## Textual Document: Case Study on the Effects of Question Paraphrasing ### Overview The image presents a side-by-side comparison of two versions of a word problem – an original question and a paraphrased question – along with their respective solution steps. The document also indicates the "ground truth" answer for both problems is 8. Each problem's solution is followed by a visual indicator (a red 'X' or a green checkmark) signifying whether the provided solution is correct. ### Components/Axes The document is structured into two columns. Each column contains: 1. A question (labeled "Original question:" or "Paraphrased question:") 2. A statement of the "ground truth answer" 3. A "Response:" section detailing the solution steps. 4. A visual indicator of solution correctness. ### Detailed Analysis or Content Details **Original 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)" **Original Question 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. Therefore, Jane played 4 rounds. (Marked with a red 'X') **Paraphrased 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)" **Paraphrased Question 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 green checkmark) ### Key Observations * The original question's solution is incorrect, while the paraphrased question's solution is correct. * The paraphrased question uses more complex language ("advantage," "x rounds") compared to the original question. * The original question focuses on rounds played, while the paraphrased question focuses on games won. * The visual indicators (X and checkmark) clearly denote the correctness of each solution. ### Interpretation This document demonstrates the impact of question paraphrasing on problem-solving accuracy. The original question, while simpler in wording, leads to an incorrect solution (4 rounds). The paraphrased question, despite being more complex, guides the solver towards the correct answer (8 games won). This suggests that the way a question is framed can significantly influence a person's ability to understand and solve it. The paraphrasing appears to clarify the underlying mathematical relationship, leading to a more accurate result. The use of 'x' in the paraphrased question may encourage a more algebraic approach, which is appropriate for the problem. The document serves as a case study highlighting the importance of careful question design and the potential pitfalls of ambiguous or poorly worded problems. The red 'X' and green checkmark provide a clear visual assessment of the solution's validity, reinforcing the learning objective.