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References
- Aké, L. (2013). Evaluation and development of elementary algebraic reasoning in teachers in training [PhD thesis, University of Granada]. https://www.ugr.es/~jgodino/Tesis_doctorales/Lilia_Ake_tesis.pdf
- Ball, D. L., & Bass, H. (2009). With an Eye on the Mathematical Horizon: Knowing Mathematics for Teaching to Learners’ Mathematical Futures. In M. Neubrand (Ed.), Beiträge zum Mathematikunterricht 2009 (pp. 11-29). WTM-Verlag.
- Ball, D.L., Hill, H.C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(3), 14-22 and 43-46.
- Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes it Special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
- Barboza, L. C., Pazuch, V., & Ribeiro, A. J. (2021). Tasks for learning teachers who teach mathematics in the elementary school. Zetetike, 29, 1-25. https://doi.org/10.20396/zet.v29i00.8656716
- Barboza, L. C., Ribeiro, A. J., & Pazuch, V. (2020). Primary school teacher’s professional learning: exploring different meanings of the equals signal. Acta Scientiae. (Canoas), 22(4), 71-120. https://doi.org/10.17648/acta.scientiae.5418
- Bernardo, R. D., Carotenuto, G., Mellone, M., & Ribeiro, M. (2017). Prospective Teachers’ Interpretative Knowledge on Early Algebra. Cadernos de Pesquisa, 24(esp.), 208-222. https://doi.org/10.18764/2178-2229.v24n.especialp208-222
- Blanton, M. L., & Kaput J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446.
- Blanton, M. L., & Kaput J. (2011). Functional Thinking as a route into algebra in the elementary grades. In J. Cai & E. Knuth (eds.), Early Algebraization, Advances in Mathematics Education (pp. 5-23), Springer. http://doi.org/10.1007/978-3-642-17735-4_2
- Blanton, M. L., Levi, L., Crites, T., & Dougherty, B. (Eds.). (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. National Council of Teachers of Mathematics.
- Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.S. (2015). The Development of Children’s Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade. Journal for Research in Mathematics Education, 46(1), 39-87. https://doi.org/10.5951/jresematheduc.46.1.0039
- Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries: A review of the state of research. ZDM, 44(3), 223-247. https://doi.org/10.1007/s11858-012-0429-7
- Carraher, D. W., & Schliemann, A. D. (2019) Early algebraic thinking and the US mathematics standards for grades K to 5. Infancia y Aprendizaje, 42(3), 479-522. https://doi.org/10.1080/02103702.2019.1638570
- Castro, W. F. (2011). Evaluation and development of didactic analysis skills of tasks on elementary algebraic reasoning in future teachers [PhD thesis, University of Granada]. https://www.ugr.es/~jgodino/Tesis_doctorales/Walter_Castro_tesis.pdf
- Cohen, L., Manion, L., & Morrison, K. (2011). Research methods education. Routledge.
- Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. (4th edition). Sage Publications.
- Demonty, I., Vlassis, J. & Fagnant, A. (2018). Algebraic thinking, pattern activities and knowledge for teaching at the transition between primary and secondary school. Educational Studies in Mathematics, 99, 1–19. https://doi.org/10.1007/s10649-018-9820-9
- Ferreira, M. C. N., Ribeiro, M., & Ribeiro, A. J. (2017). Conhecimento matemático para ensinar álgebra nos anos iniciais do ensino fundamental. Zetetiké, 25(3), 496-514. https://doi.org/10.20396/zet.v25i3.8648585
- Gellert, U. (2005). La formación docente entre lo teórico y lo práctico. In I. Gómex-Chacón & E. Planchart (Eds.), Educación Matemática y formación de profesores. Propuestas para Europa y Latinoamérica (pp. 73-83). Universidad de Deusto.
- Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas. UNIÓN: Revista Iberoamericana de Educación Matemática, 20, 13-31. https://union.fespm.es/index.php/UNION/article/view/1063
- Godino, J. D., Aké, L. P., Contreras, Á., Díaz, C., Estepa, A., Fernández, Mª. T., Lacasta, E., Lasa, A., Neto, T., Oliveras, L., & Wilhelmi, M. R. (2015a). Diseño de un cuestionario para evaluar conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental. Enseñanza de las Ciencias, 33(1), 127-150. https://doi.org/10.5565/rev/ensciencias.1468
- Godino, J.D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education 39, 127-135. https://doi.org/10.1007/s11858-006-0004-1
- Godino, J. D., Wilhelmi, M. R., Neto, T., Blanco, T. F., Contreras, Á., Díaz-Batanero, C., Estepa, A., & Lasa, A. (2015b). Evaluación de conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental de futuros maestros. Revista de Educación, 370, 199-228. https://doi.org/10.4438/1988-592X-RE-2015-370-303
- Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-specific Knowledge of Students. Journal for Research in Mathematics Education, 39(4), 372-400. https://doi.org/10.5951/jresematheduc.39.4.0372
- Hohensee, C. (2017). Preparing elementary prospective teachers to teach early algebra. Journal of Mathematics Teacher Education, 20(3), 231-257. https://doi.org/10.1007/s10857-015-9324-9
- Kaput, J. J. (2008). 1 What Is Algebra? What Is Algebraic Reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra In The Early Grades (1st ed., pp. 5-18). Routledge. https://doi.org/10.4324/9781315097435-2
- Katz, V. J. (2007). Algebra: Gateway to a Technological Future. The Mathematical Association of America.
- Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8, 139-151.
- López, E., & Sanz, R. (2021). Construcción y validación del cuestionario de autopercepción sobre las Competencias docentes del profesorado. Educatio Siglo XXI, 39(3), 157-186. https://doi.org/10.6018/educatio.427461
- McAuliffe, S., & Lubben, F. (2013). Perspectives on pre-service teacher knowledge for teaching early algebra. Perspectives in Education, 31(3), 155-169.
- Mejías, C. (2019). Assessment of the Knowledge for the Teaching of Algebra in Teachers in Exercise of Primary Education [PhD thesis, University of Girona]. https://dugi-doc.udg.edu/handle/10256/17137
- Molina, M., Castro, E., & Castro, E. (2009). Elementary students’ understanding of the equal sign in number sentences. Electronic Journal of Research in Educational Psychology, 17, 7(1), 341-368. https://doi.org/10.25115/ejrep.v7i17.1345
- Montero, I., & León, O.G. (2002). Clasificación y descripción de las metodologías de investigación en psicología. Revista Internacional de Psicología Clínica y de la Salud, 2(3), 503-508.
- Muñiz, J. (2017). Teoría clásica de los test. Segunda Edición. Pirámide.
- Ng, D. (2011). Indonesian primary teachers' mathematical knowledge for teaching geometry: implications for educational policy and teacher preparation programs. Asia-Pacific Journal of Teacher Education, 39(2), 151-164. https://doi.org/10.1080/1359866X.2011.560648
- Oliveira, H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: a focus on functional thinking. Journal on Mathematics Education, 12(2), 257-278. https://doi.org/10.22342/jme.12.2.13745.257-278
- Oviedo, H. C., & Campo‐Arias, A. (2005). Aproximación al uso del coeficiente alfa de Cronbach; An Approach to the Use of Cronbach's Alfa. Revista colombiana de Psiquiatría, 34(4), 572‐580. https://doi.org/10.7705/biomedica.v26i4.327
- Pincheira, N., & Alsina, Á. (2021a). Hacia una caracterización del álgebra temprana a partir del análisis de los currículos contemporáneos de Educación Infantil y Primaria. Revista Educación Matemática 33(1), 153-180. https://doi.org/10.24844/EM3301.06
- Pincheira, N., & Alsina, Á. (2021b). Teachers’ mathematics knowledge for teaching early algebra: a systematic review from the MKT perspective. Mathematics, 9, 2590. https://doi.org/10.3390/math9202590
- Schliemann, A., Carraher D. W., & Brizuela B. M. (2012). Algebra in elementary school. In L. Coulange & J. P. Drouhard (Eds.), Enseignement de l’algèbre élémentaire: Bilan et perspectives (pp. 109-124). Special Issue of Recherches en Didactique des Mathématiques.
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.2307/1175860
- Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
- Strand, K., & Mills, B. (2014). Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Algebra. The Mathematics Enthusiast, 11(2), 385-432. https://scholarworks.umt.edu/tme/vol11/iss2/8
- Tanisli, D., & Kose, N. Y. (2013). Pre-Service Mathematic Teachers’ Knowledge of Students about the Algebraic Concepts. Australian Journal of Teacher Education, 38(2). http://dx.doi.org/10.14221/ajte.2013v38n2.1
- Trivilin, L. R., & Ribeiro, A. J. (2015). Mathematical Knowledge for Teaching Different Meanings of the Equal Sign: a study carried out with Elementary School Teachers. Bolema: Boletim de Educação Matemática, 29(51), 38-59. https://doi.org/10.1590/1980-4415v29n51a03
- Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397-428. https://doi.org/10.1007/s10857-013-9251-6
- Zapatera, A., & Callejo, M. L. (2017). Mathematical knowledge and professional noticing of prospective teachers in the context of pattern generalization. Characterization of Profiles. Revista Complutense de Educación, 24(1), 35-38. https://doi.org/10.5209/RCED.55070
References
Aké, L. (2013). Evaluation and development of elementary algebraic reasoning in teachers in training [PhD thesis, University of Granada]. https://www.ugr.es/~jgodino/Tesis_doctorales/Lilia_Ake_tesis.pdf
Ball, D. L., & Bass, H. (2009). With an Eye on the Mathematical Horizon: Knowing Mathematics for Teaching to Learners’ Mathematical Futures. In M. Neubrand (Ed.), Beiträge zum Mathematikunterricht 2009 (pp. 11-29). WTM-Verlag.
Ball, D.L., Hill, H.C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(3), 14-22 and 43-46.
Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes it Special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
Barboza, L. C., Pazuch, V., & Ribeiro, A. J. (2021). Tasks for learning teachers who teach mathematics in the elementary school. Zetetike, 29, 1-25. https://doi.org/10.20396/zet.v29i00.8656716
Barboza, L. C., Ribeiro, A. J., & Pazuch, V. (2020). Primary school teacher’s professional learning: exploring different meanings of the equals signal. Acta Scientiae. (Canoas), 22(4), 71-120. https://doi.org/10.17648/acta.scientiae.5418
Bernardo, R. D., Carotenuto, G., Mellone, M., & Ribeiro, M. (2017). Prospective Teachers’ Interpretative Knowledge on Early Algebra. Cadernos de Pesquisa, 24(esp.), 208-222. https://doi.org/10.18764/2178-2229.v24n.especialp208-222
Blanton, M. L., & Kaput J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446.
Blanton, M. L., & Kaput J. (2011). Functional Thinking as a route into algebra in the elementary grades. In J. Cai & E. Knuth (eds.), Early Algebraization, Advances in Mathematics Education (pp. 5-23), Springer. http://doi.org/10.1007/978-3-642-17735-4_2
Blanton, M. L., Levi, L., Crites, T., & Dougherty, B. (Eds.). (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. National Council of Teachers of Mathematics.
Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.S. (2015). The Development of Children’s Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade. Journal for Research in Mathematics Education, 46(1), 39-87. https://doi.org/10.5951/jresematheduc.46.1.0039
Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries: A review of the state of research. ZDM, 44(3), 223-247. https://doi.org/10.1007/s11858-012-0429-7
Carraher, D. W., & Schliemann, A. D. (2019) Early algebraic thinking and the US mathematics standards for grades K to 5. Infancia y Aprendizaje, 42(3), 479-522. https://doi.org/10.1080/02103702.2019.1638570
Castro, W. F. (2011). Evaluation and development of didactic analysis skills of tasks on elementary algebraic reasoning in future teachers [PhD thesis, University of Granada]. https://www.ugr.es/~jgodino/Tesis_doctorales/Walter_Castro_tesis.pdf
Cohen, L., Manion, L., & Morrison, K. (2011). Research methods education. Routledge.
Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. (4th edition). Sage Publications.
Demonty, I., Vlassis, J. & Fagnant, A. (2018). Algebraic thinking, pattern activities and knowledge for teaching at the transition between primary and secondary school. Educational Studies in Mathematics, 99, 1–19. https://doi.org/10.1007/s10649-018-9820-9
Ferreira, M. C. N., Ribeiro, M., & Ribeiro, A. J. (2017). Conhecimento matemático para ensinar álgebra nos anos iniciais do ensino fundamental. Zetetiké, 25(3), 496-514. https://doi.org/10.20396/zet.v25i3.8648585
Gellert, U. (2005). La formación docente entre lo teórico y lo práctico. In I. Gómex-Chacón & E. Planchart (Eds.), Educación Matemática y formación de profesores. Propuestas para Europa y Latinoamérica (pp. 73-83). Universidad de Deusto.
Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas. UNIÓN: Revista Iberoamericana de Educación Matemática, 20, 13-31. https://union.fespm.es/index.php/UNION/article/view/1063
Godino, J. D., Aké, L. P., Contreras, Á., Díaz, C., Estepa, A., Fernández, Mª. T., Lacasta, E., Lasa, A., Neto, T., Oliveras, L., & Wilhelmi, M. R. (2015a). Diseño de un cuestionario para evaluar conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental. Enseñanza de las Ciencias, 33(1), 127-150. https://doi.org/10.5565/rev/ensciencias.1468
Godino, J.D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education 39, 127-135. https://doi.org/10.1007/s11858-006-0004-1
Godino, J. D., Wilhelmi, M. R., Neto, T., Blanco, T. F., Contreras, Á., Díaz-Batanero, C., Estepa, A., & Lasa, A. (2015b). Evaluación de conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental de futuros maestros. Revista de Educación, 370, 199-228. https://doi.org/10.4438/1988-592X-RE-2015-370-303
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-specific Knowledge of Students. Journal for Research in Mathematics Education, 39(4), 372-400. https://doi.org/10.5951/jresematheduc.39.4.0372
Hohensee, C. (2017). Preparing elementary prospective teachers to teach early algebra. Journal of Mathematics Teacher Education, 20(3), 231-257. https://doi.org/10.1007/s10857-015-9324-9
Kaput, J. J. (2008). 1 What Is Algebra? What Is Algebraic Reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra In The Early Grades (1st ed., pp. 5-18). Routledge. https://doi.org/10.4324/9781315097435-2
Katz, V. J. (2007). Algebra: Gateway to a Technological Future. The Mathematical Association of America.
Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8, 139-151.
López, E., & Sanz, R. (2021). Construcción y validación del cuestionario de autopercepción sobre las Competencias docentes del profesorado. Educatio Siglo XXI, 39(3), 157-186. https://doi.org/10.6018/educatio.427461
McAuliffe, S., & Lubben, F. (2013). Perspectives on pre-service teacher knowledge for teaching early algebra. Perspectives in Education, 31(3), 155-169.
Mejías, C. (2019). Assessment of the Knowledge for the Teaching of Algebra in Teachers in Exercise of Primary Education [PhD thesis, University of Girona]. https://dugi-doc.udg.edu/handle/10256/17137
Molina, M., Castro, E., & Castro, E. (2009). Elementary students’ understanding of the equal sign in number sentences. Electronic Journal of Research in Educational Psychology, 17, 7(1), 341-368. https://doi.org/10.25115/ejrep.v7i17.1345
Montero, I., & León, O.G. (2002). Clasificación y descripción de las metodologías de investigación en psicología. Revista Internacional de Psicología Clínica y de la Salud, 2(3), 503-508.
Muñiz, J. (2017). Teoría clásica de los test. Segunda Edición. Pirámide.
Ng, D. (2011). Indonesian primary teachers' mathematical knowledge for teaching geometry: implications for educational policy and teacher preparation programs. Asia-Pacific Journal of Teacher Education, 39(2), 151-164. https://doi.org/10.1080/1359866X.2011.560648
Oliveira, H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: a focus on functional thinking. Journal on Mathematics Education, 12(2), 257-278. https://doi.org/10.22342/jme.12.2.13745.257-278
Oviedo, H. C., & Campo‐Arias, A. (2005). Aproximación al uso del coeficiente alfa de Cronbach; An Approach to the Use of Cronbach's Alfa. Revista colombiana de Psiquiatría, 34(4), 572‐580. https://doi.org/10.7705/biomedica.v26i4.327
Pincheira, N., & Alsina, Á. (2021a). Hacia una caracterización del álgebra temprana a partir del análisis de los currículos contemporáneos de Educación Infantil y Primaria. Revista Educación Matemática 33(1), 153-180. https://doi.org/10.24844/EM3301.06
Pincheira, N., & Alsina, Á. (2021b). Teachers’ mathematics knowledge for teaching early algebra: a systematic review from the MKT perspective. Mathematics, 9, 2590. https://doi.org/10.3390/math9202590
Schliemann, A., Carraher D. W., & Brizuela B. M. (2012). Algebra in elementary school. In L. Coulange & J. P. Drouhard (Eds.), Enseignement de l’algèbre élémentaire: Bilan et perspectives (pp. 109-124). Special Issue of Recherches en Didactique des Mathématiques.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.2307/1175860
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Strand, K., & Mills, B. (2014). Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Algebra. The Mathematics Enthusiast, 11(2), 385-432. https://scholarworks.umt.edu/tme/vol11/iss2/8
Tanisli, D., & Kose, N. Y. (2013). Pre-Service Mathematic Teachers’ Knowledge of Students about the Algebraic Concepts. Australian Journal of Teacher Education, 38(2). http://dx.doi.org/10.14221/ajte.2013v38n2.1
Trivilin, L. R., & Ribeiro, A. J. (2015). Mathematical Knowledge for Teaching Different Meanings of the Equal Sign: a study carried out with Elementary School Teachers. Bolema: Boletim de Educação Matemática, 29(51), 38-59. https://doi.org/10.1590/1980-4415v29n51a03
Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397-428. https://doi.org/10.1007/s10857-013-9251-6
Zapatera, A., & Callejo, M. L. (2017). Mathematical knowledge and professional noticing of prospective teachers in the context of pattern generalization. Characterization of Profiles. Revista Complutense de Educación, 24(1), 35-38. https://doi.org/10.5209/RCED.55070