Learning to Form Accurate Mental Models

Hand gestures are one means of illustrating geological concepts, like the orientation of these fractures in 2.5-billion-year-old rocks in Dales Gorge, Hamersley Basin, Australia. A recent study showed that students master spatial concepts more quickly when they make concrete illustrations of their mental images and then receive immediate feedback on how closely these concepts mirror physical reality. Credit: Thomas Shipley


From Cross Sections to 3D Structures
Students have great difficulty reasoning about diagrams [Hegarty, 2014], particularly diagrams that convey three-dimensional spatial information (https://eos.org/project-updates/visualizing-cross-sectional-data-in-areal-world-context),such as geological block diagrams (Figure 1), which make up approximately 17% of all visualizations in introductory textbooks [Atit et al., 2015].Students often have trouble coordinating information on the orthogonal faces of a block model to accurately estimate 3-D internal structures; many students simply assume that what is seen on one face is what would be seen inside the volume [Alles and Riggs, 2011].This difficulty in visualizing 3-D structures extends beyond the classroom.For example, on a field trip, a student might generate erroneous predictions about how outcrops connect below the surface.
To examine whether generating a prediction and immediately comparing the prediction to the correct solution could facilitate diagram understanding, Gagnier et al. [2017] asked non-geology major students in a one-on-one experimental psychology laboratory setting to view a series of images of block models, each with an indicated cut through the interior (Figure 2).The students were then asked to sketch their prediction for the resulting cross section.Immediately afterward, students were shown the correct answer (the block model after the cut) and asked to compare their prediction to the correct answer.In this way, students received information that either confirmed their prediction or provided spatial information about the nature of the error that could be used to improve the next prediction.The results indicated that after 45 minutes and after as many as 12 tries at generating a spatial prediction diagram and comparing it to the correct answer, students improved by a half of a standard deviation on a measure of geologic block diagram understanding compared to students who viewed the correct answer but did not generate a predictive diagram.

Reasoning About Deep Time
Another area where students struggle is in understanding the magnitude of deep time (https://eos.org/opinions/taking-the-pulse-of-the-earths-surface-systems),which leads to incorrect estimates of the rates of geologic events.Students' estimates of events that occurred in Earth's history can be off by as much as five orders of magnitude [Catley and Novick, 2008].
To examine whether making a prediction with spatial feedback could facilitate understanding geologic

A Versatile Approach
Despite different content, the interventions share a design that led to improved learning.First, students in both studies were asked to generate an external representation of a prediction (in the form of a sketch or answer choice) that could be compared against the correct answer.Second, students were immediately shown the correct answer and asked to spatially compare their prediction to the correct answer.We argue that these factors are critical in facilitating spatial learning, which, in turn, leads to the development of more accurate mental models.
The prediction-comparison-feedback cycle was successful in both studies despite their structural differences, suggesting that this cycle could be adapted to a range of pedagogical settings.For example, the block diagram intervention requires a full class period to complete, whereas the deep time intervention required only about 3 minutes of lecture time.Prediction can be manifested in two ways (Figure 4): internally, where the prediction is expressed mentally, and externally, where students select a multiple-choice answer or draw, voice, or gesture their predictions.We suggest four ways in which students gain by externalizing their predictions: Students must commit to their prediction.
Externalizing provides a lasting record of their thinking.
Students can make a deliberate comparison between the prediction and the correct answer, which provides a spatial error signal.
Faculty can use this external representation for formative assessment.In a typical lecture class, students view slides and take notes.Although the note-taking may seem active, it is mentally passive, as it involves no active prediction or inferences on the part of the student and provides no way to check if the students' and instructor's understandings match.

Applying This Method to Course Work
Several lessons from cognitive science research help us understand why the prediction-comparisonfeedback cycle improves student learning (for a review, see Resnick et al. [2017]): Viewing the prediction and correct answer at the same time helps the student detect differences.
Students get immediate self-generated feedback to compare with their active mental representation; this is superior to delayed-feedback methods like graded exams and homework.
When students can repeat the process, through multiple opportunities to make relevant comparisons, this repetition reinforces the correct representation and corrects incorrect representations.
When faculty ask students to engage in this prediction-comparison-feedback cycle, they must choose the type of external representation students make (e.g., a sketch or a multiple choice answer).The optimal choice will likely depend on whether common types of errors on the task can be anticipated.If the errors are well known, then a multiple-choice test (with likely errors used as foils) is likely to facilitate efficient learning.If the foils represent common misconceptions, then students will be forced to engage in a deeper comparison to make their selection, which should promote learning.However, in cases where the errors are unknown, it may be best to ask students to generate their own representations.
Our research suggests an effective method for incorporating sketching into the classroom in a way that requires minimal investment from the instructor.Sketches may be time-consuming for an instructor or teaching assistant to correct, but the instructor only needs to prepare the solution sketch.Individual students can evaluate their own sketches in only a few minutes.The student's prediction and subsequent comparison can facilitate learning and help guide the student's internal representation even in the absence of one-on-one teacher interaction.
This concept may be broadly applied to a diverse array of topics and content areas but is particularly useful for complex spatial concepts for which the misconceptions in the students' internal models may be varied or unknown.Faculty designing activities should have students independently make a sketch, receive a correct sketch from the instructor, and then follow up with a reflection on how their sketch differed from the "correct" sketch, with multiple opportunities to generate predictions for similar problems.

Fig. 1 .
Fig. 1.Geophysics students frequently encounter block diagrams like the one shown here in their textbooks, but they may have difficulty conceptualizing how subsurface features continue on into the interior of the solid, behind the cross-sectional slice.Credit: KDS4444/Wikimedia Commons, CC-BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)

Fig. 2 .
Fig. 2. Students (1) viewed a block model and (2) generated a sketch predicting what the model would look like after cut 1.Students then (3) viewed the correct answer and sketch and (4) compared their prediction to the correct answers.
time (https://eos.org/editors-vox/here-comes-the-anthropocene),Resnicket al. [2017]  conducted an experiment in six large general education classes over three semesters.During class lectures, students were presented with their textbook's geologic timescale, which compresses the space representing the Precambrian and expands the space representing the time since the Precambrian when fossilized life is preserved and abundant (Figure3).

Fig. 3 .
Fig. 3. Students in a classroom viewed a slide showing a nonlinear representation of the geologic timescale.Numerical values are shown for the beginning and end of the Hadean period (dark green, 4.6 billion years ago to 3.8 billion years ago) and the Archean period (light green, 3.8 billion years ago to 2.3 billion years ago).(top) In an instant poll, students chose among Fig. 4. The prediction-comparison-feedback cycle is an iterative process by which a student's internal representation is repeatedly corrected, working toward an increasingly accurate representation of Earth or the model.
Accurate Mental Models -Eos https://eos.org/features/learning-to-form-accurate-mental-models8/10 Accurate Mental Models -Eos https://eos.org/features/learning-to-form-accurate-mental-models9/10 A model made by stacking layers of colored modeling clay is cut to demonstrate how the interior of a 3-D structure appears on various cross-sectional surfaces.Credit: Kristin Gagnier Building a Learning Framework This cycle can scaffold geoscience learning and ultimately set students on a course toward the type of hypothesis testing required in scientific inquiry.Generating a prediction and then comparing the prediction to the correct answer provides a scaffold for spatial learning with minimal time requirement.Students develop understanding of spatial problems by engaging in a cycle of learning in which they form a prediction, express it outwardly, and then compare their prediction to the correct answer.This process lets them receive immediate feedback on their prediction.This cycle can scaffold geoscience learning and ultimately set students on a course toward the type of hypothesis testing required in scientific inquiry.