Appendix A Correlation matrices between measures aimed to measure similar constructs

Regarding the indifference points, we observe that the 1- vs 2 indifference point relates positively only to 3-back performance and negatively to teacher assessed cognitive ability.. Pea

Correlations Table A.1 indicates that most measures of cognitive ability correlate positively with each

other Regarding the indifference points, we observe that the 1- vs 2 indifference point relates

positively only to 3-back performance and negatively to teacher assessed cognitive ability The 1- vs 3 indifference point showed no relation to any measure of cognitive ability

Table A.1 Pearson correlations between indifference points and all measures of cognitive 

ability.

IDP12 IDP13 d’

1-back

d’ 2-back

d’ 3-back

Dutch English Math Raven Ability NCS

IDP13 55** 1

d’ 1-back 10 04 1

d’ 2-back 13* 01 31** 1

d’ 3-back 14* 08 31** 46** 1

Raven 00 -.05 40** 44** 35** 22** 24** 17** 1

Ability -.17** -.07 26** 21** 16* 44** 32** 33** 34** 1

Note: *p <.05, **p<.01 Ability represents ability as rated by a teacher of the students.

Table A.2 shows that most measures of self-regulated motivation correlate positively with each other (i.e the intrinsic and identified autonomous SRQ subscales and the least controlled (i.e introjected) SRQ subscale) and also with real life measures (i.e homework time and mentor-rated motivation)

NCS, homework time and teacher evaluated cognitive motivation The indifference points do not correlate with most measures, except for the relation between the 1- vs 3 indifference point and the NCS

Table A.2 Pearson correlations between indifference points and all measures of (cognitive)  motivation.

IDP12 IDP13 NCS SRQ_i

ntri

SRQ_in tro

SRQ_ex tr

SRQ_id ent

Homewo rk

Motivation

SRQ_intri 00 10 53** 1

SRQ_intro -.03 01 21** 29** 1

Motivation -.03 02 30** 23** 17** -.23** 21** 09 1

Note: *p <.05, **p<.01 Motivation represents motivation as rated by a teacher of the students.

Appendix B: Self­constructed questions used for obtaining teacher­ratings

a) How do you rate the motivation for cognitively challenging tasks for this student? Indicate the most  applicable answer by circling the appropriate number, where 1 = absolutely not motivated and 10 =  very motivated

Original Dutch formulation: 

Hoe schat u de motivatie voor cognitief uitdagende taken in bij deze leerling? Omcirkel het antwoord 

dat volgens u het meest van toepassing is op de lijn, waarbij 1 = absoluut niet gemotiveerd en 10 =  heel erg gemotiveerd. 

b) How do you rate the cognitive abilities of this student? Indicate the most applicable answer by  circling the appropriate number, where 1 = very low and 10 = very high. 

Original Dutch formulation:

Hoe schat u de cognitieve vaardigheden in van deze leerling? Omcirkel het antwoord dat volgens u het meest van toepassing is op de lijn, waarbij 1 = zeer laag en 10 = zeer hoog

Appendix C: words used as stimuli in the N­back task

Words used in N­back tasks Criteria for neutral words were: a) One syllable b) four different letters c)  not obviously related to some subject that may or may not be interesting to people

 1. lamp (lamp in English)

2. trui (sweater in English) 

3. deur (door in English) 

4. huis (house in English)

Supplementary Materials: exploratory analyses

S1: Exploratory analyses on gender and age

In a repeated-measures (RM) ANOVA on the indifference points with cognitive-load as

within-variable and gender as between-subjects within-variable, we found no main effect from gender, F(1, 291) = 2.928, p = 088, nor an interaction between gender and the indifference points, F(1, 291) = 0.376, p =

540

In a RM-ANOVA with indifference points as within-variable and age as covariate, we found no main

effect from age, F(1, 291) = 1.641, p = 201, nor an interaction between age and the indifference points, F(1, 291) = 0.788, p = 375.

In a RM-ANOVA with on the indifference points with cognitive-load as within-variable, gender as

between-subjects variable and age as covariate, we found no main effects from gender, F(1, 289) = 0.404, p = 525, or age, F(1, 289) = 2.009, p = 157, nor an interaction between gender and age, F(1, 289) = 0.512, p = 475.

An independent t-test on teacher ratings of ability with gender as grouping variable, revealed no significant effect from gender, t(269) = 0.179, p = 858 (Mfemales = 7.06, Mmales = 7.02) Another

independent t-test on teacher ratings of motivation with gender as grouping variable, also revealed no significant effect from gender, t(269) = 0.328, p = 743 (Mfemales = 6.63, Mmales = 6.56)

A RM-ANOVA on the indifference points with cognitive-load as within-variable and teacher ratings of motivation as well as teacher ratings of ability as covariates and gender as between-subjects variable, revealed a significant interaction effect between gender and teacher ratings of ability on the

indifference points, F(1, 265) = 4.890, p = 008 Follow-up tests indicated that females with higher

teacher ratings of cognitive ability, showed lower indifference points, for the 1- vs 2 indifference point

β = -0.113, p = 006, and for the 1- vs 3 indifference point, -0.120, p = 007, whereas we did not find this for males, 1- vs 2 indifference point β = -0.044, p = 275, 1- vs 3 indifference point, -0.020, p =

647 No other interactions were found

S2: Exploratory analyses controlling for n-back performance

To assess whether effects of our independent variables were still present after controlling for n-back performance, we repeated our RM-ANOVAs on the indifference points with mean n-back performance score as covariate Table 1 indicates that the effect of NCS becomes non-significant after controlling for n-back performance In addition, we found a significant effect of teacher ratings of cognitive

ability (Table 1) Follow-up tests indicated that adolescents with higher teacher ratings of cognitive

ability, showed lower 1- vs 2 indifference points, β = -0.085, p = 002, but not 1- vs 3 indifference points, β = -0.049, p = 118.

Table S1 Main effects on the indifference points while controlling for n-back performance.

NCS

n-back performance

2.827

.071 094

.011 010

SRQ-A intrinsic

n-back performance

5.271

.244

.022

.005 018

SRQ-A introjected

n-back performance

4.873

.801

.028

.000

.017

SRQ-A intrinsic

n-back performance

4.767

.401

.030

.002 016

SRQ-A identified

n-back performance

4.615

.661

.033

.001 016

Homework hours

n-back performance

5.027

.139

.026

.008 017

PAES

n-back performance

4.171

.202

.042

.006 014

Raven

n-back performance

6.654

.120

.010

.009 023

Teacher ratings motivation

n-back performance

3.876

.720

.050

.000 014

Teacher ratings ability

n-back performance

6.823

.010 010

.025 025

Dutch grade

n-back performance

5.519

.229

.019

.005 019

English grade

n-back performance

3.587

.232 059

.005 012

Math grade

n-back performance

4.822

.865

.029

.000 016

S3: Exploratory analyses on the relation between motivation and academic achievement

We performed canonical correlation analysis with motivation measures on the one hand (indifference points, NCS, 4 subscale SRQ-A scores and teacher ratings of motivation) and academic achievement measures on the other hand (grades for the courses Dutch, English and math)

We found one significant canonical variate, r = 485, p <.001 (eigenvalue = 0.307, F = 3.881) Table 2

and 3 present the canonical loadings Results showed that the canonical variate consisting of

motivation measures (set 1) predicted 11.10% variance in the canonical variate consisting of the academic achievement measures (set 2) Taking a loading of cut-off of 1, the canonical motivation variable consisted of NCS, SRQ extrinsic (reverse loading), SRQ identified and teacher rating of motivation The canonical achievement variable consisted of the grades for Dutch, English and Math

Table S2 Canonical loadings from the motivation measures (set 1). 

Teacher rating motivation 924

Table S3 Canonical loadings from the academic achievement measures (set 2)

S4: Exploratory analyses assessing incentivizing values between pilot and main experiment

To assess whether our (hypothetical) incentives from the pilot study were less motivating than the (monetary) incentives used in the main experiment, we first compared the degree to which the 1-back (low-effort) option was chosen in the pilot versus the main experiment A t-test revealed a significant

difference between the pilot and main experiment, t(127.02) = 4.3988, p < 001 (Mpilot = 2.64, Mmain

= 1.62), indicating that participants chose more often for the easy task in the pilot study

Second, we calculated per indifference point the ratio of the variance in the pilot and main experiment For the 1- vs 2 indifference point this was 0.376/0.133 = 2.828 This F-value is larger than the critical F(69, 293) = 1.318, indicating a significant difference For the 1- vs 3 indifference point we followed the same procedure, 0.440/0.119 = 3.700 As this value is also larger than the critical F-value,

we conclude that for both indifference points, there was more variance in the main than the pilot experiment

Supplementary Materials: Pilot­Study 

This pilot-study was preregistered on Aspredicted.org and can be found here:

https://aspredicted.org/ff6id.pdf All materials and methods were exactly the same as in the

preregistration

Method

Participants

A G*Power (version 3.1.9.2; Faul, Erdfelder, Lang, & Buchner, 2007) analysis indicated that a total of

67 participants was required to achieve an intended power of 0.80, using a correlational bivariate normal model with an expected correlation of 0.3 (medium: as in Westbrook et al., 2013 and

Chevalier, 2017) and a one-tailed hypothesis (positive correlation) A total of 93 high school students participated in this study The students were recruited from a school in a medium-sized city in the Netherlands The level of the school being at the average level of the Dutch school system The study was approved by the Ethics Review Board of the [blinded] All students consented to participate, and

in addition, parental passive informed consent was obtained

A total of 13 participants were excluded from the analyses: 6 because of technical issues, (i.e the laptop stopped working), and 7 participants were excluded due to extreme values on one of the

independent variables (>/< 3 SD from the mean) Our final sample consisted of 70 participants

between 13 and 16 years (M = 15.01 years, SD = 0.92 years, Nfemales = 40).

Procedure

Participation in this study involved two experimental sessions: both sessions took place at the school 

of the students. In the first session, participants performed the COG­ED task on their own laptop in  small groups of five to seven students. The COG-ED task was programmed and administered using Presentation® software (Version 20.1, Neurobehavioral Systems, Inc., Berkeley, CA,

www.neurobs.com) and took between 30 and 45 minutes. During the second session, participants  underwent a cognitive ability task and filled out several questionnaires on a computer in a computer­ room in groups of 18 to 23 students. All measures in the second session were administered using Qualtrics Survey Software (Qualtrics, Provo, UT) This session took between 25 and 40 minutes In addition, during test-taking a teacher rated academic motivation and cognitive ability for each student

COG-ED task

The COG-ED task administered here was similar to the COG-ED task described in the main article However, instead of monetary rewards we used points during the effort-discounting phase It was  indicated that all points were valuable and the reward­value of the chosen option would be transferred  into a chance of winning a 20 euro­voucher In addition, as this was the first time the COG-ED task was administered in adolescents, we wanted to assess short-term reliability of their discounting choices Therefore, we had participants perform the effort discounting task twice

Questionnaires

We also administered the Academic Self-Regulation Questionnaire (SRQ-A), the Need for Cognition Scale (NCS), the Raven’s Standard Progressive Matrices, and the BAS reward sensitivity and drive scales Finally, we let teachers rate students’ cognitive motivation and cognitive ability

Statistical analyses

The indifference points are the main dependent variable within the COG-ED task Each participant has

2 indifference points: a 1- vs 2-back indifference point representing how willing the participant was to redo the 2-back task compared to the 1-back task, and a 1- vs 3-back indifference point representing how willing the participant was to redo the 3-back task compared to the 1-back task As mentioned earlier, we wanted to assess the short-term reliability of participants’ discounting choices and therefore

we had them perform phase 2 twice To assess short-term reliability, we first calculated correlations between the indifference points from these two assessments

Next, we calculated participants’ N-back performance as a measure of cognitive ability We used the d’ statistic as is often used in signal-detection theory The d’ statistic is preferred over other

measures such as percentage correct, because it also takes into account whether participants made a correct rejection or false alarm (i.e it takes guessing into account) and is therefore a more sensitive measure of response bias (MacMillan, & Creelman, 1991) The higher the d’, the better participant is

at discriminating targets from non-targets and thus the better their performance on the N-back tasks

We ran several manipulation checks We first tested whether performance on N-back tasks decreased, and reaction times and perceived task-demands increased as cognitive load-level (n) increased, using separate repeated measures (RM) ANOVAs to test linear effects of within-variable load level (1-back, 2-back, 3-back) on performance (d’), reaction times and NASA-TLX scores If we found a significant effect, tests were followed-up by post-hoc t-tests between 1- and 2-back differences and 2- and 3-back differences Next, we tested whether the indifference points were affected by sensitivity to reward and drive by performing a RM-ANOVA on the indifference points with load-level

as within variable (1- vs 2-back and 1- vs 3-back choices) and scores on the BAS sensitivity to reward scale as between variable Thereafter, we performed the same analysis, but now with BAS drive scores

as between variable

To investigate whether willingness to investigate cognitive effort is related to need for

cognition, we performed a RM-ANOVA on the indifference points with cognitive load-level (1- vs 2-back, 1-vs 3-back choices) as within variable, and NCS scores as between variable Next, to examine

separate RM-ANOVAs on the indifference points with cognitive load-level (1- vs 2-back, 1-vs 3-back choices) as within variable, but now with SRQ-A scores on subscales and teacher ratings of student motivation respectively as between variables Finally, to investigate whether willingness to invest cognitive effort is related to cognitive ability we performed separate RM-ANOVAs on the indifference points with cognitive load-level (1- vs 2-back, 1-vs 3-back choices) as within variable with Raven scores, N-back performance, and teacher ratings of student cognitive ability as between variables respectively If the assumption of sphericity was violated in any of the RM-ANOVAs, analyses were Greenhouse-Geisser corrected All analyses were performed in IBM SPSS statistics version 24.0

Results

Manipulation checks

First we tested whether participants’ discounting choices were reliable over the two repeated

assessments and were sensitive to the different cognitive loads from the 2- and 3 N-back tasks We found a significant positive correlation between the two assessments of the 1- vs 2-back indifference

points, r = 78, p <.001, and also between the two assessments of the 1- vs 3-back indifference points,

r = 64, p <.001, indicating that indifference points showed acceptable to large short-term reliability

(Chen & Popovich, 2002) As such we averaged the indifference points over the repeated assessments and used these as dependent variables in subsequent analyses In addition, a paired t-test between the 1- vs 2-back and 1-vs 3-back indifference points indicated that, as expected, willingness to invest

effort significantly decreased as N-back load-level increased, t(69) = 4.541, p <.01 (Figure 2a) This

indicated that, as expected, adolescents show a lower willingness to exert effort for more effortful tasks and confirms the validity of the effort-discounting paradigm in this population

Next, we assessed whether the performance and subjective experience of effort during the N-back tasks were sensitive to N-N-back load level That is, higher working memory loads are expected to lower performance as measured with d’ and lead to more reported feelings of effort Linear-contrasts

RM-ANOVAs indicated that performance decreased as N-back load-level increased, F(1, 69) =