Complementing Mathematics Teachers’ Horizon Content Knowledge with an Elementary-on-Advanced Aspect

Abstract

Although Ball and her colleagues provided empirical evidence to support the existence of the six subdomains in mathematical knowledge for teaching (MKT) and further explained or defined the majority of these sub-domains, there were few explanations of what horizon content knowledge (HCK) embedded in MKT meant and they merely provided ideas about HCK. Many researchers attempted to provide some teaching incidents and exemplification to interpret the construct of HCK. Moreover, they thought teachers' studies of tertiary mathematics are useful for classroom teaching practice. Their discourse and instantiation of HCK was correspondent with a higher perspective on elementary mathematics mentioned by Felix Klein (1924), but was not entirely coincide with a kind of elementary perspective on advanced knowledge introduced by . This study lasted 1 years, and data collection included in-depth interviews, classroom observation and video analysis. We provide a shared classroom teaching incidence and illustrations to explain and to describe the construct of HCK. HCK not only is a kind of elementary perspective on advanced mathematical knowledge, but also complements to a higher perspective on elementary mathematics. Furthermore, HCK could be seen as a reciprocal pathway between the elementary and advanced mathematical knowledge.

Effect of Augmented Reality and Simulation on the Achievement of Mathematics and Visual Thinking Among Students

“…This can be observed through feelings of these learners when they face an arithmetical problem, or a simple math question (Abu Odeh, 2018). Many studies and researches have talked about the difficulty of mathematics, and learners' anxiety and fear of studying it (Cho & Tee, 2018; Venkatesan & Karimi, 2009). The hardness of mathematics makes it more complicated, so students alienate from it.…”

“…Although the majority of educational staff are convinced of the importance of developing students' thinking skills, and they emphasize that the school's mission is not filling students' minds with information, as much as it is a stimulation of thinking and creativity. Despite of that, these educators live with the practices in our schools, without trying to break the familiar wall or breaking it up (Ersoy & Guner 2015).…”

Subject Matter Knowledge of Prospective Mathematics Teachers on Quadratic Functions Using Problem-Based Learning

“…However, there is still something that needs to be improved in the HCK aspect, namely the ability to connect mathematics with everyday life. HCK can be said to be a broader set of mathematical ideas that become an idea (Cho & Tee, 2018). A teacher's HCK will lead students to learn broader mathematical knowledge, so it cannot be denied that this knowledge needs to include a type of transformation that is pedagogically useful.…”

Methodology of Teaching Graphic Methods for Solving Problems with Parameters as a Means to Achieve High Mathematics Learning Outcomes at School

“…Most of the works are collections of problems with parameters, where a large number of examples of their solution are considered and the basic techniques and methods are highlighted. An extensive class of such problems is presented by Yastrebinetsky (1986), Gornshtein, Polonsky and Yakir (1992), Shestakov and Yurchenko (1993), Amelkin and Rabtsevich (2004), Gorbachev (1998), Natyaganov and Luzhina (2003), Vavilov et al (2007), Golubev (2007), Lee, Lee, and Park (2016), Cho and Tee (2018), Pinho and Carvalho (2016), Muthelo and Chigonga (2018), etc. The authors have presented a wide variety of equations, inequalities and their systems containing a parameter.…”