Questioning That Develops Layers of Math Knowledge

The Common Core and Project-based Learning
There has been a renewed emphasis on Project-based Learning (PBL) in light of the advent of the Common Core State Standards (CCSS). PBL emphasizes real-world connections to classroom-based scenarios.  Through PBLs, students are able to draw parallels between their everyday context and abstract math concepts, creating meaningful learning.  The CCSS highlight the need not only to use math to understand the world but also to use the world to understand math. Mathematical practice 4, modeling, serves as the vehicle to explore this relationship through PBL.

Putting It into Practice
Let’s consider the case of Ms. LeDuff, a sixth-grade teacher at Wright STEAM Magnet and her practical PBL application.

I was teaching a unit on geometry that would help students understand the area of polygons by decomposing them into right triangles and other known quadrilaterals.   Understanding the implications of finding the area of composite shapes on configuring rooms and the connection to other fields such as engineering and architecture, I asked the following exploratory questions: How might you make use of known shapes (polygons) to determine the area of your bedroom?  What model might you use? Explain your argument.

This created the unregulated space for students to explore a real world problem in a project-based setting.

Modeling
Mathematical practice 4 (MP4) provides the structure for this exploration. MP4 creates a cyclical process of a) examining a real world phenomena; b) creating a real model that possibly represents this occurrence; c) abstracting and computing the mathematics associating with the model; d)checking the reasonableness of the results; and e) refining the model as needed to f) eventually present a viable argument explaining the phenomena.

Students began to ask questions such as: What type of shape best represents my room (examining a real world phenomena)?  How can I represent this shape with standard right triangles and rectangles (creating a model)?  What will I do with the space that is left over?  How can I change the dimensions of the right triangles and rectangles to have less space left over (refine model as needed)?

These questions not only aid in developing understanding of this PBL but also provide starting points for future PBLs.

Project-based learning is a practical application of mathematical practice 4 and incorporates other math practices such as MP3 (constructing viable arguments) and MP2 (reasoning abstractly and quantitatively).  PBL provides an opportunity for students to respond to an open-ended question using various resources. We increase the likelihood that students will value mathematics when they understand how it is applicable to their lives.

Your Turn
Think of your upcoming math unit of study.  What investigative questions might you ask to trigger a real-world problem-based exploration?