Project Title:

1. Introduction
2. Detailed Project Plan
3. Example of the curriculum on visual and spatial reasoning
4. Evaluation Plan
5. Dissemination of Results
6. Instrumentation Requests
7. Prior NSF Support
8. Institutional Support
9. Experience and Capability of the Principal Investigator
10. Timetable for Proposed Work
11. References Cited

1. Introduction

Students in science and engineering can benefit from developing spatial and visual abilities. For example, we depend on students¹ abilities to read and comprehend visual material. The diagrams, graphs, and scientific illustrations in Scientific American magazine, any textbook, or professional journal article testify to our widespread dependence on visual representations to communicate complex concepts in science, mathematics, and engineering. Amazingly, nowhere in the college curriculum do students in these disciplines learn to make visual representations to think and communicate. This represents a significant omission in the education of young scientists, mathematicians, and engineers and an opportunity for enhancing comprehension and creative ability.

The need for visual and spatial thinking
The ability to think and reason visually and spatially plays an important role in science and engineering discovery. Stories abound of creative discovery or problem solving in chemistry, mathematics and engineering. Among the most familiar, Kekulé described his insight of the benzene molecule structure with his 'mental eye' seeing the 'atoms gamboling' in groups with twining and twisting in snakelike motion. The revelation of benzene's ring structure came to him when he 'saw' the snake seize its own tail to form a whirling circle [1]. Interestingly, Kekulé originally studied architecture [2] before he switched to chemistry. His training in visual thinking may have helped him to 'see' the solution configurations in the reasoning process.

Visual skills are important not only in creative discovery, but in ordinary problem solving as well. George Polya in 'How to Solve It' [3] suggested making diagrams to solve a mathematical problem. Einstein sketched a diagram (circle and lines) in a letter to an astronomer [4] to show how gravity would deflect light near the sun. Feynman's well-known diagrams illustrate the interactions between charged particles moving through time and space. The diagrams 'were intended to represent physical process and the mathematical expressions used to describe them' [5]. Tesla was known for his ability to visualize and test his inventions in his Œmind¹s eye.¹ He argued [6] that visualization forces concentration and makes it easier to gain insights of underlying principle instead of paying attention to the details of apparatus. Anecdotes like these suggest that spatial and visual reasoning play an important role in science, mathematics, and engineering.

We are called on constantly throughout our intellectual life to exercise spatial and visual reasoning. As children we play with shape and color blocks and intelligence tests ask us to see spatial analogies among configurations of geometric shapes (figure A is to figure B as figure C is to ?). So-called Œbrain teasers¹ ask us to solve spatial configuration and topological puzzles. Impossible figures (such as M.C. Escher¹s famous woodcuts [7]) play with the conventions of projecting three dimensions into the plane and challenge our visual imagination [8, 9]. In geometry we draw a figure to help understand a problem that is stated in words, and occasionally we learn to introduce graphical notations to solve specific problems in other areas of mathematics and science. All these activities exercise our spatial abilities; however, because our culture (which, ironically, is intensely visual) tends to distrust the visual as a source of knowledge, we often tend to think of these activities as illustrative but intuitive, peripheral to ³real² problem solving. As with any kind of thinking, there is an intuitive component to visual and spatial thinking, but the ability to read, make, and use diagrams in thinking is to a large degree a matter of practice, not talent.

Neuropsychological Basis of Visual and Spatial Reasoning
It is widely acknowledged in neuroscience and psychology research that problem solving abilities [10, 11] rely not only on language-analytical reasoning but also temporal-spatial engineering design by visualizing the problems [12]. Clinical and empirical evidence shows that different areas of brain cells (in the left and right cortex) are activated in tasks such as planning, mathematics and language (humor) comprehension [13, 14]. Research done by Pascual-Leone and Kosslyn [15] demonstrates that Œmental images¹ are activated consistently in certain brain cells. Neurological research [16] shows that learning of fractions and ratios in elementary school mathematics can be enhanced though spatial-temporal training. Attention and performance studies [17, 18] also show that spatial perception is linked to motor skills.

Research on Diagrammatic Reasoning
In Visual Thinking, psychologist Rudolf Arnheim asserted that "perceiving and thinking are indivisibly intertwined" [19] and he argues for an ³intelligence of visual perception². Recently, researchers in psychology, artificial intelligence, and design have begun to seriously explore the role of diagrams in representation and reasoning. The goal of research in this area is to examine whether diagrams support thinking, and if so how and under what circumstances. Methods of inquiry range from protocol analysis of people solving problems with diagrams to computational modeling of diagram based reasoning; the task domains range from mathematics and physics to design. Early results in this emerging area of study have been published [20] and are discussed at conferences such as Thinking With Diagrams, Diagrams 2000: International Conference on the Theory and Application of Diagrams (http://morpheus.hartford.edu/~d2k/), and the American Association of Artificial Intelligence (AAAI) symposia on Diagrammatic Reasoning and Representation, and Spatial and Visual Reasoning. In short, although in the past visual reasoning has not been the subject of serious scrutiny, a number of efforts are now underway that may shed light on how visual reasoning works.

Specifically, what is ³visual and spatial thinking and reasoning²?
By visual and spatial reasoning we mean the ability to:

• Make graphical and three-dimensional representations of problem situations.
• Manipulate these representations (project, rotate, reflect, and invert figures, fold and unfold three dimensional objects and surfaces, etc.).
• Reason about spatial properties and relations within these representations (identify relative positions, shapes, fill in missing information that can be logically derived).

The need for teaching it
It isn't taught.
Freshman college students‹much less science and engineering majors‹seldom see any kind of visual and spatial reasoning courses. The closest are the drawing courses offered for art and architecture students, some of which are taught in our home department.

It can be taught.
Experience in teaching students of architecture to solve spatial problems shows how visual and spatial ability can be learned. However, visual instruction in the arts and architecture typically focuses on training students to practice in these fields. We plan to teach these same skills with a focus on science, engineering, and mathematics problem solving.

It should be taught.
We believe that enhancing this ability can provide students studying science, mathematics, and engineering with an additional cognitive support for problem solving‹and perhaps also creative insight. At this stage we cannot support this belief with solid evidence. That is one reason we seek to develop and deliver this course: to see whether we can make a case that teaching these skills to science, mathematics, and engineering students will offer them an advantage in solving problems.

Project goal: Enhance visual thinking skills of first year college students
We propose to provide first year college students with compelling opportunities to develop their visual thinking and spatial reasoning skills through hands-on, interactive exercises. The interactive tools include: learning modules and exercises on making drawings and diagrams by hand, computational drawing environments that allow students to see relationships between two and three dimensional representations, and explorations in the 'virtual world' of making things, taking them apart, and reasoning about the relationships among objects.

Science, mathematics, and engineering students sometimes enroll in art and architecture classes either to satisfy university distribution requirements, to explore a divergent interest, or to relax from the intellectually rigorous coursework in their major. The cultural divisions that C.P. Snow wrote about in ³The Two Cultures² [21] remain so firmly ingrained in our academic disciplines that students and instructors often fail to connect what they learn in the drawing or sculpture course to science, mathematics, and engineering. This proposal seeks to help students make that connection, by applying what we know about teaching architects drawing, modeling, and visual skill in the development of basic visual thinking materials for science, math, and engineering.

We intend to teach drawing (both physical and digital) as a means to explore and illustrate science and engineering principles and problems in terms of visual and spatial reasoning in general education, not as an isolated or target discipline or career alternative. This exposure could reach out to a larger population of students, expand their horizons as they seek a major, and build their spatial reasoning abilities. Regardless whether students select science and engineering as their career, they would be better equipped with a useful cognitive support.

Information technology is transforming the traditional passive classroom into a stimulating, interactive environment for learning. With multi-media presentation software and tools for drawing and making 3D models, learning can become an active, exciting and engaging 'hands-on' experience. In addition to traditional drawing, modeling, and puzzle-solving exercises, the seminar will employ 2D and 3D drawing software, both commercial packages and experimental software developed in the PI¹s laboratory (see Supplementary Materials provided with this grant proposal).

This proof-of-concept project will explore (and we expect, demonstrate) the feasibility and effectiveness of teaching visual and spatial skills to first year science and engineering college students. The project capitalizes on the PI¹s experience in teaching these skills to students of architecture and in developing interactive graphical software for drawing and design.

What we plan to do
We plan to demonstrate that basic skills in visual and spatial reasoning can be taught and learned through a sequence of hands-on drawing, modeling, and interactive computer based exercises. The ultimate goal is to show that developing these skills can enhance students¹ performance in basic science, mathematics, and engineering problem solving. This exploratory project will develop materials and lay groundwork for a (future) larger investigation that develops these materials in greater depth and engages in a fuller assessment of the applicability in specific science, mathematics, and engineering tasks, of visual skills gained. Our project has five major components:

• We will develop learning materials in visual and spatial thinking for scientists and engineers.
• We will deploy these materials in a freshman seminar directed broadly at pre-major students in sciences and engineering (twice, with refinements in year two). As we teach the seminar, we will specifically ask students to bring problems from their science, mathematics, and engineering coursework as materials to consider for visual problem solving. In year two, we intend to integrate some of these domain specific problems into the seminar curriculum.
• We will assess the learning experience and the role that the materials played in this experience using on-campus educational evaluators in the University of Washington¹s Center for Instructional Development and Research (CIDR) unit.
• We will bring together a seminar of small core of faculty members from diverse disciplines interested in visual and spatial reasoning and who could potentially develop the project to the next stage of implementation. In particular, we will draw on this group¹s domain expertise to look for ways to transfer general visual and spatial abilities to specific problems in their home disciplines. Our initial roster includes faculty members from mechanical engineering, computer science, and electrical engineering who have expressed interest in participating in this seminar.
• We will disseminate our results through articles in peer-reviewed outlets and by posting the learning materials we develop on a project Web site.

The exercises for year 1 are described in the following. The second year's curriculum exercises will be modified according to lessons learned in the formative assessment and course evaluation questionnaire from the first year's experience. Additional software developed in response to these evaluations will be included as well.

Exercise 1: 2D (flatland) ­ Tangrams, 2D representations, puzzle solving in 2D
The first exercise involves the exploration of two-dimensional spatial reasoning: arranging Tangram puzzles to form different shape configurations and recording the solutions by making diagrams. Class discussion will focus on notation making for diagramming puzzle solutions and the reasoning and comparison among shapes and scales. After the diagramming the puzzle solutions, the students will select a problem in their own home disciplines (or an area of interest) and to diagram a solution. Small groups will engage in presentations, evaluations and discussions of the effectiveness and possible improvements for their diagram making.

Exercise 2 Drawing ­ Using drawing to reason three dimensionally about problems
The second exercise will teach students how to draw on paper (2D) to represent three-dimensional form and space. The basic theory of visual sight lines, perception and perspective drawing will be introduced. Required readings will include works on visual perception and graphics representation principles (e.g., [22-26])

These first two exercises will explore using drawing as a vehicle for understanding three-dimensional positioning of objects in space, relative dimension of objects.

Exercise 3: Sketch-VR - 1
Sketch-VR [27, 28] is a freehand sketching software developed to enable students to quickly generate 3D models without using complicated drafting or modeling software. Students who have used the software found the instant feedback of 3D rewarding and fun. We plan to use Sketch-VR as scaffolding for students to make representations of 3D objects and spatial relations.

Exercise 4: Sketch-VR - 2
We will use Sketch-VR (adding functional extensions such as curves and 3D surfaces) for students to further explore spatial relations and visual perception of 3D objects. The UW Mechanical Engineering department has several computer numerically controlled rapid prototyping machines. We plan to use three-dimensional output devices to produce models of students' creations to further explore the understanding of objects in space.

Exercise 5 - Manipulation of physical objects
Students in this exercise will dissect the computer-output physical models and recompose them to make new spatial configurations. This exercise will also include wooden puzzle solving. Students will practice various three-dimensional (topological and spatial) puzzle solving and use drawing to represent puzzle solutions.

Exercise 6 - Model making - assembling 3D models using physical materials
This exercise will engage students in making 3D models using paper folding (origami) and computational paper-folding exercise using HyperGami software. The HyperGami software has been used successfully in K-12 education (Eisenberg, 1999). Students can use the software to design and color the geometric shapes and then construct the polyhedra from paper printouts.

Exercise 7 - Model-making using computer graphics (simple Form€Z exercises)
We will introduce students to a geometric modeling program called Form€Z (Autodessys) and learn to do simple form generation. The exercise will include positioning objects according to a coordinate system, and the manipulation of viewpoints (and possibly folding and unfolding of surface models).

Exercise 8 - FormWriter - generating 3D form using simple codes
FormWriter [29] is experimental software written to generate three-dimensional forms using mathematics expressions. (It was used in a course on three-dimensional geometry in Islamic architecture.) The exercise will engage students to write different formula and generate 3D objects that can be viewed from any angle. Students can write simple routines to generate kits of parts and use them to make a complex whole, for example making arches and ribs to form a dome or a vase.

Exercise 9 - 12 - problem-solving in science
The material and exercise will be developed jointly with domain experts, colleagues from UW campus who participated in the course (CS, ME, or EE, etc). For example, one exercise could diagram flow charts to implement a mechanical system or a software program. Sketches of Edison's phonograph design, diagrams of the plate theory of earth movements and faulting, Galileo's sketch of sunspots, and blood circulation diagrams over heart and lungs are good examples of using drawings as a means to reason about scientific concepts [32].

Two different types of evaluation and data collection methods will be used to evaluate the quality and impact of the proposed visual and spatial reasoning curriculum. The questions are: (1) how effective are the exercises and the software tools in supporting learning of visual thinking, and (2) what other kinds of exercises and software tools might be useful for learning the visual and spatial thinking skills. We will use standard classroom assessment techniques such as Attitude Survey, Concept Tests, Concept Mapping, and Interviews [33].

We will use formative evaluation methods [34, 35] to assess ongoing project activities and the impact our curriculum materials have on student learning. Assessments will be measured at several points, e.g., every 1-2 exercises) during the course of teaching/learning. We will take a variety of forms such as questioning, comment on presentation, or interviewing to analyze student progress to the learning objectives to guide and inform the directions and adjustments of the teaching material. We will employ both implementation evaluation and progress evaluation during the course of instruction. Summative evaluation will also be conducted at the end of the course. The students at the University of Washington are already required to evaluate all courses by anonymous scoring and comment. These Faculty Course Evaluation (FCE) forms are developed by the University's CIDR (Center for Instructional Development and Research, http://depts.washington.edu/cidrweb/). Several variations of the form assess different types of learning and skill acquisition. When appropriate, we will enlist help from CIDR to modify, design and conduct more formal and informal questionnaires, qualitative analysis, collecting and analyzing information, and testing of materials developed in the visual and spatial curriculum. We will use the information collected to evaluate the course material and any specific commentary on our exercises or software tools developed for the course.

The timetable for executing the project involves two iterations of a develop-deliver-evaluate cycle. In Year One, we will prepare materials for a freshman seminar, deliver the seminar, and evaluate the learning experience. In light of the evaluation data, we will modify and extend the learning materials and deliver the seminar again in Year Two, and again evaluate the learning experience. In parallel with this develop-deliver-evaluate cycle we will form a core group of faculty members from diverse disciplines who will take an active interest in visual and spatial thinking in science in general, and the seminar in particular.

Year 1: Initial development of spatial and visual reasoning curriculum, software for drawing, and assessment materials. Summer quarter will be the seminar material preparation. Freshman seminar will be taught at the autumn quarter. Winter quarter will be used to conduct first round of testing, analysis and assessment of the results of the freshman seminar from previous quarter. Spring quarter will be devoted to develop additional computer-based teaching materials.

Year 2: Revision and continuing development and assessment of curriculum material. Continue development of additional software to aid visual and spatial reasoning activities with drawing. The materials will be made available on the World Wide Web. Summer quarter will be used to develop additional computer-based teaching materials. Autumn quarter the PI will teach the freshman seminar again. Winter quarter will be for assessment analysis and spring quarter to prepare and package materials for publication (on the Web and in print).

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