Is pre-algebra needed?

[lulalu]

It has been many many years, but I don't think I had a pre-algebra class. I had a regular 8th grade math class and then did Algebra 1 in 9th grade. 

Is pre-algebra needed? What is gained in doing a pre-algebra course? 

We used Miquon in k-3 grade, and have worked through Hands on Equations. We have a little more to go in HOE and fractions next year. And we have done a lot of Gattengo's math books. These have all included a lot of early algebra concepts. So maybe we really don't need to add more pre-algebra. 

[Shoes+Ships+SealingWax]

PreAlgebra is a good opportunity to run back through elementary arithmetic at a faster clip to shore up that foundation before moving on to higher-level mathematics. For many students, it’s also an opportunity to adjust to working more independently & communicating clearly without also wrestling with entirely new material. I wouldn’t say it’s strictly necessary, but it is widely useful. 

[SoCal_Bear]

It all depends on the student, and it depends on how you define pre-algebra. Art of Problem Solving pre-algebra looks so incredibly different and at such a depth that I hesitate to even call it just pre-algebra. I use pre-algebra to do a lot of other math topics, so for us, we did a lot of other exploration in math topics outside of arithmetic and traditional math sequence before moving on to higher level mathematics. Even doing that, we will be getting to pre-calc in 8th grade.

[8filltheheart]

There is a really big leap in complexity of abstract thinking between HOE and a solid alg 1 course.   HOE is really very simplistic in terms of concepts covered in alg 1.  I have never actually used a course labeled pre-alg, but use MUS's alg as pre-alg bc it is also very simplistic in terms of applying algebraic concepts  (and doesn't get to the quadratic formula in alg 1.)

It is really going to depend on the student as to whether or not they are going to be able to jump from basic elementary math concepts into a full blown algebra course without a bridge.  I know that for my kids that going straight into Foerster's might have plausible, but it would not have been good for their confidence or building a strong foundation.  Giving them the extra yr for a genter introduction into alg before high school content was better for them.  My current 6th grader is in Foerster's right now and she has had a few sections where some of challenging problems have been frustrating for her.  (She is used to math being easy.  MUS alg certainly was.)  She would have been defeated last yr.

[mathmarm]

No, prealgebra is not needed. Especially not in a school environment where the quality and caliber of teaching and the accepted student output is carefully and deliberately taught, expected and inspected. You don't need to do a course dedicated to training students to work neatly and systematically before they get to algebra.  The skills students need to thrive in algebra can be systematically taught and mastered between 4th-middle school grades.

• learning to copy problems onto notebook paper
• working 3 step calculations with accuracy
• gaining fluency in showing work (ie, writing a full-solution)
• making quality notes in mathematics
• referring to mathematics notes appropriately
• using mathematics to check their work/verify their "answers"
• the ability to keep track of minor calculations, signs and symbols ("book-keeping")
• Mastering math facts and basic arithmetic beforehand
• Teaching children to see and understand relational "big-ideas" and patterns in mathematics

In a homeschool you can teach (and grade) for good habits and final result all throughout Arithmetic. There's no reason to let bad-habits sink in for weeks, let alone for years.

[8filltheheart]

@mathmarmThat is a great list of necessary skills.  But I am going to add 1 more vital skill--the ability to understand abstractions in math.  I am currently working with 2 very different math ability kids.  One is a gifted 6th grader, the other an avg 5th grader.  Yesterday I was working with the 5th grader on division by fractions.  With manipulatives sitting in front of her working through problems, she still struggled with grasping what was going on mathematically and she could see it.  Algebra requires abstract thinking and some kids take time to mentally mature into that level of understanding.

[mathmarm]

1 hour ago, 8filltheheart said:

@mathmarmThat is a great list of necessary skills.  But I am going to add 1 more vital skill--the ability to understand abstractions in math.  I am currently working with 2 very different math ability kids.  One is a gifted 6th grader, the other an avg 5th grader.  Yesterday I was working with the 5th grader on division by fractions.  With manipulatives sitting in front of her working through problems, she still struggled with grasping what was going on mathematically and she could see it.  Algebra requires abstract thinking and some kids take time to mentally mature into that level of understanding.

In my mind, "abstractions in math" are under the umbrella of relational "big ideas" and patterns.

 

 

[lulalu]

16 hours ago, calbear said:

It all depends on the student, and it depends on how you define pre-algebra. Art of Problem Solving pre-algebra looks so incredibly different and at such a depth that I hesitate to even call it just pre-algebra. I use pre-algebra to do a lot of other math topics, so for us, we did a lot of other exploration in math topics outside of arithmetic and traditional math sequence before moving on to higher level mathematics. Even doing that, we will be getting to pre-calc in 8th grade.

I don't want to do AOPS now. Maybe later on. My DS is a language guy, and that is where the bulk of his time goes during school. That and he is a perfectionist, so I don't think AOPS would be a good fit right now. 

We have spent time on a lot of topics outside of arithmetic so maybe that is why I feel no real drive to do a pre-algebra year. 

[lulalu]

15 hours ago, 8filltheheart said:

There is a really big leap in complexity of abstract thinking between HOE and a solid alg 1 course.   HOE is really very simplistic in terms of concepts covered in alg 1.  I have never actually used a course labeled pre-alg, but use MUS's alg as pre-alg bc it is also very simplistic in terms of applying algebraic concepts  (and doesn't get to the quadratic formula in alg 1.)

It is really going to depend on the student as to whether or not they are going to be able to jump from basic elementary math concepts into a full blown algebra course without a bridge.  I know that for my kids that going straight into Foerster's might have plausible, but it would not have been good for their confidence or building a strong foundation.  Giving them the extra yr for a genter introduction into alg before high school content was better for them.  My current 6th grader is in Foerster's right now and she has had a few sections where some of challenging problems have been frustrating for her.  (She is used to math being easy.  MUS alg certainly was.)  She would have been defeated last yr.

Gattengo has a lot more algebraic problems than HOE. We have worked through a lot with those. Gattengo has an algebra book, but it doesn't look as complete as some others I have looked through. HOE jist provided us another way to visually see problems, and we have enjoyed the word problems a lot. 

MUS uses blocks differently than Gattengo otherwise I would look into that, but I think it would be too confusing for the both of us to change now. 

[lulalu]

16 hours ago, Shoes+Ships+SealingWax said:

PreAlgebra is a good opportunity to run back through elementary arithmetic at a faster clip to shore up that foundation before moving on to higher-level mathematics. For many students, it’s also an opportunity to adjust to working more independently & communicating clearly without also wrestling with entirely new material. I wouldn’t say it’s strictly necessary, but it is widely useful. 

Yes, that is the reason I am hesitant. I really don't feel DS need another go through of elementary arithmetic. He has a great foundation, we have worked at his speed, and he has mastered elementary arithmetic well. 

[lulalu]

14 hours ago, mathmarm said:

No, prealgebra is not needed. Especially not in a school environment where the quality and caliber of teaching and the accepted student output is carefully and deliberately taught, expected and inspected. You don't need to do a course dedicated to training students to work neatly and systematically before they get to algebra.  The skills students need to thrive in algebra can be systematically taught and mastered between 4th-middle school grades.

• learning to copy problems onto notebook paper
• working 3 step calculations with accuracy
• gaining fluency in showing work (ie, writing a full-solution)
• making quality notes in mathematics
• referring to mathematics notes appropriately
• using mathematics to check their work/verify their "answers"
• the ability to keep track of minor calculations, signs and symbols ("book-keeping")
• Mastering math facts and basic arithmetic beforehand
• Teaching children to see and understand relational "big-ideas" and patterns in mathematics

In a homeschool you can teach (and grade) for good habits and final result all throughout Arithmetic. There's no reason to let bad-habits sink in for weeks, let alone for years.

That's a good list. Most of those we have worked through with using Gattengo and the work I have created. These were my thoughts about what the purpose of pre-algebra was. 

[8filltheheart]

15 minutes ago, lulalu said:

Gattengo has a lot more algebraic problems than HOE. We have worked through a lot with those. Gattengo has an algebra book, but it doesn't look as complete as some others I have looked through. HOE jist provided us another way to visually see problems, and we have enjoyed the word problems a lot. 

MUS uses blocks differently than Gattengo otherwise I would look into that, but I think it would be too confusing for the both of us to change now. 

I have never used MUS's blocks.  I simply teach the content and they do the worksheets.  I have never seen Gattengo, so no comparison.  

[lulalu]

22 minutes ago, 8filltheheart said:

I have never used MUS's blocks.  I simply teach the content and they do the worksheets.  I have never seen Gattengo, so no comparison.  

Well then I guess I should look at it. I have just written it off as unusable without looking at it. But guess I should give it a glance. I didn't realize you can use it without the blocks. 

[8filltheheart]

The books have a lot of white space. That is what makes it visually "easy" for younger kids. My kids would have been overwhelmed by a wall of text. Using it as a prealg vs alg has been a good way to solidly the simple equation aspect of alg so that when they move to Foerster's they can focus on application.

[ScoutTN]

For some kids, maybe not. For most, probably. Placement tests are a good thing, flawed, but useful!

Way, way back in the dark ages, I did not have fabulous late elementary math and then was dumped into Alg 1 without PreA.  Utterly ruined my high school math. Utterly. 

I'd rather a student be over-prepared than under for Alg 1 and I see a lot of kids being rushed into Alg 1 these days. 

[8filltheheart]

1 hour ago, ScoutTN said:

For some kids, maybe not. For most, probably. Placement tests are a good thing, flawed, but useful!

Way, way back in the dark ages, I did not have fabulous late elementary math and then was dumped into Alg 1 without PreA.  Utterly ruined my high school math. Utterly. 

I'd rather a student be over-prepared than under for Alg 1 and I see a lot of kids being rushed into Alg 1 these days. 

I agree 100%.  It is one of the reasons I like going through alg twice with progressively harder texts.  I have done that with 6 kids who have graduated and my 2 current kids at home.  They have all been rock solid in math (even my weaker academic kids)  

It is the foundation for every single math and science class going forward.

 

Edited February 20, 2022 by 8filltheheart

[Lucy the Valiant]

We used pre-algebra as a review of Singapore 1A - 6B, and also as a full year to transition to a standard math curriculum (vs. SM-style). In retrospect, I think it was a good decision, for a variety of reasons. 

 

[Shoes+Ships+SealingWax]

5 hours ago, lulalu said:

Yes, that is the reason I am hesitant. I really don't feel DS need another go through of elementary arithmetic. He has a great foundation, we have worked at his speed, and he has mastered elementary arithmetic well. 

In this case, I wouldn’t worry about it. or I’d do something that has both PreA & Algebra components, like the Arbor Center series. 

We will be starting AOPS PreAlgebra sometime next spring, when DS is 4th grade by age. He has thrived with the challenge of Beast Academy, so I want him to continue with AOPS if it suits him but he’s just begun developing some of those skills @mathmarm mentioned - neatly writing out his work, clearly explaining his thinking, & checking his work - this school year.

He’s come a long way, but I definitely feel it would be beneficial for him to spend a year learning to navigate a textbook, adjusting to the challenging discovery model, & getting acquainted with Alcumus without also juggling completely new material. In our case, I don’t feel it would be beneficial to jump straight to Algebra. 

Edited February 20, 2022 by Shoes+Ships+SealingWax

[Farrar]

Just putting in another vote for the Arbor series for the kid you're describing. A "language" lover who went through and thrived with Miquon is pretty much exactly who I think those books are for.

I agree with the idea that a separate pre-algebra is often not technically necessary. However, for this student, it sounds like he will definitely need more time solidifying these concepts and getting ready to make the leap to algebra. And that's exactly what a pre-algebra course is for - reviewing key tricky concepts in arithmetic and pushing a little further.

[lulalu]

On 2/19/2022 at 8:08 PM, Farrar said:

Just putting in another vote for the Arbor series for the kid you're describing. A "language" lover who went through and thrived with Miquon is pretty much exactly who I think those books are for.

I agree with the idea that a separate pre-algebra is often not technically necessary. However, for this student, it sounds like he will definitely need more time solidifying these concepts and getting ready to make the leap to algebra. And that's exactly what a pre-algebra course is for - reviewing key tricky concepts in arithmetic and pushing a little further.

The Arbor series looks amazing! Looks like it will be perfect for DS. 

[JennyD]

On 2/19/2022 at 4:58 PM, ScoutTN said:

I'd rather a student be over-prepared than under for Alg 1 

 

On 2/19/2022 at 8:08 PM, Farrar said:

And that's exactly what a pre-algebra course is for - reviewing key tricky concepts in arithmetic and pushing a little further.

Agree with both of these.  I have only used AoPS Pre-algebra so far but have found that to be a year very well spent.  

[Sarah0000]

Well, no. I waited and waited to start algebra for fear of not being ready but prealgebra just looked so simple. My 10yo recently started Jacob's Algebra. It's easy for him! Ugh. I had read it's a solid algebra course but the problems are on the easier side. There are benefits to that. While the operational math is easy it gives him a chance to focus on organization, writing out problems, being independent, etc. and still strongly learn the concepts and practices in algebra. It could be a good fit in your situation.

[2_girls_mommy]

We used Rod and Staff 8th grade math as our PreAlgebra with both of my kids, not a separate pre Alg curriculum, then moved into Alg. 1. with both of mine.  It had a couple of chapters labeled PreAlgebra towards the end, but most of the book was just really reviewing fractions and all of arithmetic getting ready for Algebra.  It worked ok for us. 

[lulalu]

4 hours ago, Sarah0000 said:

Well, no. I waited and waited to start algebra for fear of not being ready but prealgebra just looked so simple. My 10yo recently started Jacob's Algebra. It's easy for him! Ugh. I had read it's a solid algebra course but the problems are on the easier side. There are benefits to that. While the operational math is easy it gives him a chance to focus on organization, writing out problems, being independent, etc. and still strongly learn the concepts and practices in algebra. It could be a good fit in your situation.

Jacobs is what I was looking at for Algebra. It looks exactly like something DS would thrive with. 

[2_girls_mommy]

On 2/19/2022 at 6:49 PM, 8filltheheart said:

I agree 100%.  It is one of the reasons I like going through alg twice with progressively harder texts.  I have done that with 6 kids who have graduated and my 2 current kids at home.  They have all been rock solid in math (even my weaker academic kids)  

It is the foundation for every single math and science class going forward.

 

I haven't done this with more than one text, but have definitely taken math slowly and not tried to rush Alg 1 in 1 year with both of mine so far so as to make sure they got it.