• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• School Mathematics
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• v.14 no.3
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• pp.357-375
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• 2012

This research intends to examine how 6th graders (age 12) generalize various increasing patterns. In this research, 6 problems corresponding to the ax, x+a, ax+c, ax2, and ax2+c patterns were given to 290 students. Students' generalization methods were analysed by the generalization level suggested by Radford(2006), such as arithmetic and algebraic (factual, contextual, and symbolic) generalization. As the results of the study, we identified that students revealed the most high performance in the ax pattern in the aspect of the algebraic generalization, and lower performance in the ax2, x+a, ax+c, ax2+c in order. Also we identified that students' generalization methods differed in the same increasing patterns. This imply that we need to provide students with the pattern generalization activities in various contexts.

• Spatial Information Research
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• v.6 no.1
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• pp.11-23
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• 1998

Map generalization functions to visualize the spatial data or to change their scale by changing the level of details of data. Until recently, the studies on map generalization have concentrated more on line features than on point features. However, point features are one of the essential components of digital maps and cannnot be ignored because of the great amount of information they carry. This study, therefore, aimed to find out a detailed procedure of point features' generalization. Particularly, this work chose the distribution pattern of point features as the most important factor in the point generalization in investigating the geometric characteristics of source data. First, it attempted to find out the characteristics of distribution pattern of point features through quadrat analysis with Grieg-Smith method and nearest-neighbour analysis. It then generalized point features through the generalization threshold which did not alter the characteristics of distribution pattern and the removal of redudant point feautres. Therefore, the generalization procedure of point features provided by this work maintained the geometric characteristics as much as possible.

• The Transactions of the Korea Information Processing Society
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• v.4 no.12
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• pp.3063-3068
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• 1997

In this paper, we have extended the generalization back-propagation algorithm to multi-layer polynomial higher order neural networks. The purpose of this paper is to describe various pattern recognition using polynomial higher-order neural network. And we have applied shift position T-C test pattern for invariant pattern recognition and measured generalization by mirror symmetry problem. simulation result shows that the ability for invariant pattern recognition increase with the proposed technique. Recognition rate of invariant T-C pattern is 90% effective and of mirror symmetry problem is 70% effective when the proposed technique is utilized. These results are much better than those by the conventional methods.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.399-428
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• 2009

2007 Renewed Korea Elementary Mathematics Curriculum introduce algebra 6th grade. According to many studies about introducing algebra, it is desirable to teach 6th graders algebra through generalization of patterns. In this study, 6th graders' understanding processes and difficulties in pattern generalization were analyzed and possiblities of introducing algebra to 6th graders through pattern generalization were examined.

• The KIPS Transactions:PartD
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• v.10D no.7
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• pp.1103-1114
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• 2003

Currently, one of the most critical issues in developing the service support system for various spatio-temporal applications is the discoverying of meaningful knowledge from the large volume of moving object data. This sort of knowledge refers to the spatiotemporal moving pattern. To discovery such knowledge, various relationships between moving objects such as temporal, spatial and spatiotemporal topological relationships needs to be considered in knowledge discovery. In this paper, we proposed an efficient method, MPMine, for discoverying spatiotemporal moving patterns. The method not only has considered both temporal constraint and spatial constrain but also performs the spatial generalization using a spatial topological operation, contain(). Different from the previous temporal pattern methods, the proposed method is able to save the search space by using the location summarization and generalization of the moving object data. Therefore, Efficient discoverying of the useful moving patterns is possible.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.7
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• pp.1705-1720
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• 2013

Human face gender recognition requires fast image processing with high accuracy. Existing face gender recognition methods used traditional local features and machine learning methods have shortcomings of low accuracy or slow speed. In this paper, a new framework for face gender recognition to reach fast face gender recognition is proposed, which is based on Local Ternary Pattern (LTP) and Extreme Learning Machine (ELM). LTP is a generalization of Local Binary Pattern (LBP) that is in the presence of monotonic illumination variations on a face image, and has high discriminative power for texture classification. It is also more discriminate and less sensitive to noise in uniform regions. On the other hand, ELM is a new learning algorithm for generalizing single hidden layer feed forward networks without tuning parameters. The main advantages of ELM are the less stringent optimization constraints, faster operations, easy implementation, and usually improved generalization performance. The experimental results on public databases show that, in comparisons with existing algorithms, the proposed method has higher precision and better generalization performance at extremely fast learning speed.

• School Mathematics
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• v.15 no.2
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• pp.459-479
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• 2013

The Purpose of this study was to explore the methods of generalization and errors pattern generated by mathematically gifted students and non-gifted students in elementary school. In this research, 6 problems corresponding to the x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns were given to 156 students. Conclusions obtained through this study are as follows. First, both group were the best in symbolically generalizing ax pattern, whereas the number of students who generalized $a^x$ pattern symbolically was the least. Second, mathematically gifted students in elementary school were able to algebraically generalize more than 79% of in x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns. However, non-gifted students succeeded in algebraically generalizing more than 79% only in x+a, ax patterns. Third, students in both groups failed in finding commonness in phased numbers, so they solved problems arithmetically depending on to what extent it was increased when they failed in reaching generalization of formula. Fourth, as for the type of error that students make mistake, technical error was the highest with 10.9% among mathematically gifted students in elementary school, also technical error was the highest as 17.1% among non-gifted students. Fifth, as for the frequency of error against the types of all patterns, mathematically gifted students in elementary school marked 17.3% and non-gifted students were 31.2%, which means that a majority of mathematically gifted students in elementary school are able to do symbolic generalization to a certain degree, but many non-gifted students did not comprehend questions on patterns and failed in symbolic generalization.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• School Mathematics
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• v.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.