{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:49:03Z","timestamp":1786981743801,"version":"3.56.0"},"reference-count":159,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100005875","name":"Kulttuurin ja Yhteiskunnan Tutkimuksen Toimikunta","doi-asserted-by":"publisher","award":["286991"],"award-info":[{"award-number":["286991"]}],"id":[{"id":"10.13039\/501100005875","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Synthese"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s11229-019-02276-9","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T02:02:31Z","timestamp":1560477751000},"page":"3221-3263","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving"],"prefix":"10.1007","volume":"198","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1078-1499","authenticated-orcid":false,"given":"Regina E.","family":"Fabry","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8572-1453","authenticated-orcid":false,"given":"Markus","family":"Pantsar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"2276_CR1","doi-asserted-by":"crossref","first-page":"261","DOI":"10.7551\/mitpress\/8009.003.0011","volume-title":"Computability: Turing, G\u00f6del, Church, and beyond","author":"S Aaronson","year":"2013","unstructured":"Aaronson, S. (2013). Why philosophers should care about computational complexity. In B. J. Copeland, C. J. Posy, & O. Shagrir (Eds.), Computability: Turing, G\u00f6del, Church, and beyond (pp. 261\u2013328). Cambridge, MA: MIT Press."},{"key":"2276_CR2","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/978-3-642-38236-9_13","volume-title":"International conference on theory and applications of models of computation","author":"NL Ackerman","year":"2013","unstructured":"Ackerman, N. L., & Freer, C. E. (2013). A notion of a computational step for partial combinatory algebras. In T.-H. H. Chan, L. C. Lau, & L. Trevisan (Eds.), International conference on theory and applications of models of computation (pp. 133\u2013143). Berlin: Springer."},{"issue":"18","key":"2276_CR3","doi-asserted-by":"publisher","first-page":"4909","DOI":"10.1073\/pnas.1603205113","volume":"113","author":"M Amalric","year":"2016","unstructured":"Amalric, M., & Dehaene, S. (2016). Origins of the brain networks for advanced mathematics in expert mathematicians. Proceedings of the National Academy of Sciences, 113(18), 4909\u20134917.","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"1740","key":"2276_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1098\/rstb.2016.0515","volume":"373","author":"M Amalric","year":"2018","unstructured":"Amalric, M., & Dehaene, S. (2018). Cortical circuits for mathematical knowledge: Evidence for a major subdivision within the brain\u2019s semantic networks. Philosophical Transactions of the Royal Society B, 373(1740), 1\u20139.","journal-title":"Philosophical Transactions of the Royal Society B"},{"key":"2276_CR5","volume-title":"The adaptive character of thought","author":"JR Anderson","year":"1990","unstructured":"Anderson, J. R. (1990). The adaptive character of thought. Hillsdale, NJ: Lawrence Erlbaum Associates."},{"issue":"3","key":"2276_CR6","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1207\/s15516709cog0000_22","volume":"29","author":"JR Anderson","year":"2005","unstructured":"Anderson, J. R. (2005). Human symbol manipulation within an integrated cognitive architecture. Cognitive Science, 29(3), 313\u2013341.","journal-title":"Cognitive Science"},{"issue":"04","key":"2276_CR7","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1017\/S0140525X10000853","volume":"33","author":"ML Anderson","year":"2010","unstructured":"Anderson, M. L. (2010). Neural reuse: A fundamental organizational principle of the brain. Behavioral and Brain Sciences, 33(04), 245\u2013266.","journal-title":"Behavioral and Brain Sciences"},{"key":"2276_CR8","volume-title":"After phrenology: Neural reuse and the interactive brain","author":"ML Anderson","year":"2015","unstructured":"Anderson, M. L. (2015). After phrenology: Neural reuse and the interactive brain. Cambridge, MA: MIT Press."},{"key":"2276_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0140525X14001356","volume":"39","author":"ML Anderson","year":"2016","unstructured":"Anderson, M. L. (2016). Pr\u00e9cis of after phrenology: Neural reuse and the interactive brain. Behavioral and Brain Sciences, 39, 1\u201345.","journal-title":"Behavioral and Brain Sciences"},{"issue":"4","key":"2276_CR10","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1038\/nrn2334","volume":"9","author":"D Ansari","year":"2008","unstructured":"Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278\u2013291.","journal-title":"Nature Reviews Neuroscience"},{"issue":"18","key":"2276_CR11","doi-asserted-by":"publisher","first-page":"4887","DOI":"10.1073\/pnas.1604758113","volume":"113","author":"D Ansari","year":"2016","unstructured":"Ansari, D. (2016). The neural roots of mathematical expertise. Proceedings of the National Academy of Sciences of the United States of America, 113(18), 4887\u20134889. https:\/\/doi.org\/10.1073\/pnas.1604758113.","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"key":"2276_CR12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804090","volume-title":"Computational complexity: A modern approach","author":"S Arora","year":"2009","unstructured":"Arora, S., & Barak, B. (2009). Computational complexity: A modern approach. Cambridge, MA: Cambridge University Press."},{"issue":"1","key":"2276_CR13","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s11229-005-4064-5","volume":"153","author":"J Avigad","year":"2006","unstructured":"Avigad, J. (2006). Mathematical method and proof. Synthese, 153(1), 105\u2013159.","journal-title":"Synthese"},{"key":"2276_CR14","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1093\/acprof:oso\/9780199296453.003.0013","volume-title":"The philosophy of mathematical practice","author":"J Avigad","year":"2008","unstructured":"Avigad, J. (2008). Understanding proofs. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 317\u2013353). Oxford: Oxford University Press."},{"issue":"2","key":"2276_CR15","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/0273-2297(84)90004-2","volume":"4","author":"AJ Baroody","year":"1984","unstructured":"Baroody, A. J. (1984). A reexamination of mental arithmetic models and data: A reply to Ashcraft. Developmental Review, 4(2), 148\u2013156.","journal-title":"Developmental Review"},{"key":"2276_CR16","first-page":"3","volume-title":"Logical reasoning with diagrams","author":"J Barwise","year":"1996","unstructured":"Barwise, J., & Etchemendy, J. (1996). Visual information and valid reasoning. In G. Allwein & J. Barwise (Eds.), Logical reasoning with diagrams (pp. 3\u201325). Oxford: Oxford University Press."},{"issue":"2","key":"2276_CR17","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1111\/tops.12141","volume":"7","author":"W Bechtel","year":"2015","unstructured":"Bechtel, W., & Shagrir, O. (2015). The non-redundant contributions of Marr\u2019s three levels of analysis for explaining information-processing mechanisms. Topics in Cognitive Science, 7(2), 312\u2013322.","journal-title":"Topics in Cognitive Science"},{"key":"2276_CR18","first-page":"1","volume":"10","author":"M Blokpoel","year":"2017","unstructured":"Blokpoel, M. (2017). Sculpting computational-level models. Topics in Cognitive Science, 10, 1\u20138.","journal-title":"Topics in Cognitive Science"},{"issue":"2","key":"2276_CR19","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1145\/321386.321395","volume":"14","author":"M Blum","year":"1967","unstructured":"Blum, M. (1967). A machine-independent theory of the complexity of recursive functions. Journal of the ACM, 14(2), 322\u2013336.","journal-title":"Journal of the ACM"},{"key":"2276_CR20","volume-title":"A history of mathematics","author":"CB Boyer","year":"1985","unstructured":"Boyer, C. B. (1985). A history of mathematics. Princeton: Princeton University Press."},{"key":"2276_CR21","volume-title":"Philosophy of mathematics: A contemporary introduction to the world of proofs and pictures","author":"JR Brown","year":"2008","unstructured":"Brown, J. R. (2008). Philosophy of mathematics: A contemporary introduction to the world of proofs and pictures (2nd ed.). New York: Routledge.","edition":"2"},{"issue":"4","key":"2276_CR22","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1207\/s15516709cog0404_3","volume":"4","author":"JS Brown","year":"1980","unstructured":"Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4(4), 379\u2013426.","journal-title":"Cognitive Science"},{"key":"2276_CR23","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780195367638.001.0001","volume-title":"The origin of concepts","author":"S Carey","year":"2009","unstructured":"Carey, S. (2009). The origin of concepts. Oxford: Oxford University Press."},{"key":"2276_CR24","first-page":"106","volume-title":"The teaching and learning of algorithms in school mathematics","author":"WM Carroll","year":"1998","unstructured":"Carroll, W. M., & Porter, D. (1998). Alternative algorithms for whole-number operations. In M. J. Kenney & L. J. Morrow (Eds.), The teaching and learning of algorithms in school mathematics (pp. 106\u2013114). Reston, VA: National Council of Teachers of Mathematics."},{"issue":"1","key":"2276_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/02698590903467085","volume":"24","author":"J Carter","year":"2010","unstructured":"Carter, J. (2010). Diagrams and proofs in analysis. International Studies in the Philosophy of Science, 24(1), 1\u201314.","journal-title":"International Studies in the Philosophy of Science"},{"key":"2276_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-017-1635-1","author":"J Carter","year":"2017","unstructured":"Carter, J. (2017). Exploring the fruitfulness of diagrams in mathematics. Synthese. https:\/\/doi.org\/10.1007\/s11229-017-1635-1.","journal-title":"Synthese"},{"issue":"12","key":"2276_CR27","doi-asserted-by":"publisher","first-page":"4693","DOI":"10.1073\/pnas.0600444103","volume":"103","author":"F Castelli","year":"2006","unstructured":"Castelli, F., Glaser, D. E., & Butterworth, B. (2006). Discrete and analogue quantity processing in the parietal lobe: A functional MRI study. Proceedings of the National Academy of Sciences of the United States of America, 103(12), 4693\u20134698.","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"key":"2276_CR28","volume-title":"A history of algorithms: From the pebble to the microchip","year":"1999","unstructured":"Chabert, J.-L. (Ed.). (1999). A history of algorithms: From the pebble to the microchip. Heidelberg: Springer."},{"key":"2276_CR29","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511791222","volume-title":"Language and mind","author":"N Chomsky","year":"2006","unstructured":"Chomsky, N. (2006). Language and mind. Cambridge: Cambridge University Press."},{"key":"2276_CR30","volume-title":"Aspects of the theory of syntax (50th anniv)","author":"N Chomsky","year":"2015","unstructured":"Chomsky, N. (2015). Aspects of the theory of syntax (50th anniv). Cambridge, MA: MIT Press."},{"issue":"2","key":"2276_CR31","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1093\/bjps\/41.2.195","volume":"41","author":"A Clark","year":"1990","unstructured":"Clark, A. (1990). Connectionism, competence, and explanation. The British Journal for the Philosophy of Science, 41(2), 195\u2013222.","journal-title":"The British Journal for the Philosophy of Science"},{"key":"2276_CR32","volume-title":"Being there: Putting brain, body, and world together again","author":"A Clark","year":"1997","unstructured":"Clark, A. (1997). Being there: Putting brain, body, and world together again. Cambridge, MA: MIT Press."},{"key":"2276_CR33","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780190217013.001.0001","volume-title":"Surfing uncertainty: Prediction, action, and the embodied mind","author":"A Clark","year":"2016","unstructured":"Clark, A. (2016). Surfing uncertainty: Prediction, action, and the embodied mind. Oxford, NY: Oxford University Press."},{"issue":"7","key":"2276_CR34","doi-asserted-by":"publisher","first-page":"13","DOI":"10.3102\/0013189X023007013","volume":"23","author":"P Cobb","year":"1994","unstructured":"Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13\u201320.","journal-title":"Educational Researcher"},{"key":"2276_CR35","first-page":"24","volume-title":"Proceedings of the 1964 congress on logic, mathematics and the methodology of science","author":"A Cobham","year":"1965","unstructured":"Cobham, A. (1965). The intrinsic computational difficulty of functions. In Y. Bar-Hillel (Ed.), Proceedings of the 1964 congress on logic, mathematics and the methodology of science (pp. 24\u201330). Amsterdam: North-Holland."},{"key":"2276_CR36","first-page":"1","volume":"10","author":"RP Cooper","year":"2017","unstructured":"Cooper, R. P., & Peebles, D. (2017). On the relation between Marr\u2019s levels: A response to Blokpoel. Topics in Cognitive Science, 10, 1\u20135.","journal-title":"Topics in Cognitive Science"},{"issue":"2","key":"2276_CR37","doi-asserted-by":"publisher","first-page":"239","DOI":"10.3758\/BF03196066","volume":"33","author":"J De Houwer","year":"2005","unstructured":"De Houwer, J., Vandorpe, S., & Beckers, T. (2005). Evidence for the role of higher order reasoning processes in cue competition and other learning phenomena. Learning & Behavior, 33(2), 239\u2013249.","journal-title":"Learning & Behavior"},{"key":"2276_CR38","doi-asserted-by":"publisher","first-page":"133","DOI":"10.7551\/mitpress\/3136.001.0001","volume-title":"From monkey brain to human brain: A Fyssen Foundation symposium","author":"S Dehaene","year":"2005","unstructured":"Dehaene, S. (2005). Evolution of human cortical circuits for reading and arithmetic: The \u201cneuronal recycling\u201d hypothesis. In S. Dehaene, J.-R. Duhamel, M. D. Hauser, & G. Rizzolatti (Eds.), From monkey brain to human brain: A Fyssen Foundation symposium (pp. 133\u2013157). Cambridge, MA: MIT Press."},{"key":"2276_CR39","volume-title":"Reading in the brain: The new science of how we read","author":"S Dehaene","year":"2010","unstructured":"Dehaene, S. (2010). Reading in the brain: The new science of how we read. New York: Penguin Books."},{"key":"2276_CR40","volume-title":"The number sense: How the mind creates mathematics","author":"S Dehaene","year":"2011","unstructured":"Dehaene, S. (2011). The number sense: How the mind creates mathematics (2nd ed.). Oxford: Oxford University Press.","edition":"2"},{"issue":"7","key":"2276_CR41","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/j.tics.2005.05.004","volume":"9","author":"S Dehaene","year":"2005","unstructured":"Dehaene, S., Cohen, L., Sigman, M., & Vinckier, F. (2005). The neural code for written words: A proposal. Trends in Cognitive Sciences, 9(7), 335\u2013341. https:\/\/doi.org\/10.1016\/j.tics.2005.05.004.","journal-title":"Trends in Cognitive Sciences"},{"issue":"4","key":"2276_CR42","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1037\/h0070405","volume":"3","author":"J Dewey","year":"1896","unstructured":"Dewey, J. (1896). The reflex arc concept in psychology. Psychological Review, 3(4), 357\u2013370.","journal-title":"Psychological Review"},{"key":"2276_CR43","volume-title":"Origins of the modern mind: Three stages in the evolution of culture and cognition","author":"M Donald","year":"1991","unstructured":"Donald, M. (1991). Origins of the modern mind: Three stages in the evolution of culture and cognition. Cambridge, MA: Harvard University Press."},{"issue":"5","key":"2276_CR44","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1037\/h0093599","volume":"58","author":"K Duncker","year":"1945","unstructured":"Duncker, K. (1945). On problem-solving. Psychological Monographs, 58(5), 1\u2013113.","journal-title":"Psychological Monographs"},{"issue":"3","key":"2276_CR45","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/s11023-011-9241-3","volume":"21","author":"F Eberhardt","year":"2011","unstructured":"Eberhardt, F., & Danks, D. (2011). Confirmation in the cognitive sciences: The problematic case of Bayesian models. Minds and Machines, 21(3), 389\u2013410.","journal-title":"Minds and Machines"},{"issue":"3","key":"2276_CR46","doi-asserted-by":"publisher","first-page":"449","DOI":"10.4153\/CJM-1965-045-4","volume":"17","author":"J Edmonds","year":"1965","unstructured":"Edmonds, J. (1965). Paths, trees, and flowers. Canadian Journal of Mathematics, 17(3), 449\u2013467.","journal-title":"Canadian Journal of Mathematics"},{"key":"2276_CR47","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1080\/09515089.2013.828569","volume":"27","author":"A Estany","year":"2014","unstructured":"Estany, A., & Mart\u00ednez, S. (2014). \u201cScaffolding\u201d and \u201caffordance\u201d as integrative concepts in the cognitive sciences. Philosophical Psychology, 27, 98\u2013111. https:\/\/doi.org\/10.1080\/09515089.2013.828569.","journal-title":"Philosophical Psychology"},{"key":"2276_CR48","doi-asserted-by":"publisher","DOI":"10.4159\/9780674979185","volume-title":"Numbers and the making of us: Counting and the course of human cultures","author":"C Everett","year":"2017","unstructured":"Everett, C. (2017). Numbers and the making of us: Counting and the course of human cultures. Cambridge, MA: Harvard University Press."},{"key":"2276_CR49","doi-asserted-by":"publisher","first-page":"1","DOI":"10.15502\/9783958573147","volume-title":"Philosophy and predictive processing","author":"RE Fabry","year":"2017","unstructured":"Fabry, R. E. (2017). Predictive processing and cognitive development. In T. K. Metzinger & W. Wiese (Eds.), Philosophy and predictive processing (pp. 1\u201318). Frankfurt am Main: MIND Group. https:\/\/doi.org\/10.15502\/9783958573147."},{"issue":"6","key":"2276_CR50","doi-asserted-by":"publisher","first-page":"2483","DOI":"10.1007\/s11229-017-1334-y","volume":"195","author":"RE Fabry","year":"2018","unstructured":"Fabry, R. E. (2018). Betwixt and between: The enculturated predictive processing approach to cognition. Synthese, 195(6), 2483\u20132518. https:\/\/doi.org\/10.1007\/s11229-017-1334-y.","journal-title":"Synthese"},{"key":"2276_CR51","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-019-02238-1","author":"RE Fabry","year":"2019","unstructured":"Fabry, R. E. (2019). The cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturated arithmetical cognition. Synthese. https:\/\/doi.org\/10.1007\/s11229-019-02238-1.","journal-title":"Synthese"},{"key":"2276_CR52","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198524793.001.0001","volume-title":"Active vision","author":"JM Findlay","year":"2003","unstructured":"Findlay, J. M., & Gilchrist, I. D. (2003). Active vision. Oxford: Oxford University Press."},{"issue":"2","key":"2276_CR53","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.cognition.2005.02.005","volume":"97","author":"WT Fitch","year":"2005","unstructured":"Fitch, W. T., Hauser, M. D., & Chomsky, N. (2005). The evolution of the language faculty: Clarifications and implications. Cognition, 97(2), 179\u2013210.","journal-title":"Cognition"},{"issue":"3","key":"2276_CR54","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1016\/j.cognition.2008.04.007","volume":"108","author":"MC Frank","year":"2008","unstructured":"Frank, M. C., Everett, D. L., Fedorenko, E., & Gibson, E. (2008). Number as a cognitive technology: Evidence from Pirah\u00e3 language and cognition. Cognition, 108(3), 819\u2013824.","journal-title":"Cognition"},{"issue":"1456","key":"2276_CR55","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1098\/rstb.2005.1622","volume":"360","author":"K Friston","year":"2005","unstructured":"Friston, K. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society B: Biological Sciences, 360(1456), 815\u2013836. https:\/\/doi.org\/10.1098\/rstb.2005.1622.","journal-title":"Philosophical Transactions of the Royal Society B: Biological Sciences"},{"issue":"2","key":"2276_CR56","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1038\/nrn2787","volume":"11","author":"K Friston","year":"2010","unstructured":"Friston, K. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, 11(2), 127\u2013138. https:\/\/doi.org\/10.1038\/nrn2787.","journal-title":"Nature Reviews Neuroscience"},{"issue":"3","key":"2276_CR57","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1023\/A:1017503201702","volume":"11","author":"M Frixione","year":"2001","unstructured":"Frixione, M. (2001). Tractable competence. Minds and Machines, 11(3), 379\u2013397.","journal-title":"Minds and Machines"},{"key":"2276_CR58","first-page":"68","volume-title":"A research companion to principles and standards for school mathematics","author":"KC Fuson","year":"2003","unstructured":"Fuson, K. C. (2003). Developing mathematical power in whole number operations. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (Vol. 1, pp. 68\u201394). Reston, VA: National Council of Teachers of Mathematics."},{"issue":"3","key":"2276_CR59","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1037\/0033-2909.105.3.331","volume":"105","author":"KM Galotti","year":"1989","unstructured":"Galotti, K. M. (1989). Approaches to studying formal and everyday reasoning. Psychological Bulletin, 105(3), 331\u2013351.","journal-title":"Psychological Bulletin"},{"key":"2276_CR60","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199285945.001.0001","volume-title":"Visual thinking in mathematics","author":"M Giaquinto","year":"2007","unstructured":"Giaquinto, M. (2007). Visual thinking in mathematics. Oxford: Oxford University Press."},{"key":"2276_CR61","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1093\/acprof:oso\/9780199296453.003.0002","volume-title":"The philosophy of mathematical practice","author":"M Giaquinto","year":"2008","unstructured":"Giaquinto, M. (2008). Visualizing in mathematics. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 22\u201342). Oxford: Oxford University Press."},{"key":"2276_CR62","unstructured":"Giaquinto, M. (2015). The epistemology of visual thinking in mathematics. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Retrieved from https:\/\/plato.stanford.edu\/archives\/win2016\/entries\/epistemology-visual-thinking\/. Accessed 02 June 2019."},{"issue":"1","key":"2276_CR63","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s11245-009-9064-5","volume":"29","author":"V Giardino","year":"2010","unstructured":"Giardino, V. (2010). Intuition and visualization in mathematical problem solving. Topoi, 29(1), 29\u201339.","journal-title":"Topoi"},{"key":"2276_CR64","first-page":"23","volume-title":"The power of the image: Emotion, expression, explanation","author":"V Giardino","year":"2014","unstructured":"Giardino, V. (2014). Diagramming: Connecting cognitive systems to improve reasoning. In A. Benedek & K. Ny\u00edri (Eds.), The power of the image: Emotion, expression, explanation (pp. 23\u201334). Frankfurt am Main: Peter Lang."},{"key":"2276_CR65","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1515\/9781501503757-004","volume-title":"Thinking with diagrams: The semiotic basis of human cognition","author":"V Giardino","year":"2016","unstructured":"Giardino, V. (2016). Behind the diagrams: Cognitive issues and open problems. In S. Kr\u00e4mer & C. Ljungberg (Eds.), Thinking with diagrams: The semiotic basis of human cognition (pp. 77\u2013101). Berlin: Walter De Gruyter."},{"key":"2276_CR66","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/978-3-319-30526-4_22","volume-title":"Springer handbook of model-based science","author":"V Giardino","year":"2017","unstructured":"Giardino, V. (2017). Diagrammatic reasoning in mathematics. In L. Magnani & T. Bertolotti (Eds.), Springer handbook of model-based science (pp. 499\u2013522). Heidelberg: Springer."},{"issue":"2","key":"2276_CR67","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1111\/j.1756-8765.2009.01055.x","volume":"2","author":"RL Goldstone","year":"2010","unstructured":"Goldstone, R. L., Landy, D. H., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2(2), 265\u2013284.","journal-title":"Topics in Cognitive Science"},{"issue":"5","key":"2276_CR68","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1177\/0963721417704888","volume":"26","author":"RL Goldstone","year":"2017","unstructured":"Goldstone, R. L., Marghetis, T., Weitnauer, E., Ottmar, E. R., & Landy, D. (2017). Adapting perception, action, and technology for mathematical reasoning. Current Directions in Psychological Science, 26(5), 434\u2013441.","journal-title":"Current Directions in Psychological Science"},{"issue":"5695","key":"2276_CR69","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1126\/science.1094492","volume":"306","author":"P Gordon","year":"2004","unstructured":"Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496\u2013499.","journal-title":"Science"},{"issue":"5","key":"2276_CR70","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1111\/1467-9280.02454","volume":"14","author":"ER Grant","year":"2003","unstructured":"Grant, E. R., & Spivey, M. J. (2003). Eye movements and problem solving: Guiding attention guides thought. Psychological Science, 14(5), 462\u2013466.","journal-title":"Psychological Science"},{"issue":"8","key":"2276_CR71","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.tics.2010.05.004","volume":"14","author":"TL Griffiths","year":"2010","unstructured":"Griffiths, T. L., Chater, N., Kemp, C., Perfors, A., & Tenenbaum, J. B. (2010). Probabilistic models of cognition: Exploring representations and inductive biases. Trends in Cognitive Sciences, 14(8), 357\u2013364.","journal-title":"Trends in Cognitive Sciences"},{"key":"2276_CR72","volume-title":"Math instruction for students with learning problems","author":"SP Gurganus","year":"2007","unstructured":"Gurganus, S. P. (2007). Math instruction for students with learning problems. Boston: Pearson\/Allyn and Bacon."},{"issue":"7","key":"2276_CR73","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1016\/j.tics.2015.05.006","volume":"19","author":"T Hannagan","year":"2015","unstructured":"Hannagan, T., Amedi, A., Cohen, L., Dehaene-Lambertz, G., & Dehaene, S. (2015). Origins of the specialization for letters and numbers in ventral occipitotemporal cortex. Trends in Cognitive Sciences, 19(7), 374\u2013382.","journal-title":"Trends in Cognitive Sciences"},{"key":"2276_CR74","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jco.2016.03.001","volume":"36","author":"D Harvey","year":"2016","unstructured":"Harvey, D., Van Der Hoeven, J., & Lecerf, G. (2016). Even faster integer multiplication. Journal of Complexity, 36, 1\u201330.","journal-title":"Journal of Complexity"},{"issue":"3","key":"2276_CR75","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1511\/2003.44.200","volume":"94","author":"B Hayes","year":"2006","unstructured":"Hayes, B. (2006). Gauss\u2019s\u00a0day of reckoning. American Scientist, 94(3), 200\u2013205.","journal-title":"American Scientist"},{"key":"2276_CR76","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/11096.001.0001","volume-title":"Foolproof and other mathematical meditations","author":"B Hayes","year":"2017","unstructured":"Hayes, B. (2017). Foolproof and other mathematical meditations. Cambridge, MA: MIT Press."},{"key":"2276_CR77","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873296","volume-title":"The secret of our success: How culture is driving human evolution, domesticating our species, and making us smarter","author":"JP Henrich","year":"2016","unstructured":"Henrich, J. P. (2016). The secret of our success: How culture is driving human evolution, domesticating our species, and making us smarter. Princeton: Princeton University Press."},{"issue":"1599","key":"2276_CR78","doi-asserted-by":"publisher","first-page":"2181","DOI":"10.1098\/rstb.2012.0120","volume":"367","author":"C Heyes","year":"2012","unstructured":"Heyes, C. (2012). Grist and mills: On the cultural origins of cultural learning. Philosophical Transactions of the Royal Society B: Biological Sciences, 367(1599), 2181\u20132191. https:\/\/doi.org\/10.1098\/rstb.2012.0120.","journal-title":"Philosophical Transactions of the Royal Society B: Biological Sciences"},{"issue":"2","key":"2276_CR79","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1177\/1745691615621276","volume":"11","author":"C Heyes","year":"2016","unstructured":"Heyes, C. (2016). Born pupils? Natural pedagogy and cultural pedagogy. Perspectives on Psychological Science, 11(2), 280\u2013295.","journal-title":"Perspectives on Psychological Science"},{"key":"2276_CR80","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199682737.001.0001","volume-title":"The predictive mind","author":"J Hohwy","year":"2013","unstructured":"Hohwy, J. (2013). The predictive mind. Oxford: Oxford University Press."},{"issue":"6","key":"2276_CR81","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1038\/nrn1684","volume":"6","author":"EM Hubbard","year":"2005","unstructured":"Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6(6), 435\u2013448.","journal-title":"Nature Reviews Neuroscience"},{"key":"2276_CR82","volume-title":"International comparisons in mathematics education","year":"2012","unstructured":"Huntly, I., Kaiser, G., & Luna, E. (Eds.). (2012). International comparisons in mathematics education. London: Routledge."},{"issue":"4","key":"2276_CR83","doi-asserted-by":"publisher","first-page":"358","DOI":"10.5951\/jresematheduc.43.4.0358","volume":"43","author":"M Inglis","year":"2012","unstructured":"Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358\u2013390.","journal-title":"Journal for Research in Mathematics Education"},{"key":"2276_CR84","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/978-3-319-06025-5_30","volume-title":"Johan van Benthem on logic and information dynamics","author":"AMC Isaac","year":"2014","unstructured":"Isaac, A. M. C., Szymanik, J., & Verbrugge, R. (2014). Logic and complexity in cognitive science. In A. Baltag & S. Smets (Eds.), Johan van Benthem on logic and information dynamics (pp. 787\u2013824). Heidelberg: Springer."},{"key":"2276_CR85","unstructured":"Karatsuba, A., & Ofman, Y. (1962). Multiplication of many-digital numbers by automatic computers. In Doklady Akademii Nauk (Vol. 145, pp. 293\u2013294)."},{"issue":"4","key":"2276_CR86","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1207\/s15516709cog1404_2","volume":"14","author":"KR Koedinger","year":"1990","unstructured":"Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14(4), 511\u2013550.","journal-title":"Cognitive Science"},{"key":"2276_CR87","volume-title":"Automata and computability","author":"DC Kozen","year":"2012","unstructured":"Kozen, D. C. (2012). Automata and computability. New York: Springer."},{"issue":"3","key":"2276_CR88","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/s13347-012-0094-3","volume":"27","author":"S Kr\u00e4mer","year":"2014","unstructured":"Kr\u00e4mer, S. (2014a). Mathematizing power, formalization, and the diagrammatical mind or: What does \u201ccomputation\u201d mean? Philosophy & Technology, 27(3), 345\u2013357.","journal-title":"Philosophy & Technology"},{"key":"2276_CR89","first-page":"3","volume-title":"The power of the image: Emotion, expression, explanation","author":"S Kr\u00e4mer","year":"2014","unstructured":"Kr\u00e4mer, S. (2014b). Trace, writing, diagram: Reflections on spatiality, intuition, graphical practices and thinking. In A. Benedek & K. Ny\u00edri (Eds.), The power of the image: Emotion, expression, explanation (pp. 3\u201322). Frankfurt am Main: Peter Lang."},{"key":"2276_CR90","volume-title":"Figuration, Anschauung, Erkenntnis: Grundlinien einer Diagrammatologie","author":"S Kr\u00e4mer","year":"2016","unstructured":"Kr\u00e4mer, S. (2016). Figuration, Anschauung, Erkenntnis: Grundlinien einer Diagrammatologie. Berlin: Suhrkamp Verlag."},{"key":"2276_CR91","volume-title":"Where mathematics comes from: How the embodied mind brings mathematics into being","author":"G Lakoff","year":"2000","unstructured":"Lakoff, G., & N\u00fa\u00f1ez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books."},{"issue":"8","key":"2276_CR92","doi-asserted-by":"publisher","first-page":"2033","DOI":"10.3758\/BF03192935","volume":"35","author":"D Landy","year":"2007","unstructured":"Landy, D., & Goldstone, R. L. (2007a). Formal notations are diagrams: Evidence from a production task. Memory & Cognition, 35(8), 2033\u20132040.","journal-title":"Memory & Cognition"},{"issue":"4","key":"2276_CR93","doi-asserted-by":"publisher","first-page":"720","DOI":"10.1037\/0278-7393.33.4.720","volume":"33","author":"D Landy","year":"2007","unstructured":"Landy, D., & Goldstone, R. L. (2007b). How abstract is symbolic thought? Journal of Experimental Psychology. Learning, Memory, and Cognition, 33(4), 720\u2013733.","journal-title":"Journal of Experimental Psychology. Learning, Memory, and Cognition"},{"issue":"10","key":"2276_CR94","doi-asserted-by":"publisher","first-page":"1953","DOI":"10.1080\/17470211003787619","volume":"63","author":"D Landy","year":"2010","unstructured":"Landy, D., & Goldstone, R. L. (2010). Proximity and precedence in arithmetic. The Quarterly Journal of Experimental Psychology, 63(10), 1953\u20131968.","journal-title":"The Quarterly Journal of Experimental Psychology"},{"key":"2276_CR95","volume-title":"Mathematical cultures: The London meetings 2012-2014","year":"2016","unstructured":"Larvor, B. (Ed.). (2016). Mathematical cultures: The London meetings 2012-2014. Basel: Birkh\u00e4user."},{"key":"2276_CR96","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1002\/9781118133880.hop204023","volume-title":"Handbook of psychology","author":"J Leighton","year":"2012","unstructured":"Leighton, J., & Sternberg, R. (2012). Reasoning and problem solving. In A. Weiner, F. Healy, & R. W. Proctor (Eds.), Handbook of psychology (2nd ed., pp. 623\u2013648). New York: Wiley. https:\/\/doi.org\/10.1002\/9781118133880.hop204023.","edition":"2"},{"issue":"2","key":"2276_CR97","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1111\/tops.12131","volume":"7","author":"BC Love","year":"2015","unstructured":"Love, B. C. (2015). The algorithmic level is the bridge between computation and brain. Topics in Cognitive Science, 7(2), 230\u2013242.","journal-title":"Topics in Cognitive Science"},{"issue":"2","key":"2276_CR98","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1002\/hbm.22641","volume":"36","author":"IM Lyons","year":"2015","unstructured":"Lyons, I. M., Ansari, D., & Beilock, S. L. (2015). Qualitatively different coding of symbolic and nonsymbolic numbers in the human brain. Human Brain Mapping, 36(2), 475\u2013488.","journal-title":"Human Brain Mapping"},{"key":"2276_CR99","volume-title":"The philosophy of mathematical practice","year":"2008","unstructured":"Mancosu, P. (Ed.). (2008). The philosophy of mathematical practice. Oxford: Oxford University Press."},{"issue":"1","key":"2276_CR100","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/0004-3702(77)90013-3","volume":"9","author":"D Marr","year":"1977","unstructured":"Marr, D. (1977). Artificial intelligence\u2014A personal view. Artificial Intelligence, 9(1), 37\u201348.","journal-title":"Artificial Intelligence"},{"key":"2276_CR101","volume-title":"Vision: A computational investigation into the human representation and processing of visual information","author":"D Marr","year":"1982","unstructured":"Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. San Francisco: W.H. Freeman and Company."},{"issue":"4","key":"2276_CR102","doi-asserted-by":"publisher","first-page":"1444","DOI":"10.1016\/j.neuroimage.2012.04.020","volume":"61","author":"M Maruyama","year":"2012","unstructured":"Maruyama, M., Pallier, C., Jobert, A., Sigman, M., & Dehaene, S. (2012). The cortical representation of simple mathematical expressions. Neuroimage, 61(4), 1444\u20131460.","journal-title":"Neuroimage"},{"issue":"7","key":"2276_CR103","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/S1364-6613(03)00134-7","volume":"7","author":"BD McCandliss","year":"2003","unstructured":"McCandliss, B. D., Cohen, L., & Dehaene, S. (2003). The visual word form area: Expertise for reading in the fusiform gyrus. Trends in Cognitive Sciences, 7(7), 293\u2013299. https:\/\/doi.org\/10.1016\/S1364-6613(03)00134-7.","journal-title":"Trends in Cognitive Sciences"},{"key":"2276_CR104","doi-asserted-by":"publisher","DOI":"10.1057\/9780230592889","volume-title":"Cognitive integration: Mind and cognition unbounded","author":"R Menary","year":"2007","unstructured":"Menary, R. (2007). Cognitive integration: Mind and cognition unbounded. Basingstoke: Palgrave Macmillan."},{"issue":"4","key":"2276_CR105","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1007\/s11097-010-9186-7","volume":"9","author":"R Menary","year":"2010","unstructured":"Menary, R. (2010). Dimensions of mind. Phenomenology and the Cognitive Sciences, 9(4), 561\u2013578. https:\/\/doi.org\/10.1007\/s11097-010-9186-7.","journal-title":"Phenomenology and the Cognitive Sciences"},{"key":"2276_CR106","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.cogsys.2013.05.002","volume":"25\u201326","author":"R Menary","year":"2013","unstructured":"Menary, R. (2013a). Cognitive integration, enculturated cognition and the socially extended mind. Cognitive Systems Research, 25\u201326, 26\u201334. https:\/\/doi.org\/10.1016\/j.cogsys.2013.05.002.","journal-title":"Cognitive Systems Research"},{"key":"2276_CR107","first-page":"349","volume-title":"The hand, an organ of the mind: What the manual tells the mental","author":"R Menary","year":"2013","unstructured":"Menary, R. (2013b). The enculturated hand. In Z. Radman (Ed.), The hand, an organ of the mind: What the manual tells the mental (pp. 349\u2013367). Cambridge, MA: MIT Press."},{"issue":"3","key":"2276_CR108","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1111\/mila.12051","volume":"29","author":"R Menary","year":"2014","unstructured":"Menary, R. (2014). Neural plasticity, neuronal recycling and niche construction. Mind and Language, 29(3), 286\u2013303. https:\/\/doi.org\/10.1111\/mila.12051.","journal-title":"Mind and Language"},{"key":"2276_CR109","doi-asserted-by":"publisher","first-page":"1","DOI":"10.15502\/9783958570818","volume-title":"Open MIND","author":"R Menary","year":"2015","unstructured":"Menary, R. (2015). Mathematical cognition: A case of enculturation. In T. Metzinger & J. M. Windt (Eds.), Open MIND (pp. 1\u201320). Frankfurt am Main: MIND Group. https:\/\/doi.org\/10.15502\/9783958570818."},{"key":"2276_CR110","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.cobeha.2016.04.006","volume":"10","author":"R Merkley","year":"2016","unstructured":"Merkley, R., & Ansari, D. (2016). Why numerical symbols count in the development of mathematical skills: Evidence from brain and behavior. Current Opinion in Behavioral Sciences, 10, 14\u201320.","journal-title":"Current Opinion in Behavioral Sciences"},{"issue":"1","key":"2276_CR111","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1111\/j.1467-9280.1995.tb00305.x","volume":"6","author":"KF Miller","year":"1995","unstructured":"Miller, K. F., Smith, C. M., Zhu, J., & Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science, 6(1), 56\u201360.","journal-title":"Psychological Science"},{"issue":"8","key":"2276_CR112","doi-asserted-by":"publisher","first-page":"914","DOI":"10.1177\/0956797612437427","volume":"23","author":"MM Monti","year":"2012","unstructured":"Monti, M. M., Parsons, L. M., & Osherson, D. N. (2012). Thought beyond language: Neural dissociation of algebra and natural language. Psychological Science, 23(8), 914\u2013922.","journal-title":"Psychological Science"},{"issue":"2","key":"2276_CR113","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1207\/s15516709cog0402_2","volume":"4","author":"A Newell","year":"1980","unstructured":"Newell, A. (1980). Physical symbol systems. Cognitive Science, 4(2), 135\u2013183.","journal-title":"Cognitive Science"},{"issue":"1","key":"2276_CR114","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0004-3702(82)90012-1","volume":"18","author":"A Newell","year":"1982","unstructured":"Newell, A. (1982). The knowledge level. Artificial Intelligence, 18(1), 87\u2013127.","journal-title":"Artificial Intelligence"},{"issue":"3","key":"2276_CR115","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1145\/360018.360022","volume":"19","author":"A Newell","year":"1976","unstructured":"Newell, A., & Simon, H. A. (1976). Computer science as empirical inquiry (The 1975 ACM turing award lecture). Communications of the ACM, 19(3), 113\u2013126.","journal-title":"Communications of the ACM"},{"key":"2276_CR116","first-page":"106","volume-title":"The Oxford handbook of numerical cognition","author":"H Nuerk","year":"2015","unstructured":"Nuerk, H., Moeller, K., & Willmes, K. (2015). Multi-digit number processing: Overview, conceptual clarifications, and language influences. In R. C. Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 106\u2013139). Oxford: Oxford University Press."},{"key":"2276_CR117","volume-title":"The world on paper: The conceptual and cognitive implications of writing and reading","author":"DR Olson","year":"1994","unstructured":"Olson, D. R. (1994). The world on paper: The conceptual and cognitive implications of writing and reading. Cambridge, Mass.: Cambridge University Press."},{"key":"2276_CR118","volume-title":"Orality and literacy: The technologizing of the word","author":"WJ Ong","year":"2012","unstructured":"Ong, W. J. (2012). Orality and literacy: The technologizing of the word. London: Routledge."},{"issue":"17","key":"2276_CR119","doi-asserted-by":"publisher","first-page":"4201","DOI":"10.1007\/s11229-014-0526-y","volume":"191","author":"M Pantsar","year":"2014","unstructured":"Pantsar, M. (2014). An empirically feasible approach to the epistemology of arithmetic. Synthese, 191(17), 4201\u20134229.","journal-title":"Synthese"},{"issue":"8","key":"2276_CR120","doi-asserted-by":"publisher","first-page":"2489","DOI":"10.1007\/s11229-015-0775-4","volume":"192","author":"M Pantsar","year":"2015","unstructured":"Pantsar, M. (2015). In search of aleph-null: How infinity can be created. Synthese, 192(8), 2489\u20132511.","journal-title":"Synthese"},{"key":"2276_CR121","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-3-319-31644-4_5","volume-title":"Objectivity, realism, and proof","author":"M Pantsar","year":"2016","unstructured":"Pantsar, M. (2016). The modal status of contextually a priori arithmetical truths. In F. Boccuni & A. Sereni (Eds.), Objectivity, realism, and proof (pp. 67\u201379). Cham: Springer."},{"issue":"2","key":"2276_CR122","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1387\/theoria.17682","volume":"33","author":"M Pantsar","year":"2018","unstructured":"Pantsar, M. (2018). Early numerical cognition and mathematical processes. Theoria, 33(2), 285\u2013304.","journal-title":"Theoria"},{"key":"2276_CR123","unstructured":"Pantsar, M. (under review). Cognitive complexity and mathematical problem solving. Erkenntnis."},{"key":"2276_CR124","unstructured":"Pantsar, M. (in press). The enculturated move from proto-arithmetic to arithmetic. Frontiers in Psychology."},{"key":"2276_CR125","first-page":"260","volume-title":"Encyclopedia of computer science","author":"CH Papadimitriou","year":"2003","unstructured":"Papadimitriou, C. H. (2003). Computational complexity. In A. Ralston, E. D. Reilly, & D. Hemmendinger (Eds.), Encyclopedia of computer science (4th ed., pp. 260\u2013265). Chichester: Wiley.","edition":"4"},{"key":"2276_CR126","first-page":"260","volume-title":"Encyclopedia of computer science","author":"CS Peirce","year":"1960","unstructured":"Peirce, C. S. (1960\u20131966). Collected papers of Charles Sanders Peirce. In C. Hartshorne, P. Weiss, & A. W. Burks, (Eds.), (Vol. 1\u20138). Cambridge, MA: Belknap Press of Harvard University Press.","edition":"4"},{"issue":"4","key":"2276_CR159","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1037\/a0039980","volume":"123","author":"ST Piantadosi","year":"2016","unstructured":"Piantadosi, S. T., Tenenbaum, J. B., & Goodman, N. D. (2016). The logical primitives of thought: Empirical foundations for compositional cognitive models. Psychological Review, 123(4), 392.","journal-title":"Psychological Review"},{"issue":"3","key":"2276_CR127","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1016\/S1053-8119(03)00084-3","volume":"19","author":"CJ Price","year":"2003","unstructured":"Price, C. J., & Devlin, J. T. (2003). The myth of the visual word form area. NeuroImage, 19(3), 473\u2013481. https:\/\/doi.org\/10.1016\/S1053-8119(03)00084-3.","journal-title":"NeuroImage"},{"issue":"1","key":"2276_CR128","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1016\/j.neuroimage.2004.01.018","volume":"22","author":"CJ Price","year":"2004","unstructured":"Price, C. J., & Devlin, J. T. (2004). The pro and cons of labelling a left occipitotemporal region \u201cthe visual word form area\u201d. NeuroImage, 22(1), 477\u2013479.","journal-title":"NeuroImage"},{"key":"2276_CR129","doi-asserted-by":"publisher","first-page":"4197","DOI":"10.1007\/s11229-014-0644-6","volume":"194","author":"W Ramsey","year":"2017","unstructured":"Ramsey, W. (2017). Must cognition be representational? Synthese, 194, 4197\u20134214. https:\/\/doi.org\/10.1007\/s11229-014-0644-6.","journal-title":"Synthese"},{"issue":"8","key":"2276_CR130","doi-asserted-by":"publisher","first-page":"480","DOI":"10.5951\/TCM.7.8.0480","volume":"7","author":"TD Randolph","year":"2001","unstructured":"Randolph, T. D., & Sherman, H. J. (2001). Alternative algorithms: Increasing options, reducing errors. Teaching Children Mathematics, 7(8), 480\u2013484.","journal-title":"Teaching Children Mathematics"},{"key":"2276_CR131","first-page":"1004","volume-title":"Proceedings of the 39th annual conference of the cognitive science society","author":"J Relaford-Doyle","year":"2017","unstructured":"Relaford-Doyle, J., N\u00fa\u00f1ez, R., Howes, A., & Tenbrink, T. (2017). When does a \u2018visual proof by induction\u2019serve a proof-like function in mathematics? In E. Davelaar & G. Gunzelmann (Eds.), Proceedings of the 39th annual conference of the cognitive science society (pp. 1004\u20131009). Austin, TX: Cognitive Science Society."},{"key":"2276_CR132","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511583261","volume-title":"The body in mind: Understanding cognitive processes","author":"M Rowlands","year":"1999","unstructured":"Rowlands, M. (1999). The body in mind: Understanding cognitive processes. Cambridge, MA: Cambridge University Press."},{"key":"2276_CR133","doi-asserted-by":"publisher","first-page":"3","DOI":"10.7551\/mitpress\/5236.001.0001","volume-title":"Parallel distributed processing: Explorations in the microstructures of cognition","author":"DE Rumelhart","year":"1986","unstructured":"Rumelhart, D. E., Smolensky, P., McClelland, J. L., & Hinton, G. (1986). Sequential thought processes in PDP models. In J. L. McClelland & D. E. Rumelhart (Eds.), Parallel distributed processing: Explorations in the microstructures of cognition (Vol. 2, pp. 3\u201357). Cambridge, MA: MIT Press."},{"issue":"3","key":"2276_CR134","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1016\/j.cognition.2012.06.015","volume":"125","author":"E Schneider","year":"2012","unstructured":"Schneider, E., Maruyama, M., Dehaene, S., & Sigman, M. (2012). Eye gaze reveals a fast, parallel extraction of the syntax of arithmetic formulas. Cognition, 125(3), 475\u2013490.","journal-title":"Cognition"},{"issue":"3\u20134","key":"2276_CR135","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/BF02242355","volume":"7","author":"A Sch\u00f6nhage","year":"1971","unstructured":"Sch\u00f6nhage, A., & Strassen, V. (1971). Schnelle Multiplikation gro\u00dfer Zahlen. Computing, 7(3\u20134), 281\u2013292.","journal-title":"Computing"},{"issue":"2","key":"2276_CR136","doi-asserted-by":"publisher","first-page":"328","DOI":"10.3758\/PBR.16.2.328","volume":"16","author":"S Shaki","year":"2009","unstructured":"Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin & Review, 16(2), 328\u2013331.","journal-title":"Psychonomic Bulletin & Review"},{"issue":"3","key":"2276_CR137","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1080\/17470210601000581","volume":"60","author":"DR Shanks","year":"2007","unstructured":"Shanks, D. R. (2007). Associationism and cognition: Human contingency learning at 25. The Quarterly Journal of Experimental Psychology, 60(3), 291\u2013309.","journal-title":"The Quarterly Journal of Experimental Psychology"},{"key":"2276_CR138","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1146\/annurev.psych.093008.100519","volume":"61","author":"DR Shanks","year":"2010","unstructured":"Shanks, D. R. (2010). Learning: From association to cognition. Annual Review of Psychology, 61, 273\u2013301.","journal-title":"Annual Review of Psychology"},{"issue":"1","key":"2276_CR139","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s11229-012-0075-1","volume":"186","author":"S-J Shin","year":"2012","unstructured":"Shin, S.-J. (2012). The forgotten individual: Diagrammatic reasoning in mathematics. Synthese, 186(1), 149\u2013168.","journal-title":"Synthese"},{"key":"2276_CR140","volume-title":"The sciences of the artificial","author":"HA Simon","year":"1996","unstructured":"Simon, H. A. (1996). The sciences of the artificial (2nd ed.). Cambridge, MA: MIT Press.","edition":"2"},{"issue":"11","key":"2276_CR141","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1037\/0003-066X.55.11.1233","volume":"55","author":"ES Spelke","year":"2000","unstructured":"Spelke, E. S. (2000). Core knowledge. American Psychologist, 55(11), 1233\u20131243.","journal-title":"American Psychologist"},{"key":"2276_CR142","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9780262016797.001.0001","volume-title":"The evolved apprentice: How evolution made humans unique","author":"K Sterelny","year":"2012","unstructured":"Sterelny, K. (2012). The evolved apprentice: How evolution made humans unique. Cambridge, MA: MIT Press."},{"key":"2276_CR143","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1515\/9781501503757-005","volume-title":"Thinking with diagrams: The semiotic basis of human cognition","author":"F Stjernfelt","year":"2016","unstructured":"Stjernfelt, F., & \u00d8stergaard, S. (2016). Diagrammatic problem solving. In S. Kr\u00e4mer & C. Ljungberg (Eds.), Thinking with diagrams: The semiotic basis of human cognition (pp. 103\u2013119). Berlin: Walter De Gruyter."},{"key":"2276_CR144","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-28749-2","volume-title":"Quantifiers and cognition: Logical and computational perspectives","author":"J Szymanik","year":"2016","unstructured":"Szymanik, J. (2016). Quantifiers and cognition: Logical and computational perspectives. Heidelberg: Springer."},{"key":"2276_CR145","unstructured":"Tamburrini, G. (1997). Mechanistic theories in cognitive science: The import of Turing\u2019s Thesis. In M. L. Dalla Chiara, K. Doets, D. Mundici, & J. van Benthem (Eds.), Logic and scientific methods: The tenth international congress of logic, methodology and philosophy of science, Florence, August 1995 (pp. 239\u2013257). Dordrecht: Springer."},{"issue":"28","key":"2276_CR146","doi-asserted-by":"publisher","first-page":"10775","DOI":"10.1073\/pnas.0604416103","volume":"103","author":"Y Tang","year":"2006","unstructured":"Tang, Y., Zhang, W., Chen, K., Feng, S., Ji, Y., Shen, J., et al. (2006). Arithmetic processing in the brain shaped by cultures. Proceedings of the National Academy of Sciences, 103(28), 10775\u201310780.","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2276_CR147","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/1-4020-3335-4_8","volume-title":"Visualization, explanation and reasoning styles in mathematics","author":"J Tappenden","year":"2005","unstructured":"Tappenden, J. (2005). Proof style and understanding in mathematics I: Visualization, unification and axiom choice. In P. Mancosu, K. F. J\u00f8rgensen, & S. A. Pedersen (Eds.), Visualization, explanation and reasoning styles in mathematics (pp. 147\u2013214). Dordrecht: Springer."},{"issue":"4","key":"2276_CR148","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1111\/j.1468-0017.1986.tb00328.x","volume":"1","author":"N Tennant","year":"1986","unstructured":"Tennant, N. (1986). The withering away of formal semantics? Mind and Language, 1(4), 302\u2013318.","journal-title":"Mind and Language"},{"issue":"4","key":"2276_CR149","doi-asserted-by":"publisher","first-page":"3139","DOI":"10.1016\/j.neuroimage.2011.11.037","volume":"59","author":"N Tschentscher","year":"2012","unstructured":"Tschentscher, N., Hauk, O., Fischer, M. H., & Pulverm\u00fcller, F. (2012). You can count on the motor cortex: Finger counting habits modulate motor cortex activation evoked by numbers. Neuroimage, 59(4), 3139\u20133148.","journal-title":"Neuroimage"},{"key":"2276_CR150","first-page":"230","volume":"42","author":"AM Turing","year":"1936","unstructured":"Turing, A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42, 230\u2013265.","journal-title":"Proceedings of the London Mathematical Society"},{"issue":"2","key":"2276_CR151","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1075\/pc.22.2.06tyl","volume":"22","author":"K Tyl\u00e9n","year":"2014","unstructured":"Tyl\u00e9n, K., Fusaroli, R., Bj\u00f8rndahl, J. S., Raczaszek-Leonardi, J., \u2205stergaard, S., & Stjernfelt, F. (2014). Diagrammatic reasoning: abstraction, interaction, and insight. Pragmatics & Cognition, 22(2), 264\u2013283.","journal-title":"Pragmatics & Cognition"},{"issue":"6","key":"2276_CR152","doi-asserted-by":"publisher","first-page":"939","DOI":"10.1080\/03640210801897856","volume":"32","author":"I Van Rooij","year":"2008","unstructured":"Van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32(6), 939\u2013984.","journal-title":"Cognitive Science"},{"key":"2276_CR153","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3389\/fpsyg.2014.00440","volume":"5","author":"S Varma","year":"2014","unstructured":"Varma, S. (2014). The subjective meaning of cognitive architecture: A Marrian analysis. Frontiers in Psychology, 5, 1\u20139. https:\/\/doi.org\/10.3389\/fpsyg.2014.00440.","journal-title":"Frontiers in Psychology"},{"issue":"12","key":"2276_CR154","doi-asserted-by":"publisher","first-page":"2715","DOI":"10.1093\/cercor\/bhr295","volume":"22","author":"AC Vogel","year":"2012","unstructured":"Vogel, A. C., Petersen, S. E., & Schlaggar, B. L. (2012). The left occipitotemporal cortex does not show preferential activity for words. Cerebral Cortex, 22(12), 2715\u20132732.","journal-title":"Cerebral Cortex"},{"key":"2276_CR155","doi-asserted-by":"publisher","DOI":"10.3389\/fnhum.2014.00088","author":"AC Vogel","year":"2014","unstructured":"Vogel, A. C., Petersen, S. E., & Schlaggar, B. L. (2014). The VWFA: It\u2019s not just for words anymore. Frontiers in Human Neuroscience. https:\/\/doi.org\/10.3389\/fnhum.2014.00088.","journal-title":"Frontiers in Human Neuroscience"},{"key":"2276_CR156","first-page":"211","volume-title":"The Oxford handbook of cognitive science","author":"MM Walsh","year":"2016","unstructured":"Walsh, M. M., & Lovett, M. C. (2016). The cognitive science approach to learning and memory. In S. E. F. Chipman (Ed.), The Oxford handbook of cognitive science (pp. 211\u2013230). Oxford: Oxford University Press."},{"issue":"2","key":"2276_CR157","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1111\/j.1469-7610.1976.tb00381.x","volume":"17","author":"D Wood","year":"1976","unstructured":"Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17(2), 89\u2013100.","journal-title":"Journal of Child Psychology and Psychiatry"},{"issue":"12","key":"2276_CR158","doi-asserted-by":"publisher","first-page":"3951","DOI":"10.1007\/s11229-016-1180-3","volume":"193","author":"C Zednik","year":"2016","unstructured":"Zednik, C., & J\u00e4kel, F. (2016). Bayesian reverse-engineering considered as a research strategy for cognitive science. Synthese, 193(12), 3951\u20133985.","journal-title":"Synthese"}],"container-title":["Synthese"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11229-019-02276-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11229-019-02276-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11229-019-02276-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T08:36:44Z","timestamp":1694939804000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11229-019-02276-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,14]]},"references-count":159,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["2276"],"URL":"https:\/\/doi.org\/10.1007\/s11229-019-02276-9","relation":{},"ISSN":["0039-7857","1573-0964"],"issn-type":[{"value":"0039-7857","type":"print"},{"value":"1573-0964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,14]]},"assertion":[{"value":"6 July 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}