Question

question 1-6
passage 2: drill practice for mathematical literacy
1 there is currently a heated debate among teachers and educators about the best way to teach math to students. on one side, proponents are reared practice, or \drills.\ are thought to create the strongest math students. on the other side, there is problem-solving based instruction in which students take a mathematical concept and apply it to a real-world issue, thus going into more depth with the concept to solve the problem.
2 arguments are strong on both sides, but it is clear that drill and practice are the essential building blocks for a student to achieve mathematical fluency.
3 with problem-solving based instruction, students may be thrust into a complex problem and be expected to have enough math knowledge to apply it to the situation. without repeated practice, a student can become overwhelmed by the complexity of the task itself.
4 additionally, students can waste valuable time computing answers to simple problems, such as multiplication or division, and make little to no progress on solving the more complex problems because they are tied up doing calculations. for example, if students are using the subtraction method to do a division problem instead of knowing their division facts, they may fall behind the others working the problem who already know their facts. many students just \give up\ at this point. when students have repeated drill and practice with, for example, multiplication and division facts, they are quick and accurate in doing calculations. it frees up mental space to focus their efforts on more complex problems.
5 furthermore, having ample practice time is crucial for students who have trouble grasping mathematical concepts. there are some students who need the structure and predictability of doing exercises found in drills. in problem - solving based instruction, students can get lost and cannot
read the following excerpt from passage 2, paragraph 7:
the results of a 2017 survey found that the unit ranked 38th out of 71 countries in math. with th push to make problem - solving based curriculum instruction for schools, it’s clear that this form o is not doing much to help our students and very contributing to our country’s mathematical illitei
how does the use of fallacious reasoning weaken the author’s argument about math instruction?
after referring to recent changes, the author presents a direct link between the survey data and student outcomes.
after identifying the surveyed students, the author explains the data does not reflect drill and practice outcomes.
after providing a context for understanding the math data, the author says the outcomes reflect problem - solving instruction.
after citing the outcomes of a survey, the author leaps to make a larger generalization than the data indicates.

Explanation:

To determine how fallacious reasoning weakens the argument, we analyze each option:

• Option 1: The author doesn't present a direct link; instead, they make a hasty generalization.
• Option 2: The author doesn't explain the data not reflecting drill/practice outcomes.
• Option 3: The author says the outcomes reflect problem - solving instruction being ineffective, but the fallacy is about over - generalizing, not this.
• Option 4: The author cites a 2017 survey (the US ranked 38th in math) and then leaps to the conclusion that problem - solving based curriculum is not helping and contributing to illiteracy. The survey data alone doesn't fully support such a broad and direct conclusion about the curriculum's ineffectiveness (there could be other factors affecting math performance), so this is a hasty generalization (fallacious reasoning) where the author makes a larger generalization than the data indicates.

Answer:

After citing the outcomes of a survey, the author leaps to make a larger generalization than the data indicates.