The correctness criteria can include any of the representations computed by CogSketch. If a fact is marked as important, it is included in the correctness criteria for the sketch. Quantitative ink constraints are defined separately because, unlike visual and conceptual relationships between existing glyphs, there is no cognitive model for automatically proposing them, so they must be defined explicitly by the author for each applicable glyph.
There have been 49 different worksheets used in classroom settings so far. These worksheets span three general domains: biology 4 , engineering 19 , and geoscience The four biology worksheets involve drawing and labeling parts and flows of the human circulatory system and use a combination of conceptual relationships e. The engineering worksheets involve exercises in free body diagrams and drawing orthographic projections. Although the engineering worksheets are within the same general domain, they use different types of representations.
The free body diagrams use force arrows to convey assumptions about forces. The force arrows are represented qualitatively because the students are not required to enter numerical values for them. Instead, the arrows they draw need to be oriented in the correct qualitative direction, and they need to have the appropriate relative length. This allows the worksheet author to identify correctness criteria at the level of individual edges, either qualitatively e. In turn, the worksheet tutor can provide students with more detailed, targeted feedback. Many of the geoscience worksheets involve annotating a background image to identify relevant geologic features and any conceptual relationships that might hold between them.
Quantitative ink constraints are useful for such worksheets, as are conceptual relationships that can be used to convey movement and physical transfer e. In many cases, both types of representations are used in a single worksheet. This section describes the visual and analogical processing underlying Sketch Worksheets.
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We have, in other experiments, modeled such reasoning e. This section explains how that works. The goal of CogSketch's visual processing routines is to produce structured, relational representations that correspond reasonably well to what people are using, so that the visual distinctions that experts find relevant are detected reliably. Given the differences between today's computers and human visual processing capabilities, we have not attempted to model the details of human visual processing. CogSketch automatically computes topological relations between all glyphs in a sketch.
The rest of the visual relations can be computed on demand, depending on whether or not they are needed to understand the contents of the worksheet. These properties may include spatial relationships that are not computed by default. To gain access to those relationships, the worksheet author can ask CogSketch to elaborate its representations of the sketch. For example, in orthographic projection worksheets bottom right, Fig. The author can request that more detailed representations be computed so that some of them may be marked as important.
Crucially, when the student's sketch is evaluated with respect to the solution, the elaboration requests made by the author are used on the student sketch to ensure that the information needed to evaluate the student's sketch is available. When a student requests feedback, his or her sketch is compared to the solution sketch via analogy. This requires a comparison mechanism that can support the wide range of student sketches possible. The student may request feedback from the software at any time, so his or her sketch may be nearly complete with one or two differences from the solution or it may be wildly different with incorrectly labeled items or missing glyphs.
It is therefore important that the comparison process focuses on relevant visual and conceptual information, even when there are many differences. SME takes as input the solution sketch and the student sketch and creates a mapping between the two. Each mapping consists of 1 correspondences , which indicate how things in the solution correspond to things in the student sketch; 2 candidate inferences , which indicate important differences between the solution and the student sketch; and 3 a structural evaluation score , which is used to select the best mapping if there is more than one.
The correspondences and candidate inferences are used to determine what advice should be given to the student.
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The correspondences of the mapping are used to generate advice based on violated quantitative ink constraints. If a glyph in the solution sketch has a quantitative ink constraint associated with it, and it has a corresponding glyph in the student sketch, then the student's glyph is evaluated with respect to the solution glyph's quantitative ink constraint.
The candidate inferences of the mapping indicate visually and conceptually salient differences. If one of the differences involves a fact that was marked as important by the worksheet author, then it triggers the natural language advice string associated with it. Keying advice to differences in correctness criteria means that only relevant visual aspects of a sketch matter.
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This provides considerable flexibility and robustness. Consider again the Greenhouse Effect worksheet Fig. The relative positions of the Sun and the Earth don't matter. The Earth could be drawn as seen from a distance, for example, a sphere, or from a closer view. Since the relationships here are all conceptual relationships, and there aren't spatial relationships among the key facts for the worksheet, it could even be drawn as a concept map!
As long as the entities and relationships are correctly labeled, it means that the student understands it Fig. This general approach works well in most cases.
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However, in expanding to wider range of tasks, we have found that the matching process is even more robust if we constrain analogical mappings with conceptual and quantitative information, and use recursive, hierarchical matching for different levels of representation. We discuss these in turn. For example, in the fault identification worksheet Fig.
Where there are multiple glyphs of the same type e. However, in worksheets where the student is drawing on a background image or diagram, we have found that quantitative ink constraints can provide evidence for putting two particular entities into correspondence. In other words, given more than one possible mapping, we prefer matches where quantitative ink constraints are satisfied. This is done by looking at the competing correspondences constructed by SME, and evaluating them with respect to quantitative matching, when available.
Close quantitative matches are translated into additional match constraints requiring those entities to be placed into correspondence in subsequent comparisons. This allows the matching process to, in effect, take quantitative spatial information into account when it is relevant to the task. Some worksheets, such as engineering drawing worksheets e. Carrying out matches at multiple levels at once can lead to mismatches, and even when matches are perfectly accurate, deluge students with too much advice.
To increase accuracy in mapping, we use matches between more abstract representations to guide matches involving more detailed representations. For example, the engineering drawing worksheets Fig. This causes CogSketch to restrict comparisons to glyphs found in the same ink segmentation glyphs. At the level of glyph matching, if tutoring advice is generated, then that advice is given to the student and no further attention is paid to that pair. Otherwise, the worksheet tutor drills down to the edge level of representation.
It first looks for differences in edge cycle properties, for example, if it should be straight but isn't, that are worth addressing.
When the edge cycle level representations provide no guidance, comparisons between particular edges for that cycle are carried out, to give more detailed feedback when the author has provided important distinctions at that level. Sometimes there are canonical misconceptions in a domain.
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For example, in identifying the four chambers of the heart Fig. To enable authors to communicate such misconceptions and provide advice based on them, sketch worksheets also support misconception sketches in addition to the solution sketch. When a worksheet has misconception sketches, the tutor first checks if the student's sketch was a strong match for a known misconception.
If so, it provides advice specific to that misconception that was provided by the author.
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This provides the opportunity to give much more informative feedback. Our research on the utility of sketch worksheets is ongoing, but we already have some insights as to what types of activities have been successful, based on our experience in both observing students in laboratory experiments and in working with instructors and students in classroom experiments. Sketch worksheets have shown promise in helping students learn spatial layouts, conceptual relationships that can be conveyed visually, and scaling when qualitative differences in quantity can be readily observed and aligned visually.
In contrast, sketch worksheets do not appear to be the right platform for exercises where quantities or relationships are represented abstractly and not grounded visually. The worksheets that have been developed on the human circulatory system Fig.
Over a series of four worksheets, students are asked to draw and label the four chambers of the heart, use arrows to indicate how blood flows, and use arrows to indicate when oxygen is added to and removed from blood. They improved their ability to correctly identify chambers of the heart and accurately identify how blood flows through the circulatory system.
They did not make significant gains on an assessment on oxygen flow. Interestingly, the oxygen flow assessment was the only one of the three that did not have a visual component. We suspect that one factor in the success of these worksheets was the detection of common mistakes via misconception sketches, which enabled the worksheet tutor to provide more targeted feedback. In working with instructors and students in classroom studies e. For example, in teaching students about the geologic time scale, one approach might be to have geologic events plotted on a single time scale, with the ability to zoom in and out to detect small differences in geologic time e.
However, zooming in to one particular order of magnitude makes quantities from other orders of magnitude invisible. Instead of this approach, geoscience worksheets about scale have multiple scales aligned visually i. To support the wide range of possible student answers, it is important that advice is flexible enough to let the student know what is wrong and how it might be fixed.
For these worksheets, positional relations between student glyphs and quantitative ink constraints were used to provide hints about how the location of the student glyph should change e. Note that the worksheet tutor does not understand the interpretation of visual properties in terms of temporal relationships in the domain being taught—that mapping is the responsibility of the worksheet author, to keep the tutor as general as possible. We have also observed that worksheets where quantities are expressed completely independent of ink are not as effective.
For example, in a worksheet on the Earth's carbon cycle, students used arrows to indicate carbon transfers and used quantity annotations to denote the amount of carbon transferred.
Each carbon mass annotation could be drawn in any way. Some students used dots, others wrote numeric symbols, and others used more arrows. However, the ink did not spatially correspond to the magnitude of the annotation, and students found this confusing or not useful.
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