Implications for future research

This dissertation provides valuable new insights into how the relevance of mathematics can be conveyed in the classroom. Future researchers are invited to build upon this work by further exploring students’ competence beliefs and value beliefs in the classroom. Most centrally, replicating the current studies with different samples and for different academic subjects, and including long-term outcomes (e.g., motivational beliefs across school years, course choices, career choices, etc.) would be necessary to gain insight into the generalizability of the findings and the long-term impact of relevance-oriented teaching and interventions.

In future, researchers could consider using additional instruments and variables to investigate ways to convey relevance in everyday instructional practice. The inclusion of both teachers’ and students’ reports on relevance-oriented teaching strategies would be helpful to disentangle the relative importance of different views on mathematics instruction for students’

value development. Observer ratings, experience sampling data, and qualitative measures (e.g., coding mathematics exercise sheets) might be helpful to assess relevance-oriented instruction in a less biased way than by using questionnaires (e.g., Fahrenberg et al., 2007). Furthermore,

DISCUSSION OF THE FINDINGS FROM THE EMPIRICAL STUDIES

163 interviews with teachers have revealed that it might be difficult to convey the direct relevance of some mathematics topics and tasks to students’ lives (Turner et al., 2011). Therefore, it would be interesting to examine in addition the influence of emphasizing the general value of learning for students’ current and future value development in mathematics (see also Brophy, 1999; Wentzel

& Brophy, 2014).

Second, the results of the studies conducted for this dissertation indicate that assessing students’ competence beliefs and value beliefs in a comprehensive and differentiated way is crucial to understand better the nature and development of, and relationship between, students’

competence beliefs and value beliefs. More precisely, the effects found in Studies 1 and 2 differed according to the value component (intrinsic, attainment, utility, or cost) and type of competence belief (domain- or task-specific) investigated. By differentiating the four value components also in the future, inconsistencies in the measurement of students’ academic values could eventually be overcome (see 1.3.1) and more detailed knowledge about contextual influences on single value components could be gained. Similarly, future research framed in EVT could profit from distinguishing students’ domain- and task-specific competence beliefs as distinct outcomes of relevance interventions. Beyond that, to understand better the directional influences between students’ competence beliefs and students’ value beliefs, competence beliefs and value beliefs should both be assessed in a differentiated way when either of them constitutes the target of an intervention. Despite the huge number of competence experiments, intervention effects have not yet been reported on all components of students’ value beliefs simultaneously (for reviews, see Haney & Durlak, 1998; O'Mara et al., 2006).

Third, to explore further how relevance can be conveyed successfully in the classroom through short scientific interventions, the quotations condition could be developed further and compared with previous approaches. Instead of using a writing activity to personalize the message of the intervention (cf., Yeager & Walton, 2011), researchers could, for example, develop partner activities where students first summarize previously obtained utility information (e.g., from statements made by older peers) and then explain the personal usefulness of mathematics to their partners. Combining such replication and production tasks as partner activities is an effective way to promote meaningful knowledge structures (cf., research on generative learning strategies, e.g., Fiorella & Mayer, 2016). In addition, following SDT (Ryan

& Deci, 2000), meta-analyses of cooperative learning (e.g., Kyndt et al., 2013; Lou et al., 1996), and findings on increasing peer-orientation during adolescence (e.g., Kindermann et al., 1996), such partner activities could enhance students’ motivation to engage in the task and, in turn, enhance students’ responsiveness to the intervention.

Fourth, assessing and investigating intervention fidelity (e.g., students’ responsiveness to intervention tasks) should be standard in classroom-based experimental research. Until now, students’ responsiveness to relevance interventions has been assessed primarily to examine why an intervention did not produce any effects (Husman et al., 2017; Karabenick et al., 2017) or produced weaker effects than a corresponding laboratory-based intervention (Hulleman &

GENERAL DISCUSSION

164

Cordray, 2009). However, to learn about the mechanisms leading to effects, intervention fidelity also must be studied in effective intervention programs. Causal effects analyses (e.g., CACE models, Jo, 2002) are crucial to determine what happens if students do not complete inter-vention activities as intended (e.g., by arguing against the usefulness of mathematics), and to characterize these students to better meet their motivational needs in the future. Furthermore, in future interventions, researchers could assess students’ responsiveness not only to the part involving the generation of utility information (e.g., writing essays), but also to activities aimed at communicating utility information (e.g., listening to a presentation, reading quotations).

Individual factors such as emotional states or cognitive activation, which might correspond with students’ engagement in the intervention activities, could be assessed, for example, through computerized experience sampling methods (e.g., Pekrun & Linnenbrink-Garcia, 2012).

Fifth, the importance of various modes and sources of communicating utility information to students during relevance interventions could be disentangled by conducting laboratory experiments. The quotations condition included utility information communicated by an adult (listening activity) or communicated by peers (reading activity). Combining activities appealing to different channels (auditory, visual) might have contributed to the effectiveness of the quotations condition (cf., research on multimedia learning and memory processing, e.g., Mayer &

Moreno, 1998). In future research, the mode of communicating utility value could be varied by creating different experimental conditions including live presentations, audio recordings, or video material vs. a condition involving written material (or combined conditions). Similarly, experimental studies using varying sources of utility information such as same-age peers, slightly older peers, and adults could provide further insight into the most effective modes and sources of communicated utility value (cf., Hoogerheide, van Wermeskerken, Loyens, & van Gog, 2016, who compared the effectiveness of identical explanations when delivered by peers to when delivered by adults for learning science).

Sixth, to pave the way for relevance interventions to enter educational practice, future research is needed in which teachers are included in the implementation process of relevance intervention programs. The effectiveness of the MoMa interventions could be tested and compared when implemented in the same standardized way by teachers as opposed to researchers. However, following a design-based research approach (e.g., Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003), the MoMa intervention material also could be refined in close collaboration between scientists and teachers using several cycles of implementation, evaluation, and individual adaptation. During these cycles, teachers or researchers might propose new intervention elements, distribute elements of the 90-minute MoMa program over several lessons, and thus reduce the standardization of the intervention material. This is how, on the one hand, teachers can bring in their own ideas of how to integrate researcher-developed intervention activities in everyday instructional practice (cf., importance of teachers' beliefs for instructional behaviors, e.g., Reeve et al., 2014; Turner et al., 2011). On the other hand, in such collaboration, teachers also could be informed about how to enhance students’ competence

DISCUSSION OF THE FINDINGS FROM THE EMPIRICAL STUDIES

165 beliefs and value beliefs on a regular basis, for example, by regularly using relevance-oriented teaching strategies and being sensitive to group dynamics regarding mathematics-related value beliefs (cf., Study 1; see also Woolley et al., 2013). Teachers also could be trained on how to enhance the overall motivational quality of their teaching by including, for example, autonomy support or high structuredness—which might even reinforce the intervention effects (cf., Jang et al., 2010; Lazarides & Ittel, 2012; see also 2.1). As a result, the effectiveness of different implementations could be compared: (a) standardized vs. adapted use of relevance intervention material by teachers, (b) one-time vs. continuous integration of relevance information in teachers’ mathematics instruction, and (c) providing relevance information without vs. within an overall autonomy-supportive and/or structured mathematics teaching style.

Lastly, further research is needed on how students can be encouraged to support each other’s mathematics-related value beliefs on a regular basis. In fact, tutoring programs in which students help classmates or younger fellows in learning activities (Topping, 2000) have been shown to improve students’ achievement, attitudes towards school, and classroom behavior.

Interestingly in the subject of mathematics, these effects were found for both tutors (i.e., students assisting others) and tutees (i.e., students receiving help), with slightly stronger effects for reciprocal than for unidirectional tutoring (for reviews, see e.g., Ramani, Zippert, & Daubert, 2016; Robinson, Schofield, & Steers-Wentzell, 2005).These effects often have been framed within role theory assuming that tutors adopt behaviors and attitudes consistent with the role identity of a teacher (e.g., conveying new information, using verbal reinforcements, liking the subjects taught, valuing school in general; e.g., Allen & Feldman, 1976; Sarbin, 1976; Turner, 2006). Due to statutory equality, tutees also may identify more with peer tutors than with teachers; in turn, tutors who are aware that they act as role models may show more socially desired academic behaviors (Allen & Feldman, 1976). In previous peer tutoring programs, tutors rarely have been encouraged to actively transmit the norms and values of learning mathematics to their tutees, which might be very important in adolescence (cf., Ramani et al., 2016). Thus, in future research analysis could be made of whether peer tutoring programs in which tutors are advised to consciously convey information on the relevance of mathematics to their tutees has the power to improve students’ mathematics-related value beliefs and value-related behaviors.