• Stimulation and investigation of thought processes for the acquisition of arithmetic and algebraic structures with a focus on secondary schools and the initial study phase.

• Stimulation and investigation of learning processes of student teachers in the development of diagnostic competences for teaching conducive to learning.

• Fischer, A. & Hößle, C. & Krause, U. & Michaelis, J. & Niesel, V. (2017): Curricular interlocking and didactic-methodological design of subject-didactic and educational science training sequences to build diagnostic competence .In: Selter, Ch., Hußmann, S., Hößle, C., Knipping, Ch., Lengnink, K. & Michaelis, J. (eds.) Diagnose und Förderung heterogener Lerngruppen Theorien, Konzepte und Beispiele aus der MINT-Lehrerbildung. Münster: Waxmann 2017. p. 169 - 190.

• Brauer, L. & Fischer, A. & Hößle, C. & Niesel, V. & Voß, S. & Warnstedt, J. (2017): Vignette-based instruments to promote the diagnostic skills of students with the subjects biology and maths (lower secondary level). In: Selter, Ch., Hußmann, S., Hößle, C., Knipping, Ch., Lengnink, K. & Michaelis, J. (eds.) Diagnose und Förderung heterogener Lerngruppen Theorien, Konzepte und Beispiele aus der MINT-Lehrerbildung. Münster: Waxmann 2017. p. 257 - 276.

• Winkler, I. & Heinrich, M. & Fischer, A. & Krause, U. (2016). Multi-perspectivity in teacher education. Interdisciplinary learning in maths and German didactics. In: Winkler, Iris/Schmidt, Frederike (eds.): Interdisciplinary research in German didactics. "Foreign sisters" in dialogue. Frankfurt a. M.: Lang. S. 181-199.

• Fischer, A. (2016): Making mathematical knowledge development tangible using the example of cube symmetries - Proposal for a bridge course to introduce the mathematical culture of higher education. In: Hoppenbrock, A.; Biehler, R.; Hochmuth, R. & Rück, H.-G. (eds.): Lehren und Lernen von Mathematik in der Studieneingangsphase, Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik. Wiesbaden: Springer Fachmedien. S. 165 - 180.

• Fischer, A. & Sjuts, J. (2014): Process diagnostics in mathematics. In: Fischer, A.; Hößle, C.; Jahnke-Klein, S.; Kiper, H.; Komorek, M.; Michaelis, J. & Sjuts, J. (Eds.) Diagnostics for effective learning. Baltmannsweiler: Schneider-Verlag. S. 251 - 276.

• Meyer, A. & Fischer, A. (2013): Symbolic algebraic thinking - conceptualisation of a model In: Journal für Mathematik-Didaktik 34(2). S. 177 - 208.

• Fischer, A. (2013): Experiencing mathematical thinking processes - Proposal for a bridge course for the introduction to the mathematical culture of higher education. In: Hoppenbrock, A.; Schreiber, S; Göller, R.; Biehler, R.; Büchler, B.; Hochmuth, R.; Rück; H.-G. (Eds.): Mathematik im Übergang Schule/Hochschule und im ersten Studienjahr. Extended Abstracts of the 2nd khdm conference 20.02. - 23.02.2013. Kassel: Centre of Excellence for University Didactics in Mathematics. S. 49 - 50.

• Prediger, S., Komorek, M., Fischer, A., Hinz, R., Hußmann, S., Moschner, B., Ralle, B., Thiele, J. (2013): The long road to lesson design. On the justification and implementation of subject-specific didactic research and development programmes. In: Komorek, M. & Prediger, S. (eds.): Der lange Weg zum Unterrichtsdesign - Zur Begründung und Umsetzung genuin fachdidaktischer Forschungs- und Entwicklungsprogramme. S. 5 - 18.

• Komorek, M., Fischer, A. & Moschner, B. (2013): Subject-didactic structuring as a basis for lesson designs. In: Komorek, M. & Prediger, S. (eds.): Der lange Weg zum Unterrichtsdesign - Zur Begründung und Umsetzung genuin fachdidaktischer Forschungs- und Entwicklungsprogramme. S. 37 - 57.

• Fischer, A. & Sjuts, J. (2013): How effective is inquiry-based learning for building diagnostic skills? In: Greefrath, G.; Käpnick, F. & Stein, M. (Eds.): Beiträge zum Mathematikunterricht 2013. Münster: WTM-Verlag 2013.

• Fischer, A. (2013): Mathematical knowledge development through exercises. In: Chr. Ableitinger, J. Kramer, S. Prediger (eds.). On the double continuity in secondary school teacher education. Wiesbaden: Springer. S. 95 - 116.

• Fischer, A. & Sjuts; J. (2012): Initiatives and impulses for the dovetailing of teacher training phases and for the further development of diagnostic competence. In: Mitteilungen der Gesellschaft für Didaktik der Mathematik No. 93, 2012. p. 33 - 36.

• Fischer, A., Niesel, V. & Sjuts, J. (2012): OLAW: Teacher training in a network - developing diagnostic and support skills in the classroom and in teaching-learning laboratories. In: Freitag, Ch. & von Bargen, I. (Eds.). Practical research in teacher education. Berlin: LIT-Verlag. S. 95 - 104.

• Fischer, A. & Komorek, M (2012): Conception and implementation of the joint project OLAW. In: Bertholt, S. (ed.). Concepts of subject-didactic structuring for the classroom. Society for Didactics of Chemistry and Physics. Annual conference in Oldenburg 2011. p. 152 - 154.

• Fischer, A. & Sjuts, J. (2012): Development of diagnostic and remedial competence in mathematics - a model project to dovetail the teacher training phases. In: Ludwig, M. & Kleine, M. (eds.): Beiträge zum Mathematikunterricht 2012. Münster: WTM-Verlag 2012. p. 253 - 256.

• Fischer, A. & Sjuts, J. (2011): Development of diagnostic and support competence in the subject of mathematics - Results of a model project on the interlinking of teacher training phases. In: SEMINAR - Teacher training and school. Issue 4, 2011. p. 31 - 47.

• Fischer, A. (2011): Teaching-learning laboratories in the subject of mathematics for students and prospective teachers. In: Fischer, A. & Niesel, V. & Sjuts, J. (Eds.) (2011): Teaching-learning laboratories and their significance for schools and teacher training. A review of the OLAW joint project. Proceedings of the symposium on 31 March 2011. Oldenburg: BIS-Verlag der University of Oldenburg. S. 93 - 97.

• Fischer, A. (2011): From school back to university: How does studying mathematics prepare maths teachers for mathematical demands? In: Contributions to mathematics education. Hildesheim: Franzbecker. S. 251 - 254.

• Fischer, A. & Sjuts, J. (2011): Diagnostic competence and the difficulty of assessment. In: Contributions to mathematics education. Hildesheim: Franzbecker. PP. 259 - 262.

• Fischer, A. (2010): Difficulties in diagrammatic reasoning - a case study. In: Kadunz, G. (ed.): Language and signs. The use of linguistics and semiotics in mathematics didactics. Hildesheim: Franzbecker. S. 83 - 108.

• Siebel, F. & Fischer, A. (2010): Communicating a Sense of Elementary Algebra to Preservice Primary Teachers. In: Proceedings of the sixth Congress of the European Society for Research in Mathematics Education.

• Fischer, A. (2010): Algebraic thinking tools in analytic geometry. In: Praxis Mathematik (33). S. 30 - 35.

• Fischer, A.; Hefendehl-Hebeker, L. & Prediger, S. (2010): More than reshaping: Making rich algebraic thinking actions visible in the learning process. In: Praxis Mathematik (33). S. 1 - 7.

• Fischer, A. (2010): Drawings as thinking tools. In: The teaching of mathematics (1/10). S. 23 - 33.

• Fischer, A. (2009): Between definite and indefinite numbers - children's concepts of numbers and variables. In: Journal for Mathematics Didactics 30(1). S. 3 - 29.

• Berlin, T.; Fischer, A.; Hefendehl-Hebeker, L. & Melzig, D. (2009): From arithmetic to arithmetic schema. Building an algebraic perspective in arithmetic lessons. In: Fritz, A. & Schmidt, S. (eds.) Fördernder Mathematikunterricht in der Sekundarstufe I . Recognising and overcoming arithmetic difficulties. Weinheim: Beltz. S. 271 - 292.

• Fischer, A.; Heinze, A. & Wagner, D. (2009): Learning maths at school - learning maths at university: learners' difficulties in the transition to university. In: Heinze, A. (ed.) Learning mathematics from kindergarten to university: continuity and coherence as a challenge for mathematics teaching. Münster: Waxmann. S. 243 - 262.

• Fischer, A. & Wagner, D. (2009): Learning mathematics at upper secondary level and in higher education: Summary and research desiderata. In: Heinze, A. (ed.) Learning mathematics from kindergarten to university: Continuity and coherence as a challenge for mathematics teaching. Münster: Waxmann. S. 263 - 266.

• Fischer, A. (2009): Simplifying terms: Imitation of action routines or mental penetration of contexts? In: Contributions to mathematics education. Hildesheim: Franzbecker.

• Fischer, A. & Hefendehl-Hebeker, L. (2009): On the algebra-specific characterisation of mathematical thought processes. In: Contributions to mathematics education. Hildesheim: Franzbecker.

• Fischer, A. (2008): Drawings as tools for visualising structures. In: Barzel, B. (ed.), Berlin, T. (ed.), Bertalan, D. (ed.), Fischer, A. (ed.): Algebraisches Denken. Festschrift for Lisa Hefendehl-Hebeker. S. 61 - 69.

• Fischer, A. (2008): Representing mathematical structures with the help of graphic diagrams. In: Contributions to mathematics teaching. Hildesheim: Franzbecker.

• Fischer, A. (2007): Signs Used as Algebraic Tools - A Case Study. In: Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education. S. 872 - 881.

• Fischer, A. & Hefendehl-Hebeker, L. (2007): Negative numbers as a mental construction. In: Büchter, A. (ed.), Humenberger, H. (ed.), Hußmann, S. (ed.) & Prediger, S. (ed.): Realitätsnaher Mathematikunterricht - vom Fach aus und für die Praxis. Festschrift for Hans-Wolfgang Henn. P. 120 - 129. Hildesheim: Franzbecker.

• Fischer, A. (2007): Individual cases and structure - using visual aids to grasp arithmetical regularities. In: Contributions to mathematics teaching. Hildesheim: Franzbecker. S. 120 - 123.

• Fischer, A. (2007): Mutual influences of representations and ideas on the concept of vector space. In: Journal für Mathematik-Didaktik 28(3/4). S. 311 - 330.

• Fischer, A. (2006): The use of signs as tools for the mental construction of abstract objects. In: Journal for Mathematics Didactics 27(3/4). S. 180 - 199.

• Fischer, A. (2006): Conceptions of linear algebra: Students' construction processes and outcomes. In: Journal for Mathematics Didactics 27(2). S. 163 - 164.

• Fischer, A. (2006): Mental Models of the Concept of Vector Space. In: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education. P. 1830a - 1830j.

• Fischer, A. (2006): The construction of ideas about linear algebra. In: Contributions to mathematics education. Hildesheim: Franzbecker.

• Fischer, A. (2006): Conceptions of linear algebra: Students' construction processes and results. Dissertation, University of Dortmund, 2006.

• Fischer, A. (2003): Mental models of the concept of vector space. First results of an empirical study among students. In: mathematica didactica 26 (2) (2003). S. 91 -114.

Published conference and edited volumes and journals

• Fischer, A.; Hößle, C.; Jahnke-Klein, S.; Kiper, H.; Komorek, M.; Michaelis, J. & Sjuts, J. (eds.) (2014): Diagnostics for learning-effective teaching. Baltmannsweiler: Schneider-Verlag.

• Fischer, A. & Niesel, V. & Sjuts, J. (Eds.) (2011): Teaching-learning laboratories and their significance for schools and teacher training. A review of the OLAW joint project. Conference proceedings from 31 March 2011.Oldenburg: BIS-Verlag der University of Oldenburg.

• Fischer, A.; Hefendehl-Hebeker, L. & Prediger, S. (eds.) (2010): More than transforming - thinking algebraically. Praxis Mathematik (33).

• Barzel, B. & Berlin, T. & Bertalan, D. & Fischer, A. (Eds.) (2008): Algebraic thinking. Festschrift for Lisa Hefendehl-Hebeker. Hildesheim: Franzbecker.