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References
- Adler, J. (2001). Teaching mathematics in multilingual classrooms. Kluwer.
- Aksu, M. (1997). Student performance in dealing with fractions. Journal of Educational Research, 90(6), 375–380. https://doi.org/10.1080/00220671.1997.10544595
- Behr, M. J., Harel, G., Post, T. R., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296–332). Mac¬millan.
- Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment. Journal for Research in Mathematics Education, 15(5), 323–341. https://doi.org/10.2307/748423
- Bruner, J. (1967). Toward a theory of instruction. Harvard University Press.
- Buttlar, A.-C. (2019). Sequenzielle Analysen interaktiver Verfahren des lehrerseitigen Umgangs mit Schü¬leräußerungen [Sequential analyses of interactive procedures of teachers‘ dealing with students' utterances]. In K. Verrière & L. Schäfer (Eds.), Interaktion im Klassenzimmer (pp. 97–117). Springer.
- Chazan, D., & Ball, D. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2-10. http://www.jstor.org/stable/40248293
- Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127–138. https://doi.org/10.1007/s10649-009-9198-9
- Clarkson, P. C. (2009). Mathematics teaching in Australian multilingual classrooms: Developing an ap¬proach to the use of classroom languages. In R. Barwell (Ed.), Multilingualism in mathematics classrooms: Global perspectives (pp. 145-160). Multilingual Matters.
- Clements, D. H., & Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thinking and Learning, 6(2), 81–89. https://doi.org/10.1207/s15327833mtl0602_1
- Confrey, J. (2006). The evolution of design studies as methodology. In K. R. Sawyer (Ed.), The Cam¬bridge Handbook of the Learning Sciences (pp. 135–152). Cambridge University Press.
- Corno, L. (2008). On teaching adaptively. Educational Psychologist, 43(3), 161–173. https://doi.org/10.1080/00461520802178466
- Corno, L., & Snow, R. E. (1986). Adapting teaching to individual differences among learners. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 605–629). Macmillan.
- DIME - Diversity in Mathematics Education Center for Learning and Teaching (2007). Culture, race, power in mathematics education. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 405-433). Information Age.
- Erath, K., & Prediger, S. (2021). Quality dimensions for activation and participation in language-respon¬sive mathematics classrooms. In N. Planas, M. Schütte, & C. Morgan (Eds.), Classroom research on mathematics and language - seeing learners and teachers differently (pp. 167-183). Routledge. https://doi.org/10.4324/9780429260889-12
- Erath, K., Prediger, S., Quasthoff, U., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99(2), 161–179. https://doi.org.10.1007/s10649-018-9830-7
- Gallagher, M. A., Parsons, S. A., & Vaughn, M. (2020). Adaptive teaching in mathematics: a review of the literature. Educational Review, 1–23. https://doi.org.10.1080/00131911.2020.1722065
- Gibbons, P. (2002). Scaffolding Language, Scaffolding Learning. Teaching Second Language Learners in the Mainstream Classroom. Heinemann.
- Hardy, I., Decristan, J., & Klieme, E. (2019). Adaptive teaching in research on learning and instruction. Journal for Educational Research Online, 11(2), 169–191. https://doi.org/10.25656/01:18004
- Hattie, J. (2009). Visible learning: A synthesis of over 800 meta analyses relating to achievement. Routledge.
- Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: classroom-based fac¬tors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549. https://doi.org/10.2307/749690
- Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 65–97). Macmillan.
- Huang, R., & Li, Y. (2012). What Matters Most: A Comparison of Expert and Novice Teachers' Noticing of Mathematics Classroom Events. School Science and Mathematics, 112(7), 420–432. https://doi.org.10.1111/j.1949-8594.2012.00161.x
- Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM – Mathematics Education, 48(1), 185–97. https://doi.org.10.1007/s11858 -015-0717-0
- Lawrence-Brown, D. (2004). Differentiated Instruction: Inclusive Strategies for standard-based learning that benefit the whole class. American Secondary Education, 32(3), 34–62. http://www.jstor.org/stable/41064522
- Lim, W., Lee, J.-E., Tyson, K., Kim, H.-J., & Kim, J. (2020). An Integral Part of Facilitating Mathematical Discussions: Follow-up Questioning. International Journal of Science and Mathematics Education, 18(2), 377–398. https://doi.org.10.1007/s10763-019-09966-3
- Loibl, K., & Leuders, T. (2019). How to make failure productive: Fostering learning from errors through elaboration prompts. Learning and Instruction, 62, 1-10. https://doi.org.10.1016/j.learnin¬struc.2019.03.002
- Moschkovich, J. (2015). Academic literacy in mathematics for English Learners. The Journal of Mathe¬matical Behavior, 40(A), 43–62. https://doi.org/10.1016/j.jmathb.2015.01.005
- Munson, J. (2019). After Eliciting: Variation in Elementary Mathematics Teachers’ Discursive Pathways during Collaborative Problem Solving. The Journal of Mathematical Behavior, 56, 1–18. https://doi.org/10.1016/j.jmathb.2019.100736
- Nathan, M., & Kim, S. (2009). Regulation of Teacher Elicitations in the Mathematics Classroom. Cognition and Instruction, 27(2), 91–120. https://doi.org.10.1080/07370000902797304
- Parsons, S. A., Vaughn, M., Scales, R. Q., Gallagher, M. A., Parsons, A. W., Davis, S. D., . . . Allen, M. (2018). Teachers’ instructional adaptations: A research synthesis. Review of Educational Re¬search, 88(2), 205–242. https://doi.org.10.3102/0034654317743198
- Prediger, S., & Erath, K. (2014). Content or Interaction, or both? Synthesizing two German traditions in a video study on learning to explain in mathematics classroom microcultures. Eurasia Journal of Mathematics, Science & Technology Education, 10(4), 313–327. https://doi.org.10.12973/eura¬sia.2014.1085a
- Prediger, S., & Pöhler, B. (2015). The interplay of micro- and macro-scaffolding: an empirical reconstruc¬tion for the case of an intervention on percentages. ZDM – Mathematics Education, 47(7), 1179–1194. https://doi.org.10.1007/s11858-015-0723-2
- Prediger, S., & Wessel, L. (2013). Fostering German language learners’ constructions of meanings for fractions – Design and effects of a language- and mathematics-integrated intervention. Mathemat¬ics Education Research Journal, 25(3), 435–456. https://doi.org.10.1007/s13394-013-0079-2
- Prediger, S., Erath, K., Weinert, H., & Quabeck, K. (2022, in press). Only for multilingual students at risk? Differential effects of language-responsive mathematics instruction in a cluster-randomized con¬trolled trial on fractions. Journal for Research in Mathematics Education.
- Quabeck, K., & Erath, K. (2020). Individuelle Strukturierungen zur Gleichwertigkeit von Brüchen [Indivi¬dual conceptions of the equivalence of fractions]. In H.-S. Siller, W. Weigel, & J. F. Wörler (eds.), Beiträge zum Mathematikunterricht (pp. 733–736). WTM.
- Schwarz, C. V., Braaten, M., Haverly, C., & Xeng de los Santos, E. (2021). Using sense-making moments to understand how elementary teachers’ interactions expand, maintain, or shut down sense-mak¬ing in science. Cognition and Instruction, 39(2), 113–148. https://doi.org.10.1080/07370008. 2020.1763349
- Siemon, D., Horne, M., Clements, D., Confrey, J., Maloney, A., Samara, J., Tzur, R., & Watson, A. (2017). Researching and using learning progressions (trajectories) in mathematics education. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 109–136). Singapore: PME.
- Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749205
- Smith, M. S., & Stein, M. K. (2018). Five practices for orchestrating productive mathematics discussions (2nd ed.). NCTM.
- van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in Teacher–Student Interaction: A Dec¬ade of Research. Educational Psychology Review, 22(3), 271–296. https://doi.org/10.1007/ s10648-010-9127-6
References
Adler, J. (2001). Teaching mathematics in multilingual classrooms. Kluwer.
Aksu, M. (1997). Student performance in dealing with fractions. Journal of Educational Research, 90(6), 375–380. https://doi.org/10.1080/00220671.1997.10544595
Behr, M. J., Harel, G., Post, T. R., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296–332). Mac¬millan.
Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment. Journal for Research in Mathematics Education, 15(5), 323–341. https://doi.org/10.2307/748423
Bruner, J. (1967). Toward a theory of instruction. Harvard University Press.
Buttlar, A.-C. (2019). Sequenzielle Analysen interaktiver Verfahren des lehrerseitigen Umgangs mit Schü¬leräußerungen [Sequential analyses of interactive procedures of teachers‘ dealing with students' utterances]. In K. Verrière & L. Schäfer (Eds.), Interaktion im Klassenzimmer (pp. 97–117). Springer.
Chazan, D., & Ball, D. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2-10. http://www.jstor.org/stable/40248293
Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127–138. https://doi.org/10.1007/s10649-009-9198-9
Clarkson, P. C. (2009). Mathematics teaching in Australian multilingual classrooms: Developing an ap¬proach to the use of classroom languages. In R. Barwell (Ed.), Multilingualism in mathematics classrooms: Global perspectives (pp. 145-160). Multilingual Matters.
Clements, D. H., & Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thinking and Learning, 6(2), 81–89. https://doi.org/10.1207/s15327833mtl0602_1
Confrey, J. (2006). The evolution of design studies as methodology. In K. R. Sawyer (Ed.), The Cam¬bridge Handbook of the Learning Sciences (pp. 135–152). Cambridge University Press.
Corno, L. (2008). On teaching adaptively. Educational Psychologist, 43(3), 161–173. https://doi.org/10.1080/00461520802178466
Corno, L., & Snow, R. E. (1986). Adapting teaching to individual differences among learners. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 605–629). Macmillan.
DIME - Diversity in Mathematics Education Center for Learning and Teaching (2007). Culture, race, power in mathematics education. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 405-433). Information Age.
Erath, K., & Prediger, S. (2021). Quality dimensions for activation and participation in language-respon¬sive mathematics classrooms. In N. Planas, M. Schütte, & C. Morgan (Eds.), Classroom research on mathematics and language - seeing learners and teachers differently (pp. 167-183). Routledge. https://doi.org/10.4324/9780429260889-12
Erath, K., Prediger, S., Quasthoff, U., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99(2), 161–179. https://doi.org.10.1007/s10649-018-9830-7
Gallagher, M. A., Parsons, S. A., & Vaughn, M. (2020). Adaptive teaching in mathematics: a review of the literature. Educational Review, 1–23. https://doi.org.10.1080/00131911.2020.1722065
Gibbons, P. (2002). Scaffolding Language, Scaffolding Learning. Teaching Second Language Learners in the Mainstream Classroom. Heinemann.
Hardy, I., Decristan, J., & Klieme, E. (2019). Adaptive teaching in research on learning and instruction. Journal for Educational Research Online, 11(2), 169–191. https://doi.org/10.25656/01:18004
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta analyses relating to achievement. Routledge.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: classroom-based fac¬tors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549. https://doi.org/10.2307/749690
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 65–97). Macmillan.
Huang, R., & Li, Y. (2012). What Matters Most: A Comparison of Expert and Novice Teachers' Noticing of Mathematics Classroom Events. School Science and Mathematics, 112(7), 420–432. https://doi.org.10.1111/j.1949-8594.2012.00161.x
Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM – Mathematics Education, 48(1), 185–97. https://doi.org.10.1007/s11858 -015-0717-0
Lawrence-Brown, D. (2004). Differentiated Instruction: Inclusive Strategies for standard-based learning that benefit the whole class. American Secondary Education, 32(3), 34–62. http://www.jstor.org/stable/41064522
Lim, W., Lee, J.-E., Tyson, K., Kim, H.-J., & Kim, J. (2020). An Integral Part of Facilitating Mathematical Discussions: Follow-up Questioning. International Journal of Science and Mathematics Education, 18(2), 377–398. https://doi.org.10.1007/s10763-019-09966-3
Loibl, K., & Leuders, T. (2019). How to make failure productive: Fostering learning from errors through elaboration prompts. Learning and Instruction, 62, 1-10. https://doi.org.10.1016/j.learnin¬struc.2019.03.002
Moschkovich, J. (2015). Academic literacy in mathematics for English Learners. The Journal of Mathe¬matical Behavior, 40(A), 43–62. https://doi.org/10.1016/j.jmathb.2015.01.005
Munson, J. (2019). After Eliciting: Variation in Elementary Mathematics Teachers’ Discursive Pathways during Collaborative Problem Solving. The Journal of Mathematical Behavior, 56, 1–18. https://doi.org/10.1016/j.jmathb.2019.100736
Nathan, M., & Kim, S. (2009). Regulation of Teacher Elicitations in the Mathematics Classroom. Cognition and Instruction, 27(2), 91–120. https://doi.org.10.1080/07370000902797304
Parsons, S. A., Vaughn, M., Scales, R. Q., Gallagher, M. A., Parsons, A. W., Davis, S. D., . . . Allen, M. (2018). Teachers’ instructional adaptations: A research synthesis. Review of Educational Re¬search, 88(2), 205–242. https://doi.org.10.3102/0034654317743198
Prediger, S., & Erath, K. (2014). Content or Interaction, or both? Synthesizing two German traditions in a video study on learning to explain in mathematics classroom microcultures. Eurasia Journal of Mathematics, Science & Technology Education, 10(4), 313–327. https://doi.org.10.12973/eura¬sia.2014.1085a
Prediger, S., & Pöhler, B. (2015). The interplay of micro- and macro-scaffolding: an empirical reconstruc¬tion for the case of an intervention on percentages. ZDM – Mathematics Education, 47(7), 1179–1194. https://doi.org.10.1007/s11858-015-0723-2
Prediger, S., & Wessel, L. (2013). Fostering German language learners’ constructions of meanings for fractions – Design and effects of a language- and mathematics-integrated intervention. Mathemat¬ics Education Research Journal, 25(3), 435–456. https://doi.org.10.1007/s13394-013-0079-2
Prediger, S., Erath, K., Weinert, H., & Quabeck, K. (2022, in press). Only for multilingual students at risk? Differential effects of language-responsive mathematics instruction in a cluster-randomized con¬trolled trial on fractions. Journal for Research in Mathematics Education.
Quabeck, K., & Erath, K. (2020). Individuelle Strukturierungen zur Gleichwertigkeit von Brüchen [Indivi¬dual conceptions of the equivalence of fractions]. In H.-S. Siller, W. Weigel, & J. F. Wörler (eds.), Beiträge zum Mathematikunterricht (pp. 733–736). WTM.
Schwarz, C. V., Braaten, M., Haverly, C., & Xeng de los Santos, E. (2021). Using sense-making moments to understand how elementary teachers’ interactions expand, maintain, or shut down sense-mak¬ing in science. Cognition and Instruction, 39(2), 113–148. https://doi.org.10.1080/07370008. 2020.1763349
Siemon, D., Horne, M., Clements, D., Confrey, J., Maloney, A., Samara, J., Tzur, R., & Watson, A. (2017). Researching and using learning progressions (trajectories) in mathematics education. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 109–136). Singapore: PME.
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749205
Smith, M. S., & Stein, M. K. (2018). Five practices for orchestrating productive mathematics discussions (2nd ed.). NCTM.
van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in Teacher–Student Interaction: A Dec¬ade of Research. Educational Psychology Review, 22(3), 271–296. https://doi.org/10.1007/ s10648-010-9127-6