## Philosophy

The development philosophy of MathScape centers around the belief that mathematics is inextricably linked to the human experience. Humans use mathematics to explore their surroundings, build structures and communities, and to seek to understand the world around them. The MathScape curriculum provides meaningful mathematical investigations that allow students to experience these different uses of mathematics and, in so doing, to build mathematical competence

The MathScape curriculum reflects the following principles about mathematics:

### Mathematics is a way of thinking

A good mathematician can fuse pieces of content knowledge in creative ways to arrive at mathematical results. Mathematicians develop habits of mind such as abstracting essential elements from situations and seeking patterns and relations; mathematicians who have developed habits of mind have an intuitive sense for how to approach new problems. MathScape activities aim to develop productive habits of mind in students; all activities are designed to get students to think critically and creatively about mathematical topics.

### Mathematics is connected to other subjects both in and out of school

Almost all MathScape activities are set in a context meant to make the mathematics more meaningful for students; many contexts are large-scale and extend through an entire unit, while others are on a smaller scale. For example, in Gulliver’s Worlds, a sixth-grade unit, students examine measurement and scaling as they visit the lands of giants and tiny people. To facilitate forging connections across disciplines, each teacher guide contains a page with pointers to resources that can be used to link the context of the unit to other disciplines.

### Topics within mathematics are connected to one another

MathScape attempts to make these connections apparent to students in two ways:

• First, each of the four content strands receives significant treatment in each grade. By learning about mathematics in each content strand each year, students’ minds are primed to find connections across the content strands.
• Second, many investigations are structured to make connections between mathematical fields obvious. For example, an activity in Patterns in Numbers and Shapes, a sixth-grade unit, asks students to describe a pattern of growing squares. This activity gives students practice building rules and thinking algebraically while also involving geometry. Many students approach this problem geometrically with an area model and then use geometry to come up with an algebraic expression expressing the relationship. It is these kinds of connections that are found throughout the MathScape curriculum.

### Questions can be posed about mathematical topics

Mathematics is not a series of procedural questions students must answer; rather, mathematics has an underlying structure about which questions can be asked. MathScape frames activities to leave room for students to wonder about their own mathematical questions. For example, in The Language of Numbers, a sixth-grade unit, students construct their own number system. After thinking about some specific questions related to what their number system can do, students are asked to pose their own questions about their number systems and number systems in general.

## Resources

Teacher Tips here