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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Research in Mathematical Education
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Korea Society of Mathematical Education
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Volume & Issues
Volume 14, Issue 4 - Dec 2010
Volume 14, Issue 3 - Sep 2010
Volume 14, Issue 2 - Jun 2010
Volume 14, Issue 1 - Mar 2010
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Teaching the Derivation of Area Formulas for Polygonal Regions through Dissection-Motion-Operations (DMO): A Visual Reasoning Approach
Rahim, Medhat H. ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 195~209
Utilizing a structure of operations known as Dissection-Motion-Operations (DMO), a set of mathematics propositions or area-formulas in school mathematics will be introduced through shape-to-shape transforms. The underlying theme for DMO is problem-solving through visual reasoning and proving manipulatively or electronically vs. rote learning and memorization. Visual reasoning is the focus here where two operations that constitute DMO are utilized. One operation is known as Dissection (or Decomposition) operation that operates on a given region in 2D or 3D and dissects it into a number of subregions. The second operation is known as Motion (or Composition) operation applied on the resultant sub-regions to form a distinct area (or volume)-equivalent region. In 2D for example, DMO can transform a given polygon into a variety of new and distinct polygons each of which is area-equivalent to the original polygon (cf [Rahim, M. H. & Sawada, D. (1986). Revitalizing school geometry through Dissection-Motion Operations. Sch. Sci. Math. 86(3), 235-246] and [Rahim, M. H. & Sawada, D. (1990). The duality of qualitative and quantitative knowing in school geometry, International Journal of Mathematical Education in Science and Technology 21(2), 303-308]).
A Few Problems for the Intellectual Development of Students in High Schools and Community Colleges
Mulyukov, Rustem ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 211~218
It is a truism that mathematics is about relations (cf. [Halford, G. S. (1999). The properties of representations used in higher cognitive processes: Developmental implications. In: Sigel, I. E. (Ed.), The Development of Mental Representation: Theories and Applications (pp. 147-168). Mahwah, New Jersey: Erlbaum]). In this article we are considering few problems related to the Viviani's and Routh's Theorems. All Problems are connected by the relation which exists between the distances of the point inside the triangle to it sides. We show how reasoning about the relations could lead the student's problem solving process and give easy to understand solutions of the problems. Among the problems being considered are the proof of the Converse to Viviani's Theorem, the formulas for areas of all figures formed by the sides of triangle and its cevians.
Students Approaches in Constructing Convincing Arguments in Geometry Using Technology: A Case Study
Rahim, Medhat H. ; Siddo, Radcliffe A. ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 219~231
Mathematically, a proof is to create a convincing argument through logical reasoning towards a given proposition or a given statement. Mathematics educators have been working diligently to create environments that will assist students to perform proofs. One of such environments is the use of dynamic-geometry-software in the classroom. This paper reports on a case study and intends to probe into students' own thinking, patterns they used in completing certain tasks, and the extent to which they have utilized technology. Their tasks were to explore the shape-to-shape, shape-to-part, and part-to-part interrelationships of geometric objects when dealing with certain geometric problem-solving situations utilizing dissection-motion-operation (DMO).
Pre-service teachers' perceptions of Mathematics as a language
Timor, Tsafi ; Patkin, Dorit ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 233~247
The article deals with the perceptions of Mathematics as a language of pre-service teachers of Mathematics in a College of Education in Israel. The formal language of studying in the College of Education is Hebrew. The goals of the study were to examine the perceptions of pre-service teachers on the following issues: the language components involved in learning Mathematics, the basic cognitive skills required for learning Mathematics, and the perception of Mathematics as a language (PML). Findings indicated that due to new attitudes in mathematical training, pre-service teachers of Mathematics perceived Mathematics as a language regarding all language components.
Impact of Inquiry-Based Teaching on Student Attitude toward Mathematics
Kim, Taik-H. ; Pan, Wei ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 249~262
Large Midwest university faculty members proposed the Science and Technology Enhancement Program Project (STEP) to improve students' learning in the secondary mathematics classroom using modules of inquiry-based teaching. The purpose of this study was to determine the impact of the STEP Project on students' attitude toward mathematics. Hierarchical linear models (HLM) were used to evaluate the impact of the STEP Project. The sample group for the study was 130 ninth grade students enrolled in Integrated Algebra I in a large urban school district. The school was one of eight secondary schools that participated in the STEP Project. The classes in the treatment group were three of five classes ordered in terms of the highest, middle, and lowest mean GPA. The control group consisted of two other middle GPA classes. The classes had an average of 25 students. Teachers who previously had been involved in the STEP Project taught all treatment and control classes. The inquiry-based teaching activities provided by the project were confined to the treatment classes. The survey measuring students' attitudes toward mathematics were obtained for both groups of students. The inquiry-based teaching affected students' attitudes toward mathematics (p < 0.07, ES = 3.07). Especially, students who had preexisting low attitudes toward mathematics were significantly affected by treatment (p < 0.02, ES = 0.02), while the treatment positively affected African American students overall at p < 0.08 (ES = 0.58).
The Role of "Personal Knowledge" in Solid Geometry among Primary School Mathematics Teachers
Patkin, Dorit ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 263~279
Teachers' personal knowledge (PK) is an element in their pedagogic-practical knowledge. This study exposes the PK of primary school mathematics teachers regarding solid geometry through reflection. Students are exposed to solid geometry on various levels, from kindergarten age and above. Previous studies attested to the fact that students encounter difficulties-strong dislike and fear engendered by geometry. A good number of teachers have strong dislike to solid geometry, as well. Therefore, those engaged in teaching the subject must address the problem and try to overcome these difficulties. In this paper we have introduced the reflective process among teachers in primary school, including application of Van-Hiele's theory to solid geometry.
The Use of Feedback in Written Reports and Portfolio: An Assessment for Learning Strategy
Santos, Leonor ; Pinto, Jorge ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 281~297
This paper pretends to study the potentialities of feedback, particularly in the development of a written report in two phases and in portfolio; and the main difficulties that teachers has to face concerning this assessment practice. Through a meta-analysis concerning different studies, it is possible to say that oral or written feedback, intentionally provided to students of several ages, may enable them to develop their self-assessment capacity and to get close of the expected product. However, the type of student and his or her perceptions may influence the effectiveness of feedback. Even for experience teachers, this practice maintains complex.
Research on Gender Differences of Mathematics Achievement from the Views of Gender Socialization
Zhang, Xiaoui ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 299~308
The gender differences of mathematics achievement exists in many counties in the world. Some Chinese scholars think that the differences also exist in China. The researchers explain the gender differences of mathematics learning mainly from the individual psychology and education. This paper, firstly, introduces an investigation of the gender differences of mathematics achievement in grade 1-9 in three areas (Hefei urban area, Cuozhen area, and Chenji area) of Hefei in China. The investigation found that the gender differences of mathematics achievement exist but are different in these areas. Then, the results are explained from the theory of the gender socialization.
What is Learning in the Mathematics Classroom?
Patton, Barba Aldis ; Hutto, Nora Nelson ;
Research in Mathematical Education, volume 14, issue 3, 2010, Pages 309~322
What is learning in the math classroom? Does a new term need to be coined for learning? Is the term over-used and it has lost it meaning? The responses of one hundred five teacher-candidates and graduate students were coded using the five levels researcher designed rubric which was modeled after Bloom's Taxonomy for depth of knowledge. The effects of understanding learning include the preparation of lesson plans, classroom instruction, the guiding of student learning, and the professional development of teacher leaders.