Dim 1: Math

Students’ understanding of a discipline is shaped in fundamental ways by their classroom experience of it. If, for example, a reading class is focused on decoding text, a history class on memorizing dates of major events, or a mathematics class on memorizing procedures, there is little chance that the students in that class will emerge from it with either an appreciation of the discipline or the understandings they need.

Learning to “think like a historian,” or like a scientist, or a practitioner of any discipline, means coming to grips with the concepts and practices of that discipline – approaching phenomena through a disciplinary lens, with a broad spectrum of knowledge and tools at one’s disposal. Historians “place themselves in context” to understand the motivations and actions of historical figures. Writers having a sense of purpose and a sense of audience when writing, as well as relevant factual and grammatical knowledge. Scientists and mathematicians inquire into “what makes things tick,” using reason, equations, representations, and models in the service of sense making. This combination of disciplinary orientations, knowledge (including concepts and tools), practices and habits of mind is what we refer to in shorthand as the “content” of the discipline. Students need to experience that content in its full richness if they are to become disciplinary thinkers.

Every major discipline has produced one or more sets of standards – statements regarding the essential understandings that students should develop. This is not the place to review such documents, but simply to note that if the activities in a classroom do not live up to the relevant disciplinary standards, it is hard to imagine that the students who emerge from that classroom will have a deep sense of the discipline or be able to use their knowledge effectively.

The tools section of this document provides descriptions of tools such as the TRU Conversation and Observation Guides, which offer ways to inquire into and reflect on the richness of the disciplinary content offered to students.

Rich content, however, is just a beginning. The primary idea behind TRU is that what counts in instruction is how students encounter the content – how they are or are not positioned to take advantage of the riches the discipline has to offer. We have all been in classes where, for example, the content was “over our heads” or we failed to connect to it for some reason; no matter how beautiful it may have been, we were lost. That is why dimensions 2 through 5 of the TRU framework – how students themselves experience the discipline – are so important.