{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:12:16Z","timestamp":1761581536486,"version":"3.37.3"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,3,23]],"date-time":"2017-03-23T00:00:00Z","timestamp":1490227200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003509","name":"\u00d6rebro University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003509","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Ed Res J"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s13394-017-0202-x","type":"journal-article","created":{"date-parts":[[2017,3,24]],"date-time":"2017-03-24T04:56:16Z","timestamp":1490331376000},"page":"471-492","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Sixth-grade students\u2019 reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis"],"prefix":"10.1007","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9530-4151","authenticated-orcid":false,"given":"Maike","family":"Schindler","sequence":"first","affiliation":[]},{"given":"Stephan","family":"Hu\u00dfmann","sequence":"additional","affiliation":[]},{"given":"Per","family":"Nilsson","sequence":"additional","affiliation":[]},{"given":"Arthur","family":"Bakker","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,3,23]]},"reference":[{"key":"202_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/9781444395600","volume-title":"The formation of reason","author":"D Bakhurst","year":"2011","unstructured":"Bakhurst, D. (2011). The formation of reason. Oxford: Wiley-Blackwell."},{"issue":"1\u20132","key":"202_CR2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1080\/10986065.2011.538293","volume":"13","author":"A Bakker","year":"2011","unstructured":"Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1\u20132), 5\u201326.","journal-title":"Mathematical Thinking and Learning"},{"key":"202_CR3","first-page":"219","volume-title":"Proceedings of the 32nd annual meeting of the North American chapter of the international group for the psychology of mathematics education","author":"R Beatty","year":"2010","unstructured":"Beatty, R. (2010). Behind and below zero: sixth grade students use linear graphs to explore negative numbers. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 219\u2013226). Columbus: The Ohio State University."},{"key":"202_CR4","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/978-3-642-00742-2_46","volume-title":"Theories of mathematics education. Seeking new frontiers","author":"A Bikner-Ahsbahs","year":"2010","unstructured":"Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories\u2014an approach for exploiting the diversity. In B. Sriraman & L. English (Eds.), Theories of mathematics education. Seeking new frontiers (pp. 483\u2013512). Berlin: Springer."},{"issue":"2","key":"202_CR5","doi-asserted-by":"crossref","first-page":"194","DOI":"10.5951\/jresematheduc.45.2.0194","volume":"45","author":"L Bofferding","year":"2014","unstructured":"Bofferding, L. (2014). Negative integer understanding: characterizing first graders\u2019 mental models. Journal for Research in Mathematics Education, 45(2), 194\u2013245.","journal-title":"Journal for Research in Mathematics Education"},{"key":"202_CR6","first-page":"703","volume-title":"Proceedings of the 32nd annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education","author":"L Bofferding","year":"2010","unstructured":"Bofferding, L. (2010). Addition and subtraction with negatives: acknowledging the multiple meanings of the minus sign. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 703\u2013710). Columbus: The Ohio State University."},{"key":"202_CR7","unstructured":"Borba, R. E. (1995). Understanding and operating with integers: Difficulties and obstacles. In L. Meira. & D. Carraher (Eds.), Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 226\u2013231). Recife."},{"key":"202_CR8","doi-asserted-by":"crossref","DOI":"10.4159\/9780674028739","volume-title":"Articulating reasons: an introduction to inferentialism","author":"R Brandom","year":"2000","unstructured":"Brandom, R. (2000). Articulating reasons: an introduction to inferentialism. Cambridge, MA: Harvard University Press."},{"key":"202_CR9","volume-title":"Making it explicit: reasoning, representing, and discursive commitment","author":"R Brandom","year":"1994","unstructured":"Brandom, R. (1994). Making it explicit: reasoning, representing, and discursive commitment. Cambridge, MA: Harvard University Press."},{"issue":"1","key":"202_CR10","first-page":"415","volume":"4","author":"A Bruno","year":"2001","unstructured":"Bruno, A. (2001). La ense\u00f1anza de los n\u00fameros negativos: formalismo y significado. La Gaceta de la Real Sociedad Matem\u00e1tica Espa\u00f1ola, 4(1), 415\u2013427.","journal-title":"La Gaceta de la Real Sociedad Matem\u00e1tica Espa\u00f1ola"},{"key":"202_CR11","first-page":"5","volume":"29","author":"A Bruno","year":"1997","unstructured":"Bruno, A. (1997). La ense\u00f1anza de los n\u00fameros negativos: aportaciones de una investigaci\u00f3n. Revista de did\u00e1ctica de las matem\u00e1ticas, 29, 5\u201318.","journal-title":"Revista de did\u00e1ctica de las matem\u00e1ticas"},{"issue":"2","key":"202_CR12","first-page":"25","volume":"14","author":"A Bruno","year":"2005","unstructured":"Bruno, A., & Cabrera, N. (2005). Una experiencia sobre la representaci\u00f3n en la recta de n\u00fameros negativos. Quadrante: Revista te\u00f3rica e de investiga\u00e7\u00e3o, 14(2), 25\u201341.","journal-title":"Quadrante: Revista te\u00f3rica e de investiga\u00e7\u00e3o"},{"issue":"2","key":"202_CR13","first-page":"249","volume":"15","author":"A Bruno","year":"1997","unstructured":"Bruno, A., & Martin\u00f3n, A. (1997). Procedimientos de resoluci\u00f3n de problemas aditivos con n\u00fameros negativos. Ense\u00f1anza de las Ciencias, 15(2), 249\u2013258.","journal-title":"Ense\u00f1anza de las Ciencias"},{"key":"202_CR14","first-page":"98","volume":"9","author":"A Bruno","year":"1996","unstructured":"Bruno, A., & Martin\u00f3n, A. (1996). N\u00fameros negativos: una revisi\u00f3n de investigaciones. Revista de Did\u00e1ctica de las Matem\u00e1ticas, 9, 98\u2013108.","journal-title":"Revista de Did\u00e1ctica de las Matem\u00e1ticas"},{"key":"202_CR15","first-page":"83","volume":"37","author":"A Bruno","year":"2001","unstructured":"Bruno, A., Martin\u00f3n, A., & Vel\u00e1zquez, F. (2001). Algunas dificultades en los problemas aditivos. Suma. Revista para la ense\u00f1anza y aprendizaje de las matem\u00e1ticas, 37, 83\u201394.","journal-title":"Suma. Revista para la ense\u00f1anza y aprendizaje de las matem\u00e1ticas"},{"issue":"2\u20133","key":"202_CR16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1080\/10986065.2001.9679970","volume":"3","author":"MM Chiu","year":"2001","unstructured":"Chiu, M. M. (2001). Using metaphors to understand and solve arithmetic problems: novices and experts working with negative numbers. Mathematical Thinking and Learning, 3(2\u20133), 93\u2013124.","journal-title":"Mathematical Thinking and Learning"},{"key":"202_CR17","unstructured":"Davidson, P. M. (1987). How should non-positive integers be introduced in elementary mathematics? In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th International Conference for the Psychology of Mathematics Education (Vol. 2, pp. 430\u2013436). Montreal, Canada: University of Montreal."},{"issue":"1\/2","key":"202_CR18","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s10649-006-0400-z","volume":"61","author":"R Duval","year":"2006","unstructured":"Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1\/2), 103\u2013131.","journal-title":"Educational Studies in Mathematics"},{"key":"202_CR19","unstructured":"Gallardo, A. (1995). Negative numbers in the teaching of arithmetic: Repercussions in elementary algebra. In D. Owens, M. Reeds, & G. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 158\u2013163). Columbus."},{"key":"202_CR20","unstructured":"Human, P., & Murray, H. (1987). Non-concrete approaches to integer arithmetic. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the international conference on the psychology of mathematics education (pp. 437\u2013443). Montreal."},{"key":"202_CR21","unstructured":"Hu\u00dfmann, S., Leuders, T., Prediger, S., & Barzel, B. (2011). Kontexte f\u00fcr sinnstiftendes Mathematiklernen (KOSIMA)\u2014ein fachdidaktisches Forschungs- und Entwicklungsprojekt. In R. Haug & L. Holz\u00e4pfel (Eds.), Beitr\u00e4ge zum Mathematikunterricht (pp. 419\u2013422). M\u00fcnster, Germany: wtm."},{"key":"202_CR22","first-page":"47","volume-title":"Mathewerkstatt 3 [Maths studio 3]","author":"S Hu\u00dfmann","year":"2014","unstructured":"Hu\u00dfmann, S., & Schindler, M. (2014a). \u201cRaus aus den Schulden\u201d\u2014Mit negativen Zahlen rechnen [out of the debts\u2014calculating on negative numbers]. In T. Leuders, S. Prediger, B. Barzel, & S. Hu\u00dfmann (Eds.), Mathewerkstatt 3 [Maths studio 3] (pp. 47\u201378). Berlin: Cornelsen."},{"key":"202_CR23","first-page":"28","volume":"183","author":"S Hu\u00dfmann","year":"2014","unstructured":"Hu\u00dfmann, S., & Schindler, M. (2014b). Ein Kontext f\u00fcr negative Zahlen\u2014auch f\u00fcr die Multiplikation [a context for negative numbers\u2014also for multiplication]. Mathematik lehren, 183, 28\u201332.","journal-title":"Mathematik lehren"},{"key":"202_CR24","volume-title":"Kritik der reinen Vernunft [critique of pure reason]","author":"I Kant","year":"1781","unstructured":"Kant, I. (1781). Kritik der reinen Vernunft [critique of pure reason]. Cologne: Parkland."},{"key":"202_CR25","unstructured":"Kiryushchenko, V. (2015). Semantic contents and pragmatic perspectives: the idea of objectivity in Robert Brandom\u2019s normative pragmatism. Paper presented at the \u201c epc2: European Pragmatism Conference II \u201c. Retrieved from http:\/\/epc2.sciencesconf.org\/54871"},{"key":"202_CR26","doi-asserted-by":"crossref","unstructured":"Mackrell, K., & Pratt, D. (2017). Constructionism and the space of reasons. Mathematics Education Research Journal.","DOI":"10.1007\/s13394-017-0194-6"},{"key":"202_CR27","first-page":"259","volume-title":"Kognitive Aspekte mathematischer Begriffsentwicklung [cognitive aspects of mathematical concept formation]","author":"G Malle","year":"1988","unstructured":"Malle, G. (1988). Die Entstehung neuer Denkgegenst\u00e4nde\u2014untersucht am Beispiel der negativen Zahlen [the formation of new \u2018mental objects\u2019\u2014investigated using the concept of negative numbers]. In W. D\u00f6rfler (Ed.), Kognitive Aspekte mathematischer Begriffsentwicklung [cognitive aspects of mathematical concept formation] (pp. 259\u2013319). Vienna: H\u00f6lder-Pichler-Tempsky."},{"key":"202_CR28","first-page":"1055","volume-title":"International handbook of mathematics education","author":"J Mason","year":"1996","unstructured":"Mason, J., & Waywood, A. (1996). The role of theory in mathematics education and research. In A. J. Bishop et al. (Eds.), International handbook of mathematics education (pp. 1055\u20131089). Dordrecht, NL: Kluwer."},{"key":"202_CR29","first-page":"35","volume":"5","author":"S Mukhopadhyay","year":"1997","unstructured":"Mukhopadhyay, S. (1997). Story telling as sense-making: children\u2019s ideas about negative numbers. Hiroshima Journal of Mathematics Education, 5, 35\u201350.","journal-title":"Hiroshima Journal of Mathematics Education"},{"key":"202_CR30","unstructured":"Mukhopadhyay, S., Resnick, L. B. & Schauble, L. (1990). Social sense-making in mathematics: Children\u2019s ideas of negative numbers. In G. Booker, P. Cobb, & T. De Mendicuti (Eds.), Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education with the North American Chapter 12th PME-NA Conference (pp. 281\u2013288). Mexico."},{"key":"202_CR31","first-page":"147","volume-title":"Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education","author":"JC Murray","year":"1985","unstructured":"Murray, J. C. (1985). Children\u2018s informal conceptions of integer arithmetic. In L. Streefland (Ed.), Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 147\u2013153). Noordwijkerhout, NL: Technipress Culemborg."},{"key":"202_CR32","doi-asserted-by":"publisher","unstructured":"Noorloos, R., Taylor, S., Bakker, A., & Derry, J. (2017). Inferentialism as an alternative to socioconstructivism in mathematics education. Mathematics Education Research Journal, 1\u201317. doi: 10.1007\/s13394-017-0189-3","DOI":"10.1007\/s13394-017-0189-3"},{"key":"202_CR33","unstructured":"Peled, I. (1991). Levels of knowledge about negative numbers: effects of age and ability. In F. Furinghetti (Ed.), Proceedings of the Fifteenth Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 145\u2013152). Assisi, Italy: Conference Committee."},{"key":"202_CR34","first-page":"106","volume-title":"Proceedings of the Thirteenth Annual Meeting of the International Group for the Psychology of Mathematics Education","author":"I Peled","year":"1989","unstructured":"Peled, I., Mukhopadhyay, S., & Resnick, L. B. (1989). Formal and informal sources of mental models for negative numbers. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the Thirteenth Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 106\u2013110). Paris: France."},{"issue":"7","key":"202_CR35","doi-asserted-by":"crossref","first-page":"5","DOI":"10.3102\/0013189X024007005","volume":"24","author":"DC Phillips","year":"1995","unstructured":"Phillips, D. C. (1995). The good, the bad, and the ugly: the many faces of constructivism. Educational Researcher, 24(7), 5\u201312.","journal-title":"Educational Researcher"},{"issue":"1","key":"202_CR36","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s10649-013-9519-x","volume":"86","author":"J Pierson Bishop","year":"2014","unstructured":"Pierson Bishop, J., Lamb, L. L., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2014a). Using order to reason about negative numbers: the case of Violet. Educational Studies of Mathematics, 86(1), 39\u201359.","journal-title":"Educational Studies of Mathematics"},{"issue":"1","key":"202_CR37","doi-asserted-by":"crossref","first-page":"19","DOI":"10.5951\/jresematheduc.45.1.0019","volume":"45","author":"J Pierson Bishop","year":"2014","unstructured":"Pierson Bishop, J., Lamb, L. L., Philipp, R. A., Whitacre, I., Schappelle, B. P., & Lewis, M. L. (2014b). Obstacles and affordances for integer reasoning: an analysis of children\u2019s thinking and the history of mathematics. Journal for Research in Mathematics Education, 45(1), 19\u201361.","journal-title":"Journal for Research in Mathematics Education"},{"key":"202_CR38","volume-title":"Concrete human psychology","author":"W-M Roth","year":"2016","unstructured":"Roth, W.-M. (2016a). Concrete human psychology. New York: Routledge."},{"issue":"1","key":"202_CR39","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1007\/s12124-015-9331-5","volume":"50","author":"W-M Roth","year":"2016","unstructured":"Roth, W.-M. (2016b). The primacy of the social and sociogenesis. Integrative Psychological and Behavioral Science, 50(1), 122\u2013141.","journal-title":"Integrative Psychological and Behavioral Science"},{"key":"202_CR40","first-page":"112","volume-title":"Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education","author":"C Sackur","year":"1997","unstructured":"Sackur, C., & Drouhard, J. P. (1997). Algebraic expressions and equations: an example of the evolution of the notions. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 112\u2013119). Lahti: University of Helsinki."},{"key":"202_CR41","doi-asserted-by":"crossref","unstructured":"Schindler, M. (2014). Auf dem Weg zum Begriff der negativen Zahlen: Empirische Studie zur Ordnungsrelation f\u00fcr ganze Zahlen aus inferentieller Perspektive. [On the way to the concept of negative number. An empirical study on order relations for integers from an inferential point of view.] Wiesbaden, Germany: Springer Spektrum.","DOI":"10.1007\/978-3-658-04375-9"},{"key":"202_CR42","volume-title":"Wie Kinder rechnen [how children do arithmetic]","author":"C Selter","year":"1997","unstructured":"Selter, C., & Spiegel, H. (1997). Wie Kinder rechnen [how children do arithmetic]. Leipzig: Klett."},{"key":"202_CR43","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511499944","volume-title":"Thinking as communicating. Human development, the growth of discourses, and mathematizing","author":"A Sfard","year":"2008","unstructured":"Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press."},{"issue":"4","key":"202_CR44","doi-asserted-by":"crossref","first-page":"428","DOI":"10.5951\/jresematheduc.43.4.0428","volume":"43","author":"M Stephan","year":"2012","unstructured":"Stephan, M., & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428\u2013464.","journal-title":"Journal for Research in Mathematics Education"},{"issue":"2","key":"202_CR45","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1080\/07370008.2015.1038539","volume":"33","author":"JM Tsang","year":"2015","unstructured":"Tsang, J. M., Blair, K. P., Bofferding, L., & Schwartz, D. L. (2015). Learning to \u201csee\u201d less than nothing: putting perceptual skills to work for learning numerical structure. Cognition and Instruction, 33(2), 154\u2013197.","journal-title":"Cognition and Instruction"},{"issue":"4","key":"202_CR46","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1080\/09515080802285552","volume":"21","author":"J Vlassis","year":"2008","unstructured":"Vlassis, J. (2008). The role of mathematical symbols in the development of number conceptualization: The case of the minus sign. Philosophical Psychology, 21(4), 555\u2013570.","journal-title":"Philosophical Psychology"},{"key":"202_CR47","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.learninstruc.2004.06.012","volume":"14","author":"J Vlassis","year":"2004","unstructured":"Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in \u2018negativity\u2019. Learning and Instruction, 14, 469\u2013484.","journal-title":"Learning and Instruction"},{"key":"202_CR48","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.jmathb.2010.11.004","volume":"30","author":"W Widjaja","year":"2011","unstructured":"Widjaja, W., Stacey, K., & Steinle, V. (2011). Locating negative decimals in the number line: insights into the thinking of pre-service primary teachers. Journal of Mathematical Behavior, 30, 80\u201391.","journal-title":"Journal of Mathematical Behavior"}],"container-title":["Mathematics Education Research Journal"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13394-017-0202-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13394-017-0202-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13394-017-0202-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T21:02:14Z","timestamp":1658869334000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13394-017-0202-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,23]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["202"],"URL":"https:\/\/doi.org\/10.1007\/s13394-017-0202-x","relation":{},"ISSN":["1033-2170","2211-050X"],"issn-type":[{"type":"print","value":"1033-2170"},{"type":"electronic","value":"2211-050X"}],"subject":[],"published":{"date-parts":[[2017,3,23]]}}}