How to teach a child advance math.

[wasab]

I would like to teach my 10 year old sister advance math. (she is currently in 5th grade).

 

My plan is to have her learn the prerequisite like basic algebraic operations, elementary number theory, as well as elementary geometry and trig to prepare her for high school math. After that, I will have her learn High school algebra, high school geometry, high school algebra II and trigonometry. After that, i will get my dusty college books off my closet and start teaching her derivative calculus, integral calculus, multivariable calculus, discrete mathematics, linear algebra, and differential equations. The pace depends on how well she is learning the materials but i hope that she will master the prerequisite for high school level math bfeore middle school and all high school level subjects before 8th grade then i will start teaching her college level materials from there.

 

I spoke with my parents and they agree to this madness. My sister may not like it but she is quite bright and i believe she can certainly do it. I am now thinking whats the best way to go about doing this. Right now i am just thinking getting a blackboard and a marker and then spend one hour explaining concepts and go over examples and afterwards assigning her exercises for her to finish. That pretty much means tutoring her daily. I can find more time during my spring break and summer. 

 

Is that the correct way to go about it? I do not have much experience teaching anyone so if you happen to be a professional educators, I would like to hear your thoughts. 

[Guest]

I think starting with basic algebra is a great way to start. Algebra itself is very simple. Just find X. 

 

X= 5

17+5=X

so on. 

Then in American School, we progressed through several levels of algebra. Then did geometry. Then Algebra &trigpnometry, then precalculus, then the various levels of calculus. You can branch offf to do linear algebra or differential equations at some point in your calculus experience. I stopped after algebra and trigonometry so I don’t know how the rest goes. 

[dalekphalm]

1 hour ago, wasab said:

I would like to teach my 10 year old sister advance math. (she is currently in 5th grade).

 

My plan is to have her learn the prerequisite like basic algebraic operations, elementary number theory, as well as elementary geometry and trig to prepare her for high school math. After that, I will have her learn High school algebra, high school geometry, high school algebra II and trigonometry. After that, i will get my dusty college books off my closet and start teaching her derivative calculus, integral calculus, multivariable calculus, discrete mathematics, linear algebra, and differential equations. The pace depends on how well she is learning the materials but i hope that she will master the prerequisite for high school level math bfeore middle school and all high school level subjects before 8th grade then i will start teaching her college level materials from there.

 

I spoke with my parents and they agree to this madness. My sister may not like it but she is quite bright and i believe she can certainly do it. I am now thinking whats the best way to go about doing this. Right now i am just thinking getting a blackboard and a marker and then spend one hour explaining concepts and go over examples and afterwards assigning her exercises for her to finish. That pretty much means tutoring her daily. I can find more time during my spring break and summer. 

 

Is that the correct way to go about it? I do not have much experience teaching anyone so if you happen to be a professional educators, I would like to hear your thoughts. 

Just out of curiosity, is there a particular reason you're trying to teach your 10 year old sister high school math concepts before she even enters middle school?

 

If she's actually Mensa level genius, sure, but if that's the case, she'll pick up a lot of it on her own.

 

I certainly wouldn't advocate for daily 1 hour long tutoring sessions.

 

Does your sister even have a particular interest in advanced mathematics?

[wasab]

7 minutes ago, dalekphalm said:

Just out of curiosity, is there a particular reason you're trying to teach your 10 year old sister high school math concepts before she even enters middle school?

 

If she's actually Mensa level genius, sure, but if that's the case, she'll pick up a lot of it on her own.

 

I certainly wouldn't advocate for daily 1 hour long tutoring sessions.

 

Does your sister even have a particular interest in advanced mathematics?

well, it's because we wish to home school her on math. American public school system is very slow in teaching mathematics. My parents are immigrants and they said the American public high school are teaching what they were learning in middle school so we do not believe my sister is being challenge enough. 

 

Plus, even if she struggles, which i doubt she will because she is quite bright(perfect marks on everything), she will have exposure to these materials so when she learns in the public school system, it will be a cake walk for her. Education isn't merely up to the school teachers. Children should be learning at home as well. 

 

 

[wasab]

19 minutes ago, fpo said:

I think starting with basic algebra is a great way to start. Algebra itself is very simple. Just find X. 

 

X= 5

17+5=X

so on. 

Then in American School, we progressed through several levels of algebra. Then did geometry. Then Algebra &trigpnometry, then precalculus, then the various levels of calculus. You can branch offf to do linear algebra or differential equations at some point in your calculus experience. I stopped after algebra and trigonometry so I don’t know how the rest goes. 

yeah i know, i attended American high school myself. I know the curriculum. In fact, i have all the old tests and homework. I can use these to figure out what materials to teach her and questions to go over. My only question is how to effectively teach the materials. should i just follow the general method of have her watch how i do it and then have her do it herself? 

[Ithanul]

If she interested in any hobbies that use math or fields, sure, teach her some of the higher Math like Algebra and Trig.   Otherwise, could be a huge waste of time.  Math is not a bad subject to learn, but the higher stuff can be questionable to learn considering not all jobs utilize it or just use a computer to do the hard stuff faster.

 

Myself, have a basic associate CS.  Took college level Algebra and Trig, don't use one lick of it at work; instead, I do use it in my hobbies like HAM radio and building stuff, so the Algebra basics help out there.

[dalekphalm]

2 minutes ago, wasab said:

well, it's because we wish to home school her on math. American public school system is very slow in teaching mathematics. My parents are immigrants and they said the American public high school are teaching what they were learning in middle school so we do not believe my sister is being challenge enough. 

 

Plus, even if she struggles, which i doubt she will because she is quite bright(perfect marks on everything), she will have exposure to these materials so when she learns in the public school system, it will be a cake walk for her. Education isn't merely up to the school teachers. Children should be learning at home as well. 

 

 

Well if that works for you, certainly.

 

But I would be very hesitant to force this upon her, at least, beyond small amounts. Start with once a week, and if that works out, increase the amount slowly, until you hit an equilibrium. That equilibrium could be 5 days a week, 7, or 3, or none (worst case).

[Guest]

Then that’s what I’d do. Just one class at a time until she gets it. 

 

I think it mostly takes practice and a good explanation of every step. 

 

I was told that 2nd graders (7-8 year olds) started doing basic algebra (which was first introduced in 7th grade to me. 12-13) I hope i helped. I’m not a teacher so I did the best I could with what i know. I want to teach my kids high level math too when I get some. Another bright kid I met just read math textbooks for fun in his free time. 

[Ithanul]

Just now, fpo said:

Then that’s what I’d do. Just one class at a time until she gets it. 

 

I think it mostly takes practice and a good explanation of every step. 

 

I was told that 2nd graders (7-8 year olds) started doing basic algebra (which was first introduced in 7th grade to me. 12-13) I hope i helped. I’m not a teacher so I did the best I could with what i know. I want to teach my kids high level math too when I get some. Another bright kid I met just read math textbooks for fun in his free time. 

Darn, 2nd grade now?  I remember only being introduce to multiplying and division in 4th grade.  Then again, each public school is different.

 

Myself, I don't really plan to have kids, but if I did have one or two, I teach them Math that can be used in applications such as building with wood, metal, or electronics (not just have them do numbers on paper, but actually applying it in life).

[wasab]

13 minutes ago, dalekphalm said:

Well if that works for you, certainly.

 

But I would be very hesitant to force this upon her, at least, beyond small amounts. Start with once a week, and if that works out, increase the amount slowly, until you hit an equilibrium. That equilibrium could be 5 days a week, 7, or 3, or none (worst case).

yeah, i will go slow and a little at a time. The pace all depends on her really.

 

15 minutes ago, Ithanul said:

If she interested in any hobbies that use math or fields, sure, teach her some of the higher Math like Algebra and Trig.   Otherwise, could be a huge waste of time.  Math is not a bad subject to learn, but the higher stuff can be questionable to learn considering not all jobs utilize it or just use a computer to do the hard stuff faster.

 

Myself, have a basic associate CS.  Took college level Algebra and Trig, don't use one lick of it at work; instead, I do use it in my hobbies like HAM radio and building stuff, so the Algebra basics help out there.

no, it isn't about preparing her for a job. I am not even sure if she is interested in math and or what she would like to pursue as an occupation as she grows up 

 

what I am sure is that she will be learning these, especially high school math, regardless what occupation interests her and making sure she is academically competent and prepared for it is the goal. Also, calculus recently has been like a general requirement in most universities regardless if you are majoring in rocket nuclearing or underwater basket weaving. Its purpose is also to develop critical thinking and problem solving. 

[Guest]

16 minutes ago, Ithanul said:

Darn, 2nd grade now?  I remember only being introduce to multiplying and division in 4th grade.  Then again, each public school is different.

 

Myself, I don't really plan to have kids, but if I did have one or two, I teach them Math that can be used in applications such as building with wood, metal, or electronics (not just have them do numbers on paper, but actually applying it in life).

I learned division and multiplication in 4th grade (8/9 years old) 

but from the beginning with basic algebra you can do it with addition and subtraction. Only difference is that you just put x after the equal sign. 

In elementary school i’d Get problems like this:

 

5+6=

 

to make it algebra you just add an x after the equal sign  

[Ithanul]

6 minutes ago, wasab said:

yeah, i will go slow and a little at a time. The pace all depends on her really.

 

no, it isn't about preparing her for a job. I am not even sure if she is interested in math and or what she would like to pursue as an occupation as she grows up 

 

what I am sure is that she will be learning these, especially high school math, regardless what occupation interests her and making sure she is academically competent and prepared for it is the goal. Also, calculus recently has been like a general requirement in most universities regardless if you are majoring in rocket nuclearing or underwater basket weaving. Its purpose is also to develop critical thinking and problem solving. 

Then probably best to just ask her.  Yeah, she is ten, but she should have something that has her attention or interest.  Something that can be used as a stepping stone in teaching.

 

Not all Universities are equal in curriculum.  In one that I went to, not one lick of calculus was required for the Bachelors but Speech and writing was a big deal.  The second one I went to, there was pre-cal in the Algebra and Trig, but was not a big focus at all (hardly any of the calculus was taught); instead, writing and speeches where the big deal along with small debating and idea sharing.  Now, there where degrees with Calculus as a requirement, but not all degrees required it.

[Ithanul]

6 minutes ago, fpo said:

I learned division and multiplication in 4th grade (8/9 years old) 

but from the beginning with basic algebra you can do it with addition and subtraction. Only difference is that you just put x after the equal sign. 

In elementary school i’d Get problems like this:

 

5+6=

 

to make it algebra you just add an x after the equal sign  

Yeah, that usually the first way of introducing the use of a variable.  Then again, my parents bought this device that had Math problems in it (had problems all the way to doing Ratios).  Even though I was like eight when I had it, I thought thing was a toy and just messed with it for hours (somehow in messing with it, I figured out how to do the Ratio problems, but was still crappy at doing the division ones).  Though, the school also had those fun little computer games that had us solve Math problems.  So, maybe the OP can make a Math game to grab her attention.

[Guest]

11 minutes ago, Ithanul said:

Yeah, that usually the first way of introducing the use of a variable.  Then again, my parents bought this device that had Math problems in it (had problems all the way to doing Ratios).  Even though I was like eight when I had it, I thought thing was a toy and just messed with it for hours (somehow in messing with it, I figured out how to do the Ratio problems, but was still crappy at doing the division ones).  Though, the school also had those fun little computer games that had us solve Math problems.  So, maybe the OP can make a Math game to grab her attention.

That’s a great idea!!! 

 

I had this “lead frog” thing. It had games you could load and you use the book with the electronics to play learning games like math, or reading. 

 

I don’t know if your sister is “too old for toys” (I’m not. I love fidget spinners :P) but a lot of toy stores like “Toys R Us” have learning toy sections with age appropriate numbers listed on the boxes. 

[Guest]

I’m a fan of the YouTube series, Khan Academy. If one vetts it first, it can be a valuable tool for anyone learning (or teaching) math and/or science and/or ...

 

Just my 2 cents...

[Canada EH]

Just show her how to use Youtube

and its best to get them taught young, especially languages like speech languages not code

[wasab]

40 minutes ago, Canada EH said:

Just show her how to use Youtube

and its best to get them taught young, especially languages like speech languages not code

youtube is good at introducing concept but practices are what really reinforces mastery. I am going to have her work example problems step by step. 

 

i wont be trying to confuse her too much with theories and everything. I will just show her the steps in the algebras and calclations. If shes interested in the theorems and proves, i guess i can teach it to her. 

 

I know pretty well what to teach for high school materials. Middle school prerequisite however, i am a bit vague. I believe it is mainly algebraic expressions involving decimals, inequality, fractions, integers(negative and positive), percentage, graphing method using tables and so on. There can be some basic trig like hypotenuse theorem and tangent, sin, cosine represented as right angles. basically, pre-algebra stuffs. I can go over them in  3 months plus summer quite quick. By the time she attends middle school, she can just jump straight into algebra. She can learn that in half a school year i am pretty sure(heck, i myself learn it in 8th grade in just 2 month and a half. My middle school does this early NY regent examination for qualified students) 

 

High school materials i have pretty good ideas. Radicals, linear equations , system of equations, quadratics ect. 

Geometry would be angle formulas, formula of circle, ovals, right angles, ect plus some basic logic in the beginning like mollus peons and contrapostive I think, which will be cover more rigorously in college level discrete mathematics. 

 

 

Trig and algebra II are also straight forward. mainly algebras involving higher degree polynomials, square root of negatives/complex numbers operations, trig as represented by unit circle, trig equations, inverse trig functions, trig identities, ect. 

 

I am not going to teach pre calculus. Things learned there like matrices, asymptomatic functions, and polar graphs will be cover in differential and integral calculus anyhow. Vectors, scalars, and cross product multiplication will be cover in multivariable calculus and college level linear algebra in similar fashion. 

 

Those are what i can recall from the top of my head. I will check the US common core standards to make sure all appropriate subjects are covered. 

Perhaps i can also sneak in sciences in there like classical physics mechanics and electromagnetism but expecting her to understand all that would be a bit too opportunistic. I am going to start teach this Friday after searching what materials i need go over. 

 

[Tsuki]

im gonna be honest, i'd suggest against doing this.

 

They teach things differently in schools than they used to.  if you teach her how to do it the way you learned it, then when she gets to that point in school and they try to teach her a different way, its going to confuse the fuck out of her and can actually cause problems.

 

"yea you got the answer right but your work is all wrong because we want you to do it this way instead"

 

thats why i stopped helping my kids with math(unless the exact directions are on the worksheet), i can teach them how i learned, which is easier and faster, but its not the way the teachers want them to do it.