Design Principles

The MathScape curriculum reflects the following principles about teaching and learning mathematics:

All students can be successful at learning mathematics

Humans naturally order, quantify, sort, and describe, and mathematics is a language that serves to organize and make sense out of our human experience. All children possess the ability to think and learn mathematically.

Mathematics is meaningful to students when it is embedded within their own experience

When students are able to connect their learning to something that has meaning to them, they both understand it and retain it better than when the learning is disconnected. By relating mathematical investigations to middle school students’ experiences, MathScape promotes meaningful learning for students.

Deep understanding of mathematics content is achieved best through drawing out students’ mathematical thinking and using their thinking as a basis for planning instruction

Students learn by constructing knowledge from an experience and relating that new knowledge to the existing body of knowledge they have. Within mathematics, this means that students must grapple with concepts by formulating their own ideas and by examining, discussing and testing them. Students’ mathematical thinking is a vital component to MathScape lessons.

There is often more than one way to solve a problem, and it is important to examine and explore these alternative approaches

By analyzing different solution methods for a problem, teachers validate students’ different ways of thinking. This affirmation can motivate students and encourage further learning. In addition, students gain flexibility in solving problems and develop a repertoire of mathematical methods from which to draw when faced with a new problem.

Studying mathematics topics in depth is preferable to addressing a breadth of coverage; mastery is achieved after sustained and varied work with a concept and the opportunity to apply a concept in different contexts

A study of topics in depth involves:

  1. allotting adequate time for students to build meaning;
  2. presenting a topic in a variety of ways so that different learning styles are accommodated and, hence, more children gain understanding;
  3. making connections to other areas of mathematics and to other disciplines. These circumstances allow for deep understanding to develop in students in ways that are not possible when many topics are addressed at a cursory level.

Assessment both informs instruction and evaluates student learning

In order to base instruction on students’ understanding of the material, a teacher needs frequent formal and informal ways to assess that understanding. Curriculum materials can provide a variety of methods for teachers to use in gathering such information. These methods include whole-class discussion, small-group work observed by the teacher, students’ narrative written work and mathematical problem-solving. Curriculum materials must also provide evaluative tools to measure what students have learned.

A curriculum can serve as a learning vehicle for teachers as well as for students

When a curriculum presents interesting contexts and views for working with mathematical concepts and skills, there is the opportunity for both students and teachers to make new connections between what may be familiar pieces of content.