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01-04-2025 | Research

Switch cost in arithmetic operations and its relation to math anxiety

Auteurs: Yarden Gliksman, Shir Levy

Gepubliceerd in: Psychological Research | Uitgave 2/2025

Abstract

Math fluency is the ability to efficiently solve known arithmetic exercises, and it is one of the building blocks for academic achievements and daily use. Math fluency is assessed by how many exercises individuals can solve correctly in a limited time, requiring switching from one exercise to another. Switching is one of the executive functions and involves flexibility and adaptation to changing circumstances. Switching is measured through switch cost, which represents the difference in performance between executing the same task sequentially and switching between tasks. The current study examines the switch cost in math fluency. Participants, students from higher academic institutions, performed a math fluency test applied by the Ben-Gurion University Math Fluency (BGU-MF) tool, which included simple arithmetic exercises of addition, subtraction, multiplication and division. In Experiment 1, we examined the switch cost for each operation, and between pairs of operations, among 135 students (age 19 to 34). Results showed that the switch cost differs among different operations. Moreover, switch costs occur when alternating between complementary operations, but not between operations that rely on the same cognitive mechanisms, such as retrieval or calculation. In Experiment 2, we examined the switch cost in math fluency among 54 students (age 21 to 34) with high- vs. low- math anxiety. High math anxiety participants presented poorer performance in math fluency, as measured by accuracy rates and reaction times, and a larger switch cost. Our results fit the Attentional Control Theory (ACT) which suggests that anxiety impairs the executive functions. The effects of dominance, familiarity, difficulty, mental sets and executive functions on the switch cost in math fluency are discussed.

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De Agostini, R. (2020). The role of working memory and inhibition efficiency in mathematics anxiety. [doctoral dissertation, University of York]. https://etheses.whiterose.ac.uk/28135

Aldrup, K., Klusmann, U., & Lüdtke, O. (2020). Reciprocal associations between students’ mathematics anxiety and achievement: Can teacher sensitivity make a difference? Journal of Educational Psychology, 112(4), 735–750. https://doi.org/10.1037/edu0000398CrossRef

Allport, D. A., Styles, E. A., & Hsieh, S. (1994). Shifting intentional set: Exploring the dynamic control of tasks. In C. Umiltà & M. Moscovitch (Eds.), Attention and performance 15: Conscious and nonconscious information processing (pp. 421–452). The MIT Press.

Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291. https://doi.org/10.1038/nrn2334CrossRefPubMed

Ansari, T. L., Derakshan, N., & Richards, A. (2008). Effects of anxiety on task switching: Evidence from the mixed antisaccade task. Cognitive, Affective, & Behavioral Neuroscience, 8(3), 229–238. https://doi.org/10.3758/CABN.8.3.229CrossRef

Arend, I., & Botella, J. (2002). Emotional stimuli reduce the attentional blink in sub-clinical anxious subjects. Psicothema, 14(2), 209–214.

Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition & Emotion, 8(2), 97–125. https://doi.org/10.1080/02699939408408931CrossRef

Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224–237. https://doi.org/10.1037/0096-3445.130.2.224CrossRefPubMed

Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181–185.CrossRef

Baroody, A. J. (1999). Children’s Relational Knowledge of Addition and Subtraction. Cognition and Instruction, 17(2), 137–175. https://doi.org/10.1207/S1532690XCI170201CrossRef

Bjälkebring, P., & Peters, E. (2021). Money matters (especially if you are good at math): Numeracy, verbal intelligence, education, and income in satisfaction judgments. PLoS ONE, 16(11), e0259331. https://doi.org/10.1371/journal.pone.0259331CrossRefPubMedPubMedCentral

Blair, C., & Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78(2), 647–663. https://doi.org/10.1111/j.1467-8624.2007.01019.xCrossRefPubMed

Button, K. S., Ioannidis, J. P., Mokrysz, C., Nosek, B. A., Flint, J., Robinson, E. S., & Munafò, M. R. (2013). Power failure: Why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience, 14(5), 365–376. https://doi.org/10.1038/nrn3475CrossRefPubMed

Campbell, J. I. D., & Arbuthnott, K. D. (2010). Effects of mixing and cueing simple addition and multiplication. European Journal of Cognitive Psychology, 22(3), 422–442. https://doi.org/10.1080/09541440902903629CrossRef

Carey, E., Hill, F., Devine, A., & Szücs, D. (2016). The Chicken or the Egg? The direction of the relationship between mathematics anxiety and mathematics performance. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2015.01987CrossRefPubMedPubMedCentral

Chang, H., & Beilock, S. L. (2016). The math anxiety-math performance link and its relation to individual and environmental factors: A review of current behavioral and psychophysiological research. Current Opinion in Behavioral Sciences, 10, 33–38. https://doi.org/10.1016/j.cobeha.2016.04.011CrossRef

Clark, C. A. C., Pritchard, V. E., & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46(5), 1176–1191. https://doi.org/10.1037/a0019672CrossRefPubMed

Clarke, B., Nelson, N., & Shanley, L. (2016). Mathematics fluency—More than the weekly timed test. In K. D. Cummings & Y. Petscher (Eds.), The Fluency Construct (pp. 67–89). NY: Springer.CrossRef

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Routledge.

Corbetta, M., & Shulman, G. L. (2002). Control of goal-directed and stimulus-driven attention in the brain. Nature Reviews Neuroscience, 3(3), 201–215. https://doi.org/10.1038/nrn755CrossRefPubMed

Cummings, K. D., & Petscher, Y. (2015). The fluency construct: Curriculum-based measurement concepts and applications. Springer. https://doi.org/10.1007/978-1-4939-2803-3CrossRefPubMedCentral

Curtis, E. (2012). Switching between simple addition and multiplication: Asymmetrical switch costs due to problem difficulty. [Master's thesis, Carleton University]. https://doi.org/10.22215/etd/2012-06790

Daches Cohen, L., Korem, N., & Rubinsten, O. (2021). Math anxiety is related to math difficulties and composed of emotion regulation and anxiety predisposition: A network analysis study. Brain Sciences, 11(12), 1609. https://doi.org/10.3390/brainsci11121609CrossRefPubMedPubMedCentral

Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1(1), 83–120.

Dehaene, S., Molko, N., Cohen, L., & Wilson, A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14(2), 218–224. https://doi.org/10.1016/j.conb.2004.03.008CrossRefPubMed

Derakshan, N., Ansari, T. L., Hansard, M., Shoker, L., & Eysenck, M. W. (2009). Anxiety, inhibition, efficiency, and effectiveness: An investigation using the antisaccade task. Experimental Psychology, 56(1), 48–55. https://doi.org/10.1027/1618-3169.56.1.48CrossRefPubMed

Diamond, A. (2013). Executive Functions. Annual Review of Psychology, 64(1), 135–168. https://doi.org/10.1146/annurev-psych-113011-143750CrossRefPubMed

Ellefson, M. R., Shapiro, L. R., & Chater, N. (2006). Asymmetrical switch costs in children. Cognitive Development, 21(2), 108–130. https://doi.org/10.1016/j.cogdev.2006.01.002CrossRef

Eysenck, M. W., Derakshan, N., Santos, R., & Calvo, M. G. (2007). Anxiety and cognitive performance: Attentional control theory. Emotion, 7(2), 336–353. https://doi.org/10.1037/1528-3542.7.2.336CrossRefPubMed

Farhi, M., Gliksman, Y., & Shalev, L. (2024). Cognitive control among primary- and middle-school students and their associations with math achievement. Education Sciences, 14(2), 159. https://doi.org/10.3390/educsci14020159CrossRef

Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods, 41(4), 1149–1160. https://doi.org/10.3758/BRM.41.4.1149CrossRefPubMed

Finell, J., Sammallahti, E., Korhonen, J., Eklöf, H., & Jonsson, B. (2022). Working Memory and its mediating role on the relationship of math anxiety and math performance: A meta-analysis. Frontiers in Psychology, 12. https://doi.org/10.3389/fpsyg.2021.798090

Foley, A. E., Herts, J. B., Borgonovi, F., Guerriero, S., Levine, S. C., & Beilock, S. L. (2017). The math anxiety-performance link: A global phenomenon. Current Directions in Psychological Science, 26(1), 52–58. https://doi.org/10.1177/0963721416672463CrossRef

Fox, E., Russo, R., & Georgiou, G. A. (2005). Anxiety modulates the degree of attentive resources required to process emotional faces. Cognitive, Affective, & Behavioral Neuroscience, 5(4), 396–404. https://doi.org/10.3758/CABN.5.4.396CrossRef

Friedman, N. P., & Miyake, A. (2017). Unity and diversity of executive functions: Individual differences as a window on cognitive structure. Cortex, 86, 186–204. https://doi.org/10.1016/j.cortex.2016.04.023CrossRefPubMed

Giner-Sorolla, R., Montoya, A. K., Reifman, A., Carpenter, T., Lewis, N. A., Jr., Aberson, C. L., & Soderberg, C. (2024). Power to detect what? Considerations for planning and evaluating sample size. Personality and Social Psychology Review, 28(3), 276–301. https://doi.org/10.31234/osf.io/rv3kwCrossRefPubMedPubMedCentral

Gliksman, Y., Kreiner, H., & Gamliel, E. Attribute framing and numeric cognition. (under review).

Gliksman, Y., Schwarz, I., & Naparstek, S. (under review). Math fluency, verbal fluency and individual differences in young and old adults.

Gliksman, Y., Berebbi, S., & Henik, A. (2022a). Math fluency during primary school. Brain Sciences, 12(3), 371. https://doi.org/10.3390/brainsci12030371CrossRefPubMedPubMedCentral

Gliksman, Y., Berebbi, S., Hershman, R., & Henik, A. (2022b). BGU-MF: Ben-Gurion University math fluency test. Applied Cognitive Psychology, 36(2), 293–305. https://doi.org/10.1002/acp.3918CrossRef

González-Gómez, B., Núñez-Peña, M. I., & Colomé, À. (2023). Math anxiety and the shifting function: An event-related potential study of arithmetic task switching. European Journal of Neuroscience, 57(11), 1848–1869. https://doi.org/10.1111/ejn.15984CrossRefPubMed

Grabner, R. H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F., & Neuper, C. (2009). To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia, 47(2), 604–608. https://doi.org/10.1016/j.neuropsychologia.2008.10.013CrossRefPubMed

Gunderson, E. A., Park, D., Maloney, E. A., Beilock, S. L., & Levine, S. C. (2018). Reciprocal relations among motivational frameworks, math anxiety, and math achievement in early elementary school. Journal of Cognition and Development, 19(1), 21–46. https://doi.org/10.1080/15248372.2017.1421538CrossRef

Hackett, G. (1985). Role of mathematics self-efficacy in the choice of math-related majors of college women and men: A path analysis. Journal of Counseling Psychology, 32(1), 47–56. https://doi.org/10.1037/0022-0167.32.1.47CrossRef

Hart, S. A., & Ganley, C. M. (2019). The nature of math anxiety in adults: Prevalence and correlates. Journal of Numerical Cognition, 5(2), 122–139. https://doi.org/10.5964/jnc.v5i2.195CrossRefPubMedPubMedCentral

Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21(1), 33–46. https://doi.org/10.5951/jresematheduc.21.1.0033CrossRef

Imbo, I., & Vandierendonck, A. (2007). Do multiplication and division strategies rely on executive and phonological working memory resources? Memory & Cognition, 35(7), 1759–1771. https://doi.org/10.3758/BF03193508CrossRef

Jansen, B. R. J., Louwerse, J., Straatemeier, M., Van der Ven, S. H. G., Klinkenberg, S., & Van der Maas, H. L. J. (2013). The influence of experiencing success in math on math anxiety, perceived math competence, and math performance. Learning and Individual Differences, 24, 190–197. https://doi.org/10.1016/j.lindif.2012.12.014

Katzir, M., & Posten, A. C. (2023). Are there dominant response tendencies for social reactions? Trust trumps mistrust—evidence from a Dominant Behavior Measure (DBM). Journal of Personality and Social Psychology, 125(1), 57–81. https://doi.org/10.1037/pspa0000334CrossRefPubMed

Loenneker, H., Cipora, K., Artemenko, C., Soltanlou, M., Bellon, E., De Smedt, B., García-Orza, J., Giannouli, V., Gutiérrez-Cordero, I., Lipowska, K., Van Dijck, J. P., Yao, X., Nuerk, H. C., & Huber, J. (2024). Math4Speed—A freely available normed measure of arithmetic fluency. Canadian Journal of Experimental Psychology. https://doi.org/10.31219/osf.io/8mtpeCrossRef

Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex “frontal lobe” tasks: A latent variable analysis. Cognitive Psychology, 41(1), 49–100. https://doi.org/10.1006/cogp.1999.0734CrossRefPubMed

Molzhon, A. (2010). Predicting arithmetic performance from age and executive function skills. [Master's thesis, Virginia Commonwealth University]. https://scholarscompass.vcu.edu/etd/2314/?show=full

Monsell, S. (1996). Control of mental processes. In V. Bruce (Ed.), Unsolved mysteries of the mind: Tutorial essays in cognition (pp. 93–148). London: Psycology Press. https://doi.org/10.4324/9781315784960-4CrossRef

Nesher, P. Mauntwitan, M; Oberman, J; Albert, J. Weis, R. Amit, M. Fridlender, A.;Koren, M.;Rasalan, A. & Steinberg, R. Arithmetic Curriculum for Elementary School; Report; Ministry of Education: Jerusalem, Israel, 2006. Available online: https://meyda.education.gov.il/files/Tochniyot_Limudim/Math/Yesodi/mavo1.pdf (accessed on 18 April 2024).

Pelegrina, S., Martín-Puga, M. E., Lechuga, M. T., Justicia-Galiano, M. J., & Linares, R. (2024). Role of executive functions in the relations of state-and trait-math anxiety with math performance. Annals of the New York Academy of Sciences, 1535(1), 76–91. https://doi.org/10.1111/nyas.15140CrossRefPubMed

Peters, E., & Shoots-Reinhard, B. (2023). Better decision making through objective numeracy and numeric self-efficacy. Advances in Experimental Social Psychology, 68(1), 1–75. https://doi.org/10.1016/bs.aesp.2023.03.002CrossRef

Pizzie, R. G., & Kraemer, D. J. (2021). The association between emotion regulation, physiological arousal, and performance in math anxiety. Frontiers in Psychology, 12, 639448. https://doi.org/10.3389/fpsyg.2021.639448CrossRefPubMedPubMedCentral

Ramirez, G., Chang, H., Maloney, E. A., Levine, S. C., & Beilock, S. L. (2016). On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies. Journal of Experimental Child Psychology, 141, 83–100. https://doi.org/10.1016/j.jecp.2015.07.014CrossRefPubMed

Rolison, J. J., Morsanyi, K., & O’Connor, P. A. (2016). Can I count on getting better? Association between math anxiety and poorer understanding of medical risk reductions. Medical Decision Making, 36(7), 876–886. https://doi.org/10.1177/0272989X15602000CrossRefPubMed

Rubinstein, J. S., Meyer, D. E., & Evans, J. E. (2001). Executive control of cognitive processes in task switching. Journal of Experimental Psychology: Human Perception and Performance, 27(4), 763–797. https://doi.org/10.1037/0096-1523.27.4.763CrossRefPubMed

Sánchez-Pérez, N., Fuentes, L. J., & González-Salinas, C. (2021). Assessing math anxiety in elementary schoolchildren through a Spanish version of the Scale for Early Mathematics Anxiety (SEMA). PLoS ONE, 16(8), e0255777. https://doi.org/10.1371/journal.pone.0255777CrossRefPubMedPubMedCentral

Santos, F. H., Hunt, T., & Ansari, D. (in print). The intersection of cognitive and emotional factors in diagnosing and treating developmental dyscalculia. In Y. Gliksman, L. Kaufmann, & A. Henik (Eds.), Developmental dyscalculia: From brain mechanisms to educational applications. Elsevier

Schneider, D. W., & Anderson, J. R. (2010). Asymmetric switch costs as sequential difficulty effects. Quarterly Journal of Experimental Psychology, 63(10), 1873–1894. https://doi.org/10.1080/17470211003624010CrossRef

Schwaighofer, M., Bühner, M., & Fischer, F. (2016). Executive functions as moderators of the worked example effect: When shifting is more important than working memory capacity. Journal of Educational Psychology, 108(7), 982–1000. https://doi.org/10.1037/edu0000115CrossRef

Sherer, J. Z., & Grunow, A. (2010) 90-Day Cycle: Exploration of math intensives as a strategy to move more community college students out of developmental math courses. Carnegie Foundation for the Advancement of Teaching

Skagerlund, K., Forsblad, M., Slovic, P., & Västfjäll, D. (2020). The affect heuristic and risk perception—Stability across elicitation methods and individual cognitive abilities. Frontiers in Psychology, 11, 970. https://doi.org/10.3389/fpsyg.2020.00970CrossRefPubMedPubMedCentral

Skagerlund, K., Skagenholt, M., & Träff, U. (2024). Mathematics anxiety and number processing: The link between executive functions, cardinality, and ordinality. Quarterly Journal of Experimental Psychology. https://doi.org/10.1177/17470218241234041CrossRef

Sokolowski, H. M., Hawes, Z., & Ansari, D. (2023). The neural correlates of retrieval and procedural strategies in mental arithmetic: A functional neuroimaging meta-analysis. Human Brain Mapping, 44(1), 229–244. https://doi.org/10.1002/hbm.26082CrossRefPubMed

Sowinski, C., Dunbar, K., & LeFevre, J. (2014). Calculation Fluency Test, unpublished technical report, Math Lab, Carleton University, Ottawa, Canada. https://carleton.ca/cacr/?p=316

Sunardi, S., Yudianto, E., Susanto, S., Kurniati, D., Cahyo, R. D., & Subanji, S. (2019). Anxiety of students in visualization, analysis, and informal deduction levels to solve geometry problems. International Journal of Learning, Teaching and Educational Research, 18(4), 171–185. https://doi.org/10.26803/ijlter.18.4.10CrossRef

Thibault, R. T., Zavalis, E. A., Malički, M., & Pedder, H. (2024). An evaluation of reproducibility and errors in published sample size calculations performed using G* Power. medRxiv. https://doi.org/10.1101/2024.07.15.24310458CrossRef

Tzelgov, J., Henik, A., Sneg, R., & Baruch, O. (1996). Unintentional word reading via the phonological route: The Stroop effect with cross-script homophones. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22(2), 336–349. https://doi.org/10.1037/0278-7393.22.2.336CrossRef

Tzelgov, J., Meyer, J., & Henik, A. (1992). Automatic and intentional processing of numerical information. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18(1), 166–179. https://doi.org/10.1037/0278-7393.18.1.166CrossRef

Van der Ven, S. H., Kroesbergen, E. H., Boom, J., & Leseman, P. P. (2012). The development of executive functions and early mathematics: A dynamic relationship. British Journal of Educational Psychology, 82(1), 100–119. https://doi.org/10.1111/j.2044-8279.2011.02035.xCrossRefPubMed

Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson III tests of achievement. Itasca, IL: Riverside Publishing.

Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749–750. https://doi.org/10.1038/358749a0

Yeung, N., & Monsell, S. (2003). Switching between tasks of unequal familiarity: The role of stimulus-attribute and response-set selection. Journal of Experimental Psychology: Human Perception and Performance, 29(2), 455–469. https://doi.org/10.1037/0096-1523.29.2.455CrossRefPubMed

Titel: Switch cost in arithmetic operations and its relation to math anxiety
Auteurs: Yarden Gliksman
Shir Levy
Publicatiedatum: 01-04-2025
Uitgeverij: Springer Berlin Heidelberg
Gepubliceerd in: Psychological Research / Uitgave 2/2025
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-025-02086-4

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Switch cost in arithmetic operations and its relation to math anxiety

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The effect of response inhibition on the aftereffects of completed prospective memory

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