for the learning of mathematics   vol. 41 num. 3 (2021) an international journal of mathematics education

-   front cover                           0 Lisa Lunney Borden ,  Evan Throop-Robinson ,  Ellen Carter ,  Suzanna Prosper   Sets of, rows of, jumps of: verbing multiplication ABSTRACT                 2 Paola Ramírez   Observing how a student becomes coherently aware in mathematics ABSTRACT                 9 Daniel Edelen ,  Ashley Schmidt ,  Richard Cox ,  Sarah B. Bush   A closer examination into elementary students’ mathematics discourse: the role of language games                           14 Elena Polotskaia ,  Annie Savard ,  Catherine Nadon   La résolution de problèmes mathématiques et l’art de la représentation                           16 Elena Polotskaia ,  Annie Savard ,  Catherine Nadon   Mathematical problem solving and the art of representation (online only)                           19 Omid Khatin-Zadeh ,  Babak Yazdani-Fazlabadi ,  Zahra Eskandari   The grounding of mathematical concepts through fictive motion, gesture and the motor system                           19 Alison Mirin ,  Fabio Augusto Milner ,  Nicholas Wasserman ,  Keith Weber   On two definitions of ‘function’                           22 Tim Rowland   Mathematics teaching—joy in times of trouble? ABSTRACT                 25 Roza Leikin ,  Regina Ovodenko   Stepped tasks for complex problem solving: top-down-structured mathematical activity ABSTRACT                 30 John Paul Cook ,  Paul Christian Dawkins ,  Zackery Reed   Explicating interpretations of equivalence in measurement contexts ABSTRACT                 36 Gila Hanna ,  Xiaoheng Yan   Opening a discussion on teaching proof with automated theorem provers ABSTRACT                 42 Paul Ernest   A dialogue on the deep ethics of mathematics ABSTRACT                 47 Luis Felipe Prieto-Martínez   Unsolved problems in plane geometry ABSTRACT                 53 -   Index to Volume 41                           54 -   Contributors                           56

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