• Although performance was far better than in Study 1,it remained far from ceiling. Errors were greater onstrike (13°) than rod (7°) and were lower when correctlines paralleled walls’ axes (see samples).

• As expected, strike errors were smaller in the highWLG than in low WLG (11° vs. 15°). Furthermore,medium and low WLG did worse on strike if it was first.

• Dip data – as in Study 1 – showed systematicoverestimates of the steepness of the (model)outcrops. These data fit Proffitt’s (2006) finding thatadults overestimate hills’ inclines.

The Role of Basic Spatial Concepts in Education: What Learners Bring to the ClassroomLynn S. Libena Kim A. Kastensb & Adam E. Christensena

aThe Pennsylvania State University (Department of Psychology); bColumbia University (Lamont-Doherty Earth Observatory, Department of Earth & Environmental Sciences)

Background

Task Modifications

Study 1 was designed to study whether college studentswho have difficulty on the WLT also have difficultylearning strike and dip.

• Students were giveninstructions (a) on strike anddip based on US GeologicalSurvey explanations.

• Students were taken to anartificial outcrop made ofplywood, similar to thatshown in (b), and installed ina sloping area near acampus building (c).

Rod Lines

Study 1

Strike LinesImportance of Spatial Thinking in Science

Spatial thinking is a core cognitivedomain. It has been increasinglyrecognized as critical for science andmath education, e.g., the recent NRCreport on Learning to Think Spatially

Many students – from kindergarteners to undergraduates– have trouble with even basic spatial concepts such asunderstanding Euclidean horizontal and verticalcoordinate axes.

Illustrative is research on the “water level task” (WLT)showing that many college students (especially females)have difficulty representing the invariant horizontality ofliquid.

Conclusions

The data suggest that educators should not presumethat all students arrive at their classrooms with thebasic spatial skills needed to understand andrepresent phenomena central to many sciencedisciplines. Additional research is needed to test thepotential value of providing instruction in basic spatialskills as a foundation on which to build scienceeducation.

Acknowledgments

This research was supported by NSF Grants to Libenand Kastens, REC #04-11686 and #04-11823,respectively. The opinions are those of the authors,and no endorsement by NSF should be inferred.Correspondence may be addressed to liben@psu.edu.

Spatial Concepts

Water Level Sample Item

Draw a line to show bottle half full.

Spatial Thinking in Geology

We hypothesized that these spatial concepts are neededby field geologists as they observe and record on a maprock outcrops’ strike and dip.

Strike is the line at the intersection between thehorizontal plane and the plane of the rock surface,recorded by a line on a map.

Dip is the angle between the horizontal plane and theplane of the rock surface, measured within the verticalplane.

Textbook illustration showing relevance ofhorizontality and verticality for strike & dip

Participants

We screened roughly 600 undergraduates enrolled inintroductory psychology courses for their understandingof horizontality on a 6-item WLT. Males and femalesfrom each of the following WL Groups (~20/cell; N = 125)were then given geology instruction.

High WLG: all 6 water lines correctMedium WLG: mixed correct & incorrectLow WLG: all 6 water lines incorrect

Geology Instructions & Tasks

• Students were asked todraw the strike line on a mapof the nearby area of campus(d), to show dip direction,and to estimate dip indegrees.

• They were also asked todraw a line on another copyof the same map to indicatethe orientation of a rod (e).

Key Findings: Study 1

• Students varied greatly in theirsuccess in orienting the strikeline on the map correctly. 41% oflines were off by 30° or more.Many students seemed to berecording the long axis of outcroprather than strike. Males’ errors,24° were significantly smallerthan females’, 31°.

Dip Lines & Numbers

• Students generally over-estimated dip by 20°. The modalresponse was 45° (correct: 30°).Some gave impossibleresponses of over 90°.

• Again, performance was highlyvariable, with 34% deviating fromcorrect by 30° or more. On rod,performance differed both by sex(right), males’ error, 24° females’error 43° and WLG (below),high, medium, low, respectively:15°, 36°, 49°

Study 2

Study 2 was designed to pinpoint students’ difficulties bysimplifying tasks to remove challenges we judgedperipheral to core spatial concepts. Again, we enrolledstudents based on WLT scores (N = 94).

• Tasks were given indoors (simpler,smaller, more rectilinear environment);model/small rod on a table replacedburied outcrop/large rod outside.

• Horizontal (strike) lines were drawnon models and direct instructions (“draw a line on the mapto show the location and direction of this line/rod”) weresubstituted for geology instructions. 8 rod, 8 strike, and 5dip.

Key Findings: Study 2

(a)

(b) (c)

(e)

(d)

FIGURE 14.10 A. The geometricprinciples used to measure the directionand angle of tilt of an inclined plane. B.Strike and direction and angle of dip.Note the symbol used by geologists toindicate strike and dip.

From Skinner et al., 1995, The Dynamic Earth.

N

N

View direction