Math books with excellent explanations

[Heather in VA]

For pre-algebra and up, what would you say are some of the best math with clear, readable teaching in the book rather than via video or teachers manual? It doesn't have to be the most advanced program, just solid.

[EKS]

Lial has good explanations and problems that don't stray too far from the teaching.

Edited April 11, 2017 by EKS

[regentrude]

I found AoPS excellent. It is written to be used without a teacher. The book says every word a good teacher would say in the classroom (which is why some people consider it 'wordy".)

[JoJosMom]

I would second Lial's books for solid and easy to follow.

 

I disagree about AoPS as a general recommendation for self-study; I really think AoPS depends on the type of learner.  I would suggest finding a physical copy and taking it for a test-drive before buying.  ;)  (And it's what we use!  It wouldn't work for me, but my DD loves it.)

[Clemsondana]

We have used AoPS, but my kid has enjoyed the Jousting Armadillos, Crocodiles to Coconuts, and Chuckles the Rocket Dog books more. It is written in a very conversational tone that seems easy to understand. As far as I know, they only have algebra - actually, the first book might be considered pre-algebra, but at any rate the series ends after you do polynomials.

[Heather in VA]

Thanks all - I did want to clarify that I'm not looking for a pure self-study. My daughter seems to do better when she can read the lesson herself and then I can help her with what she didn't understand clearly enough. So I figure the better the initial explanation, the better it will go. We are currently using Derek Owens pre-algebra and it's going ok but when she doesn't understand she shuts down and doesn't want me to help her because she's already watched videos and maxed out her "lesson" tolerance. She has ADD/Executive functioning issues and math is her weakness so she had a set amount of time she can engage in math before she shuts off. The videos take a lot out of her. 

[Guest]

Dolciani. I rarely consulted my teacher, and my son found it quite clear. He was very happy to have the visuals.

[Mike in SA]

I must say, "excellent explanations" is very subjective. Most mathematicians would prefer direct, concise derivations over verbose descriptions requiring interpretation. I have found that many students want spoon-feeding which they are unlikely to find in the best texts.

 

So, how would you characterize "excellent?"

[kiana]

Honestly I liked the explanations in Algebra: A Fresh Approach, and I think the more linear style of explanation would suit her better.

 

Most of the college textbooks for beginning algebra are okay too (Lial/Gustafson/Larson/Martin-Gay/probably others) but I think the pages with all the sidebars and notes would probably be a bit overwhelming for an ADD kid. 

[Heather in VA]

Honestly I liked the explanations in Algebra: A Fresh Approach, and I think the more linear style of explanation would suit her better.

 

Most of the college textbooks for beginning algebra are okay too (Lial/Gustafson/Larson/Martin-Gay/probably others) but I think the pages with all the sidebars and notes would probably be a bit overwhelming for an ADD kid. 

 

Thanks - I've been looking at that one for a while and like it. Did you use it? If so, what did you use before it? I kind of want one more layer of pre-algebra before moving on to give her a little more time for her analytical thinking to mature. 

[daijobu]

Another vote for AoPS.  The explanations take you through slowly and carefully without skipping a single step.  Read and savor every word!  

[wapiti]

When my kids ask for help for algebra 1 or geometry, I usually reach for AoPS first, especially if they need some instruction on the concept.  If I don't find what I want there, I'll pull out a Dolciani (late 80s/early 90s editions; or for geometry, Jurgensen).

 

For a refresher on the procedure only, I'll go to the Glencoe McGraw Hill study guide for their school text (available on random school websites).

[madteaparty]

Well, AOPS is excellent for this.

But AOPS didn't work for us. Just plain solutions has worked thus far with Foerster.

[MamaSprout]

IMO Foerster works well for this. Dd does it on her own mostly, and it works great if she reads and does the sample problems. Not so great if she say "oh yeah, I got this" and jumps in. We have the videos, but I watch them in case she needs help so I don't have to play catch up to answer a quick question.

[MamaSprout]

DP

Edited April 11, 2017 by elladarcy

[EKS]

I must say, "excellent explanations" is very subjective. Most mathematicians would prefer direct, concise derivations over verbose descriptions requiring interpretation. I have found that many students want spoon-feeding which they are unlikely to find in the best texts.

 

The best text for a mathematician (expert) is not going to be the same as the best text for a student (novice).  Most students, especially when they first encounter a concept, need help connecting the dots.  They simply can't extract the same information that an expert would.

 

I suspect that what you're calling "spoon-feeding" is what I refer to as "communication."

[Heather in VA]

The best text for a mathematician (expert) is not going to be the same as the best text for a student (novice).  Most students, especially when they first encounter a concept, need help connecting the dots.  They simply can't extract the same information that an expert would.

 

I suspect that what you're calling "spoon-feeding" is what I refer to as "communication."

 

I agree with this so I guess by this definition I want spoon-feeding. I don't think that is the same thing as not requiring the student to think.

[kiana]

Thanks - I've been looking at that one for a while and like it. Did you use it? If so, what did you use before it? I kind of want one more layer of pre-algebra before moving on to give her a little more time for her analytical thinking to mature. 

 

I haven't used it, sorry. But you should be able to download the first chapter from her website and test-drive it before committing. That chapter is review from pre-algebra so it shouldn't be too challenging even if you end up postponing the algebra course for a bit. 

[Mike in SA]

The best text for a mathematician (expert) is not going to be the same as the best text for a student (novice).  Most students, especially when they first encounter a concept, need help connecting the dots.  They simply can't extract the same information that an expert would.

 

I suspect that what you're calling "spoon-feeding" is what I refer to as "communication."

 

This was my point, except by "spoon-feeding," I really meant "spoon-feeding": so chopped up that thought is not required, and mastery is never garnered.  This is from my own experience as a teacher.

 

I honestly believe that students are best off somewhere in the middle of the two extremes.  But, that still leaves a wide range of preferences to select from.

 

[Mom22ns]

A couple comments on Lial's. First I think their explanations are really good up through Algebra 2 (Intermediate Algebra), but not nearly so good at the pre-calc or college algebra level. Second, I completely agree that the pages are too busy and the layout too overwhelming for an ADD kid, or many younger kids. They are designed for college age students. We used them and liked them, but I thought I'd throw out those caveats.