Explain Worked Solutions
|Explain Worked Solutions|
|Contributors||Paul Salvador Inventado, Peter Scupelli|
|Last modification||June 6, 2017|
|Source||Inventado and Scupelli (2016).|
|Pattern formats||OPR Alexandrian|
Provide students with clearly explained worked solutions when they are unable to answer problems correctly despite receiving support.
Students are asked to answer problems in a math online learning system to practice a particular skill. The system provides students with different types of learning support to help them solve the problem such as hints generated using the Mastery Learning Templates and Mastery Learning Exercise Generator design patterns or guide questions built with the Scaffold Problems with Guide Questions design pattern.
Students may be unable to solve a problem even after making answer attempts and receiving learning support.
- Prior knowledge. Students cannot solve a problem if they lack the knowledge or skills necessary to solve it.
- Learning opportunity. Students lose a learning opportunity if they are not taught how to solve a problem they failed to answer.
- Disengagement. Students may disengage from the learning activity when they get stuck too long trying to solve a problem.
Therefore, allow students to request for worked solutions if they tried to answer a problem and requested help, but were still unable to solve it. The worked solution should show each step in the solution process that starts with the given problem until it is solved. Each step should be explained clearly so students understand how the result of one step relates to the next step. Students may have a better chance of understanding the process and applying it to similar problems if they understand the process. Students may learn more from a worked solution because: (a) they are familiar with the problem (as they already tried to solve it), (b) they may be able to figure out what step they did incorrectly or did not perform, and (c) concise worked solutions guide student learning and do not introduce extraneous information that may cause additional cognitive load. Students may feel a sense of accomplishment when they recognize the steps they performed in the worked solution. There may be more than one way to solve a problem, but it may be a good idea to present only one worked solution at a time to avoid confusion. Consider using the One Concept Several Implementations design pattern by presenting different worked solutions for different variations of a problem so students become aware of different ways to solve it.
- Worked solutions may help students acquire or relearn knowledge, which they can organize and store in long-term memory for later retrieval.
- Providing clear explanations in the worked solution will help learners understand and apply what they learned to solve similar problems in the future
- Worked solutions may help students get unstuck from the current problem. Understanding the solution may also help them avoid getting stuck on similar problems in the future.
- Students may overlook critical information in the worked solution unless they are highlighted
- Content creators will need to create a worked solution for each problem they create.
- Students may miss a learning opportunity when they ask for worked solutions too soon because the worked solution gives away the answer.
- Students might not learn how to construct solutions on their own if they are used to having worked solutions.
- Students may get the impression that a particular worked solution is the only way to solve the problem unless otherwise specified (e.g., explicitly stating there are other solutions, showing other solutions in other problems, asking students to compare their answers with their peers who might have used a different solution).
- Learners need to recognize and understand the solution before they are able to apply it
- Several studies were conducted to compare the effects of various feedback types on learning such as no feedback, knowledge of response, knowledge of correct response, and elaborate feedback. Many of these studies reported that elaborate feedback resulted in higher learning gains.
- Worked solutions can help students recall previously acquired knowledge or help them acquire new knowledge that they can use to solve similar problems in the future.
- Worked solutions can help students learn concepts effectively by reducing unnecessary cognitive load from extraneous information.
- Students can assess their knowledge-gaps more accurately when they try to solve problems before they receive instruction, which may also help prepare them for future learning.
Data was collected from the ASSISTments online learning system between September 2012 and September 2013. One of the features in the data set was students’ average frustration, which described how likely students experienced frustration while answering a problem in ASSISTments. Student frustration was predicted by an affect detector using features like the number of previous incorrect answers, time taken to solve problems, and number of hint requests. An analysis of frustration instances in the ASSISTments data set showed that some problems were more challenging than others based on the small number of students who answered it correctly. The analysis also revealed an interesting behavior wherein some students continually requested for hints until it showed them the solution and the correct answer, paused for a moment, submitted the correct answer, then moved on to the next problem. The next time these students encountered a similar problem, they answered it correctly on the first attempt. Students’ usage of hints, when taken together, resembled a worked solution. This may indicate students’ preference to learn from worked solutions, and its positive effects on their learning. More details about the data used, the methodology used for analysis, and the results are presented in.
The Explain Worked Solutions design pattern closely resembles the Worked Examples design pattern, but provides the answer to the current problem solved by the student. The Explain Worked Solutions design pattern can be used with the Try It Yourself design pattern to provide students with learning support while they answer problem-solving activities that promote better understanding of a given topic. Encoding worked solutions for problem variations may be tedious to write. Content creators may use the Mastery Learning Exercise Generator and Mastery Learning Templates design patterns to generate worked solutions automatically. It may be good idea to delay the presentation of worked solutions until students have attempted to solve the problem or tried to request basic hints as described in the Increasing Hint Specificity design pattern. The Image-Enhanced Hint design pattern. can be used to clarify worked solutions. If applicable, remember to implement the One Concept Several Implementations design pattern to make students aware of other solutions that may solve the problem.
Many math textbooks and workbooks provide worked solutions in the back of the book so students can check their answers and see the correct solution. Several learning systems also provide students with worked solutions when they are unable to solve the problem such as ASSISTments and SQL-Tutor. ASSISTments, in particular, uses a variety of mediums to present worked solutions such as text and image explanations, video explanations, or short video lectures.
Figure 1 illustrates a worked solution for a math problem about solving the sum of interior angles of triangles. The relevant concepts and the steps in the solution are explained so students can understand the process more easily. A better understanding of the problem and solution may enable them to apply this knowledge to similar problems.
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