20 Y S. Lai et al. Fig. 1. The system architecture CIs of numbers and quantities in mathematical field in Grade 1-9 Curriculum are in order. Each competence indicator is divided into several detailed subitems according to different grades. The serial numbers of CIs are in order. The small serial number should be learned first and the large one should be learned later. According to different grades, each competence indicator sets up different detailed subitems of different grades with different levels. Detailed subitems of different grades refer to the levels of teaching materials in different grades in the same competence indicator, such as CIs: N-1-01: being capable of counting, reading, listening and writing the numbers less than ten thousand, comparing their size and conversing calculation of the units. Symbol N represents the numbers and quantities of head line, 1 represents the first stage (grade 1 to 3 in elementary school) and 01 is the serial number of competence indicator. Two of the detailed subitems of N-1-01 are found below: 1-n-01: able to perform counting within range of 100, and name one-digit and two-digit numbers. 1-n-02: able to apply numbers to express quantity, size, and order. Symbol 1 represents grade 1, n represents the key subject (Numbers) of lowercase letter, and 01, 02 are the serial numbers of detailed subitems of CIs. Following the advances achieved through the teaching, the students, in accordance with the spiral curriculum structure, learn basic capabilities designated by detailed subitems of CIs. Fig. 2 expresses the relationship graph of the flow of learning time and detailed subitems of the CIs when the students of grade 3 are studying the subjects of number and quantity. Exploring a Computer-Assisted Managing System with Competence Indicators 21 N umber and q uantit y of Com p etence Indicators for the first sta g e a t g rade 3 The flow of learning time Fig. 2. The relationship graph of the flow of learning time and detailed subitems of the CIs 2.3 System Components Interface agent. The interface agent supplies teachers and students with a friendly and succinct screen. The functions include: account management, authorization, and en- quiries. After teachers register and enter the system, they can upload the teaching elements, upload evaluation components, inquire or use every component and students’ learning conditions. After students register and enter the system, they can browse the teaching components, accept evaluation, and check their learning conditions. Because the contents of the category system are classified based on Competence Identifiers, teachers and students can find the adaptive current instruction needed, progress in- strument and evaluation elements, easily. The students can, in accordance with the current instrumental advancement and contents, learn on the Internet and take tests to determine their degrees of learning. Learning component module. Learning component is a kind of outward knowledge. Detailed subitems at different grades can be treated as knowledge map. IT management can be applied to management. The teacher users uploads teaching and learning components through WWW and the system classifies the teaching components up- loaded by the teachers according to general classification standard of detailed subitems at different grades which can avoid the complexity generated by programmed teaching method on detailed item classification of teaching materials. The system treats the detailed subitems at different grades of CIs in Grade 1-9 Curriculum as the base for classification and provides unified form for the users. The teachers can surf, check and cite the teaching components for the use of teaching and the students can check and surf teaching components according to current teaching progress, which allows them to acquire the expected capacities [11] [12]. Evaluation component module. Test is the most convenient method for teachers to collect students’ competences and learning conditions in short time [13], and the teaching evaluation should be explored from three dimensions: evaluation duration, 22 Y S. Lai et al. level of educational goal and degree of clearness [14]. Skinner believed that strength- ening training is the main mechanism of the organism’s learning process. When a stimulus is presented repetitively and it can cause proper reaction, the reaction is con- sidered to be controlled by the stimulus. The construction of stimulus control depends on two conditions: (1) active practices: practicing several times for the right reaction; (2) following enhancement: after practices, enhancement should be operated. The answer of the previous question is the base of the next concept. Learning feedback module. The current learning position of the student is in the ADL. The system records the students’ learning conditions in the database to provide evaluation items on learning effects. Fig. 3 shows that if the student could complete the test within the expected time and achieve the skilled level, the student is considered achieving the level of realistic development. Then, the system provides teaching components of the Competence Indicator for the next stage, which goes into the ZPD. The learning components provided by the system are regarded as the new framework. In a test, if the student gives a wrong answer, the system will display an error message, or an encouraging message if answered correctly, so that students could have feedback immediately. It could be used as the reference of correction for continuous learning activity. When the student fails the test, the system guides the student back to the pre- vious Competence Indicator item. Fig. 3. The feedback flow chart of learning and test 3 Method 3.1 Experimental Environment After teachers sign up for an account and login the system, they can use it. When teachers upload learning components with various file formats, the system stores them in the course database according to the selected detailed subitems of the CIs for teachers’ or students’ usage. Teachers select the uploading files and give detailed subitems of CIs. Then the system stores learning components in the course database according to detailed subitems of the CIs. When the teacher clicks the link of a com- ponent, the system searches for the component in the database, and transmits the Exploring a Computer-Assisted Managing System with Competence Indicators 23 component to the teacher’s computer screen. After students login the system, it pro- vides students with a teaching material list based on their learning conditions. Students select one of the teaching materials and the system will transmit the elements to the students’ monitors. Fig. 4 expresses an example of students browsing learning com- ponents. After students login the system, it provides students with an evaluation list based on their learning conditions. Students click to accept evaluation and the system provides students with questions in random order, and one by one. Students have to complete all of the questions in a limited time (ex: fifteen minutes) or they have to start from the beginning again. The system’s evaluation components adopt the selection form, and every question can include a help file. If needed, each choice can also be inserted into the help file. Score Time Ex p osition Materials sel ection Fig. 4. Students browse the learning component 3.2 Participants There are thirty-two third-grade students randomly selected from an elementary school participate in this experiment. The system provides course units for students’ practice in number and quantity. These course units are not given yet in official programs in the school. Students spent one hour on the practice for related courses at noon break or after school every day. After two months, students take a test for their third-grade mathe- matical learning effects. 3.3 Equipment This study is to ascertain students’ learning effects with Mathematical Achievement Test which is edited referring to Elementary Schools’ Mathematics Curriculum Stan- dard and the guidelines of grade 3 Mathematics Instruction. The CIs range from 3-n-01 to 3-n-10. The test has two of learning categories of numbers and quantities of 24 Y S. Lai et al. mathematics. It contains 40 questions including three parts: Subtest One for mathe- matics concepts (13 questions), Subtest Two for arithmetic operations (14 questions), and Subtest Three for conceptual application ability (13 questions). The test-retest reliability of the test is 0.80 and the split reliability is 0.89. The validity of the test accuracy was analyzed and tested by the mathematical scholars, experienced test de- signers, and two-way testing table; therefore, it has content validity. 4 Results This study takes statistical software package to analyze data. Data are analyzed by the method of descriptive and inferential statistics including mean, standard deviations, and t test. In order to compare the difference between control and experiment groups for the system, the independent t-test is applied and the significant level is 0.05. The mean and standard deviation of scores of the mathematical tests are listed in Table 1. We conduct a t-test for the pre- and post-test scores in the experimental and control groups. Table 1. Mean (M) and standard deviation (SD) of the pre- and post-tests Pretest Post-test Students n Test M SD M SD t value Subtest One 37.56 21.56 43.66 23.36 0.08 Grade 3 32 Subtest Two 34.38 21.36 42.34 23.92 0.00* Subtest Three 41.60 23.01 49.38 19.71 0.04* Total 36.88 20.42 43.25 18.87 0.02* *α<0.05 This study adopts t statistical tests of difference of mean from two dependent sam- ples to test whether the difference of mean between pre-tests and post-tests is equal, or whether the difference of mean reaches statistical significance. According to the guidance of Mathematical Achievement Test, the students’ original total test scores and subtest scores should be transformed into percentage scores referred to normal model when applying or interpreting the test results. The mean (M) and standard deviations (SD) of the translated percentage scores are shown in Table 1. After Subtest One’s original scores are transformed into percentage scores. The scores in the pre-tests (M = 43.66, SD = 23.36) are significantly better than those in the post-test ones (M = 37.56, SD = 21.56) .The α value of t-test is 0.483. It shows that the scores in pre-tests and post-tests are not different (t = 0.08, α > 0.05). It indicates that the system is not helpful for students in the teaching of mathematical concepts. After Subtest Two’s original scores are transformed into percentage scores. The scores in the pre-tests (M = 42.34, SD = 23.92) are significantly better than those in the post-test ones (M = 34.38, SD = 21.36) .The α value of t-test is 0.00. It shows that the scores in pre-tests and post-tests are different (t = 0.00, α < 0.05). It indicates that the system has a . refer to the levels of teaching materials in different grades in the same competence indicator, such as CIs: N-1-01: being capable of counting, reading, listening and writing the numbers less than. component in the database, and transmits the Exploring a Computer- Assisted Managing System with Competence Indicators 23 component to the teacher’s computer screen. After students login the system,. learning time and detailed subitems of the CIs when the students of grade 3 are studying the subjects of number and quantity. Exploring a Computer- Assisted Managing System with Competence Indicators