Mathematical and Computational Thinking: Practice 5

Are you asking, “What is mathematical and computation thinking?”  If so, you are not alone.” This practice may even sound a little intimidating to some. It shouldn’t be cause for alarm.

Mathematical and computational thinking includes things like finding patterns in numbers, measuring, identifying characteristics of data sets, graphing. . . and much more. Mathematical and computational thinking is a key science and engineering practice.  The first step in helping students gain these important skills is to be sure that as educators we understand what is included in this practice. Here’s how the Framework describes the progression of mathematical and computational thinking.

Increasing students’ familiarity with the role of mathematics in science is central to developing a deeper understanding of how science works. As soon as students learn to count, they can begin using numbers to find or describe patterns in nature. At appropriate grade levels, they should learn to use such instruments as rulers, protractors, and thermometers for the measurement of variables that are best represented by a continuous numerical scale, to apply mathematics to interpolate values, and to identify features—such as maximum, minimum, range, average, and median—of simple data sets.

A significant advance comes when relationships are expressed using equalities first in words and then in algebraic symbols—for example, shifting from distance traveled equals velocity multiplied by time elapsed to s = vt. Students should have opportunities to explore how such symbolic representations can be used to represent data, to predict outcomes, and eventually to derive further relationships using mathematics. Students should gain experience in using computers to record measurements taken with computer-connected probes or instruments, thereby recognizing how this process allows multiple measurements to be made rapidly and recurrently. Likewise, students should gain experience in using computer programs to transform their data between various tabular and graphical forms, thereby aiding in the identification of patterns.

Students should thus be encouraged to explore the use of computers for data analysis, using simple data sets, at an early age. For example, they could use spreadsheets to record data and then perform simple and recurring calculations from those data, such as the calculation of average speed from measurements of positions at multiple times. Later work should introduce them to the use of mathematical relationships to build simple computer models, using appropriate supporting programs or information and computer technology tools. As students progress in their understanding of mathematics and computation, at every level the science classroom should be a place where these tools are progressively exploited.

The MLTI devices include tools that can support students in developing mathematical and computational thinking.

Students can use spreadsheets and graphing programs of Bento, Grapher, Geogebra, Data Studio, Logger Pro and Omni Graph Sketcher to find patterns in numbers and data, and predict outcomes, describe features of data sets (maximum and minimum), relate mathematic relationships to sets of numbers (x+3=7), and relate these to science phenomena like the growth of a plant or the increasing temperature of heating water.

Students can use Net Logo and Maine Explorer to explore and manipulate computer models.

You can learn more about mathematical and computational thinking by listening to the NSTA webinar by Robert Mayes and Bryan Shader.