Abstract
With the adoption and implementation of the Common Core State Standards for Mathematics and the Next Generation Science Standards, teachers are being called upon now more than ever before to regularly utilize and incorporate mathematics, science, and engineering practices in order to deepen students' understanding of the content they are learning, make broader connections to the STEM disciplines, and to ultimately help to strengthen the STEM pipeline. This chapter describes how teachers can use SketchUp as a tool to implement the practices through creative design into their own classrooms. The premise and basics of SketchUp are shared as well as a rich creative design project that develops spatial reasoning in middle grades students.
TopIntroduction
Every person is born with a certain amount of innate spatial reasoning; it is an essential part of our everyday life. While we use it regularly by positioning and orienting ourselves in everyday environments, it is important to continue to develop it, especially when visualizing and moving between 3-dimensional objects to 2-dimensional and conversely.
Transforming mental images is a spatial skill that engineers and designers depend on. When a hiker pauses with a map and compass, it is the spatial intelligence that conceptualizes the path. Through the spatial sense, a painter “feels” the tension, balance and composition of a painting. Spatial ability is also the more abstract intelligence of a chess master, a battle commander, or a theoretical physicist, as well as the familiar ability to recognize objects, faces and details. (Grow, 1990, para. 2)
Spatial reasoning is formally introduced in school curricula and standards as early as kindergarten. For example, throughout the Common Core State Standards for Mathematics [CCSSM] (Council of Chief State School Officers [CCSSO], 2010), one would find multiple emphases placed on “modeling”, “decomposing”, and “applying” concepts to real world situations (e.g., M.GM-1, H.GM-1) – terms that we often use to be more explicit in what we mean by “spatial reasoning”. Moreover, there is an explicit focus on spatial reasoning, especially modeling, through the intentional use and structure of the eight Standards for Mathematical Practice.
In combination, the Next Generation Science Standards [NGSS] (NGSS Lead States, 2013) emphasize not only the eight Standards for Mathematical Practice through cross-cutting concepts, but also lay out the eight Science and Engineering Practices (Table 1). Students need to be exposed not only to the scientific facts, but also the processes that engineers and scientists use in developing knowledge and understanding the world around them. Through interaction and exploration with the world around them, students gain valuable understanding of how the scientific community performs their work.
Table 1. Standards for mathematical practice and science and engineering practices
| Standards for Mathematical Practice [CCSSM] | Science and Engineering Practices [NGSS] |
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning. | 1. Asking questions (for science) and defining problems (for engineering).
2. Developing and using models.
3. Planning and carrying out investigations.
4. Analyzing and interpreting data.
5. Using mathematics and computational thinking.
6. Constructing explanations (for science) and designing solutions (for engineering).
7. Engaging in argument from evidence.
8. Obtaining, evaluating, and communicating information. |
Key Terms in this Chapter
SketchUp: A software package for three-dimensional modeling and computer-aided design currently available at http://www.sketchup.com/ .
Geometry: The school study of Euclidean plane and solid geometry, both with and without coordinates.
Dynamic Geometry Software: Interactive software in which the user can create and manipulate geometric constructions.
Engineering Design: The process of creating, designing, implementing, and revisiting a plan to help create a product that has specified performance goals.
Spatial Visualization: The process of constructing and manipulating mental models of 2- and 3-dimensional objects and locations.
Modeling: “Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions” (CCSSO, 2011 AU21: The in-text citation "CCSSO, 2011" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. , p. 72).
Computer-Aided Design (CAD): The use of computer software to create virtual representations of objects in 2- or 3-dimensional space.