The anchoring effect is a psychological phenomenon wherein individuals heavily rely on a previously presented anchor when making decisions. This anchor, often a numerical cue presented at the beginning, influences the perception and evaluation of subsequent information by serving as a reference point. The extent to which this effect plays a role in the assessment of cognitive load in educational psychology is not yet known. Particularly, when students need to indicate cognitive load multiple times during problem-solving, they may use heuristics to simplify the cognitively demanding assessment process. Therefore, the purpose of this work was to determine whether the cognitive heuristic of anchoring biases the assessment of cognitive load. In three experiments (N1 = 100, N2 = 87, N3 = 80), participants were asked to assess the complexity of a task environment with task units varying in complexity (low, moderate, and high) multiple times during problem-solving. In each experiment, the sequence of complexity was varied to investigate whether the first impression of complexity affects the immediately following assessment. The results are ambivalent, as the first impression of complexity did not have the expected influence on the immediately following assessment in Experiments 1 and 2. However, the hypothesized anchoring effect was demonstrated in Experiment 3. The results suggest that the anchoring effect occurs only when students are initially confronted with a highly complex task and that this has the strongest influence on the subsequent assessment.