April 2012 Volume 15 Number 2 - Educational Technology & Society

Participants and Experimental Procedure
The participants of this study are elementary school fifth graders in Taiwan. Four classes are chosen to participate in
this study, two classes are assigned as the experimental group randomly, and the other two are assigned as the control
group. There are originally 122 students in the four classes. However, 4 students are unable to complete the tests;
thus, the effective sampling population is reduced to 118 students, with 59 in the experimental group and 59 in the
control group. The experimental group is taught using “the adaptive U-learning math path learning activity,” while
the control group learned using “the traditional paper-and-pencil based math path learning activity”. The experiment
process is shown in Table 2:
Process
(time)
Test 1
(one lesson)
Teaching activities
(six lessons)
Test 2
(one lesson)
Remedial activities
(one lesson)
Test 3
(one lesson)
Mathematical
connection ability
questionnaire
(twenty minutes)
Table 2. The experiment process
Experimental group
computerized adaptive diagnostic test
adaptive U-learning math path teaching
process
computerized adaptive diagnostic test
adaptive U-learning remedial lessons
computerized adaptive diagnostic test
paper-and-pencil test
Control group
computerized adaptive diagnostic test
traditional math path teaching process
computerized adaptive diagnostic test
traditional remedial lessons
computerized adaptive diagnostic test
paper-and-pencil test
As shown in Table 2, there are three computerized diagnostic tests of “looking for patterns” unit and a mathematical
connection ability questionnaire used as evaluation tools. The three tests are Test1, Test2 and Test3, each with 30
questions. They are parallel forms with a Cronbach α reliability coefficient of 0.75, indicating that the difficulty rates
of the test questions are between 31.3% and 96.0%. The coefficient of determination ranged between 0.3 and 0.5,
and the validity is assessed by field experts.
In order to combine ubiquitous learning, campus math path and the knowledge structure based adaptive testing
system. Test1, Test2 and Test3 are all administered by KSAT. The adaptive testing algorithm of KSAT is based on
the students’ item structure. This structure is estimated by ordering theory (Airasian & Bart, 1973). As shown in
Figure 11, if the subject gets a top skill (item C) correct then it is inferred that he or she also understands its
prerequisites (items F, G, H, I). This algorithm can predict students’ profiles using fewer items than in original
paper-and-pencil based tests.
Figure 11. The students’ item structure
The mathematical connection ability questionnaire is developed based on mathematical connection competence
indicators of Grade 1-9 Curriculum Guidelines in Taiwan (Ministry of Education of the R.O.C., 2009). There are 3
dimensions in this questionnaire: the first dimension assesses the students’ abilities to connect mathematics to real
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