effects: the worked-example effect, the guidance fading effect, and the expertise-reversal effect. Criticism of discovery-based teaching techniques Mayer (2004) argues against discovery-based teaching techniques and provides an extensive review to support this argument. Mayer's arguments are against pure discovery, and are not specifically aimed at constructivism: "Nothing in this article should be construed as arguing against the view of learning as knowledge construction or against using hands-on inquiry or group discussion that promotes the process of knowledge construction in learners. The main conclusion I draw from the three research literatures I have reviewed is that it would be a mistake to interpret the current constructivist view of learning as a rationale for reviving pure discovery as a method of instruction." Mayer's concern is how one applies discovery-based teaching techniques. He provides empirical research as evidence that discovery-based teaching techniques are inadequate. Here he cites this literature and makes his point "For example, a recent replication is research showing that students learn to become better at solving mathematics problems when they study worked-out examples rather than when they solely engage in hands-on problem solving. Today's proponents of discovery methods, who claim to draw their support from constructivist philosophy, are making inroads into educational practice. Yet a dispassionate review of the relevant research literature shows that discovery-based practice is not as effective as guided discovery." Mayer's point is that people often misuse constructivism to promote pure discovery-based teaching techniques. He proposes that the instructional design recommendations of constructivism are too often aimed at discovery-based practice. Sweller (1988) found evidence that practice by novices during early schema acquisition, distracts these learners with unnecessary search-based activity, when the learner's attention should be focused on understanding (acquiring schemas). The study by Kirschner et al. from which the quote at the beginning of this section was taken has been widely cited and is important for showing the limits of minimally-guided instruction. Hmelo-Silver et al. responded, pointing out that Kirschner et al. conflated constructivist teaching techniques such as inquiry learning with "discovery learning". (See the preceding two sections of this article.) This would agree with Mayer's viewpoint that even though constructivism as a theory and teaching techniques incorporating guidance are likely valid applications of this theory, nevertheless a tradition of misunderstanding has led to some question "pure discovery" techniques. The math wars and discovery-based teaching techniques The math wars controversy in the United States is an example