Defining Core Practices for MM Teacher Designers. In detailing the teachers’ enactments of the MM lessons and reflections on the
MM process using several of the lesson episodes, the researcher found four main categories of mathematical modeling core teaching practices that emerged as being central to the success of enacting mathematical modeling in the elementary classroom: a) Questioning practices: Developing student questioning competence; b) Data Practices: Connecting relevant data with formulating the problem and eliciting student thinking about important variables and assumption in a problem situation; c) Modeling Practices: Building a solution that can be communicated to others through uses of records of student work, concrete tools, written and verbal explanations, number sentences and pictorial representations; d) Analytic and Interpretive Practices: Facilitating productive analysis of a model for the purpose of refining the model (See article in press here)
Suh et al., (In press) reported ways in which researchers are collaborating with teacher designers to develop personally relevant and rigorous MM tasks for elementary students. These design skills include : 1) Leveraging problem posing routines: When posing a MM problem, teacher-designers adopted instructional routines for problem posing and worked on developing teacher and student questioning competence; 2) Connecting familiar context that engages students: Teachers, as designers, looked for situational features that warranted mathematizing and searched for contexts that were relevant and important to support students engagement in modeling. In addition, teachers elicited students to think about how their solution was shareable, reuseable, or generalizable, in order to evaluate whether a systematic model was created; 3) Connecting context with content: Teachers connected the need for mathematics in a modeling task with the curricular objectives of their grade level; 4) Considering categories of MM tasks: The modeling tasks tended to fall into four general categories where a mathematical solution or model could be used to describe, predict, optimize, and make decisions about real world situations.
- Descriptive Modeling- Using math to describe, represent and analyze a situation or a phenomenon.
- Optimization Modeling -Using data to find the “best” by optimizing or in some cases minimizing some variable(i.e., cost, space) in a situation.
- Rating and ranking- Using a criteria where one assigns weights or mathematical measures as a way to rate and rank options to make decisions.
- Predictive Modeling- Using trends and data analysis to predict an outcome or use patterns (data analysis and algebra) to predict a situation and make decisions. In some tasks, probability and statistical modeling is used to search for patterns in data to explain a phenomenon (i.e., scientific phenomenon used in STEM contexts).