If we provide a student with a process to frame a subject we can begin their steps towards asking questions about the subject and eventually solving problems within the discipline. One natural way to observe the subject is to measure it. Immediately, we encounter a set of questions about the subject itself. What can be measured or counted? What are the tools needed? What are the units of measurement? These initial questions can provoke deeper reading and engagement into the situation and provide a process for generating inquiry around a topic. If students are able to measure and collect data themselves, this allows for immediate engagement.
Another route into math and data is seeing. Math can be extremely visual, using graphs, tables, and geometric diagrams. In general, these objects can intimidate students and so a graph may not initially stimulate a student's curiosity. There is often too much to see for one to immediately perceive patterns. Mathematical visuals are densely packed information. A process for unpacking visual information can be vital to help our students to react productively to a visual stimulus.
To assist students to frame a subject through examining visuals also requires a process. Questions that can help students to unpack meaning are as useful as the framing questions above. Who or what is being measured? What are the units of measurement? In addition, students should deconstruct the two-dimensions of the graph. What does the x-axis show us as well as the y-axis? How are the actual measurements coded to fit into the graphic? What does each visual unit on the graph correspond to in the actual data?
Students who have begun to engage in the topic either through measured data or looking at graphs should be given the opportunity to formulate a pathway of inquiry. In the classroom a process for stimulating questions is necessary and should not be expected to arise naturally. Based on the book, "Make Just One Change: Teach Students to Ask Their Own Questions" by Dan Rothstein and Luz Santana, a
Question Formation Technique
can be used to stimulate student conversation around the topic and to formulate questions that can later be refined.
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In this process, students will work in groups with each other to generate as many questions as they can. The goal here is to ask unfiltered questions. The purpose of this process is to provide a safe space for asking questions, a place where questions are respected and rewarded, and practice in changing observations and statements into questions, so that students learn explicitly how to inquire.
Following the initial brainstorming of questions, students should share the group questions. A new phase can begin as the groups discuss the types of questions that have arisen, perhaps categorizing them in various ways. Some ways of grouping questions are as open versus closed, measurable versus opinion-based, and "answerable now" versus "needs more research."