## Case Study: Effects of Question Paraphrasing ### Overview The image presents a case study examining the effects of question paraphrasing on problem-solving. It compares the solution process for an original question and a paraphrased version of the same question. The problem involves calculating the number of rounds Jane played in a game, given her points earned and lost. ### Components/Axes The image is divided into two main sections: 1. **Original Question:** Presents the initial problem statement and its step-by-step solution. 2. **Paraphrased Question:** Presents a reworded version of the problem and its corresponding solution. Each section includes: * **Question:** The problem statement. * **Response:** A step-by-step breakdown of the solution. * **Ground Truth Answer:** The correct answer to the problem (8). * A checkmark or X indicating if the solution is correct. ### Detailed Analysis **Original Question:** * **Question:** "In a card game, you are awarded 10 points if you win one round. While playing, Jane ends up with 60 points. If she lost 20 points, then how many rounds did she play? (ground truth answer: 8)" * **Response:** * Step 1: "Determine the total points Jane earned by subtracting the points she lost from her final score. Total points earned = Final score - Points lost. Total points earned = 60 - 20. Total points earned = 40." * Step 2: "Since Jane earns 10 points for each round she wins, we can find the number of rounds she played by dividing the total points earned by the points earned per round. Number of rounds = Total points earned / Points earned per round. Number of rounds = 40 / 10. Number of rounds = 4." * Conclusion: "Therefore, Jane played 4 rounds." (Marked with an "X", indicating an incorrect answer) **Paraphrased Question:** * **Question:** "At a bridge competition, every game won grants the player 10 points. Unfortunately, Jane started with an advantage but ended up losing 20 points and scoring only 60 points. If she had won x rounds and lost none, what would be the value of x? (ground truth answer: 8)" * **Response:** * Step 1: "Understand the given information. Jane started with an advantage but ended up losing 20 points. She scored a total of 60 points. Every game won grants the player 10 points." * Step 2: "Determine the total points Jane would have had if she hadn't lost any points. Since she lost 20 points, we need to add 20 to her total score to find out how many points she would have had if she hadn't lost any points. Total points without loss = 60 + 20 = 80 points." * Step 3: "Calculate the number of games Jane won. Since every game won grants the player 10 points, we can divide the total points without loss by 10 to find the number of games she won. Number of games won = Total points without loss / 10 = 8. The number of games she won is equal to 8." (Marked with a checkmark, indicating a correct answer) ### Key Observations * The original question's solution incorrectly calculates the total points earned by subtracting the points lost from the final score, leading to an incorrect number of rounds played (4). * The paraphrased question's solution correctly calculates the total points without loss by adding the points lost to the final score, leading to the correct number of games won (8). * The ground truth answer is 8 for both questions. ### Interpretation The case study demonstrates that question paraphrasing can significantly impact problem-solving accuracy. The original question's wording may have led to a misunderstanding of how to calculate the total points earned, resulting in an incorrect solution. The paraphrased question, by explicitly stating that Jane started with an advantage and lost points, guided the solver to correctly calculate the total points without loss and arrive at the correct answer. This highlights the importance of clear and unambiguous question wording in problem-solving contexts.