Investigating the Relationship Between the Problem and the Solver: Who Decides What Math Gets Used?

Disciplinary Learning From an Authentic Engineering Context

“…(p. 4) Tasks that are descriptive of a goal state, such as a mathematical model, but which are not prescriptive of the paths students must take to reach it, may tap the same mathematical content in many different types of studentsalthough the content may vary in maturity. Carmona and Greenstein (2013) showed this phenomenon by testing the same MEA on two radically different groups of students (40 third-graders and eight science post-baccalaureates) and examining the models that each participant group produced. Carmona and Greenstein found that, despite the radical difference in level of schooling between the participant groups, certain types of mathematics used in the models emerged in both groups.…”

Pre-Service Teachers as Researchers: A Mentorship Model

“…Unlike traditional instruction where teachers often demonstrate procedural strategies and techniques, the role of the teacher when implementing modeling tasks is to encourage students to choose, develop, and apply mathematical approaches and help students think about how they might approach the problem to improve their models (COMAP & SIAM, 2016). Mathematical modeling tasks are helpful in revealing student thinking and they enable students to interpret, invent, and find solutions with students from different performing levels (e.g., Aguilar Batista, 2017;Carmona & Greenstein, 2010;Koellner-Clark & Lesh 2003;Mousoulides, Pittalis, Christou, & Sriraman, 2010).…”

What Is Known about Elementary Grades Mathematical Modelling

“…The largest amount of content connections was in the measurement and data/statistics category. The content included interpreting and dealing with multiple tables of data (e.g., [30][31][32]), quantifying qualitative data [6,33], operationally defining constructs [6], exploring relationships and trends (e.g., [34]), representing and structuring findings/data in visual and text forms (e.g., [35,36]), selecting, ranking, and aggregating data (e.g., [33]), weighted ranks (e.g., [30]), sampling [6], identifying variation in data [34,37,38], using an optimization model that uses a two-dimensional coordinate grid [39], area [17], developing a survey and collecting data [35,40], volume measurement [28], and simple randomization distribution to test a hypothesis about the nature of ESP [40].…”

“…Across different studies it was found that elementary students can successfully participate in mathematical modelling [17,20,30,33,39,42,44]. With a modelling activity focused on determining what are important 6 Education Research International factors in buying a pair of sneakers, students used multiple interpretations and approaches and developed mathematics content [44].…”