Previous research has shown that naïve views of math and science concepts coexist with more formal views. The current study extended this finding to the domain of mathematical equivalence and tested whether inhibitory control relates to using more formal views over naïve ones. In the current study, we report two experiments in which undergraduate students (n = 125 for Study 1 and n = 184 for Study 2) completed a priming task involving inhibitory control and math items, an inhibitory control flanker measure, and a comprehensive mathematical equivalence assessment. We found quantitative and qualitative evidence that adults hold both naïve operational views and formal relational views of equivalence across multiple measures and under timed and untimed conditions. In contrast to our hypotheses, we did not find evidence to support a strong association between individual differences in inhibitory control and mathematical equivalence knowledge. The results call into question the role of this domain-general cognitive skill in contributing to adults’ expression of naïve operational thinking.
AllanN. P.HumeL. E.AllanD. M.FarringtonA. L.LoniganC. J. (2014). Relations between inhibitory control and the development of academic skills in preschool and kindergarten: A meta-analysis. Developmental Psychology, 50(10), 2368–2379. https://doi.org/10.1037/a0037493
2.
AvgerinouV. A.TolmieA. (2020). Inhibition and cognitive load in fractions and decimals. British Journal of Educational Psychology, 90(S1), 240–256. https://doi.org/10.1111/bjep.12321
3.
BorstG.PoirelN.PineauA.CassottiM.HoudéO. (2012). Inhibitory control in number- conservation and class-inclusion tasks: A neo-Piagetian inter-task priming study. Cognitive Development, 27(3), 283–298. https://doi.org/10.1016/j.cogdev.2012.02.004
4.
BraemS.BuggJ. M.SchmidtJ. R.CrumpM. J. C.WeissmanD. H.NotebaertW.EgnerT. (2019). Measuring adaptive control in conflict tasks. Trends in Cognitive Science, 23(9), 769–783. https://doi.org/10.1016/j.tics.2019.07.002
5.
CareyS. (2009). The origin of concepts. Oxford University Press.
6.
CareyS.SpelkeE. (1994). Domain-specific knowledge and conceptual change. In HirschfeldL. A.GelmanS. A. (Eds.), Mapping the mind: Domain specificity in cognition and culture (pp. 169–200). Cambridge University Press. https://doi.org/10.1017/CBO9780511752902
7.
CarpenterT. P.FrankeM. L.LeviL. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.
8.
ChesneyD. L.McNeilN. M.BrockmoleJ. R.KelleyK. (2013). An eye for relations: Eye-tracking indicates long-term negative effects of operational thinking on understanding of math equivalence. Memory & Cognition, 41(7), 1079–1095. https://doi.org/10.3758/s13421-013-0315-8
9.
ChesneyD. L.McNeilN. M.MatthewsP. G.ByrdC. E.PetersenL. A.WheelerM. C.FyfeE. R.DunwiddieA. E. (2014). Organization matters: Mental organization of addition knowledge relates to understanding math equivalence in symbolic form. Cognitive Development, 30, 30–46. https://doi.org/10.1016/j.cogdev.2014.01.001
10.
ChiM. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. In VosniadouS. (Ed.), International handbook of research on conceptual change (pp. 61–82). Erlbaum.
11.
CoulangesL.Abreu-MendozaR. A.VarmaS.UncapherM. R.GazzaleyA.AngueraJ.Rosenberg-LeeM. (2021). Linking inhibitory control to math achievement via comparison of conflicting decimal numbers. Cognition, 214, 104767. https://doi.org/10.1016/j.cognition.2021.104767
12.
CraggL.GilmoreC. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3(2), 63–68. https://doi.org/10.1016/j.tine.2013.12.001
13.
DevlinB. L.HornburgC. B.McNeilN. M. (2023). Kindergarteners predictors of formal understanding of mathematical equivalence in second grade. Developmental Psychology, 59(8), 1426–1439. https://dx.doi.org/10.1037/dev0001559
DuthooW.AbrahamseE. L.BraemS.BroehlerC. N.NotebaertW. (2014). The congruency sequence effect 3.0: A critical test of conflict adaptation. PLOS ONE, 9(10), Article e110462. https://doi.org/10.1371/journal.pone.0110462
17.
EavesJ.AttridgeN.GilmoreC. (2022). The Role of Domain-General and Domain-Specific Skills in the Identification of Arithmetic Strategies. Journal of Numerical Cognition, 8(3), 335–350. https://doi.org/10.5964/jnc.7459
FyfeE. R.MatthewsP. G.AmselE. (2020). College developmental math students’ knowledge of the equal sign. Educational Studies in Mathematics, 104, 65–85. https://doi.org/10.1007/s10649-020-09947-2
20.
FyfeE. R.Rittle-JohnsonB. (2017). Mathematics practice without feedback: A desirable difficulty in a classroom setting. Instructional Science, 45, 177–194. https://doi.org/10.1007/s11251-016-9401-1
GómezD. M.JiménezA.BobadillaR.ReyesC.DartnellP. (2015). The effect of inhibitory control on general mathematics achievement and fraction comparison in middle school children. ZDM Mathematics Education, 47, 801–811. https://doi.org/10.1007/s11858-015-0685-4
23.
GrenellA.NelsonL. J.GardnerB.FyfeE. R. (2022). Children’s confidence using incorrect strategies on mathematical equivalence problems. Cognitive Development, 62, 101167. https://doi.org/10.1016/j.cogdev.2022.101167
24.
HornburgC. B.DevlinB. L.McNeilN. M. (2022). Earlier understanding of mathematical equivalence in elementary school predicts greater algebra readiness in middle school. Journal of Educational Psychology, 114(3), 540–559. https://doi.org/10.1037/edu0000683
KieranC. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317–326. https://doi.org/10.1007/BF00311062
27.
LaskiE. V.DulaneyA. (2015). When prior knowledge interferes, inhibitory control matters for learning: The case of numerical magnitude representations. Journal of Educational Psychology, 107(4), 1035–1050. https://doi.org/10.1037/edu0000034
28.
LeeK.BullR. (2016). Developmental changes in working memory, updating, and math achievement. Journal of Educational Psychology, 108(6), 869–882. https://doi.org/10.1037/edu0000090
29.
LeeK.LeeH. 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
30.
LeeM. D.WagenmakersE.-J. (2014). Bayesian cognitive modeling: A practical course. Cambridge University Press.
31.
LeibE. R.StarrA.YoungerJ. W.BungeS. A.UncapherM. R.Rosenberg-LeeM. (2023). Testing the Whole Number Interference Hypothesis: Contributions of Inhibitory Control and Whole Number Knowledge to Fraction Understanding. Developmental Psychology, 59(8), 1407–1425. https://doi.org/10.1037/dev0001557
32.
LinchevskiL. (1995). Algebra with numbers and arithmetic with letters: A definition of pre- algebra. Journal of Mathematical Behavior, 14, 113–120. https://doi.org/10.1016/0732-3123(95)90026-8
33.
LinzariniA.HoudéO.BorstG. (2015). When Stroop helps Piaget: An inter-task positive priming paradigm in 9-year-old children. Journal of Experimental Child Psychology, 139, 71–82. https://doi.org/10.1016/j.jecp.2015.05.010
34.
MacLeodC. M. (1991). Half a century of research on the Stroop effect: An integrative review. Psychological Bulletin, 109(2), 163–203. https://doi.org/10.1037/0033-2909.109.2.163
35.
MatthewsP. G.FuchsL. S. (2020). Keys to the gate? Equal sign knowledge at second grade predicts fourth grade algebra competence. Child Development, 91, 14–28. https://doi.org/10.1111/cdev.13144
36.
MatthewsP. G.Rittle-JohnsonB.McEldoonK.RogerT. (2012). Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316–350. https://doi.org/10.5951/jresematheduc.43.3.0316
37.
McNeilN. M. (2014). A change–resistance account of children’s difficulties understanding mathematical equivalence. Child Development Perspectives, 8, 42–47. https://doi.org/10.1111/cdep.12062
38.
McNeilN. M.AlibaliM. W. (2005a). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development, 6(2), 285–306. https://doi.org/10.1207/s15327647jcd0602_6
39.
McNeilN. M.AlibaliM. W. (2005b). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 883–899. https://doi.org/10.1111/j.1467-8624.2005.00884.x
40.
McNeilN. M.Rittle-JohnsonB.HattikudurS.PetersenL. A. (2010). Continuity in representation between children and adults: Arithmetic knowledge hinders undergraduates’ algebraic problem solving. Journal of Cognition and Development, 4, 437–457. https://doi.org/10.1080/15248372.2010.516421
41.
PeirceJ.GrayJ. R.SimpsonS.MacAskillM.HöchenbergerR.SogoH.KastmanE.LindeløvJ. K. (2019). PsychoPy2: Experiments in behavior made easy. Behavior Research Methods, 51, 195–203. https://doi.org/10.3758/s13428-018-01193-y
42.
PengP.NamkungJ.BarnesM.SunC. (2016). A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 108(4), 455–473. https://doi.org/10.1037/edu0000079
43.
PowellS. R. (2012). Equations and the equal sign in elementary mathematics textbooks. The Elementary School Journal, 112(4), 627–648. https://doi.org/10.1086/665009
Rittle-JohnsonB.AlibaliM. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other?Journal of Educational Psychology, 91(1), 175–189. https://doi.org/10.1037/0022-0663.91.1.175
46.
Rittle-JohnsonB.MatthewsP. G.TaylorR. S.McEldoonK. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103(1), 85–104. https://doi.org/10.1037/a0021334
47.
RobinsonK. M.DubéA. K. (2013). Children’s additive concepts: Promoting understanding and the role of inhibition. Learning and Individual Differences, 23, 101–107. https://doi.org/10.1016/j.lindif.2012.07.016
48.
RoellM.ViarougeA.HoudéO.BorstG. (2017). Inhibitory control and decimal number comparison in school-aged children. PLOS ONE, 12(11), Article e0188276. https://doi.org/10.1371/journal.pone.0188276
StrickerJ.VogelS. E.Schöneburg-LehnertS.KrohnT.DögnitzS.JudN.SprikM.WindhaberM.SchneiderM.GrabnerR. H. (2021). Interference between naïve and scientific theories occur is in mathematics and is related to mathematical achievement. Cognition, 214, 104789. https://doi.org/10.1016/j.cognition.2021.104789
53.
VamvakoussiZ.DoorenW. V.VerschaffelL. (2013). Educated adults are still affected by intuitions about the effect of arithmetical operations: Evidence from a reaction-time study. Educational Studies in Mathematics, 82, 323–330. https://doi.org/10.1007/s10649-012-9432-8
54.
Van DoorenW.InglisM. (2015). Inhibitory control in mathematical thinking, learning and problem solving: A survey. ZDM Mathematics Education, 47, 713–721. https://doi.org/10.1007/s11858-015-0715-2
55.
VosniadouS. (2014). Examining cognitive development from a conceptual change point of view: The framework theory approach. European Journal of Developmental Psychology, 11(6), 645–661. https://doi.org/10.1080/17405629.2014.921153
56.
VosniadouS.BrewerW. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24(4), 535–585. https://doi.org/10.1016/0010-0285(92)90018-W
57.
VosniadouS.PnevmatikosD.MakrisN.LepeniotiD.EikospentakiK.ChountalaA.KyrianakisG. (2018). The recruitment of shifting and inhibition in on-line science and mathematics tasks. Cognitive Science, 42(6), 1860–1886. https://doi.org/10.1111/cogs.12624
58.
VosniadouS.VamvakoussiX.SkopelitiI. (2008). The framework approach to conceptual change. In VosniadouS. (Ed.), International handbook of research on conceptual change (pp. 3–34). Routledge.
YoungA. G.ShtulmanA. (2020). Children’s cognitive reflection predicts conceptual understanding in science and mathematics. Psychological Science, 31(11), 1396–1408. https://doi.org/10.1177/0956797620954449
61.
YuX.ZhangM.ChenY.DengZ.ChenY.ZhangH.ZhangY.ChenX. (2020). The role of inhibitory control in the development of analogical reasoning: From general to specific. British Journal of Developmental Psychology, 38(4), 594–615. https://doi.org/10.1111/bjdp.12346
62.
ZaitchikD.SolomonG. E. A.TardiffN.BascandzievI. (2016). Conceptual change: Where domain-specific learning mechanisms meet domain-general cognitive resources. In BarnerD.BaronA. S. (Eds.), Core knowledge and conceptual change (pp. 73–88). Oxford University Press.
63.
ZelazoP. D.AndersonJ. E.RichlerJ.Wallner-AllenK.BeaumontJ. L.ConwayK. P.GershonR.WeintraubS. (2014). NIH Toolbox Cognition Battery (CB): Validation of executive function measures in adults. Journal of the International Neuropsychological Society, 20(6), 620–629. https://doi.org/10.1017/S13556177140004
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
