Learning objectives, especially those well defined by applying Bloom's taxonomy for Cognitive Objectives, have been widely recognized as important in various teaching and learning practices. However, many educators have difficulties developing learning objectives appropriate to the levels in Bloom's taxonomy, as they need to consider the progression of learners' skills with learning content as well as dependencies between different learning objectives. To remedy this challenge, we aimed to apply state-of-the-art computational techniques to automate the classification of learning objectives based on Bloom's taxonomy. Specifically, we collected 21,380 learning objectives from 5,558 different courses at an Australian university and manually labeled them according to the six cognitive levels of Bloom's taxonomy. Based on the labeled dataset, we applied five conventional machine learning approaches (i.e., naive Bayes, logistic regression, support vector machine, random forest, and XGBoost) and one deep learning approach based on pre-trained language model BERT to construct classifiers to automatically determine a learning objective's cognitive levels. In particular, we adopted and compared two methods in constructing the classifiers, i.e., constructing multiple binary classifiers (one for each cognitive level in Bloom's taxonomy) and constructing only one multi-class multi-label classifier to simultaneously identify all the corresponding cognitive levels. Through extensive evaluations, we demonstrated that: (i) BERT-based classifiers outperformed the others in all cognitive levels (Cohen's Kappa up to 0.93 and F1 score up to 0.95); (ii) three machine learning models – support vector machine, random forest, and XGBoost — delivered performance comparable to the BERT-based classifiers; and (iii) most of the binary BERT-based classifiers (5 out of 6) slightly outperformed the multi-class multi-label BERT-based classifier, suggesting that separating the characterization of different cognitive levels seemed to be a better choice than building only one model to identify all cognitive levels at one time.