The Influence of Teacher Education on Mathematics Teaching Knowledge: Local Implementation of Global Ideals

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“…About a third could not multiply by a 2-digit number; less than half could divide by a 2-digit number and success tended to become increasingly elusive the more advanced the mathematics questioned. The data from this study were significantly more alarming than those reported in international studies (e.g., Burghes, 2011;Tatto et al, 2015). What is new in the data detail is the degree and spread of challenge exhibited at enrolment.…”

“…Analysis of middle school students' learning of fractions (Brown & Quinn, 2006, 2007 has been well documented and it is clear from NAPLAN and international testing analysis that the pre-service teachers would have to teach and remediate fraction misconceptions as part of their early practice. Primary pre-service teachers' difficulties with fraction-based concepts have been relatively well reported (e.g., Chick, Baker, Phan, & Chen, 2006;Norton & Nesbit, 2011;Widjaja & Stacey, 2009), but similar challenges for middle school pre-service teachers have received relatively little empirical description, although international testing studies (e.g., Burghes, 2011;Tatto et al, 2015) suggest this is an area that warrants investigation. Sample questions assessing fraction fluency include Question 7, "What is 4 1 2 ÷ 1 3 "(Success rate 42%).…”

“…Theorists from various fields argue that as the complexity of the discipline knowledge being taught increases, the importance of the teacher's content knowledge and specific pedagogy becomes more profound (Chen, Kakyuga, & Sweller, 2016;Kirschner, Verschaffel, Star, & Dooren, 2017). Unfortunately, international comparison does not paint a favourable picture of Western preservice teachers' mathematical content knowledge (MCK), particularly in the primary teaching years but also extending into secondary teaching (e.g., Burghes 2011;Hine, 2015;Kim et al, 2011;Krainer, Hsieh, Peck, & Tatto, 2015;Ma, 1999;Tatto, Rodriguez, & Lu, 2015;Tatto et al, 2008). Those studies that have looked at the depth of MCK of middle school pre-service teachers, in the West in particular (e.g., Burghes, 2011;Kleickmann et al, 2013;Hind, 2015;Krainer et al, 2015;Tatto et al, 2015), indicate patchy MCK.…”

Primary Mathematics Trainee Teacher Confidence and it’s Relationship to Mathematical Knowledge

“…The majority of educational researchers who consider that knowing mathematics deeply is a key aspect of teaching (e.g., Ball & Bass, 2000;Ball et al, 2008;Hattie, 2009;Ma, 1999;Shulman, 1987;Zhang & Stephens, 2013) would be alarmed. The data on MCK add to the corpus of data related to concern about the levels of mathematics knowledge with which trainee teachers are able to commence study in Western institutions (e.g., Ball et al, 2001;Burghes, 2011;Henderson & Rodrigues, 2008;Jensen, 2012;Klein, 2005;Livy & Herbert, 2013;Ma, 1999;Ma & Kishor, 1997;Major & Perger, 2014;Tatto et al, 2015;Tatto et al, 2008). Prior to 2015 these trainee teachers would have graduated without further opportunity to remediate their levels of content or confidence.…”

“…While the models have evolved and become ever more sophisticated, it is apparent that concerns about the depth of teachers' content knowledge (MCK) remain a relatively constant theme in the Western educational research literature (e.g., Ball et al, 2001;Burghes, 2011;Henderson & Rodrigues, 2008;Ingram & Linsell, 2014;Jensen, 2012;Klein, 2005;Livy & Herbert, 2013;Ma, 1999;Ma & Kishor, 1997;Major & Perger, 2014;Tatto, Rodriguez, & Lu, 2015;Tatto et al, 2008). Not surprisingly this is mirrored by Western government concerns about the extent of teacher knowledge and teacher performance (Graven, 2002;Henderson & Rodrigues, 2008;NSW Smarter Schools National Partnership, 2010;Teacher Education Ministerial Advisory Group [TEMAG], 2014; U.S. Department of Education, 2008) including in the study state (Masters, 2009).…”