Exploring Advanced Mathematics Courses and Content for Secondary Mathematics Teachers

Connections Identified by Teacher Educators Between the Mathematics They Teach and the Mathematics Their Students Will Teach in the Future

“…When, after finishing his course of study, he became a teacher, he suddenly found himself expected to teach the traditional elementary mathematics in the old pedantic way; and, since he was scarcely able, unaided, to discern any connection between this task and his university mathematics, he soon fell in with the time honoured way of teaching, and his university studies remained only a more or less pleasant memory which had no influence upon his teaching. (Felix Klein, 1908, referred to in Winsløw & Grønbaek, 2014 Nevertheless, it is still a focus of interest in the field, as it is reported in various studies (Leikin et al, 2018;Suominen, 2018;Ticknor, 2012;Wasserman, 2018;Weber et al, 2020;Yan et al, 2021). Leikin et al (2018) conducted a study with mathematics teachers from teacher training courses at Israeli universities.…”

“…Ticknor (2012) points out teacher educators should make explicit connections between the advanced mathematics they teach and the mathematics their students, prospective teachers, will teach in secondary school. Wasserman (2018) establishes contact points between advanced mathematics and mathematics education at a secondary education level. He considers a non-exhaustive list of four different connection points in a spectrum that goes from the most linked to mathematics, to the most linked to mathematics education: content connections, disciplinary practice connections, classroom teaching connections, and modeled instruction connections.…”

“…In regards to the modeled instruction connections (Wasserman, 2018), which refer to the establishment of connections through the teaching practice itself, there are extensive studies and references made by many authors (Marshman, 2021;Rojas & Deulofeu, 2015;Rojas et al, 2021;Ticknor, 2012) pointing out the influence that teacher educators' classroom practices have in prospective teachers' future teaching practices. Many times this influence hinders the application of what is learned in methodology courses during teacher training.…”

“…We have focused on mathematical connections, though taking into consideration that other types of connections could appear. Wasserman (2018) considers the connections between the study of advanced mathematics and secondary teaching through a non-exhaustive list of four different connection points, in a spectrum that ranges from the one most linked to mathematics to the more linked to pedagogy: Content connections, disciplinary practice connections, classroom teaching connections, and modeled instruction connections. Wasserman (2018) refers to content connections as the relationship between the content of advanced mathematics and the content of school mathematics.…”

Including School Mathematics Teaching Applications in an Undergraduate Discrete Mathematics Course

“…Patterson [12] analyzed real analysis textbooks and mapped concepts within these textbooks to K-12 content standards. Wasserman [13] has worked on categorizing types of connections between advanced mathematics and school mathematics. He investigated different ways prospective teachers can engage in developing mathematical knowledge for teaching in their undergraduate mathematics major courses and articulated four different points of connections to teaching.…”