Algebra and elementary-age kiddos

[Mrs.Mom]

Hi all!

 

First let me say .. I am NOT a math teacher. (I'm a high school English teacher). I love math, loved it in school. But I have learned it is the theory of math I dig ... not so much getting accurate answers. My 10-yo is exactly the same. He is brilliant in theory - a little rough on the actual execution. But all in all, doing well. So well, in fact, we are flying through the pre-algebra curriculum. We do Teaching Textbooks. I know this is not a highly-acclaimed program here... but we needed something that worked with his personality, and our style. It fits really well and works for now. Like I said, he is 10.

 

I have a good friend who is a high school math teacher, so I often go to her with my obstacles. But when I tried to talk to her about how I thought my son would struggle with these fundamental algebraic concepts and, instead, he is ZOOMING through the material (it just makes sense to him ... it's fun, challenging and it interests him... math with a purpose, in his eyes) ... my friend said to me that there is no way a 10-yo can comprehend algebra. That the maturity just isn't there.

 

So I ask my fellow homeschooling moms.... is there truth in this?

In flipping through the rest of the text and looking at the assessments online, I think we need to scrap pre-a and just get the Alg 1 book. But her comments cause me to doubt myself. She said I should give him our state 8th grade math end-of-year test before going forward.

 

I wish I understood math education as well as I understand education in language arts. I feel confident in his knowledge and aptitude in English! :) But math, I'm feeling my way through. His is a creative type ... not so much a calculating type.

Thoughts?

 

PS - we supplement with a lot of logic and critical thinking, so it is rounding him out. He has always loathed math, so finding something he enjoys and can learn with is more important than rigor at this particular junction. But... I'm open to new ways of thinking. :)

[kiana]

Rubbish. I took algebra I/II during the year I turned ten and geometry/precalc the next year and I did just fine, tyvm.

 

If he is zooming, finds it fun, challenging and interests him, let him fly! If he starts to struggle, there will be time then to drop back and find something else.

 

However, since you already own the pre-algebra and he is currently finding it fun and challenging I would go ahead and have him finish it before starting algebra. If he were bored, frustrated, and complaining about how easy it was my advice would be different.

[wapiti]

my friend said to me that there is no way a 10-yo can comprehend algebra. That the maturity just isn't there.  

 

So I ask my fellow homeschooling moms.... is there truth in this?

 

For purposes of this discussion, I assume that you are referring to the content typically contained in "Algebra 1" rather than generic algebraic concepts.  (Algebraic concepts are certainly accessible to younger students; consider materials such as Hands On Equations just as one example.)  

 

My two cents:  the teacher made a very broad generalization.  Obviously, there are some 10 year-olds who can understand algebra 1.  It's just that they aren't so common that a high school math teacher sees many such students; indeed, by the time such young students get to high school, they may have completed much of the usual high school sequence.  Furthermore, some aspects of a typical Algebra 1 course may go more smoothly with a more mature student (e.g. writing work out and the attention span necessary to get through a typical lesson from a high school text), though those parts may be a little more flexible when homeschooling a younger student.  Most importantly, how ready a student may be for algebra may depend on an understanding of elementary arithmetic concepts, which may in turn depend not only on the student's individual ability but also on the quality of the student's elementary math education.

 

There are plenty of ways to skin the cat of math acceleration.  You may wish to consider adding depth and challenge from other resources and/or use TT Algebra 1 as more of a pre-algebra and then follow it with a more challenging Algebra 1.  That is, when your student completes what you deem to be official high school level coursework, you may wish to have that include more rigorous resources.  There is no need to race through the high school sequence (despite the discussion on another board, LOL; also consider the same author's perspective on problem solving).  Consider the big picture, the long view, of the sort of education you are planning for your ds (believe me, I am saying this as much to remind myself as I am saying to you!!).

[lewelma]

Of course there are 10 year olds who can do algebra.  In fact there are 6 year olds who can do algebra (ask me how I know).  However, and this is a very BIG however, there is a large diffference between being able to do algebraic manipulation and thinking algebraiclly. I don't know a lot about TT, but my guess is that it focuses on the first.  It is fine for your son to be working on that type of material now; but given that your son clearly has talent, I would strongly recommend that before advancing past algebra 1, you move him into a curriculum that focuses on algebraic thinking (word problems, proofs, etc). Either AoPS or Forresters would work.

 

Ruth in NZ

[quark]

How anyone can generalize like that is just beyond me. Anyone can believe what they want to. You need to believe in your son.

 

FWIW, as much as I respect RR, I sincerely believe that his advice to delay calculus still does not apply to every kid. Some kids will thrive by waiting. Some kids, perhaps more so if they are homeschooled (having the flexibility of time to go back and review, solidify and challenge themselves further plus closer parent monitoring) will thrive by going ahead even if they are not 100% solid in earlier concepts. I have one of those who is really flying by being allowed to go at his pace no matter what that pace is and he is not alone. I am meeting more and more young kids these days who are seeing their love of math return/ grow by being allowed to follow their chosen path (but with careful monitoring by a mentor/ parent).

 

I do agree with the suggestion to add more depth with problem solving and to continue the critical thinking that you are already doing.

[EKS]

A 10yo can absolutely understand algebra.  Both of my children did Algebra I at age 10, and the younger one did it in a real b&m class at a "rigorous" private school.

[Crimson Wife]

FWIW, my DD did Singapore Discovering Math 7 last year as a 10 y.o. and she found the algebra chapters easier than the pre-algebra ones. In fact, the reason I didn't move her on to DM 8 this year but instead am doing a quick run-through of MEP years 7-9 is because she isn't totally solid on certain pre-algebra topics. A lot of SAT math is actually pre-algebra and for her, I think getting a high SAT math score will be more important than taking a bunch of college math courses before H.S. graduation (right now she aspires to be a speech pathologist or perhaps a researcher on language development).

 

I don't personally think kids are done any favors by being allowed to zoom through an easy program.

[8filltheheart]

I'll just be a broken record and repeat what others have said. Your friend is wrong and it is most likely bc she has never encountered such a child. That said, like others have pointed out, an advanced math student is being poorly served if all they are doing is superficial coverage of concepts. I think when RR speaks of the Calculus Trap, he is describing a situation like taking a 10 yr old and allowing them to progress through a curriculum like TT and thinking that the student is being well-served. The student isn't. It is a false sense of achievement. Digging into concepts and really understanding what they are doing and then being able apply what they are learning to unique situations is the ultimate goal. A 10 yr old functioning on that deeper level,is prepared to forge ahead successfully.

 

You might want to look into the verbal problems book from Hands on Equations for word problems to supplement TT pre-alg. I agree with everyone that you should ultimately not move beyond alg 1 until he completes a more thorough alg course.

 

Fwiw, all my older kids have completed an easier alg course, MUS, followed by a more thorough applied course, Foerster. (I didn't know about AoPS back then. I like them both. They are both good books but go about things in very different ways.) I have a ds that by the time he started 9th grade he had completed alg 1 twice, geo, alg 2, AoPS alg 3, and their counting and probability course. He started 9th in pre-cal and has never slowed down and loves math. All that to say, those of Us in this thread all have kids that disprove the teacher. But......RR is sharing absolute truth. There is nothing gained by simply rushing forward. There is absolutely nothing to lose for your student to repeat alg 1with a better, deeper course.

 

Everything they will do in math and science in the future is built on basic elementary math and alg. If those foundations are not rock solid, then everything built on top of those skills may as well be built on sand. So, simply doing it early really doesn't mean much in and of itself. Solid understanding and application means everything.

[kohlby]

Most 10 year olds could handle the most basic Algebra.  Some 10 year olds can handle complex Algebra. My eldest started MUS Alg I in 3rd grade.  We switched out at the start of fourth grade for Art of Problem Solving.  He's now in 5th grade and will be finishing AoPS Alg II within the next month or so.  He's also done AoPS Intro to Number Theory.  His brain is very analytical.  He can easily understand theory that many kids his age can't.  I was the same way with my understanding - but stuck in traditional age-based courses.  So, that's another thing to consider - kids in public school often are stuck below where they should be.

 

If TT is working for your child, then I don't see anything wrong with continuing it right now.  However, I'd add another course later on.  I used to teach high school math and found that MUS Alg I was not even up to college prep level, even with the honors sheets.  From my understanding, TT is even more basic.  That doesn't mean not to use it - but to use it as step to a more complete math program later on.  We did use rapid acceleration with MUS with my oldest - that's what he needed and MUS did a great job of getting the basics down without gaps.  But at around Pre-Algebra, there's some depth missing. 

[Dmmetler]

My DD did LOF pre-Algebra and Key to Algebra, and is now doing AOPS pre-Algebra. I don't feel it's a wasted year for her to do two years of pre-Algebra, and don't regret doing the easier program at age 7-8 first, before AOPS at 8-9. She is likely to be in sciences somewhere (right now her plans are in the area of biology or zoology, especially herpetology), so strong math skills are a need for her, but while she likes math, and is gifted at it, she's simply not as focused on it as some kids on this board.

[laundrycrisis]

... my friend said to me that there is no way a 10-yo can comprehend algebra. That the maturity just isn't there.

 

So I ask my fellow homeschooling moms.... is there truth in this?

 

In flipping through the rest of the text and looking at the assessments online, I think we need to scrap pre-a and just get the Alg 1 book. But her comments cause me to doubt myself. She said I should give him our state 8th grade math end-of-year test before going forward.

 

Hogwash.  Your friend is very closed-minded about the process of learning.

 

Do what works for your child.  Ignore the "trained" (aka brainwashed) education professional. 

 

Enjoy your math !

[Brad S]

... my friend said to me that there is no way a 10-yo can comprehend algebra.

Your friend is mistaken. You've already received a lot of good comments, and I would just echo what lewelma and 8FillTheHeart have already written, and said so well. Good luck.

[EndOfOrdinary]

As a previous high school math teacher, I want to second what Ruth in NZ said about doing versus understanding.  I think there are very few 10 year olds on the planet who do not understand that there are 5 cookies and they have to give their sister 2 of them, how many do they get to eat?  Algebra is the sort of thing most adults (and kids) do every day with out thinking about it.  If I am also so bold as to say, it is the same thing schools teach backwards and forwards when it comes to math.

 

It depends on whether you want your son to really understand algebra or to just be able to use it. The two are very different.  Very few adults really need to understand algebra in the "get geeked out, take things apart, put them back together, twist your mind all about" sort of way.  I LOVE algebra.  I think about math totally weirdly and find such things enjoyable.  My son is all geometry and makes my head melt sometimes with how he sees the world.  Let your son explore which ever he likes - analytical or visual mathematics.  He is 10, you will not break him by letting him explore algebra, I promise.  Secondly, it isn't like he is never going to experience the concepts again as he gets older.

 

As a previous public school teacher turned homeschooler, I can say that many teachers are threatened when a young child appears to excel at subjects they have trouble reaching older children with (especially if the child is homeschooled).  It is often dismissed as "not possible."  I see this sometimes with my husband who teaches English.  My son wants to be a linguist and is currently in his second year of Latin.  For quite sometime my husband dismissed my son's knowledge of phrases/clauses, sentence diagraming, or learning roots saying he wasn't capable of grasping language at the age 8.  He said it was ridiculous.  At 9, my son is spelling with root words, crafting interesting sentences, etc and my husband is having to humble himself a bit.  When it came right down to it, it bothered him that at home our young child was excelling past my husband's high school students and it was very uncomfortable for him.

[mathwonk]

Your friend meant well, and was possibly correct about an average 10 year old, but certainly not about all, and apparently not about yours.

 

Just to give you some counterexamples, when I taught epsilon camp in summer 2011, I believe the age requirement was that only students under age of 11 could enroll, and the prerequisite for enrollment was algebra up through quadratic equations.  We enrolled 28 students.

 

In 2013, I conducted the online pre-camp program for first time campers, some much younger than 10, and we began with quadratic equations, moving on through ideas of differential calculus, which we did carefully and in detail, from various historical perspectives.  This was a small group of 5-10 very bright very young students.

 

Here are links to the notes we covered in 2013 from my web page, and to the epsilon camp page with the description of prerequisite material.

 

http://www.math.uga.edu/~roy/epsilon13.pdf

 

http://www.epsiloncamp.org/who_is_eligible.php

 

 

I hasten to add, these are very exceptional 8- 10 year olds, and only a handful worked through that online algebra and calculus material, but we are talking about unusual students here, namely yours.

 

I suspect there is almost no fundamental math concept at all that anyone can reliably say is entirely inaccessible to someone just based on that person's age.   So comments like the ones made by your friend are just statistical remarks which are mostly true, or mostly true in her experience, but have little relevance to your situation, in my opinion.  What may be true, is that if she tried teaching those concepts to a typical class of 10 year olds, she would likely have an unsuccessful class.

 

I am guilty myself of making similarly sweeping remarks of the following sort:  students who have used calculators so thoroughly, that they have missed grappling with basic arithmetic operations, like multiplication and raising to powers, are probably unable to comprehend algebra.  This however has nothing to do with age, but with background.  In this case I am also extrapolating from my teaching experience with average classes, and I could be wrong here too, in individual cases.

 

By the way, you say your son is "zooming through the material", but what does that mean?  Is he doing the problem sets correctly or just reading the text easily?  If he is consistently working both routine and challenging problems correctly, then I would say he is understanding the material, but not otherwise.  (My perspective is that of a college math teacher.)