Error analysis on factorization and the effect of online individualization classes (인수분해에 대한 오류 분석과 온라인 개별화 수업의 효과)
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- Journal of the Korean School Mathematics Society
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- v.24 no.1
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- pp.83-105
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- 2021
In this paper, we analyzed the misconceptions and errors incurred during factorization learning. We also examined whether online individualization classes had a positive effect on students' mathematical achievement. The experiment was conducted for 4 weeks (16 times in total) on middle school juniors in rural areas of Gyeonggi Province, where the influence of private extra education was small. In the class, the 'Google Classroom' was used as a LMS, the video lecture was uploaded to YouTube, and the teacher interacted with the students through "Zoom" and "Facetalk". In the online class situation, students' assignments and test answers were checked in real time through 'Google Classroom', and immediate feedback was provided to the experimental class group's students. However, for the control group students, feedback was provided only to those who desired. A total of 7 achievement evaluations were conducted in the order of pre-test, formative evaluation (5 times), and post-test to confirm the change in students' ability improvement and achievement. Through the formative evaluation analysis, it was possible to grasp the types of errors and misconceptions that occured during the factorization process. Students' errors were divided into four types: theorem or definition distortion error, functional errors such as calculation, operation, and manipulation, errors that do not verify the solution, and no response. As a result of ANCOVA, the two groups did not show any difference from the 1st to 4th formative assessment. However, the 5th formative assessment and post-test showed statistically significant differences, confirming that online individualization classes contributed to improvemed achievement.
After emergence of Internet, social media with highly interactive Web 2.0 applications has provided very user friendly means for consumers and companies to communicate with each other. Users have routinely published contents involving their opinions and interests in social media such as blogs, forums, chatting rooms, and discussion boards, and the contents are released real-time in the Internet. For that reason, many researchers and marketers regard social media contents as the source of information for business analytics to develop business insights, and many studies have reported results on mining business intelligence from Social media content. In particular, opinion mining and sentiment analysis, as a technique to extract, classify, understand, and assess the opinions implicit in text contents, are frequently applied into social media content analysis because it emphasizes determining sentiment polarity and extracting authors' opinions. A number of frameworks, methods, techniques and tools have been presented by these researchers. However, we have found some weaknesses from their methods which are often technically complicated and are not sufficiently user-friendly for helping business decisions and planning. In this study, we attempted to formulate a more comprehensive and practical approach to conduct opinion mining with visual deliverables. First, we described the entire cycle of practical opinion mining using Social media content from the initial data gathering stage to the final presentation session. Our proposed approach to opinion mining consists of four phases: collecting, qualifying, analyzing, and visualizing. In the first phase, analysts have to choose target social media. Each target media requires different ways for analysts to gain access. There are open-API, searching tools, DB2DB interface, purchasing contents, and so son. Second phase is pre-processing to generate useful materials for meaningful analysis. If we do not remove garbage data, results of social media analysis will not provide meaningful and useful business insights. To clean social media data, natural language processing techniques should be applied. The next step is the opinion mining phase where the cleansed social media content set is to be analyzed. The qualified data set includes not only user-generated contents but also content identification information such as creation date, author name, user id, content id, hit counts, review or reply, favorite, etc. Depending on the purpose of the analysis, researchers or data analysts can select a suitable mining tool. Topic extraction and buzz analysis are usually related to market trends analysis, while sentiment analysis is utilized to conduct reputation analysis. There are also various applications, such as stock prediction, product recommendation, sales forecasting, and so on. The last phase is visualization and presentation of analysis results. The major focus and purpose of this phase are to explain results of analysis and help users to comprehend its meaning. Therefore, to the extent possible, deliverables from this phase should be made simple, clear and easy to understand, rather than complex and flashy. To illustrate our approach, we conducted a case study on a leading Korean instant noodle company. We targeted the leading company, NS Food, with 66.5% of market share; the firm has kept No. 1 position in the Korean "Ramen" business for several decades. We collected a total of 11,869 pieces of contents including blogs, forum contents and news articles. After collecting social media content data, we generated instant noodle business specific language resources for data manipulation and analysis using natural language processing. In addition, we tried to classify contents in more detail categories such as marketing features, environment, reputation, etc. In those phase, we used free ware software programs such as TM, KoNLP, ggplot2 and plyr packages in R project. As the result, we presented several useful visualization outputs like domain specific lexicons, volume and sentiment graphs, topic word cloud, heat maps, valence tree map, and other visualized images to provide vivid, full-colored examples using open library software packages of the R project. Business actors can quickly detect areas by a swift glance that are weak, strong, positive, negative, quiet or loud. Heat map is able to explain movement of sentiment or volume in categories and time matrix which shows density of color on time periods. Valence tree map, one of the most comprehensive and holistic visualization models, should be very helpful for analysts and decision makers to quickly understand the "big picture" business situation with a hierarchical structure since tree-map can present buzz volume and sentiment with a visualized result in a certain period. This case study offers real-world business insights from market sensing which would demonstrate to practical-minded business users how they can use these types of results for timely decision making in response to on-going changes in the market. We believe our approach can provide practical and reliable guide to opinion mining with visualized results that are immediately useful, not just in food industry but in other industries as well.
Magnetization Transfer (MT) imaging generates contrast dependent on the phenomenon of magnetization exchange between free water proton and restricted proton in macromolecules. In biological materials in knee, MT or cross-relaxation is commonly modeled using two spin pools identified by their different T2 relaxation times. Two models for cross-relaxation emphasize the role of proton chemical exchange between protons of water and exchangeable protons on macromolecules, as well as through dipole-dipole interaction between the water and macromolecule protons. The most essential tool in medical image manipulation is the ability to adjust the contrast and intensity. Thus, it is desirable to adjust the contrast and intensity of an image interactively in the real time. The proton density (PD) and T2-weighted SE MR images allow the depiction of knee structures and can demonstrate defects and gross morphologic changes. The PD- and T2-weighted images also show the cartilage internal pathology due to the more intermediate signal of the knee joint in these sequences. Suppression of fat extends the dynamic range of tissue contrast, removes chemical shift artifacts, and decreases motion-related ghost artifacts. Like fat saturation, phase sensitive methods are also based on the difference in precession frequencies of water and fat. In this study, phase sensitive methods look at the phase difference that is accumulated in time as a result of Larmor frequency differences rather than using this difference directly. Although how MT work was given with clinical evidence that leads to quantitative model for MT in tissues, the mathematical formalism used to describe the MT effect applies to explaining to evaluate knee disorder, such as anterior cruciate ligament (ACL) tear and meniscal tear. Calculation of the effect of the effect of the MT saturation is given in the magnetization transfer ratio (MTR) which is a quantitative measure of the relative decrease in signal intensity due to the MT pulse.
Digital Convergence means integration between industry, technology, and contents, and in marketing, it usually comes with creation of new types of product and service under the base of digital technology as digitalization progress in electro-communication industries including telecommunication, home appliance, and computer industries. One can see digital convergence not only in instruments such as PC, AV appliances, cellular phone, but also in contents, network, service that are required in production, modification, distribution, re-production of information. Convergence in contents started around 1990. Convergence in network and service begins as broadcasting and telecommunication integrates and DMB(digital multimedia broadcasting), born in May, 2005 is the symbolic icon in this trend. There are some positive and negative expectations about DMB. The reason why two opposite expectations exist is that DMB does not come out from customer's need but from technology development. Therefore, customers might have hard time to interpret the real meaning of DMB. Time is quite critical to a high tech product, like DMB because another product with same function from different technology can replace the existing product within short period of time. If DMB does not positioning well to customer's mind quickly, another products like Wibro, IPTV, or HSPDA could replace it before it even spreads out. Therefore, positioning strategy is critical for success of DMB product. To make correct positioning strategy, one needs to understand how consumer interprets DMB and how consumer's interpretation can be changed via communication strategy. In this study, we try to investigate how consumer perceives a new product, like DMB and how AD strategy change consumer's perception. More specifically, the paper segment consumers into sub-groups based on their DMB perceptions and compare their characteristics in order to understand how they perceive DMB. And, expose them different printed ADs that have messages guiding consumer think DMB in specific ways, either cellular phone or personal TV. Research Question 1: Segment consumers according to perceptions about DMB and compare characteristics of segmentations. Research Question 2: Compare perceptions about DMB after AD that induces categorization of DMB in direction for each segment. If one understand and predict a direction in which consumer perceive a new product, firm can select target customers easily. We segment consumers according to their perception and analyze characteristics in order to find some variables that can influence perceptions, like prior experience, usage, or habit. And then, marketing people can use this variables to identify target customers and predict their perceptions. If one knows how customer's perception is changed via AD message, communication strategy could be constructed properly. Specially, information from segmented customers helps to develop efficient AD strategy for segment who has prior perception. Research framework consists of two measurements and one treatment, O1 X O2. First observation is for collecting information about consumer's perception and their characteristics. Based on first observation, the paper segment consumers into two groups, one group perceives DMB similar to Cellular phone and the other group perceives DMB similar to TV. And compare characteristics of two segments in order to find reason why they perceive DMB differently. Next, we expose two kinds of AD to subjects. One AD describes DMB as Cellular phone and the other Ad describes DMB as personal TV. When two ADs are exposed to subjects, consumers don't know their prior perception of DMB, in other words, which subject belongs 'similar-to-Cellular phone' segment or 'similar-to-TV' segment? However, we analyze the AD's effect differently for each segment. In research design, final observation is for investigating AD effect. Perception before AD is compared with perception after AD. Comparisons are made for each segment and for each AD. For the segment who perceives DMB similar to TV, AD that describes DMB as cellular phone could change the prior perception. And AD that describes DMB as personal TV, could enforce the prior perception. For data collection, subjects are selected from undergraduate students because they have basic knowledge about most digital equipments and have open attitude about a new product and media. Total number of subjects is 240. In order to measure perception about DMB, we use indirect measurement, comparison with other similar digital products. To select similar digital products, we pre-survey students and then finally select PDA, Car-TV, Cellular Phone, MP3 player, TV, and PSP. Quasi experiment is done at several classes under instructor's allowance. After brief introduction, prior knowledge, awareness, and usage about DMB as well as other digital instruments is asked and their similarities and perceived characteristics are measured. And then, two kinds of manipulated color-printed AD are distributed and similarities and perceived characteristics for DMB are re-measured. Finally purchase intension, AD attitude, manipulation check, and demographic variables are asked. Subjects are given small gift for participation. Stimuli are color-printed advertising. Their actual size is A4 and made after several pre-test from AD professionals and students. As results, consumers are segmented into two subgroups based on their perceptions of DMB. Similarity measure between DMB and cellular phone and similarity measure between DMB and TV are used to classify consumers. If subject whose first measure is less than the second measure, she is classified into segment A and segment A is characterized as they perceive DMB like TV. Otherwise, they are classified as segment B, who perceives DMB like cellular phone. Discriminant analysis on these groups with their characteristics of usage and attitude shows that Segment A knows much about DMB and uses a lot of digital instrument. Segment B, who thinks DMB as cellular phone doesn't know well about DMB and not familiar with other digital instruments. So, consumers with higher knowledge perceive DMB similar to TV because launching DMB advertising lead consumer think DMB as TV. Consumers with less interest on digital products don't know well about DMB AD and then think DMB as cellular phone. In order to investigate perceptions of DMB as well as other digital instruments, we apply Proxscal analysis, Multidimensional Scaling technique at SPSS statistical package. At first step, subjects are presented 21 pairs of 7 digital instruments and evaluate similarity judgments on 7 point scale. And for each segment, their similarity judgments are averaged and similarity matrix is made. Secondly, Proxscal analysis of segment A and B are done. At third stage, get similarity judgment between DMB and other digital instruments after AD exposure. Lastly, similarity judgments of group A-1, A-2, B-1, and B-2 are named as 'after DMB' and put them into matrix made at the first stage. Then apply Proxscal analysis on these matrixes and check the positional difference of DMB and after DMB. The results show that map of segment A, who perceives DMB similar as TV, shows that DMB position closer to TV than to Cellular phone as expected. Map of segment B, who perceive DMB similar as cellular phone shows that DMB position closer to Cellular phone than to TV as expected. Stress value and R-square is acceptable. And, change results after stimuli, manipulated Advertising show that AD makes DMB perception bent toward Cellular phone when Cellular phone-like AD is exposed, and that DMB positioning move towards Car-TV which is more personalized one when TV-like AD is exposed. It is true for both segment, A and B, consistently. Furthermore, the paper apply correspondence analysis to the same data and find almost the same results. The paper answers two main research questions. The first one is that perception about a new product is made mainly from prior experience. And the second one is that AD is effective in changing and enforcing perception. In addition to above, we extend perception change to purchase intention. Purchase intention is high when AD enforces original perception. AD that shows DMB like TV makes worst intention. This paper has limitations and issues to be pursed in near future. Methodologically, current methodology can't provide statistical test on the perceptual change, since classical MDS models, like Proxscal and correspondence analysis are not probability models. So, a new probability MDS model for testing hypothesis about configuration needs to be developed. Next, advertising message needs to be developed more rigorously from theoretical and managerial perspective. Also experimental procedure could be improved for more realistic data collection. For example, web-based experiment and real product stimuli and multimedia presentation could be employed. Or, one can display products together in simulated shop. In addition, demand and social desirability threats of internal validity could influence on the results. In order to handle the threats, results of the model-intended advertising and other "pseudo" advertising could be compared. Furthermore, one can try various level of innovativeness in order to check whether it make any different results (cf. Moon 2006). In addition, if one can create hypothetical product that is really innovative and new for research, it helps to make a vacant impression status and then to study how to form impression in more rigorous way.