3 ms·

What’s the alternative? How does a neophyte go about cultivating the mindset and understanding you describe?

rawgabbit 4y ago
Unfortunately, I don't have an easy answer. My son recently graduated from my high school and I noticed that while his school used Pearson's website to drill him on the mechanics. My son struggled with word problems precisely because he did not have the fundamental concepts. For example, I argued that division is more intuitive when we multiply using fractions. - Whole numbers have an implicit denominator of one. E.g., 7 is equal to 7/1. - It is more intuitive to think of division as multiplying by fractions. E.g., 7/2 is equal to (7/1) x (1/2). We multiply the numerators together. And multiply the denominators together. - Where this is helpful is when we deal with complex arithmetic like (7/2)/2. We have 7 pizzas. Divide by 2. And divide by 2 again. If you break it into fractions, this is equal to (7/1) x (1/2) x (1/2). The numerator is 7x1x1. While the denominator is 1x2x2. Putting it together, it is (7x1x1) / (1x2x2) which is equal to 7/4. This discussion usually leads to the question of what is multiplication (again)? I argued that multiplication can be thought of as a shortcut for addition or can be thought of as set theory. I have two bags of marbles and each bag contains 10 marbles each. How many marbles do I have? You can either write 10+10 (multiplication as a shortcut for addition) or you can write 2x10 (set theory). Taking it back to division. I have two bags of marbles and each bag contains 10 marbles and I have to share my marbles with my sibling (divide by two), how many marbles do I have?. You can write either (10+10)/2 or you can write 2 x 10 x (1/2).
mattwilsonn888 4y ago
This person describes an experience similar to the one which inspired my mindset. https://news.ycombinator.com/threads?id=As_You_Wish https://news.ycombinator.com/threads?id=As_You_Wish

Unfortunately, I don't have an easy answer. My son recently graduated from my high school and I noticed that while his school used Pearson's website to drill him on the mechanics. My son struggled with word problems precisely because he did not have the fundamental concepts. For example, I argued that division is more intuitive when we multiply using fractions. - Whole numbers have an implicit denominator of one. E.g., 7 is equal to 7/1. - It is more intuitive to think of division as multiplying by fractions. E.g., 7/2 is equal to (7/1) x (1/2). We multiply the numerators together. And multiply the denominators together. - Where this is helpful is when we deal with complex arithmetic like (7/2)/2. We have 7 pizzas. Divide by 2. And divide by 2 again. If you break it into fractions, this is equal to (7/1) x (1/2) x (1/2). The numerator is 7x1x1. While the denominator is 1x2x2. Putting it together, it is (7x1x1) / (1x2x2) which is equal to 7/4. This discussion usually leads to the question of what is multiplication (again)? I argued that multiplication can be thought of as a shortcut for addition or can be thought of as set theory. I have two bags of marbles and each bag contains 10 marbles each. How many marbles do I have? You can either write 10+10 (multiplication as a shortcut for addition) or you can write 2x10 (set theory). Taking it back to division. I have two bags of marbles and each bag contains 10 marbles and I have to share my marbles with my sibling (divide by two), how many marbles do I have?. You can write either (10+10)/2 or you can write 2 x 10 x (1/2).

mattwilsonn888 4y ago

This person describes an experience similar to the one which inspired my mindset. https://news.ycombinator.com/threads?id=As_You_Wish https://news.ycombinator.com/threads?id=As_You_Wish