Mathematics Teachers' Reasoning About Fractions and Decimals Using Drawn Representations

Pre-service Teachers’ Perceptions of the Use of Representations and Suggestions for Students’ Incorrect Use

“…These findings may suggest two things: (1) the PSTs might have believed that manipulatives or models would be more useful for concepts taught in the lower grades than for concepts taught in the upper grades; (2) the PSTs might have had limited content and/or pedagogical knowledge that they needed to teach advanced fraction knowledge using representations. Either possibility may corroborate the prior findings that teachers tend to have limited representational competence (Collins, 2015;Huinker, 2015;Izsák, 2008;Lee, Brown, & Orrill, 2011;Rosli et al, 2013).…”

“…While using representations is recognized as important for supporting students' sense-making processes, the literature also documents that limited uses or misuses of representations, often due to teachers' limited content knowledge, can negatively affect teaching and learning (Bosse, Lynch-Davis, Adu-Gyamfi, & Chandler, 2016;Izsák, 2008;Lee, Brown, & Orrill, 2011;Zazkis & Gadowsky, 2001). However, while adequacy of content knowledge is a necessary condition for teachers' effective use of representation, it is not sufficient.…”

“…However, many studies also have reported teachers' lack of competence in using representations to support student learning (Borko et al, 1992;Izsak, 2008;Lee, Brown, & Orrill, 2011). In particular, studies have shown that pre-service teachers who demonstrate good knowledge of fraction operations and computation skills often show low knowledge and skills in the use of representations (e.g., Lo & Lou, 2012;Rosli, Han, Capraro, & Capraro, 2013).…”

The Pseudo-Covariational Reasoning Thought Processes in Constructing Graph Function of Reversible Event Dynamics Based on Assimilation and Accommodation Frameworks

“…Problems solving are essential of teaching and learning mathematics process (Lee, Brown & Orrill, 2011;Wu & Adam, 2006;Lee, 2005). But in teaching and learning process, there are many mathematical teachers who taught the procedure without explaining why the particular procedure was used.…”

Knowledge of preservice elementary teachers on fractions

“…De manera similar a los resultados obtenidos con maestros y maestras en formación, cuando los sujetos del estudio están en ejercicio, los estudios revelaron un limitado conocimiento sobre fracciones y números racionales (Jacobson y Izsák, 2015;Klemer, Rapoport y Lev-Zamir, 2018;Lee, Brown & Orrill 2011;Rojas, Flores y Carillo, 2015). No obstante, en comparación con docentes en formación, no se han identificado diferencias significativas en el conocimiento del contenido matemático entre ambos grupos, pero sí en contenidos didácticos específicos, como selección de tareas o selección y uso de Uniciencia.…”