Research ArticlePSYCHOLOGY

Calculated avoidance: Math anxiety predicts math avoidance in effort-based decision-making

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Science Advances  20 Nov 2019:
Vol. 5, no. 11, eaay1062
DOI: 10.1126/sciadv.aay1062
  • Fig. 1 Behavioral task and hypothesis.

    (A) Choose phase of the CAST. In each CAST trial, participants were asked to choose between easy (i.e., low effort) choice cards, which always offered 2 cents, and hard (i.e., high effort) choice cards, which offered one of five possible reward amounts (2, 3, 4, 5, and 6 cents). The domain (either math or word) of the choice cards was kept the same within a trial. (B) Four example problems in the solve phase of the CAST. Participants were asked to fill the blue square to make a correct equation (math) or an English word by selecting one of three options below. In word problems, “~” is used in place of some characters to make problems harder. The problems were sorted by seven difficulty levels through a validation study (see the Supplementary Materials). Word answers: PL[A]N, EX[A]MINED. Math answers: 30[8], 2[5]84. (C) Expected reward and optimal decision-making as a function of the reward offered in the hard option (the horizontal axis). The horizontal dashed line represents the expected reward (the left vertical axis) of the easy option given the expected accuracy of 95%, and the black open circles represent the expected reward of the hard options, given the expected accuracy of 70%. The blue filled circles indicate the optimal choice probability of the hard options in each reward condition to maximize monetary reward based on expected reward values. (D) Math-specific effort avoidance hypothesis. The hard choice probability (HCP; the vertical axis) was defined by averaging the individual HCPs in the 4-, 5-, and 6-cent conditions (C). We predicted that math anxiety would be negatively correlated with the math HCP (red thick line) but not with word HCP (black line).

  • Fig. 2 Adaptive difficulty manipulation and validation.

    (A) Time courses of hard math difficulty level from two representative participants. The problem difficulty was determined by the 2-up-1-down staircase procedure (see Materials and Methods). Each circle represents a correct trial, and each × represents an incorrect trial. The difficulty trajectory around trial 120 (indicated with a dashed rectangle) is magnified in the top panel to illustrate the 2-up-1-down staircase procedure. The filled triangle and square symbols on the right indicate the average difficulty level (ADL). (B) Relationships between math/word ADL and resulting accuracy in the hard problems. Each circle represents a participant, and the horizontal dotted line at 70% indicates the target accuracy. The filled triangle and square symbols indicate the representative participants in (A). The histograms of the hard accuracy are plotted on the right vertical axes. (C) Relationship between math anxiety and math ADL. Each circle represents a participant, the solid lines are the significant regression lines [study 1 (top): Pearson’s r(134) = −0.30; 95% CI, −0.45 to −0.14; P < .001; study 2 (bottom): r(330) = −0.16; 95% CI, −.27 to −.06; P = .003], and the gray shades represent the 95% confidence bands.

  • Fig. 3 Math-specific effort avoidance.

    (A) Observed HCP as a function of the reward offered in the hard option (the horizontal axis; the easy option always offered 2 cents). The circles and squares specify the HCP in each reward condition averaged across participants, and, especially, the squares represent the conditions in which the hard choice is optimal (see Fig. 1C). Filled red symbols specify the math condition, and open black symbols specify the word condition. Error bars indicate SEM across participants. (B) Relationships between math anxiety, math HCP (left), and word HCP (right). Each circle represents a participant, the solid lines are the significant regression lines [the left Math panels; study 1: r(140) = −0.34; 95% CI, −0.48 to −0.19; P < 0.001; study 2: r(330) = −0.15; 95% CI, −0.26 to −0.05; P = 0.005], the dashed lines are the nonsignificant regression lines [the right Word panels; study 1: r(140) = −0.01; 95% CI, −0.18 to 0.15; P = 0.86; study 2: r(330) = −0.03; 95% CI, −0.14 to 0.08; P = 0.60], and the gray shades represent the 95% confidence bands. The histograms of HCP are plotted on the right vertical axes.

  • Table 1 Results of comprehensive LMM analysis for study 2.

    Dependent variable: math HCP. Independent variables were not transformed. Random effects: The random intercepts for age, gender, education level, highest level of math taken, current math taking, ethnicity, race, and income. All 332 rows (participants) were entered into the model. The maximum likelihood estimation method was used to fit the model. df = 321. Adjusted R2 = 47.04%. The 95% confidence intervals are presented in parentheses beside the βs.

    Predictorβ coefficient (95% CI)SE (β)t(321)P
    Intercept−0.11 (−0.68 to 0.46)0.29−0.380.70
    Word HCP0.74 (0.64 to 0.85)0.0514.04<0.001
    Math anxiety−0.09 (−0.14 to −0.04)0.02−3.60<0.001
    Reading anxiety0.05 (−0.00 to 0.09)0.021.930.05
    Trait anxiety−0.001 (−0.003 to 0.001)0.001−0.810.42
    Test anxiety0.003 (0.000 to 0.007)0.0022.160.03
    Easy math accuracy−0.03 (−0.62 to 0.55)0.30−0.120.91
    Easy math RT0.01 (−0.06 to 0.08)0.040.220.82
    Hard math accuracy0.14 (−0.29 to 0.57)0.220.620.53
    Hard math RT−0.03 (−0.08 to 0.02)0.03−1.300.19
    Math ADL0.08 (0.03 to 0.12)0.023.230.001

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaay1062/DC1

    Materials and Methods S1. Participants: Recruitment details

    Materials and Methods S2. The CAST: Creation and validation of the problem set

    Fig. S1. Temporal stability of the math/word ADLs and HCPs.

    Fig. S2. Test-retest reliability of the math/word ADLs and HCPs.

    Fig. S3. Relationships between math anxiety and problem-solving variables.

    Table S1. Descriptive statistics and correlation matrix of questionnaires and behavioral measures of study 1.

    Table S2. Descriptive statistics and correlation matrix of questionnaires and behavioral measures of study 2.

    Table S3. Results of study 1 LMM analysis for the math-specific effort avoidance.

    Table S4. Results of study 2 LMM analysis for the math-specific effort avoidance.

    Table S5. Results of comprehensive LMM analysis for study 1.

    Table S6. Results of confirmatory generalized regression analysis for study 1.

    Table S7. Results of confirmatory generalized regression analysis for study 2.

  • Supplementary Materials

    This PDF file includes:

    • Materials and Methods S1. Participants: Recruitment details
    • Materials and Methods S2. The CAST: Creation and validation of the problem set
    • Fig. S1. Temporal stability of the math/word ADLs and HCPs.
    • Fig. S2. Test-retest reliability of the math/word ADLs and HCPs.
    • Fig. S3. Relationships between math anxiety and problem-solving variables.
    • Table S1. Descriptive statistics and correlation matrix of questionnaires and behavioral measures of study 1.
    • Table S2. Descriptive statistics and correlation matrix of questionnaires and behavioral measures of study 2.
    • Table S3. Results of study 1 LMM analysis for the math-specific effort avoidance.
    • Table S4. Results of study 2 LMM analysis for the math-specific effort avoidance.
    • Table S5. Results of comprehensive LMM analysis for study 1.
    • Table S6. Results of confirmatory generalized regression analysis for study 1.
    • Table S7. Results of confirmatory generalized regression analysis for study 2.

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