Based on the theoretical approaches to interlanguage and discourse cohesiveness, this study examines international students' growth in discourse awareness and discourse competence in the teaching of elementary Chinese reading and writing, and explores a set of assessment methods for teaching discourse. The learners' knowledge and production of Chinese conjunctive words were assessed with multiple test methods, including the sentence sequencing test for testing learners' cognitive understanding of discourse cohesiveness, the elicitation tasks for assessing learners' production of conjunctive words, the tests of picture-based sentence writing and essay writing for evaluating learners' discourse awareness of the cohesiveness in form and meaning. 13 students were recruited by us to participate in these tests. A comprehensive discussion of the data supports that appropriate reading and writing instruction can develop learners' discourse competence and enhance their discourse awareness to a certain extent.