Abstract:

The learners’ intrinsic cognitive load (ICL) is decided by the difficulty of learning materials but not by the instructional method. Students' observation ability plays a crucial role in mathematical computation that students can understand the rules from the questions and produce effective solution procedures within a limited time; therefore, the number of steps in computation is an important indicator to observe the level of the difficulty. In traditional paper-and-pencil tests, the overall accuracy of the students can be presented, but the response time of each question and their cognitive load are less reflected. The computerized assessments can evaluate the learns' accuracy and response time accurately.

The aim of this study is that we want to know the pattern of learners' ICL from the behavioral data and self-report. We designed seven different levels of difficulty by using "unary linear equation" and "simultaneous linear equations", with computation steps. For example, Level 1 is composed of "unary linear equation (one step)". Level 1 and Level 2 are composed of "unary linear equation (1-2 steps)". Level 3 to Level 7 are composed of "simultaneous linear equations (3-7 steps)". Each level has 30 questions, and there are 210 questions totally. Forty college students (half of females) were tested. We adopted “Introducing a situation-Question presentation-Answer verification” task with “yes-no” two-alternative-forced-choice procedure, and recorded by E-prime 3.0 software. Finally, participants were asked to fill in a self-reported questionnaire about cognitive load.

The behavior results indicated that accuracy increased and reaction time decreased as the learning materials difficulty increased. For accuracy, Level 1 to Level 4 decreased in smaller difference (98.5%/95.4%/94.1%/ 90.8% in turn), and the maximum gap is 7.7%; However, there is not much difference between Level 5, Level 6, and Level 7 (71.8%/70.7%/71.5% in turn). In particular, the accuracy difference between Level 4 and Level 5 as much as 19%. For reaction time, Level 1 to Level 4 increased in smaller difference (0.95s/1.27s/1.61s/1.82s in turn) and the maximum gap is only 0.87s; However, there is not much difference between Level 6 and Level 7(3.7s/3.8s in turn). In particular, the reaction time difference between Level 5 and Level 6 (2.3s/3.7s in turn) as much as 1.4s. In correlation analysis, only the accuracy of the low score group showed a significant correlation with the factor of effort (r=0.498*).

From the view of ICL, Level 1 to Level 4 showed low cognitive load state and high-efficiency processing (higher accuracy and shorter reaction time), while Level 6 and Level 7 showed high cognitive load state and low-efficiency processing (lower accuracy and longer reaction time). However, Level 5 presents a special state of "lower accuracy but longer reaction time". This phenomenon may be due to the change in the cognitive load state which from low to high. In addition, according to the correlation between the subjective and objective measurements, the more effort the low score group, the higher the accuracy, which means that learners can get good outcomes through hard learning. Taken together, through computerized measurement and questionnaire analysis, students’ behavior responses and their cognitive load can be understood more clearly, which is helpful for teachers to make appropriate adjustments in teaching.

Keywords:

Intrinsic cognitive load, computerized assessment, mathematical computation, cognitive load theory.