What is a good way to learn the fundamentals of math?
September 2, 2018 11:02 AM Subscribe
I want real problem solving skills development for my niece.
I was always horrible at math, but I also had terrible education. I learned only memorization. As in memorizing the times table, etc. So I never really figured out how to truly problem solve. I'd like to help tutor my niece (6 years old) when she stays with me, but I only know the way I was taught.
I have heard of things called "singapore math" and "common core math" and "number sense" etc... But which is the best technique to REALLY learn math rather than just memorizing things?
I was always horrible at math, but I also had terrible education. I learned only memorization. As in memorizing the times table, etc. So I never really figured out how to truly problem solve. I'd like to help tutor my niece (6 years old) when she stays with me, but I only know the way I was taught.
I have heard of things called "singapore math" and "common core math" and "number sense" etc... But which is the best technique to REALLY learn math rather than just memorizing things?
In my opinion the heart of math is two things:
1) Understanding *why* things work. At the higher levels this means proofs, etc. At her level its understanding the ideas behind basic operations, like that addition is taking groups of similar things which you have counted and knowing how many things they make if you put them together as a single large group, subtraction is taking a certain number of things out of a group, multiplication is basically repeated addition, and division is breaking a big group into smaller sub groups and figuring out how many things are in each group (or deciding how many things should be in each subgroup and then asking how many subgroups you have). When my kids were young I discovered the Hershey Fraction Book was a fun intro to fractions that you can do with actual candy bars, and helped explain how fractions can be viewed as parts of a whole, and how those parts can combine.
So for a six year old, counting on your fingers, actually *counting* to add or subtract is actually a good thing, because it emphasizes the meaning of the operations. Later when you get to working with multi-digit numbers you want to emphasize how the digits in the numbers are powers of 10, larger powers as you go left, smaller powers as you go right, which is why, for instance, when you add in a column and get a result larger then 10, the 10 digit "carries" into the next column to the left, or when you subtract and your upper digit is less then the lower one you can "borrow" 10 from the digit to the left. Similarly, if you should get to decimals with your niece (I don't know whether we're talking days or years here) you can emphasize how the pattern continues with fractions of powers of 10 to the right of the decimal.
2) Becoming fluent with the operations. This is where memorization is helpful, since it allows you to perform these operations nearly effortlessly. Memorization without understanding is not great, but understanding without memorization isn't great either, since every problem is a struggle. For single digit addition and subtraction and memorizing times tables I'd give my kids a teacup or a small bowl, and get a bag of M&M's or Hershey's kisses or other similar small candy and put one in their teacup for each problem they got right (as we went through flash cards or whatever), with the stipulation that they couldn't eat their candies until they got at least 10. They found the candies, and just the idea of being rewarded fun.
Anyhow, I'm not an expert in math education theory for young kids, just a dad and a math tutor at the high school and college level, but that's been my experience in a nutshell.
posted by Reverend John at 11:55 AM on September 2, 2018 [3 favorites]
1) Understanding *why* things work. At the higher levels this means proofs, etc. At her level its understanding the ideas behind basic operations, like that addition is taking groups of similar things which you have counted and knowing how many things they make if you put them together as a single large group, subtraction is taking a certain number of things out of a group, multiplication is basically repeated addition, and division is breaking a big group into smaller sub groups and figuring out how many things are in each group (or deciding how many things should be in each subgroup and then asking how many subgroups you have). When my kids were young I discovered the Hershey Fraction Book was a fun intro to fractions that you can do with actual candy bars, and helped explain how fractions can be viewed as parts of a whole, and how those parts can combine.
So for a six year old, counting on your fingers, actually *counting* to add or subtract is actually a good thing, because it emphasizes the meaning of the operations. Later when you get to working with multi-digit numbers you want to emphasize how the digits in the numbers are powers of 10, larger powers as you go left, smaller powers as you go right, which is why, for instance, when you add in a column and get a result larger then 10, the 10 digit "carries" into the next column to the left, or when you subtract and your upper digit is less then the lower one you can "borrow" 10 from the digit to the left. Similarly, if you should get to decimals with your niece (I don't know whether we're talking days or years here) you can emphasize how the pattern continues with fractions of powers of 10 to the right of the decimal.
2) Becoming fluent with the operations. This is where memorization is helpful, since it allows you to perform these operations nearly effortlessly. Memorization without understanding is not great, but understanding without memorization isn't great either, since every problem is a struggle. For single digit addition and subtraction and memorizing times tables I'd give my kids a teacup or a small bowl, and get a bag of M&M's or Hershey's kisses or other similar small candy and put one in their teacup for each problem they got right (as we went through flash cards or whatever), with the stipulation that they couldn't eat their candies until they got at least 10. They found the candies, and just the idea of being rewarded fun.
Anyhow, I'm not an expert in math education theory for young kids, just a dad and a math tutor at the high school and college level, but that's been my experience in a nutshell.
posted by Reverend John at 11:55 AM on September 2, 2018 [3 favorites]
I'll second Family Math. Especially because you're working with her intermittently, it has a lot of options for activities that don't require a daily commitment to build on.
The Critical Thinking Company offers a lot of affordable workbooks that focus on mathematical reasoning rather than calculation per se. I've used them a lot with my kids, some of whom found them really fun and some of whom didn't care for them at all.
My kids also really like TOPS modules. They are also very affordable, and teach math and science with things you can find around the house (though you can also buy the materials through the site. My kids love the hands-on activities. Double-checking, I see that they don't offer anything that is math per se until older grades, but I'll mention it anyway because fun! And even the most basic science modules include elements like forming a hypothesis and keeping data. And they're fun. So fun.
posted by Orlop at 1:13 PM on September 2, 2018 [1 favorite]
The Critical Thinking Company offers a lot of affordable workbooks that focus on mathematical reasoning rather than calculation per se. I've used them a lot with my kids, some of whom found them really fun and some of whom didn't care for them at all.
My kids also really like TOPS modules. They are also very affordable, and teach math and science with things you can find around the house (though you can also buy the materials through the site. My kids love the hands-on activities. Double-checking, I see that they don't offer anything that is math per se until older grades, but I'll mention it anyway because fun! And even the most basic science modules include elements like forming a hypothesis and keeping data. And they're fun. So fun.
posted by Orlop at 1:13 PM on September 2, 2018 [1 favorite]
Kahn, for you to do to make sure you're using contemporary methods. Do the lessons for the same grade she's in, or a few grades ahead, including watching the videos.
posted by The corpse in the library at 2:55 PM on September 2, 2018 [4 favorites]
posted by The corpse in the library at 2:55 PM on September 2, 2018 [4 favorites]
I think what you want is the Art of Problem Solving. Highly recommended!
posted by peacheater at 2:56 PM on September 2, 2018 [2 favorites]
posted by peacheater at 2:56 PM on September 2, 2018 [2 favorites]
Vi Hart has a series of fun math videos. Many will be over the head of a 6 year old but exposure to a cool young lady who enjoys math and sees much beauty in it is probably a good thing.
posted by SaltySalticid at 11:27 PM on September 2, 2018 [1 favorite]
posted by SaltySalticid at 11:27 PM on September 2, 2018 [1 favorite]
This is a commendable goal but I fear the answer is it depends on the method your niece is being taught.
When we talk about number sense, that's essentially being able to quantify what six, for example, is. You can picture six--donuts or nails or hamsters--and can mentally see that. It's knowing that six will be more than four, and that ten is when you put them both together, and that a billion is super gigantic. Number sense is valuable for all of us, so when we're being consumers and the car we want is $45,000 but our budget is $12,000, we know that's far too large a gap in numbers to make work. Everyone needs number sense.
Common core math--which is NOT used in every US state-- are the mathematical standards of what all US students are expected to know. Not all states have adopted these and not all math teachers agree these standards are useful. But it's not an actual curriculum, which leads me to:
Singapore Math. This IS a content-based curriculum and (opinion here) it's completely amazing because it's model-based. Instead of the Everyday Math model where students cycle in a helix-like fashion with an endless amount of drill and kill worksheets, SM focuses on a few mathematical concepts that students master. While it seems to move more slowly than standard US math, kids learn the material far more deeply--essentially, it uses number sense.
So the best way to help your niece is to find out more about the curriculum being used, and learn about that. Millions of adults know too well the screeching of, "But that's not the way they TAUGHT it!!" and then everyone ends up hating math. Khan Academy will also be super helpful to you and your niece because they have interesting videos that explain multiple mathematical methods.
posted by yes I said yes I will Yes at 4:01 AM on September 3, 2018 [2 favorites]
When we talk about number sense, that's essentially being able to quantify what six, for example, is. You can picture six--donuts or nails or hamsters--and can mentally see that. It's knowing that six will be more than four, and that ten is when you put them both together, and that a billion is super gigantic. Number sense is valuable for all of us, so when we're being consumers and the car we want is $45,000 but our budget is $12,000, we know that's far too large a gap in numbers to make work. Everyone needs number sense.
Common core math--which is NOT used in every US state-- are the mathematical standards of what all US students are expected to know. Not all states have adopted these and not all math teachers agree these standards are useful. But it's not an actual curriculum, which leads me to:
Singapore Math. This IS a content-based curriculum and (opinion here) it's completely amazing because it's model-based. Instead of the Everyday Math model where students cycle in a helix-like fashion with an endless amount of drill and kill worksheets, SM focuses on a few mathematical concepts that students master. While it seems to move more slowly than standard US math, kids learn the material far more deeply--essentially, it uses number sense.
So the best way to help your niece is to find out more about the curriculum being used, and learn about that. Millions of adults know too well the screeching of, "But that's not the way they TAUGHT it!!" and then everyone ends up hating math. Khan Academy will also be super helpful to you and your niece because they have interesting videos that explain multiple mathematical methods.
posted by yes I said yes I will Yes at 4:01 AM on September 3, 2018 [2 favorites]
Seconding that whatever you do for number games and out-of-class learning, make sure you know what kinds of things she's learning in school, and how she's being taught to do them. If one of the things the kid takes away is that "Uncle/Auntie Fantasticness says the way the teacher is showing us is dumb" then this is not going to help their math growth as much as if you can supplement in ways that help them be proficient in class. Half of liking math is feeling like you're succeeding, and the easiest way to start hating it is getting repeatedly told you're doing it wrong.
posted by aimedwander at 7:43 AM on September 4, 2018 [2 favorites]
posted by aimedwander at 7:43 AM on September 4, 2018 [2 favorites]
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posted by puddledork at 11:48 AM on September 2, 2018 [2 favorites]