• Education of Primary School Mathematics
• /
• v.14 no.1
• /
• pp.43-55
• /
• 2011

The purpose of this study was to investigate the effects of inquiry oriented instruction on the learning of area formulas. For this purpose, current elementary mathematics textbook(2007 revised version) which deal with area formulas was reviewed and then the experimental research on inquiry oriented instruction in area formulas was conducted. The results of this study as follow; First, there was no significant effect of inquiry oriented instruction on the mathematical achievement in area formula problems. Second, there was no significant effect on the memorization of area formulas. Third, there was significant effect on the generalization of area formulas. Forth, there was significant effect on the methods of generalization of area formulas. Fifth, through inquiry activities, the students can learn mathematical ideas and develop creative mathematical ideas. Finally, implications for teaching area formulas through inquiry activity was discussed. We have to introduce new area formula through prior area formulas which had been studied, and make the students inquire the connection between each area formulas.

• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.461-472
• /
• 2015

Korean students are taught area formulas of parallelogram and triangle by inductive reasoning in current curriculum. Inductive thinking is a crucial goal in mathematics education. There are, however, many problems to understand area formula inductively. In this study, those problems are illuminated theoretically and investigated in the class of 5th graders. One way to teach area formulas is suggested by means of process of problem solving with transforming figures.

• Research in Mathematical Education
• /
• v.14 no.3
• /
• pp.195-209
• /
• 2010

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]).

• English Language & Literature Teaching
• /
• v.11 no.2
• /
• pp.111-134
• /
• 2005

This paper examines high school English textbooks to ascertain if they appropriately reflect the kinds and frequencies of routine formulas and downgraders of request act used by English native speakers. It is important to present authentic routine formulas in textbooks for students to acquire proper, efficient and safe communication strategies to communicate with other English speakers. For the analysis, currently available 7 series of 21 high school English textbooks under the $7^{th}$ National Curriculum were selected. Each series of textbooks contains 3 school grade textbooks as High School English, High School English I, and High School English II. The results show that the high school English textbooks generally demonstrate a secund reflection of the English native speakers' use of request strategies and downgraders. That is, the textbooks were found to have presented mostly casual forms of routine formulas while they have not presented sufficient coverage of elaborated polite routine formulas for requesting which English native speakers frequently use. The presence of some kinds of the frequently used downgraders was also very small in proportion in the textbooks. More effort should be given to complement the deficiency in this area by teachers and researchers.

• School Mathematics
• /
• v.8 no.3
• /
• pp.327-339
• /
• 2006

In this study, a teaching units for teaching and learning of secondary preservice teachers' mathematising is designed, focusing on reinvention of Bretschneider's formula. preservice teachers can obtain the following through this teaching units. First, preservice teachers can experience mathematising which invent a noumenon which organize a phenomenon, They can make an experience to invent Bretscheider's formula as if they invent mathematics really. Second, preservice teachers can understand one of the mechanisms of mathematics knowledge invention. As they reinvent Brahmagupta's formula and Bretschneider's formula, they understand a mechanism that new knowledge is invented Iron already known knowledge by analogy. Third, preservice teachers can understand connection between school mathematics and academic mathematics. They can understand how the school mathematics can connect academic mathematics, through the relation between the school mathematics like formulas for calculating areas of rectangle, square, rhombus, parallelogram, trapezoid and Heron's formula, and academic mathematics like Brahmagupta's formula and Bretschneider's formula.