Worked Solutions
Worked-Example Solutions
The image below is a screenshot of a typical assessment / worked example couplet generated by Learning Conductor. This particular couplet is intended to help students become more proficient in the content strand Measurement & Geometry and the topic Area, Surface Area, and Volume. As indicated by the second line of text in the image, this couplet is the 4th of 10 in this student-generated problem set.
Image 1 Caption: The area immediately above Circle 1 shows the item problem statement. The area to the left of Circle 1 displays the mathematical representation associated with this particular problem statement, which we refer to as the item-specific representation. Learning Conductor’s item-generation capability means that the quantitative values incorporated in the problem statement change from one learning episode to another. The dimensions of the new representation will also change, as students negotiate from one assessment-based problem-solving exercise to the next.
The answers listed to the left of Circle 2 displays the correct answer to the item, and three distracters. Since the values in the problem statement and the dimensions of item-specific representation are parametrically determined, the values of the correct answer and distracters will also change from problem to problem.
The area to the left of Circle 3 presents the worked-example solution to the assessment item. The solution begins by filling in the blank area of the irregularly shaped item-specific representation, thereby creating a standard rectangle. It then proceeds to illustrate how the student can use the standard formula for calculating the area the two rectangles created by this strategy. The student is then shown how the problem can be solved by computing the areas of the two rectangles, and subtracting the area of the filled in rectangle from the larger rectangle.
The worked example shown above is designed to familiarize the student with the usefulness of using his or her existing knowledge of standard area calculations to calculate the area of irregularly-shaped figures composed of n numbers of rectangles.
The image below shows an exercise / solution couplet dependent upon the production of a series of unfolding mathematical representations. Since the acquisition of normative levels of mathematical proficiency is inseparable from representational fluency, the ability to generate these types of couplets is of major pedagogical value.
We believe Conductor represents the first time an assessment-related software application has included the means for dynamically generating geometrically accurate mathematical representations.
Item Cloning
The screenshots below depict a typical Algebra and Functions assessment item. The image on the left is the source item; the one on the right is one of its “clones.” The explanatory text at the bottom of both images depicts the worked-example solution, which appears immediately after the student submits an answer to the problem.
