logo logo European Journal of Psychology and Educational Research

EJPER is is a, peer reviewed, online academic research journal.

Subscribe to

Receive Email Alerts

for special events, calls for papers, and professional development opportunities.


Publisher (HQ)

Eurasian Society of Educational Research
Eurasian Society of Educational Research
Christiaan Huygensstraat 44, Zipcode:7533XB, Enschede, THE NETHERLANDS
Eurasian Society of Educational Research
Christiaan Huygensstraat 44, Zipcode:7533XB, Enschede, THE NETHERLANDS
arithmetic operations problem size effect working memory interference control

The Effect of Problem Size on Children’s Arithmetic Performance: Interference Control in Working Memory

Selma Boz

This study investigates school-age children’s arithmetic operations performance while solving larger-size problems which produces interferences .


This study investigates school-age children’s arithmetic operations performance while solving larger-size problems which produces interferences in memory. Complex problems can trigger competing responses in working memory, which are irrelevant to a task goal and increase the likelihood of interference from previously learned problems (De Visscher et al., 2018). Interference control in working memory is required to be able to manage and suppress irrelevant information while performing cognitive tasks such as arithmetic problem-solving (Unsworth, 2010). The present study explores potential cognitive processes while performing arithmetic tasks and emphasizes the important role of interference control for better performance in such tasks. This study applied a mixed-effect model experimental design. Forty-four primary school children were involved in the study. The results showed that children’s performance in terms of correct responses was similar for both small-size and large-size problems. However, their response speed was significantly lower in larger-size problems, which created more interference in working memory.

Keywords: Arithmetic operations, problem-size effect, working memory, interference control.

cloud_download PDF
Article Metrics


Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44(1-2), 75-106. https://doi.org/10.1016/0010-0277(92)90051-I

Baddeley, A. (1992). Working memory. Science, 255(5044), 556–559. https://doi.org/10.1126/science.1736359

Berg, D. H. (2008). Working memory and arithmetic operations in children: The contributory roles of processing speed, short-term memory, and reading. Journal of Experimental Child Psychology, 99(4), 288–308. https://doi.org/10.1016/j.jecp.2007.12.002

Boz, S., & Erden, M. (2021). Çalışan belleğin farklı bileşenlerinin 3. sınıf öğrencilerinin çarpma becerisine etkisi [The Effect of different components of working memory on multiplication skills of 3rd grade children]. Hacettepe University Journal of Education/Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 36(1), 177-185. https://doi.org/10.16986/HUJE.2020058880  

Brown, L., Sherbenou, R. J., & Johnsen, S. K. (2010). TONI-4: Test of Non-Verbal Intelligence 4 (4th ed.). PRO-ED.

Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1(2), 121–164.

Campbell, J. I. D., & Oliphant, M. (1992). Representation and retrieval of arithmetic fact: A network-interference model and simulation. In J. I. D. Campbell (Ed.), Advances in psychology (Vol. 91, pp. 331–364). Elsevier. https://doi.org/10.1016/S0166-4115(08)60891-2

Campbell, J. I. D., & Tarling, D. P. M. (1996). Retrieval processes in arithmetic production and verification. Memory and Cognition, 24, 156–172. https://doi.org/10.3758/BF03200878

Cooney, J. B., Swanson, H. L., & Ladd, S. F. (1988). Acquisition of mental multiplication skill; Evidence for the transition between counting and retrieval strategies. Cognition and Instruction, 5(4), 323-345. https://doi.org/10.1207/s1532690xci0504_5

Cowan, N. (1999). An embedded-processes model of working memory. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 62-101). Cambridge University Press. https://doi.org/10.1017/CBO9781139174909.006

De Stefano, D., & LeFevre, J.-A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16(3), 353-386. https://doi.org/10.1080/09541440244000328

De Visscher, A., & Noël, M.-P. (2014). The detrimental effect of interference in multiplication facts storing: Typical development and individual differences. Journal of Experimental Psychology: General, 143(6), 2380–2400.  https://doi.org/10.1037/xge0000029

De Visscher, A., & Noël, M.-P. (2016). Similarity interference in learning and retrieving arithmetic facts. In M. Cappelletti & W. Fias (Eds.), Progress in brain research: The mathematical brain across the lifespan  (Vol. 227, pp. 131–158). Elsevier.  https://doi.org/10.1016/bs.pbr.2016.04.008

De Visscher, A., Vogel, S. E., Reishofer, G., Hassler, E., Koschutnig, K., De Smedt, B., & Grabner, R. H. (2018). Interference and problem size effect in multiplication fact solving: Individual differences in brain activations and arithmetic performance. NeuroImage, 172, 718-727. https://doi.org/10.1016/j.neuroimage.2018.01.060

Dotan, D., & Zviran-Ginat, S. (2022). Elementary math in elementary school: The effect of interference on learning the multiplication table. Cognitive Research: Principles and Implications, 7, Article 101. https://doi.org/10.1186/s41235-022-00451-0

Ecker, U. K. H., Lewandowsky, S., Oberauer, K., & Chee, A. E. H. (2010). The components of working memory updating: An experimental decomposition and individual differences. Journal of Experimental Psychology: Learning, Memory, and Cognition, 36(1), 170–189. https://doi.org/10.1037/a0017891

Engle, R. W., Tuholski, S. W., Laughlin, J. E., & Conway, A. R. A. (1999). Working memory, short-term memory, and general fluid intelligence: A latent-variable approach. Journal of Experimental Psychology: General, 128(3), 309–331. https://doi.org/10.1037/0096-3445.128.3.309

Fuchs, L. S., Fuchs, D., Stuebing, K., Fletcher, J. M., Hamlett, C. L., & Lambert, W. (2008). Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition? Journal of Educational Psychology, 100(1), 30-47. https://doi.org/10.1037/0022-0663.100.1.30

Geary, D. C. (2003). Arithmetical development: Commentary on chapters 9 through 15 and future directions. In A. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 453-464). Erlbaum.

Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510

Geary, D. C., & Brown, S. C. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27(3), 398-406. https://doi.org/10.1037/0012-1649.27.3.398

Hasher, L., Lustig, C., & Zacks, R. (2007). Inhibitory mechanisms and the control of attention. In A. R. A. Conway, C. Jarrold, M. J. Kane, & A. Miyake & J. N. Towse (Eds.), Variation in working memory (pp. 227–249). Oxford University Press.

Hasher, L., & Zacks, R. T. (1988). Working memory, comprehension, and aging: A review and new view. In G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 22, pp. 193-225). Elsevier. https://doi.org/10.1016/S0079-7421(08)60041-9

Heitz, R. P. (2014). The speed-accuracy tradeoff: History, physiology, methodology, and behavior. Frontiers in Neuroscience, 8, Article 150. https://doi.org/10.3389/fnins.2014.00150

Hubber, P. J., Gilmore, C., & Cragg, L. (2014). The roles of the central executive and visuospatial storage in mental arithmetic: A comparison across strategies. The Quarterly Journal of Experimental Psychology, 67(5), 936-954. https://doi.org/10.1080/17470218.2013.838590

Ji, Z., & Guo, K. (2023). The association between working memory and mathematical problem solving: A three-level meta-analysis. Frontiers in Psychology, 14, Article 1091126. https://doi.org/10.3389/fpsyg.2023.1091126

Jonides, J., & Nee, D. E. (2006). Brain mechanisms of proactive interference in working memory. Neuroscience, 139(1), 181-193. https://doi.org/10.1016/j.neuroscience.2005.06.042

Kane, M. J., & Engle, R. W. (2000). Working-memory capacity, proactive interference, and divided attention: Limits on long-term memory retrieval. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26(2), 336–358. https://doi.org/10.1037/0278-7393.26.2.336

Lee, K., & Lee, H. W. (2019). Inhibition and mathematical performance: Poorly correlated, poorly measured, or poorly matched? Child Development Perspectives, 13(1), 28–33. https://doi.org/10.1111/cdep.12304

LeFevre, J.-A., Bisanz, J., Daley, K. E., Buffone, L., Greenham, S. L., & Sadesky, G. S. (1996). Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology: General, 125(3), 284–306. https://doi.org/10.1037/0096-3445.125.3.284

Marton, K., Campanelli, L., Eichorn, N., Scheuer, J., & Yoon, J. (2014). Information processing and proactive interference in children with and without specific language impairment. Journal of Speech, Language, and Hearing Research, 57(1), 106–119. https://doi.org/10.1044/1092-4388(2013/12-0306)

McNeil, N. M., & Alibali, M. W. (2005). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76(4), 883–899. https://doi.org/10.1111/j.1467-8624.2005.00884.x

Ministry of National Education. (2018). Matematik dersi öğretim program (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics course curriculum (Primary and secondary school 1st, 2nd, 3rd, 4th, 5th, 6th, 7th and 8th grades)]. https://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329

Morris, N., & Jones, D. M. (1990). Memory updating in working memory: The role of the central executive. British Journal of Psychology, 81(2), 111–121. https://doi.org/10.1111/j.2044-8295.1990.tb02349.x

Nairne, J. S. (1990). A feature model of immediate memory. Memory & Cognition, 18, 251–269. https://doi.org/10.3758/BF03213879

Noël, M.-P., & De Visscher, A. (2018). Hypersensitivity-to-interference in memory as a possible cause of difficulty in arithmetic facts storing. In A. Henik & W. Fias (Eds.), Heterogeneity of function in numerical cognition (pp. 387–408). Academic Press. https://doi.org/10.1016/b978-0-12-811529-9.00018-2

Oberauer, K. (2001). Removing irrelevant information from working memory. A cognitive aging study with the modified Sternberg task. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27(4), 948–957. https://doi.org/10.1037//0278-7393.27.4.948

Oberauer, K., & Kliegl, R. (2006). A formal model of capacity limits in working memory. Journal of Memory and Language, 55(4), 601–626. https://doi.org/10.1016/j.jml.2006.08.009

Oberauer, K., & Lange, E. B. (2009). Activation and binding in verbal working memory: A dual-process model for the recognition of nonwords. Cognitive Psychology, 58(1), 102–136. https://doi.org/10.1016/j.cogpsych.2008.05.003

Oberauer, K., & Lewandowsky, S. (2008). Forgetting in immediate serial recall: Decay, temporal distinctiveness, or interference? Psychological Review, 115(3), 544-76. https://doi.org/10.1037/0033-295X.115.3.544

Oberauer, K., Lewandowsky, S., Farrell, S., Jarrold, C., & Greaves, M. (2012). Modeling working memory: An interference model of complex span. Psychonomic Bulletin & Review, 19, 779-819. https://doi.org/10.3758/s13423-012-0272-4

Palladino, P. (2006). The role of interference control in working memory: A study with children at risk of ADHD. Quarterly Journal of Experimental Psychology, 59(12), 2047–2055. https://doi.org/10.1080/17470210600917850

Psychology Software Tools. (2020). E-Prime 3 (Version 3.x) [Computer software]. Retrieved from  https://pstnet.com/products/e-prime/

Raghubar, K. P., Barnes, M. A., & Hecht, S. A. (2010). Working memory and math: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20(2), 110–122. https://doi.org/10.1016/j.lindif.2009.10.005

R Core Team. (2022). R: A language and environment for statistical computing (Version 4.2.1). R Foundation for Statistical Computing. https://www.R-project.org/

Sala, G., & Gobet, F. (2017). Working memory training in typically developing children: A meta-analysis of the available evidence. Developmental Psychology, 53(4), 671-685. https://doi.org/10.1037/dev0000265

Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Math Education, 20(4), 338-355. https://doi.org/10.2307/749440

Shipstead, Z., Redick, T. S., & Engle, R. W. (2012). Is working memory training effective? Psychological Bulletin, 138(4), 628-654. https://doi.org/10.1037/a0027473

Silver, E. (Ed.). (1985). Teaching and learning mathematical problem solving: Multiple research perspectives. Lawrence Erlbaum Associates.

Thevenot, C., Castel, C., Fanget, M., & Fayol, M. (2010). Mental subtraction in high- and lower-skilled arithmetic problem solvers: Verbal report versus operand-recognition paradigms. Experimental Psychology: Learning, Memory, and Cognition, 36(5), 1242–1255. https://doi.org/10.1037/a0020447

Unsworth, N. (2010). Interference control, working memory capacity, and cognitive abilities: A latent variable analysis. Intelligence, 38(2), 255–267. https://doi.org/10.1016/j.intell.2009.12.003  

Unsworth, N., & Engle, R. W. (2007). The nature of individual differences in working memory capacity: Active maintenance in primary memory and controlled search from secondary memory. Psychological Review, 114(1), 104−132. https://doi.org/10.1037/0033-295X.114.1.104

Zbrodoff, N. J., & Logan, G. D. (2005). What everyone finds: The problem-size effect. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 331–345). Psychology Press.