 (1) ◽  
pp. 15-27
Author(s):  
Yogi Anggraena
Keyword(s):  
Problem Solving ◽  
International Student ◽  
Mathematical Reasoning ◽  
Mathematics Learning ◽  
Student Assessment ◽  
National Council ◽  
Mathematical Literacy ◽  
Mathematical Concepts ◽  
International Student Assessment ◽  
Study Results

The Trending topic in International Mathematics and Science Study (TIMSS) and the Program for International Student Assessment (PISA) have become a new standard for mathematics learning. One of the objectives of the study from TIMSS and PISA is to know the students' abilities in reasoning, identifying, and understanding, and using the basic mathematics needed in daily life. Or in other words, students must have mathematical literacy. The concept of mathematical literacy is intended the ability of individuals to formulate, use, and interpret mathematics in various contexts. This includes mathematical reasoning and using mathematical concepts, procedures, facts, and equipment to describe, explain, and predict phenomena or events (OECD, 2013). Indonesia has participated in TIMSS and PISA studies several times, from the TIMSS and PISA study results, it shows that students have not been able to develop optimally about their thinking abilities in mathematics schools and are still low in ability (1) to understand complex information, (2) theory , analysis and problem solving, (3) using tools, procedures and problem solving and (4) conducting investigations. In 2014, the National Council of Teachers of Mathematics (NCTM) stated that learning mathematics today is still too formal, lacks connection with the meaning, understanding, and application of mathematical concepts, and fails to give sufficient attention to the ability of reasoning and solving problem. These results indicate that there needs to be a change in curriculum orientation, which is not to burden students with content but prioritize the aspects of essential abilities needed by all citizens to participate in developing their country in the 21st century. Therefore it is necessary to develop a mathematics curriculum that enhances students' abilities in reasoning and problem solving in order to improve the quality of mathematics for students knowledge and skill in this global era.

scholarly journals IbM PELATIHAN PEMBELAJARAN MATEMATIKA BERBANTUAN KOMPUTER PADA GURU-GURU SMP DI KECAMATAN TOMOHON TENGAH

2019 ◽  
Vol 1 (4) ◽  
Author(s):  
Derel Filandy Kaunang
Keyword(s):  
Mathematics Teachers ◽  
Junior High School ◽  
Mathematics Learning ◽  
Geometric Transformation ◽  
Computer Assisted ◽  
High School Mathematics ◽  
Mathematical Concepts ◽  
Learning Mathematics ◽  
Perceived Benefit ◽  
The Right

In mathematics learning using compurter is needed. Computer-Assisted Mathematics is considered necessary in helping students to understand the lessons. Usingcomputers as a medium let the students understand the materials given,of course requires the role of teachers. Therefore it is necessary to conduct training for teachers with the aim of guiding the teachers to implement the learning process in assistance of computers to understand the materials that are difficult for students.The targets of this activity are: (1) To obtain the description of the quality of junior mathematics teachers in Computer-Assisted Mathematics (2) To increase students' interest in learning mathematics and students' understanding of the correct mathematical concepts related to materials which are abstract (3) To increase the use of Computer-Assisted media in learning mathematics. The targets of this activity are junior high school mathematics teachers in the district of Central Tomohon.Based on the results of observation and evaluation on the implementation of this activity, ofthe computer-assisted mathematics training obtained the following results: First, teachers have high enthusiasm in learning about thecomputer-assisted mathematics. Second, teachers can use computer aids in the form of mathematical software such as: (1) Geometer's Sketchpad in teachinggeometry,that is to draw the right kind of triangle and prove Pythagoras theorem. (2) Geogebra in teaching geometric transformation (reflection, rotation, dilation) and seeking solutions of SPLDV and SPTLDV. (3) Yenka to teach the matters of mathematical models. (4) Macromedia Flash products inlearningmathematics especially about planes. Overall, computer-assisted mathematics training activities, in the form of utilizing mathematics softwares, provides satisfaction for the participants. In addition, the highly perceived benefit is that teachers can use the software that has been studied in computer-assisted mathematics training to facilitate the students in understanding the concept of mathematics appropriately. Keywords: Workshops, Computer-Assisted Mathematics

scholarly journals Pendampingan Kegiatan Lesson Study for Learning Community (LSLC) Guru Matematika MTS-MA-SMK Pondok Pesantren Darussholihin NW Kalijaga Lombok Timur

2021 ◽  
Vol 1 (2) ◽  
pp. 177-190
Author(s):  
Sripatmi Sripatmi ◽  
Ratih Ayu Apsari ◽  
Nourma Pramestie Wulandari ◽  
Ulfa Lu’luilmaknun ◽  
Nilza Humaira Salsabila
Keyword(s):  
Learning Community ◽  
Learning Strategies ◽  
Mathematics Teachers ◽  
Lesson Study ◽  
Mathematics Learning ◽  
Teaching Profession ◽  
Learning Assessment ◽  
Mathematical Concepts ◽  
Questions And Answers ◽  
Design Activities

As an effort to develop the teaching profession, Lesson Study for Learning Community (LSLC) emphasizes the importance of collaborative and continuous learning assessment based on the principles of collegiality and mutual learning to build a learning community. Based on discussions with the head of Darussholihin Islamic Boarding School (Ponpes) NW Kalijaga, East Lombok, principals of MTs-SMP, MA-SMA, and Vocational Schools fostered by Ponpes Darussholihin NW Kalijaga, it was revealed that: mathematics is one of the subjects that most students are less interested in. MTs-SMP, MA-SMA, SMK fostered by Ponpes Darussholihin NW Kalijaga, as well as most mathematics teachers still have difficulty planning and implementing learning strategies that can guide students in finding mathematical concepts, principles, and problem solving. To solve these problems, assistance is needed, through LSLC activities for school mathematics teachers at Ponpes Darussholihin NW Kalijaga, in order to resolve problems related to the implementation of mathematics learning. This service activity is carried out by utilizing several methods, namely: lectures, questions and answers, discussions, and providing assistance when mathematics teachers carry out the LSLC steps, including Plan, Do, See, and Re-design activities. Through mentoring activities carried out from September 18 to October 2, 2021, it was concluded that mentoring activities could: i) improve the understanding and skills of Mathematics teachers in schools at Ponpes Darussholihin NW Kalijaga in designing (plan), implementing (do), reflecting (see), and re-design of learning as regulated in the 2013 curriculum; ii) increasing collegiality among mathematics teachers at the Darussholihin Islamic Boarding School's fostered schools, NW Kalijaga.

Early Childhood Corner: Learning about “One”: Units as a Cornerstone for Head Start Mathematics

2003 ◽  
Vol 10 (4) ◽  
pp. 210-215
Author(s):  
Catherine Sophian
Keyword(s):  
Elementary School ◽  
Early Childhood ◽  
Head Start ◽  
Young Children ◽  
Mathematics Learning ◽  
Teaching Mathematics ◽  
Important Goal ◽  
Mathematical Concepts ◽  
Ways Of Thinking ◽  
Sound Foundation

An important goal of teaching mathematics to young children is to give them a sound foundation for future mathematics learning. Therefore, teachers must identify how the things they teach young children—and the ways in which they teach them—can impact students' ways of thinking about mathematical concepts that will become important in the elementary school years and beyond.

scholarly journals The Involvement of Science, Technology, Engineering, and Mathematics (STEM) Learning in an APOS Analysis of Students’ Mathematical Understanding

2020 ◽  
Vol 4 (2) ◽  
pp. p105
Author(s):  
Achmad Mudrikah ◽  
Nandang Arif Saefuloh
Keyword(s):  
High School Students ◽  
Mathematics Learning ◽  
Mathematical Understanding ◽  
Stem Learning ◽  
School Students ◽  
Mathematical Concepts ◽  
Science Technology ◽  
Action Process ◽  
And Mathematics ◽  
Theory Framework

This article was reported as a research that involved Science, Technology, Engineering and Mathematics (STEM) Learning by using APOS theory framework to investigate Students’ Mathematical Understanding of sine rule and cosine rule concept. Sine rule and cosine rule concepts are taught to eleven-grade senior high school students in Indonesia. Students’ responses to five trigonometric problems involving sine rule and cosine rule were analyzed through this article. This study has confirmed that sine rule and cosine rule concept can be understood through STEM learning engagement because it has enabled students to obtain the appropriate mental structure at the action, process, object and schema levels. However, sustainable development needs to be done to improve mathematics learning that can build mental structures needed by students to understand mathematical concepts.

scholarly journals Examining mathematical discourse to understand in-service teachers’ mathematical activities

Pythagoras ◽  
2013 ◽  
Vol 34 (1) ◽  
Author(s):  
Margot Berger
Keyword(s):  
South Africa ◽  
Mathematics Teachers ◽  
Mathematical Discourse ◽  
The Other ◽  
Digital Immigrants ◽  
Mathematical Task ◽  
Mathematical Objects ◽  
Use Of Technology ◽  
Different Characteristics ◽  
Mathematical Activities

In this article I use Sfard’s theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus) task required students to examine a function at an undefined point and to decide whether a vertical asymptote is associated with this point or not. Using the different characteristics of mathematical discourse, I argue that the words that students use really matter and show how a change in one participant’s use of the term ‘vertical asymptote’ constituted and reflected her learning. I also show how the other participant used imitation in a ritualised routine to get through the task. Furthermore I demonstrate how digital immigrants may resist the use of technology as the generator of legitimate mathematical objects.

PEMANFAATAN SOFTWARE GEOGEBRA UNTUK MENINGKATKAN KETERAMPILAN GURU MATEMATIKA SMP/MTs DI KECAMATAN LENGAYANG

2021 ◽  
Vol 1 (1) ◽  
pp. 28-37
Author(s):  
Fauziah Fauziah ◽  
Riska Amelia ◽  
Yusri Wahyuni
Keyword(s):  
Secondary School ◽  
Mathematics Teachers ◽  
Mathematics Learning ◽  
Mathematical Concepts ◽  
Teacher Skills ◽  
Learning Mathematics ◽  
Simulation And Evaluation ◽  
Teacher's Knowledge ◽  
Primary And Secondary School

The development of information technology today is so fast that it affects all aspects of life including the field of education. In the field of education, especially mathematics lessons at the primary and secondary school levels, there have been many media or tools that can be used in teaching basic mathematical concepts, one of which is using Geogebra software. Mathematics teachers in SMP / MTs in Lengayang District, Pesisir Selatan Regency still have limitations in using computers as a tool for making learning media with the help of math software. The objectives of this community service are: Increase teachers' understanding of the role of mathematics learning media, and Improve teacher skills in using geogebra applications to create mathematics learning media. GeoGebra was chosen as an alternative because it has various advantages both theoretically and based on research results. The method used is training on GeoGebra, simulation, and evaluation. PKM activities are carried out on SMP / MTs mathematics teachers in Lengayang District, Pesisir Selatan Regency. Based on the results of this training, it was concluded that the teacher's knowledge and understanding of the importance of media in learning mathematics increased and the teacher was able to design mathematics learning media using GeoGebra software.

scholarly journals PEMANFAATAN SOFTWARE GEOGEBRA UNTUK MENUNJANG PENCAPAIAN STANDAR KOMPETENSI GURU MATEMATIKA MTS DI KOTA SEMARANG

At-Taqaddum ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 95
Author(s):  
Budi Cahyono ◽  
Eva Khoirun Nisa
Keyword(s):  
Mathematics Teachers ◽  
Junior High School ◽  
Professional Competence ◽  
Mathematics Learning ◽  
Learning Material ◽  
Mathematical Concepts ◽  
Mathematical Application ◽  
Math Teachers ◽  
Media Construction ◽  
Information And Communication

<p><em>Information and communication technology (ICT) cannot be separated from education. For professional competence,  junior high school/ MTs mathematics teachers must be able to use ICT to communicate and develop themselves. At present, there are many uses of mathematical application programs in mathematics learning, one of which is Geogebra software. Geogebra can be used as a demonstration and visualization media, construction aids and the process of discovering mathematical concepts. To help MTs math teachers in the Semarang in teaching geometry that is indeed felt abstract and difficult for most students, Geogebra software training is given. With the training, MTs mathematics teachers in Semarang were able to utilize Geogebra's software in achieving competency standards by making a project correctly in the form of visualizing a learning material that could be implemented in the classroom.</em></p><p>====================================================</p><p>Teknologi informasi dan komunikasi (TIK) tidak dapat lepas dari dunia pendidikan. Untuk kompetensi profesional, guru mata pelajaran matematika SMP/MTs harus mampu memanfaatkan TIK untuk berkomunikasi dan mengembangkan diri. Saat ini, telah banyak penggunaan program aplikasi matematika dalam pembelajaran matematika salah satunya adalah software <em>Geogebra. Geogebra</em> dapat dijadikan sebagai media demonstrasi dan visualisasi, alat bantu konstruksi dan proses penemuan konsep matematika. Untuk membantu guru-guru matematika MTs di Kota Semarang dalam mengajarkan materi geometri yang memang dirasakan abstrak dan sulit bagi sebagian besar siswa maka diberikan pelatihan software <em>Geogebra</em>. Dengan adanya pelatihan tersebut, guru-guru matematika MTs di Kota Semarang mampu memanfaatkan software <em>Geogebra </em>dalam pencapaian standar kompetensi dengan membuat sebuah proyek dengan benar berupa visualisasi suatu materi pembelajaran yang dapat diimplementasikan di kelas.</p>

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