Mathematical Knowledge Application and Student Difficulties in a Design-Based Interdisciplinary Project

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

“…All students understood the context and what the problem was asking and were able to use a systematic way to check profit from room price (Aliprantis & Carmona, 2003). Other difficulties that middle school students have had with mathematical modeling include 6 th graders' discussions not refining their models (Mousoulides et al, 2007), 7 th to 9 th graders having difficulty choosing the most important variables and assumptions (Gould & Wasserman, 2014), and several studies have found that if students lack needed mathematics knowledge it could cause a blockage (Galbraith & Stillman, 2006;Ng, 2011;Stillman, Brown, & Galbraith, 2010). Galbraith & Stillman (2006) have also developed a framework for student blockages between six modeling steps with thirty-one general possible blockages.…”

What Is Known about Secondary Grades Mathematical Modelling --A Review

“…Using the same problem Stillman (2011) identified five metacognitive responses that students could have when faced with difficulties. Several studies found that if students lacked needed mathematics knowledge it could cause a blockage (Galbraith & Stillman, 2006;Galbraith et al, 2007;Ng, 2011;. Another frequent blockage was caused by understanding the real world situation Busse & Kaiser, 2003;Galbraith et al, 2007;Ng, 2011;Stillman et al, 2010).…”

“…Eleven studies looked at students' knowledge construction during mathematical modelling and mainly found that students are able to construct developing mathematical understandings (Arleback, Doerr, & O'Neil, 2013;Dunne & Galbraith, 2003;Hitt & Gonzalez-Martin, 2015;Lesh & Carmona, 2003;Lesh & Doerr, 2003a;Ng, 2011;Park, Park, Park, Cho & Lee, 2013). Six of the studies involved MEAs done in the U.S. in which students were able to reason with concepts of average rate of change with exponential functions (Arleback, Doerr, & O'Neil, 2013), inverse variation , proportionality (Lesh & Doerr, 2003a;, geometry and measurement (Lesh & Carmona, 2003), and transformational proof scheme that involves pictorial anticipation of an action not yet performed .…”

Modes of Mathematical Modelling : An analysis of how modelling is used and interpreted in and out of school settings

“…A list that captures all knowledge being taught is obviously not possible, but to describe the diversity of knowledge taught there are some examples given related to elementary arithmetic with base ten blocks (Speiser & Walter, 2010), sound intensity and brightness (Riede, 2010), ranking statistical data (Carmona & Greenstein, 2010;English, 2010;Mousolides et al, 2010), solving linear pattern tasks (Amit & Neria, 2010), solving problems with geometry (Stillman, Brown, & Galbraith, 2010), with technology (Confrey & Maloney, 2007), different representations of functions (Arzarello, Pezzi & Robutti, 2007), calculus (Araújo & Salvador, 2001), non linear situations (De Bock, Van Dooren & Janssens, 2007), multi-variable functions (Nisawa & Moriya, 2011), interdisciplinary projects (Ng, 2011), traffic models (Blomhøj & Hoff Kjeldsen, 2011), etc....…”

“…Research findings indicate that secondary students involved in modelling tasks make less overuse of linear models (De Bock, Van Dooren, & Janssens, 2007), know how to find, interpret and recognise the meaning of a mathematical solution (Sol, Giménez & Rosich, 2011), get more motivated to develop a modelling competency (Lakoma, 2007), increase their knowledge and beliefs of the usefulness of mathematics (Maass, 2010), develop a modelling competency if it is integrated in the classroom during a long period (Bracke & Geiger, 2011). Other research studies point to a lack of knowledge, for example that many students do not apply mathematical skills or concepts (Ng, 2011) or use simple mathematics (Biccard & Wessels, 2011) in the solution process. The lack of validating is a common problem among the secondary students (Biccard & Wessels, 2011;Sol et al, 2011) as well as to make generalisations (Amit & Neria, 2010;Lakoma, 2007).…”