Supplemental materials.

<div><p>Identity-based motivation theory predicts that how sure students are of attaining their academic possible identities (possible identity certainty) interacts recursively with the inferences they make thinking about schoolwork feels hard—this is important for me (difficulty-as-importance) and this is just not for me (difficulty-as-impossibility). Recursivity implies bidirectionality across time points. To date, studies primarily from the U.S. and China only document a shift up or down from one time to a second time. We address this method gap with a three-time-point, two-month study during a secondary school transition (Chinese students N = 818, Mage = 12, 44% female). We obtained prior grades (T0) and placement test scores (T1+). Students filled out questionnaires at critical junctures: a month before the placement test (T1), the day test results were announced (T2), and after learning their school placement (T3). Across three time points, structural equation model results show bidirectional paths linking academic possible identity certainty and difficulty-as-importance beliefs. Controlling for prior grades, students higher in possible identity certainty at T1 scored higher on their placement tests at T1+. Students with higher T1+ placement test scores had higher difficulty-as-importance at T2, controlling for T1 their difficulty-as-importance score. Students with higher T2 difficulty-as-importance had higher T3 possible identity certainty, controlling for their T2 possible identity certainty score. The reverse was also true—students with higher T2 possible identity certainty had higher T3 difficulty-as-importance, controlling for their T2 difficulty-as-importance score. In contrast, controlling for prior scores, from T1 to T2 and T2 to T3 possible identity certainty and difficulty-as-impossibility were unidirectionally related. Students with higher possible identity certainty had lower difficulty-as-impossibility beliefs and not the reverse. Taken together, our results support a recursive process by which difficulty-as-importance beliefs support academic goal pursuit by bolstering students’ certainty of attaining their possible identities and certainty reduces difficulty-as-impossibility beliefs.</p></div>