Classroom Supports for Generalizing

Author:
Amy B. Ellis University of Georgia

Search for other papers by Amy B. Ellis in
Current site
Google Scholar
PubMed
Close
,
Anne Waswa University of Georgia

Search for other papers by Anne Waswa in
Current site
Google Scholar
PubMed
Close
,
Halil I. Tasova California State University–San Bernadino

Search for other papers by Halil I. Tasova in
Current site
Google Scholar
PubMed
Close
,
Michael Hamilton University of Georgia

Search for other papers by Michael Hamilton in
Current site
Google Scholar
PubMed
Close
,
Kevin C. Moore University of Georgia

Search for other papers by Kevin C. Moore in
Current site
Google Scholar
PubMed
Close
, and
Aytuğ Çelik Pamukkale University

Search for other papers by Aytuğ Çelik in
Current site
Google Scholar
PubMed
Close

Generalizing is a critical aspect of mathematics learning, with researchers and policy documents highlighting generalizing as a core mathematical practice. It can also be challenging to foster in class settings, and teachers need access to better resources to teach generalizing, including an understanding of effective forms of instruction. This article proposes Classroom Supports for Generalizing (CSGs), investigating how multiple elements—such as tasks, teacher moves, student interactions, and representations—interact to meaningfully foster student generalizing. Drawing on class video data from a middle school teacher and two high school teachers, we present the CSG Framework, which identifies three categories of supports: Interactions for Generalizing, Structures for Generalizing, and Routines for Generalizing.

Footnotes

The research reported was supported by the National Science Foundation, Grant No. DRL 1920538.

A previous version of this research was presented at the 43rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

Contributor Notes

Amy B. Ellis, Department of Math, Science, and Social Studies Education, University of Georgia, Athens, GA 30602; amyellis@uga.edu

Anne Waswa, Department of Math, Science, and Social Studies Education, University of Georgia, Athens, GA 30602; anne.waswa@uga.edu

Halil I. Tasova, Department of Teacher Education and Foundations, California State University–San Bernadino, San Bernadino, CA 92407; halil.tasova@csusb.edu

Michael Hamilton, Department of Math, Science, and Social Studies Education, University of Georgia, Athens, GA 30602; mwhamilton@uga.edu

Kevin C. Moore, Department of Math, Science, and Social Studies Education, University of Georgia, Athens, GA 30602; kvcmoore@uga.edu

Aytuğ Çelik, Department of Mathematics and Science Education, Pamukkale University, Denizli, 20070, Turkey; aytug.deu@gmail.com

  • Collapse
  • Expand
Journal for Research in Mathematics Education
  • Amit, M., & Neria, D. (2008). “Rising to the challenge”: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM, 40(1), 111129. https://doi.org/10.1007/s11858-007-0069-5

    • Search Google Scholar
    • Export Citation
  • Australian Curriculum, Assessment and Reporting Authority. (2019). National report on schooling in Australia 2017. https://dataandreporting.blob.core.windows.net/anrdataportal/ANR-Documents/nationalreportonschoolinginaustralia_2017.pdf

    • Search Google Scholar
    • Export Citation
  • Bauersfeld, H. (1995). The structuring of the structures: Development and function in mathematicizing as a social practice. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 137158). Erlbaum.

    • Search Google Scholar
    • Export Citation
  • Becker, J. R., & Rivera, F. (2006). Sixth graders’ figural and numerical strategies for generalizing patterns in algebra. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 95101). Universidad Pedagógica Nacional.

    • Search Google Scholar
    • Export Citation
  • Bezemer, J., & Mavers, D. (2011). Multimodal transcription as academic practice: A social semiotic perspective. International Journal of Social Research Methodology, 14(3), 191206. https://doi.org/10.1080/13645579.2011.563616

    • Search Google Scholar
    • Export Citation
  • Blumer, H. (1969). Symbolic interactionism: Perspective and method. Prentice-Hall.

  • Brodie, K. (2009). Teaching mathematical reasoning in secondary school classrooms. Springer. https://doi.org/10.1007/978-0-387-09742-8

  • Čadež, T. H., & Kolar, V. M. (2015). Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem. Educational Studies in Mathematics, 89(2), 283306. https://doi.org/10.1007/s10649-015-9598-y

    • Search Google Scholar
    • Export Citation
  • Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309333. https://doi.org/10.1007/s10857-016-9343-1

    • Search Google Scholar
    • Export Citation
  • Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM, 40(1), 322. https://doi​.org/10.1007/s11858-007-0067-7

    • Search Google Scholar
    • Export Citation
  • Chazan, D. (2006). What if not? and teacher’s mathematics. In F. A. N. Rosamund & L. Copes (Eds.), Educational transformations: Changing our lives through mathematics (pp. 320). Author House.

    • Search Google Scholar
    • Export Citation
  • Cockburn, A. D. (2012). To generalise, or not to generalise, that is the question. In B. Maj-Tatsis & K. Tatsis (Eds.), Generalization in mathematics at all educational levels (pp. 1121). University of Rzeszow.

    • Search Google Scholar
    • Export Citation
  • Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401429. https://doi​.org/10.1007/s10649-014-9532-8

    • Search Google Scholar
    • Export Citation
  • Cooper, T. J., & Warren, E. (2008). The effect of different representations on Years 3 to 5 students’ ability to generalise. ZDM, 40(1), 2337. https://doi​.org/10.1007/s11858-007-0066-8

    • Search Google Scholar
    • Export Citation
  • Department for Education. (2021). National curriculum in England: Mathematics programmes of study. https://www.gov.uk/government/publications​/national-curriculum-in-england-mathematics-programmes-of-study/

    • Search Google Scholar
    • Export Citation
  • Dörfler, W. (2008). En route from patterns to algebra: Comments and reflections. ZDM, 40(1), 143160. https://doi.org/10.1007/s11858-007-0071-y

    • Search Google Scholar
    • Export Citation
  • Eckert, A., & Nilsson, P. (2017). Introducing a symbolic interactionist approach on teaching mathematics: The case of revoicing as an interactional strategy in the teaching of probability. Journal of Mathematics Teacher Education, 20(1), 3148. https://doi.org/10.1007/s10857-015-9313-z

    • Search Google Scholar
    • Export Citation
  • El Mouhayar, R. (2020). Triadic dialog in multilingual mathematics classrooms as a promoter of generalization during classroom talk. Mathematics Education Research Journal, 34(1), 87112. https://doi.org/10.1007/s13394-020-00325-y

    • Search Google Scholar
    • Export Citation
  • El Mouhayar, R. R., & Jurdak, M. E. (2013). Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics, 82(3), 379396. https://doi.org/10.1007/s10649-012-9434-6

    • Search Google Scholar
    • Export Citation
  • Ellis, A. B. (2007a). Connections between generalizing and justifying: Students’ reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194229.

    • Search Google Scholar
    • Export Citation
  • Ellis, A. B. (2007b). A taxonomy for categorizing generalizations: Generalizing actions and reflection generalizations. Journal of the Learning Sciences, 16(2), 221262. https://doi.org/10.1080/10508400701193705

    • Search Google Scholar
    • Export Citation
  • Ellis, A. B. (2011). Generalizing-promoting actions: How classroom collaborations can support students’ mathematical generalizations. Journal for Research in Mathematics Education, 42(4), 308345. https://doi.org/10.5951/jresematheduc.42.4.0308

    • Search Google Scholar
    • Export Citation
  • Ellis, A. B., & Grinstead, P. (2008). Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations. The Journal of Mathematical Behavior, 27(4), 277296. https://doi.org/10.1016/j.jmathb.2008.11.002

    • Search Google Scholar
    • Export Citation
  • Ellis, A. B., Lockwood, E., Tillema, E., & Moore, K. (2021). Generalization across multiple mathematical domains: relating, forming, and extending. Cognition and Instruction, 40(3), 351384. https://doi.org/10.1080/07370008.2021.2000989

    • Search Google Scholar
    • Export Citation
  • Ellis, A., Özgür, Z., & Reiten, L. (2019). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, 31(2), 107132. https://doi.org/10.1007/s13394-018-0246-6

    • Search Google Scholar
    • Export Citation
  • English, L. D., & Warren, E. A. (1995). General reasoning processes and elementary algebraic understanding: Implications for initial instruction. Focus on Learning Problems in Mathematics, 17(4), 119.

    • Search Google Scholar
    • Export Citation
  • Georgia Department of Education. (2021). Georgia’s K–12 mathematics standards 2021. https://www.gadoe.org/Curriculum-Instruction-and-Assessment/Curriculum-and-Instruction/Documents/Mathematics/Georgia-K12-Mathematics-Standards/Georgia-K-8-Mathematics-Standards​.pdf

    • Search Google Scholar
    • Export Citation
  • Gresalfi, M., Horn, I., Jasien, L., Wisittanawat, P., Ma, J. Y., Radke, S. C., Guyevskey, V., Sinclair, N., & Sfard, A. (2018). Playful mathematics learning: Beyond early childhood and sugar-coating. In J. Kay & R. Luckin (Eds.), Proceedings of the 13th International Conference of the Learning Sciences (Vol. 2, pp. 13351342). University College London.

    • Search Google Scholar
    • Export Citation
  • Hamilton, M., Moore, K., Ellis, A., Ying, Y., Tasova, H. I., Çelik, A. Ö., & Waswa, A. (2021). Supporting generalizing in the classroom: One teacher’s beliefs and instructional practice. In D. Olanoff, K. Johnson, & S. Spitzer (Eds.), Proceedings of the 43rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 15361541). PME.

    • Search Google Scholar
    • Export Citation
  • Harel, G., & Tall, D. (1991). The general, the abstract, and the generic in advanced mathematics. For the Learning of Mathematics, 11(1), 3842. https://flm-journal.org/Articles/26D7502008745BD5F027505EE1F95E.pdf

    • Search Google Scholar
    • Export Citation
  • Herbel-Eisenmann, B. (2003, April 9–12). Examining “norms” in mathematics education literature: Refining the lens [Paper presentation]. Annual meeting of the National Council of Teachers of Mathematics, research presession, San Antonio, TX, United States.

    • Search Google Scholar
    • Export Citation
  • Horn, I. S., & Little, J. W. (2010). Attending to problems of practice: Routines and resources for professional learning in teachers’ workplace interactions. American Educational Research Journal, 47(1), 181217. https://doi.org/10.3102/0002831209345158

    • Search Google Scholar
    • Export Citation
  • Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 116. https://doi.org/10.1007/s10649-017-9761-8

    • Search Google Scholar
    • Export Citation
  • Johanning, D. I. (2004). Supporting the development of algebraic thinking in middle school: A closer look at students’ informal strategies. The Journal of Mathematical Behavior, 23(4), 371388. https://doi.org/10.1016/j.jmathb.2004.09.001

    • Search Google Scholar
    • Export Citation
  • Jurow, A. S. (2004). Generalizing in interaction: Middle school mathematics students making mathematical generalizations in a population-modeling project. Mind ,Culture, and Activity, 11(4), 279300. https://doi.org/10.1207/s15327884mca1104_4

    • Search Google Scholar
    • Export Citation
  • Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133155). Erlbaum.

    • Search Google Scholar
    • Export Citation
  • Koellner, K., Pittman, M., & Frykholm, J. (2008). Talking generally or generally talking in an algebra classroom. Mathematics Teaching in the Middle School, 14(5), 304310. https://doi.org/10.5951/MTMS.14.5.0304

    • Search Google Scholar
    • Export Citation
  • Leinhardt, G., & Greeno, J. G. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 78(2), 7595. https://doi​.org/10.1037/0022-0663.78.2.75

    • Search Google Scholar
    • Export Citation
  • Leinhardt, G., & Steele, M. D. (2005). Seeing the complexity of standing to the side: Instructional dialogues. Cognition and Instruction, 23(1), 87163. https://doi.org/10.1207/s1532690xci2301_4

    • Search Google Scholar
    • Export Citation
  • Lemke, J. L. (1990). Talking science: Language, learning, and values. Ablex.

  • Lesh, R. A., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematical problem solving, learning, and teaching. Erlbaum.

    • Search Google Scholar
    • Export Citation
  • Lobato, J., Clarke, D., & Ellis, A. B. (2005). Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education, 36(2), 101136.

    • Search Google Scholar
    • Export Citation
  • Lockwood, E., & Reed, Z. (2016). Students’ meanings of a (potentially) powerful tool for generalizing in combinatorics. In T. Fukawa-Connelly, N. E. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th annual Conference on Research in Undergraduate Mathematics Education (pp. 115). RUME.

    • Search Google Scholar
    • Export Citation
  • MacGregor, M., & Stacey, K. (1993). Seeing a pattern and writing a rule. In I. Hirabayashi, N. Nohda, K. Shigematsu, & F.-L. Lin (Eds.), Proceedings of the 17th international Conference for the Psychology of Mathematics Education (pp. 181188). University of Tsukuba.

    • Search Google Scholar
    • Export Citation
  • Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. The Journal of Mathematical Behavior, 18(1), 5378. https://doi.org/10.1016/S0732-3123(99)00017-6

    • Search Google Scholar
    • Export Citation
  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bernarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 6586). Kluwer. https://doi.org/10.1007/978-94-009-1732-3_5

    • Search Google Scholar
    • Export Citation
  • Mata-Pereira, J., & da Ponte, J.-P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169186. https://doi.org/10.1007/s10649-017-9773-4

    • Search Google Scholar
    • Export Citation
  • Matthews, P. G., & Ellis, A. B. (2018). Natural alternatives to natural number: The case of ratio. Journal of Numerical Cognition, 4(1), 1958. https://doi​.org/10.5964/jnc.v4i1.97

    • Search Google Scholar
    • Export Citation
  • Melhuish, K., Thanheiser, E., & Guyot, L. (2020). Elementary school teachers’ noticing of essential mathematical reasoning forms: Justification and generalization. Journal of Mathematics Teacher Education, 23(1), 3567. https://doi.org/10.1007/s10857-018-9408-4

    • Search Google Scholar
    • Export Citation
  • Morse, J. M. (1997). “Perfectly healthy, but dead”: The myth of inter-rater reliability. Qualitative Health Research, 7(4), 445447. https://doi​.org/10.1177/104973239700700401

    • Search Google Scholar
    • Export Citation
  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. http://www.corestandards.org

    • Search Google Scholar
    • Export Citation
  • Peirce, C. S. (1956). The essence of mathematics. In J. R. Newman (Ed.), The world of mathematics (Vol. 3, pp. 17731783). Simon and Schuster.

    • Search Google Scholar
    • Export Citation
  • Pytlak, M. (2015). Learning geometry through paper-based experiences. In K. Krainer & N. Vondrová (Eds.), Proceedings of the ninth congress of the European Society for Research in Mathematics Education (pp. 571577). Charles University. https://hal.science/hal-01287017

    • Search Google Scholar
    • Export Citation
  • Radford, L. (2006). Algebraic thinking and the generalization of patterns: A semiotic perspective. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th annual meeting of International Group for the Psychology of Mathematics Education, North American Chapter (pp. 221). Universidad Pedagógica Nacional.

    • Search Google Scholar
    • Export Citation
  • Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM, 40(1), 8396. https://doi.org/10.1007/s11858-007-0061-0

    • Search Google Scholar
    • Export Citation
  • Reid, D. A. (2002). Conjectures and refutations in Grade 5 mathematics. Journal for Research in Mathematics Education, 33(1), 529. https://doi​.org/10.2307/749867

    • Search Google Scholar
    • Export Citation
  • Rivera, F. (2007). Visualizing as a mathematical way of knowing: Understanding figural generalization. The Mathematics Teacher, 101(1), 6975. https://doi.org/10.5951/MT.101.1.0069

    • Search Google Scholar
    • Export Citation
  • Rivera, F. D. (2008). On the pitfalls of abduction: Complicities and complexities in patterning activity. For the Learning of Mathematics, 28(1), 1725. https://flm-journal.org/Articles/B2FC402116BF4341B985BAA4E46CA.pdf

    • Search Google Scholar
    • Export Citation
  • Rivera, F. D., & Becker, J. R. (2007). Abduction-induction (generalization) processes of elementary majors on figural patterns in algebra. The Journal of Mathematical Behavior, 26(2), 140155. https://doi.org/10.1016/j.jmathb.2007.05.001

    • Search Google Scholar
    • Export Citation
  • Rivera, F. D., & Becker, J. R. (2008). Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns. ZDM, 40(1), 6582. https://doi.org/10.1007/s11858-007-0062-z

    • Search Google Scholar
    • Export Citation
  • Rösken, B., Hoechsmann, K., & Törner, G. (2008, March 5–8). Pedagogies in action: The role of mathematics teachers’ professional routines [Paper presentation]. Symposium on the occasion of the 100th Anniversary of ICMI, Rome, Italy.

    • Search Google Scholar
    • Export Citation
  • Roulston, K. (2010). Reflective interviewing: A guide to theory and practice. Sage. https://doi.org/10.4135/9781446288009

  • Schifter, D., & Russell, S. J. (2020). A model for teaching mathematical argument at the elementary grades. Journal of Educational Research in Mathematics, 30, 1528.

    • Search Google Scholar
    • Export Citation
  • Secretaría de Educación Pública. (2017). E010 servicios de educación superior y posgrado [Superior and postgraduate education services E010]. Subsecretaría de Planeacion, Evaluación y Coordinación, Dirección General de Evaluación de Políticas, Gobierno de México.

  • Stacey, K., & MacGregor, M. (2001). Curriculum reform and approaches to algebra. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 141153). Kluwer. https://doi.org/10.1007/0-306-47223-6_8

    • Search Google Scholar
    • Export Citation
  • Steele, D. F., & Johanning, D. I. (2004). A schematic-theoretic view of problem solving and development of algebraic thinking. Educational Studies in Mathematics, 57(1), 6590. https://doi.org/10.1023/B:EDUC.0000047054.90668.f9

    • Search Google Scholar
    • Export Citation
  • Strachota, S., Knuth, E., & Blanton, M. (2018). Cycles of generalizing activities in the classroom. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5-to 12-year-olds (pp. 351378). Springer. https://doi.org/10.1007/978-3-319-68351-5_15

    • Search Google Scholar
    • Export Citation
  • Strauss, A. L., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Sage.

  • Stylianides, G. J. (2008). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 916. https://flm-journal​.org/Articles/308086F06226BBFBA6966CF21B6EC.pdf

    • Search Google Scholar
    • Export Citation
  • Stylianides, G. J., Stylianides, A. J., & Shilling-Traina, L. N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 14631490. https://doi.org/10.1007/s10763-013-9409-9

    • Search Google Scholar
    • Export Citation
  • Syed, M., & Nelson, S. C. (2015). Guidelines for establishing reliability when coding narrative data. Emerging Adulthood, 3(6), 375387. https://doi​.org/10.1177/2167696815587648

    • Search Google Scholar
    • Export Citation
  • Tasova, H. I., Ellis, A., Hamilton, M., Moore, K., Waswa, A., Çelik, A. Ö., & Ying, Y. (2021). A serendipitous mistake: How one teacher’s beliefs and knowledge mediated her in-the-moment instruction. In D. Olanoff, K. Johnson, & S. Spitzer (Eds.), Proceedings of the 43rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 15741579). PME.

    • Search Google Scholar
    • Export Citation
  • Tuomi-Gröhn, T., & Engeström, Y. (2003). Between school and work: New perspectives on transfer and boundary-crossing. Pergamon.

  • Vlahović-Štetić, V., Pavlin-Bernardić, N., & Rajter, M. (2010). Illusion of linearity in geometry: Effect in multiple-choice problems. Mathematical Thinking and Learning, 12(1), 5467. https://doi.org/10.1080/10986060903465871

    • Search Google Scholar
    • Export Citation
  • Voigt, J. (1995). Thematic patterns of interaction and sociomathematical norms. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 163201). Erlbaum.

    • Search Google Scholar
    • Export Citation
  • Voigt, J. (1996). Negotiation of mathematical meaning in classroom processes: Social interaction and learning mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 2150). Erlbaum.

    • Search Google Scholar
    • Export Citation
  • Vygotsky, L. (1986). Thought and language (A. Kozulin, Ed. & Trans.). MIT Press.

  • Widman, S., Chang-Order, J., Penuel, W. R., & Wortman A. (2019). Using evaluation tools toward more equitable youth engagement in libraries: Measuring connected learning and beyond. Young Adult Library Services, 17(4), 3644.

    • Search Google Scholar
    • Export Citation
  • Yackel, E., & Rasmussen, C. (2002). Beliefs and norms in the mathematics classroom. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 313330). Springer. https://doi.org/10.1007/0-306-47958-3_18

    • Search Google Scholar
    • Export Citation
  • Yeap, B.-H., & Kaur, B. (2008). Elementary school students engaging in making generalisation: A glimpse from a Singapore classroom. ZDM, 40(1), 5564. https://doi.org/10.1007/s11858-007-0072-x

    • Search Google Scholar
    • Export Citation
  • Zazkis, R., Liljedahl, P., & Chernoff, E. J. (2008). The role of examples in forming and refuting generalizations. ZDM, 40(1), 131141. https://doi​.org/10.1007/s11858-007-0065-9

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 2885 2885 296
Full Text Views 287 287 47
PDF Downloads 330 330 65
EPUB Downloads 0 0 0