by David and Phyllis Whitin
January 2001
Too often in designing an interdisciplinary unit of study, teachers lament that including the mathematics is difficult. One problem in granting mathematics its rightful place in interdisciplinary studies is that it is often not recognized as a way of thinking about the world. Mathematics, like other ways of thinking, is characterized by concepts. These concepts include number, equivalence, symmetry, ratio, base, similarity, congruence, length, weight, and time. These concepts are generalizations that learners can use across contexts to examine and investigate the world.
If we want children to experience and use mathematics in a functional way, then we must give them authentic learning experiences. Two strategies for accomplishing this task are (1) having children make direct observations and then (2) posing questions or wonders that are based on those observations. We use the word wonder because it connotes an inquisitiveness, or musing, about the world that is not tied to a correct or incorrect response. If we grant children these two opportunities, then we do not need to cross our fingers and hope that the mathematics will be embedded in the questions that the children ask. Instead, it will be there because mathematics, like other forms of expression, rides the crest of an inquiring mind.
A firstgrade class in South Carolina was studying insects and went outdoors in February to look for some. The students wondered why they did not find any. Their observations began a study of life cycles (time) in the natural world. A month later, the class again went outdoors, where they found grasshoppers, ants, other insects, and spiders. These observations led them to wonder how far grasshoppers hop (length) and why spiders build webs in a corner (spatial relations). The spiderweb and the mathematics of spatial relations led them to construct maps for another class to show the best places for finding bugs. Mathematics became a purposeful tool for communicating knowledge of insects to an interested audience.
In the same South Carolina school, one fourthgrade student initiated a class study of rocks by bringing his collection to school. While observing rock samples, the class wondered about such things as, How many years ago did this rock come out of a volcano? (time) and Why do rocks break up into different shapes? (shape). To follow up on their interest in shape, their teacher led a discussion of atomic structure and constructing models of the six crystal systems (shape, symmetry). By using one of the models (triclinic) to build crystals of various sizes, they noticed that each version "got bigger but kept its shape" (similarity).
Building models and constructing maps were functional uses of mathematics in this school's interdisciplinary studies. The activities emerged from children who were making direct observations and posing questions or wonders. The concepts of spatial relations, shape, and similarity helped them describe relationships that they had experienced and wanted to share with one another. Mathematics was neither a neglected perspective nor an artificial appendage to an interdisciplinary study but rather a purposeful tool for exploring meaningful questions.
David J. Whitin and Phyllis Whitin are faculty members at Queens College, City University of New York. David teaches mathematics courses with a particular emphasis on linking mathematics with literature and science. Phyllis's teaching and research interests include children's literature and integrated curricula. The Whitins regularly collaborate with teachers in the New York City area. 
