Skip to main content
Top
Published in: Cognitive Processing 2/2023

31-01-2023 | Research Article

The influence of semantic alignment on the performance of addition and division operation: age-related differences

Authors: Yangyang Wang, Jia Gao, Tingting Wang, Bijuan Huang, Hongmin Feng, Jiwei Si

Published in: Cognitive Processing | Issue 2/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Semantic alignment refers to the cognitive tendency that people always seek for the matching of semantic relations between mathematical cognition and objects in specific situations. In developing individuals, language ability and mathematical ability are in the development stage, and the development of semantic consistency is more helpful to reveal the relationship between the two. From the perspective of semantic alignment, this study aims to explore the age-related difference in the effects of semantic relationship on arithmetic operations. Sixty-two children and 62 adults were recruited to perform an arithmetical verification task. The results showed that: (1) Compared with children, adults had shorter response times and higher accuracy in mathematical operations. (2) Both adults and children showed longer response times in division condition than that in addition condition. (3) Children are more affected by semantic alignment than adults in addition. (4) For addition operation, participants performed better under semantic consistent condition than under semantic inconsistent condition, but the opposite result was found for division operation. It indicated that semantic consistently promoted the addition operation and semantic inconsistently promoted the division operation. This suggests that teachers should pay attention to integrating mathematical conceptual knowledge and language context in future educational practice.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
go back to reference Babai R, Zilber H, Stavy R, Tirosh D (2010) The effect of intervention an accuracy of students’ responses and reaction times to geometry problems. Int J Sci Math Educ 8(1):185–201CrossRef Babai R, Zilber H, Stavy R, Tirosh D (2010) The effect of intervention an accuracy of students’ responses and reaction times to geometry problems. Int J Sci Math Educ 8(1):185–201CrossRef
go back to reference Bassok M (2001) Semantic alignments in mathematical word problems D. In: Gentner, Holyoak KJ, Kokinov BN (eds) The analogical mind: perspectives from cognitive science. The MIT Press, Cambridge, pp 199–253 Bassok M (2001) Semantic alignments in mathematical word problems D. In: Gentner, Holyoak KJ, Kokinov BN (eds) The analogical mind: perspectives from cognitive science. The MIT Press, Cambridge, pp 199–253
go back to reference Bassok M, Wu LL, Olseth KL (1995) Judging a book by its cover: Interpretative effects of content on problem-solving transfer. Mem Cognit 23(3):354–367PubMedCrossRef Bassok M, Wu LL, Olseth KL (1995) Judging a book by its cover: Interpretative effects of content on problem-solving transfer. Mem Cognit 23(3):354–367PubMedCrossRef
go back to reference Bassok M, Chase VM, Martin SA (1998) Adding apples and oranges: alignment of semantic and formal knowledge. Cogn Psychol 35(2):99–134PubMedCrossRef Bassok M, Chase VM, Martin SA (1998) Adding apples and oranges: alignment of semantic and formal knowledge. Cogn Psychol 35(2):99–134PubMedCrossRef
go back to reference Bassok M, Pedigo SF, Oskarsson AT (2008) Priming addition facts with semantic relations. J Exp Psychol Learn Mem Cognit 34(2):343–352CrossRef Bassok M, Pedigo SF, Oskarsson AT (2008) Priming addition facts with semantic relations. J Exp Psychol Learn Mem Cognit 34(2):343–352CrossRef
go back to reference Chen XQ, He BX, Zhang J (2012) The integration of arithmetic knowledge and semantic knowledge in addition facts. Acta Psychol Sin 44(06):720–734CrossRef Chen XQ, He BX, Zhang J (2012) The integration of arithmetic knowledge and semantic knowledge in addition facts. Acta Psychol Sin 44(06):720–734CrossRef
go back to reference Collins AM, Loftus EF (1975) A spreading-activation theory of semantic processing. Psychol Rev 82(6):407–428CrossRef Collins AM, Loftus EF (1975) A spreading-activation theory of semantic processing. Psychol Rev 82(6):407–428CrossRef
go back to reference Collins AM, Quillian MR (1969) Retrieval time from semantic memory. J Verbal Learn Verbal Behav 8(2):240–247CrossRef Collins AM, Quillian MR (1969) Retrieval time from semantic memory. J Verbal Learn Verbal Behav 8(2):240–247CrossRef
go back to reference Evans WS, Caplan D, Waters G (2011) Effects of concurrent arithmetical and syntactic complexity on self-paced reaction times and eye fixations. Psychon Bull Rev 18(6):1203–1211PubMedCrossRef Evans WS, Caplan D, Waters G (2011) Effects of concurrent arithmetical and syntactic complexity on self-paced reaction times and eye fixations. Psychon Bull Rev 18(6):1203–1211PubMedCrossRef
go back to reference Fedorenko E, Gibson E, Rohde D (2007) The nature of working memory in linguistic, arithmetic and spatial integration processes. J Mem Lang 56(2):246–269CrossRef Fedorenko E, Gibson E, Rohde D (2007) The nature of working memory in linguistic, arithmetic and spatial integration processes. J Mem Lang 56(2):246–269CrossRef
go back to reference Fisher KJ, Bassok M, Osterhout L (2010) When two plus two does not equal four: event-related potential responses to semantically incongruous arithmetic word problems. In: Ohlsson S, Catrambone R (Eds) Proceedings of the 32nd annual conference of the cognitive science society. Springer, Austin, pp 1571–1576 Fisher KJ, Bassok M, Osterhout L (2010) When two plus two does not equal four: event-related potential responses to semantically incongruous arithmetic word problems. In: Ohlsson S, Catrambone R (Eds) Proceedings of the 32nd annual conference of the cognitive science society. Springer, Austin, pp 1571–1576
go back to reference Fu XC, Li XD (2017) Cognitive inhibition: a new perspective on problem solving. J Psychol Sci 40(1):58–63 Fu XC, Li XD (2017) Cognitive inhibition: a new perspective on problem solving. J Psychol Sci 40(1):58–63
go back to reference Guthormsen AM, Fisher KJ, Bassok M, Osterhout L, Dewolf M, Holyoak KJ (2016) Conceptual integration of arithmetic operations with real-world knowledge: evidence from event-related potentials. Cogn Sci 40(3):723–757PubMedCrossRef Guthormsen AM, Fisher KJ, Bassok M, Osterhout L, Dewolf M, Holyoak KJ (2016) Conceptual integration of arithmetic operations with real-world knowledge: evidence from event-related potentials. Cogn Sci 40(3):723–757PubMedCrossRef
go back to reference Hauser MD, Chomsky N, Fitch WT (2002) The faculty of language: What is it, who has it, and how did it evolve? Science 298(5598):1569–1579PubMedCrossRef Hauser MD, Chomsky N, Fitch WT (2002) The faculty of language: What is it, who has it, and how did it evolve? Science 298(5598):1569–1579PubMedCrossRef
go back to reference Houdé O, Tzourio-Mazoyer N (2003) Neural foundations of logical and mathematical cognition. Nat Rev Neurosci 4(6):507–514PubMedCrossRef Houdé O, Tzourio-Mazoyer N (2003) Neural foundations of logical and mathematical cognition. Nat Rev Neurosci 4(6):507–514PubMedCrossRef
go back to reference Jarosz AF, Jaeger AJ (2019) Inconsistent operations: a weapon of math disruption. Appl Cogn Psychol 33(1):124–138CrossRef Jarosz AF, Jaeger AJ (2019) Inconsistent operations: a weapon of math disruption. Appl Cogn Psychol 33(1):124–138CrossRef
go back to reference Jiang RH, Li XD (2017) The overuse of proportional reasoning and its cognitive mechanisms: a developmental negative priming study. Acta Psychol Sin 49(6):745–758CrossRef Jiang RH, Li XD (2017) The overuse of proportional reasoning and its cognitive mechanisms: a developmental negative priming study. Acta Psychol Sin 49(6):745–758CrossRef
go back to reference Jiang RH, Li XD, Xu P, Lei Y (2020) Do teachers need to inhibit heuristic bias in mathematics problem-solving? Evidence from a negative-priming study. Curr Psychol 41: 6954–6965CrossRef Jiang RH, Li XD, Xu P, Lei Y (2020) Do teachers need to inhibit heuristic bias in mathematics problem-solving? Evidence from a negative-priming study. Curr Psychol 41: 6954–6965CrossRef
go back to reference Jordan NC, Hanich LB, Kaplan DA (2003) Longitudinal study of mathematical competencies in children with specific mathematical difficulties versus children with comorbid mathematical and reading difficulties. Child Dev 74:834–850PubMedCrossRefPubMedCentral Jordan NC, Hanich LB, Kaplan DA (2003) Longitudinal study of mathematical competencies in children with specific mathematical difficulties versus children with comorbid mathematical and reading difficulties. Child Dev 74:834–850PubMedCrossRefPubMedCentral
go back to reference Kadosh RC, Dowker A (2015) The Oxford handbook of numerical cognition. Oxford University Press, Oxford Kadosh RC, Dowker A (2015) The Oxford handbook of numerical cognition. Oxford University Press, Oxford
go back to reference Kmiecik MJ, Brisson RJ, Morrison RG (2019) The time course of semantic and relational processing during verbal analogical reasoning. Brain Cogn 129(2):25–34PubMedCrossRef Kmiecik MJ, Brisson RJ, Morrison RG (2019) The time course of semantic and relational processing during verbal analogical reasoning. Brain Cogn 129(2):25–34PubMedCrossRef
go back to reference Lavie N (1995) Perceptual load as a necessary condition for selective attention. J Exp Psychol Hum Percept Perform 21(3):451–468PubMedCrossRef Lavie N (1995) Perceptual load as a necessary condition for selective attention. J Exp Psychol Hum Percept Perform 21(3):451–468PubMedCrossRef
go back to reference Lavie N (2005) Distracted and confused? Selective attention under load. Trends Cogn Sci 9(2):75–82PubMedCrossRef Lavie N (2005) Distracted and confused? Selective attention under load. Trends Cogn Sci 9(2):75–82PubMedCrossRef
go back to reference Lavie N (2010) Attention, distraction, and cognitive control under load. Curr Dir Psychol Sci 19(3):143–148CrossRef Lavie N (2010) Attention, distraction, and cognitive control under load. Curr Dir Psychol Sci 19(3):143–148CrossRef
go back to reference Lavie N, Tsal Y (1994) Perceptual load as a major determinant of the locus of selection in visual attention. Percept Psychophys 56(2):183–197PubMedCrossRef Lavie N, Tsal Y (1994) Perceptual load as a major determinant of the locus of selection in visual attention. Percept Psychophys 56(2):183–197PubMedCrossRef
go back to reference Lee HS, Dewolf M, Bassok M, Holyoak KJ (2016) Conceptual and procedural distinctions between fractions and decimals: a cross-national comparison. Cognition 147(1):57–69PubMedCrossRef Lee HS, Dewolf M, Bassok M, Holyoak KJ (2016) Conceptual and procedural distinctions between fractions and decimals: a cross-national comparison. Cognition 147(1):57–69PubMedCrossRef
go back to reference Lubin A, Vidal J, Lanoë C, Houdé O, Borst G (2013) Inhibitory control is needed for the resolution of arithmetic word problems: a developmental negative priming study. J Educ Psychol 105(3):701–708CrossRef Lubin A, Vidal J, Lanoë C, Houdé O, Borst G (2013) Inhibitory control is needed for the resolution of arithmetic word problems: a developmental negative priming study. J Educ Psychol 105(3):701–708CrossRef
go back to reference Lubin A, Rossi S, Lanoë C, Vidal J, Houdé O, Borst G (2016) Expertise, inhibitory control and arithmetic word problems: a negative priming study in mathematics experts. Learn Instr 45:40–48CrossRef Lubin A, Rossi S, Lanoë C, Vidal J, Houdé O, Borst G (2016) Expertise, inhibitory control and arithmetic word problems: a negative priming study in mathematics experts. Learn Instr 45:40–48CrossRef
go back to reference Martin SA, Bassok M (2005) Effects of semantic cues on mathematical modeling: evidence from word-problem solving and equation construction tasks. Mem Cognit 33(3):471–478PubMedCrossRef Martin SA, Bassok M (2005) Effects of semantic cues on mathematical modeling: evidence from word-problem solving and equation construction tasks. Mem Cognit 33(3):471–478PubMedCrossRef
go back to reference McCloskey M (1992) Cognitive mechanisms in numerical processing: evidence from acquired dyscalculia. Cognition 44(1–2):107–157PubMedCrossRef McCloskey M (1992) Cognitive mechanisms in numerical processing: evidence from acquired dyscalculia. Cognition 44(1–2):107–157PubMedCrossRef
go back to reference Ministry of Education of the People’s Republic of China (2012) Compulsory education curriculum standard experimental teaching materials mathematics. Beijing Normal University Press, Beijing Ministry of Education of the People’s Republic of China (2012) Compulsory education curriculum standard experimental teaching materials mathematics. Beijing Normal University Press, Beijing
go back to reference Minzenberg MJ, Ober BA, Vinogradov S (2002) Semantic priming in schizophrenia: a review and synthesis. J Int Neuropsychol Soc 8:699–720PubMedCrossRef Minzenberg MJ, Ober BA, Vinogradov S (2002) Semantic priming in schizophrenia: a review and synthesis. J Int Neuropsychol Soc 8:699–720PubMedCrossRef
go back to reference Obersteiner A, Van Dooren W, Van Hoof J, Verschaffel L (2013) The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learn Instr 28:64–72CrossRef Obersteiner A, Van Dooren W, Van Hoof J, Verschaffel L (2013) The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learn Instr 28:64–72CrossRef
go back to reference Páchová A, Vondrová N (2021) The effect of semantic cues on the difficulty of word problems and the interplay with other complicating variables. Res Math Educ 23:85–102CrossRef Páchová A, Vondrová N (2021) The effect of semantic cues on the difficulty of word problems and the interplay with other complicating variables. Res Math Educ 23:85–102CrossRef
go back to reference Parmar RS (2003) Understanding the concept of “division”: assessment considerations. Exceptionality 11(3):177–189CrossRef Parmar RS (2003) Understanding the concept of “division”: assessment considerations. Exceptionality 11(3):177–189CrossRef
go back to reference Rapp M, Bassok M, DeWolf M, Holyoak KJ (2015) Modeling discrete and continuous entities with fractions and decimals. J Exp Psychol Appl 21(1):47–56PubMedCrossRef Rapp M, Bassok M, DeWolf M, Holyoak KJ (2015) Modeling discrete and continuous entities with fractions and decimals. J Exp Psychol Appl 21(1):47–56PubMedCrossRef
go back to reference Siegler RS (1988) Strategy choice procedures and the development of multiplication skill. J Exp Psychol Gen 117(3):258–275PubMedCrossRef Siegler RS (1988) Strategy choice procedures and the development of multiplication skill. J Exp Psychol Gen 117(3):258–275PubMedCrossRef
go back to reference Siegler RS, Shipley C (1995) Variation, selection, and cognitive change. In: Simon TJ, Halford GS (eds) Developing cognitive competence: new approaches to process modeling. Lawrence Erlbaum, Hillsdale, pp 31–76 Siegler RS, Shipley C (1995) Variation, selection, and cognitive change. In: Simon TJ, Halford GS (eds) Developing cognitive competence: new approaches to process modeling. Lawrence Erlbaum, Hillsdale, pp 31–76
go back to reference Tyumeneva YA, Larina G, Alexandrova E, DeWolf M, Bassok M, Holyoak KJ (2018) Semantic alignment across whole-number arithmetic and rational numbers: evidence from a Russian perspective. Think Reason 24(2):198–220CrossRef Tyumeneva YA, Larina G, Alexandrova E, DeWolf M, Bassok M, Holyoak KJ (2018) Semantic alignment across whole-number arithmetic and rational numbers: evidence from a Russian perspective. Think Reason 24(2):198–220CrossRef
go back to reference Varol F, Farran D (2007) Elementary school students’ mental computation proficiencies. Early Child Educ J 35(1):89–94CrossRef Varol F, Farran D (2007) Elementary school students’ mental computation proficiencies. Early Child Educ J 35(1):89–94CrossRef
go back to reference Wang J, Deng Y (2014) The effect of language system on different numerical systems in human cognition. Adv Psychol Sci 22(6):926–933CrossRef Wang J, Deng Y (2014) The effect of language system on different numerical systems in human cognition. Adv Psychol Sci 22(6):926–933CrossRef
go back to reference Zbrodoff NJ, Logan GD (2005) What everyone finds: the problem size effect. In: Campbell JID (ed) Handbook of mathematical cognition. Psychology Press, New York, pp 331–346 Zbrodoff NJ, Logan GD (2005) What everyone finds: the problem size effect. In: Campbell JID (ed) Handbook of mathematical cognition. Psychology Press, New York, pp 331–346
Metadata
Title
The influence of semantic alignment on the performance of addition and division operation: age-related differences
Authors
Yangyang Wang
Jia Gao
Tingting Wang
Bijuan Huang
Hongmin Feng
Jiwei Si
Publication date
31-01-2023
Publisher
Springer Berlin Heidelberg
Published in
Cognitive Processing / Issue 2/2023
Print ISSN: 1612-4782
Electronic ISSN: 1612-4790
DOI
https://doi.org/10.1007/s10339-023-01125-5

Other articles of this Issue 2/2023

Cognitive Processing 2/2023 Go to the issue