Gifted Issues Discussion homepage Forums General Discussion Hitting a brick wall with algebra

Related to my other post: DD12 (just turned) is in 6th grade and in a double-accelerated math track (also designed for GT students, so on the one hand enriched, but on the other they are all 6th graders). The class has been easy for her up till now, but they are hitting true Algebra 1 material now (having finished prealgebra). She is struggling. I actually see this as possibly developmental, but also possibly a result of not having all the fundamentals of algebra fully in place before moving ahead. I've got her doing Dragonbox 2 and reviewing the concepts she's striking out on on Khan Academy. Other advice or resources from the trenches? DD is FREAKING out because she has never experienced the "I just don't get this" feeling before in math. She is also declaring that she hates algebra, which is not encouraging.

Could the problem be the book?

I collect math books, and have a pretty good pile of contemporary books that are used in schools. Without exception, anything published by mainstream publishers that I have or have looked at is a dog. So, this means, "Glencoe Algebra 1" "Prentice Hall Algebra 1" "Pearson-Prentice Hall Algebra 1." The same is true for the pre-algebra books. You can recognize them because they all have lots of bright friendly colors, and lots of notes in the margins about WHY THIS MATTERS! and LINKS TO STANDARDS!

When I looked carefully at these books, I realized that the subject matter jumps around and is often presented out of logical order. As an example, I'm looking at a copy of a bad algebra book right now. Chapter 3 has sections on:

• Solving basic one-variable equations
• Similar triangles
• Functions in two variables
• Deriving square roots
• Percent error
• Rate*time=distance word problems

It's a jumbled-up incoherent mess of concepts and examples. If your daughter is stuck with a book like this, the surprising part is that she's got this far without being too confused. BTW, the pre-algebra books are just as bad. They all are, really.

This mess is part of what drove the Common Core math standards (the standards are good, but the implementation is lousy). STEM faculty at universities have seen that students are increasingly unable to solve basic math problems, and they realized that the way the subject is taught in K-12 schools is a big part of the problem.

My best advice is to buy a copy of a very old book and start your DD in that, from page 1. My son is using this pre-algebra book. I call this book "Pre-algebra for future mathematicians." It's an outstanding work that starts with set theory and moves through properties of numbers, basic number theory, and other skills that underlie algebra (but are not taught today). Some of this book will be easy for an advanced 6th grader (so she could likely move quickly through it), but it provides theory that is sorely lacking today.

Alternatively, there's the Brown algebra 1 book. Teacher's editions and other extras for that book are easy to get. The Brown geometry and algebra 2 books are also very good. They lack the theory that the first book provides, though.

The route I recommend will take more time, but will get your daughter on track to learning math properly.

I've gone on too long and will stop now!

Yes, she is using a typical moden jumbled-up book like those you describe, although the teacher (who has been around the block) supplements with her own material, which is typically better, longer, and more thorough. I've noticed, FWIW, that both her recent teachers (last year's 5th grade teacher was math-savvy) do everything out of order from what the book prescribes...

Okay, so what's different now?

The hardest part of algebra 1 for my DD was the chapter on two-variable functions, which was about 2/3 of the way through the course. Is this what your DD's class is working on now? IMO, this topic is conceptually the hardest part of algebra 1 because it's so abstract. DD had to work hard on these ideas in order to grasp them. We went over them many times.

Alternatively, did the class start with pre-algebra and move into algebra (say, at the beginning of the second semester?). The progression isn't fully outlined in your first message. If this is the case, sticking points in early algebra 1 include having to do multiple steps to solve equations (e.g. 2x +3 = 17/2 - 5x) and rate*time = distance problems. In my experience, it's normal for parts of any course to be harder than others. Algebra gets difficult when it gets abstract, which happens in steps. Both these skills involve moving abstract ideas into practice.

What kind of pre-algebra course did she do? IMO (and only my opinion), today's pre-algebra courses fail because they don't teach the theory that kids need to honestly understand algebra. Going from arithmetic to algebra is a huge conceptual jump because of the abstract ideas in algebra. Pre-algebra should be based on practice of skills AND fundamental concepts about numbers (e.g. set theory, properties like commutativity, etc.). This approach introduces abstract ideas in a basic way that prepares students for what's coming. Unfortunately, pre-algebra today is generally skills-based, and set theory isn't a "skill."

She's hanging up on systems of equations. I feel like she has JUST gotten consistent with solving basic equations and now, bam, we're there.


Yes.

Wait. To me, this means, solve the following:

2x + 6y = 54
3x - y = -10

Is that right?

If she's expected to do this stuff, it's no wonder she's having trouble. This topic is way past the beginning of this subject. If they just started algebra last month, they should at a point where they're solving things like 2x + 3 = 17 - 5x (I'm guessing that was tossed into "pre-algebra" and bundled with solving 2x + 7 = 21). They still shouldn't even be at rate * time = distance yet.

Solving systems of equations should be in last quarter of algebra 1, after functions (which starts with graphing a line).

This is what I mean about it being all jumbled up. I'm sure her teacher is trying, but if this is where they are, she's out of order.

ETA. If the course is proceeding in a jumbled up way, it's not her fault that she doesn't understand it, and hating algebra isn't surprising. I'd hate it too if someone presented it out of order.

My middle son detested math and thought he was stupid until we took him back to basics and presented the subject to him in an ordered, coherent way. Two years later, he enjoys math and says "It's my friend again."

Yes. This is exactly what she's doing, though her examples are actually harder. I personally think this is very hard for age 12 and having just finished prealgebra, but I am not mathy.

She has done graphing, but not any serious functions.

I'm mathy, and this is way beyond what students in a first-quarter algebra course should be doing. It wouldn't surprise me if a lot of the kids in class are lost.

We have a situation where the books are awful and fear encourages a focus on skills that might be on a high-stakes test. Add to it that teachers, even though they may mean well, don't understand how the subject is learned (and may not fully understand the subject itself). Ergo, they can't teach it. Very few people in the field seem to understand that if you teach the fundamentals, the kids will be able to answer the questions on the bubble tests. It's a Dunning-Kruger thing, I suspect: they don't know how clueless they truly are, and are unaware of the damage they do.

I'm going to go back to my original advice. Start her on a proper pre-algebra course like the one I linked to. If you have a local Mathnasium, they might teach it to her (the Mathnasium was the starting point for my son saying, "Math is my friend again.").

The thought of starting over may seem icky. But try to see it this way: she's not starting over because she never got started properly to begin with.

Just to clarify.. is she is a CC compressed Math 8, Algebra I class combined? If so.. Math 8 isn't "pre-algebra" it is pre-algebra the first 4-5 chapters of Algebra & some gemoetry. Thus starting "Algebra book" would be getting into 2-equations and two unknowns. Still sounds like they have skipped a bunch of important information.

Are they teaching the cookie cutter approach to math? What I mean by that is not really explaining how or why it work but just showing them here is technique A,B, and C to solve the problems.

I agree that your daughter probably needs more practice and understanding for solving for one equation before she gets to two equations.

My only suggestion for understanding two equations & two unknowns then uses graphs? Solve with graphs first. Graph the equations & see where they overlap. IMO this is one of the best ways of understanding what is going on. Graph lots & lots of different equations. Graph them on top of each other and see where they intersect. Graph the different steps, so you can see that equations that look different are really equal.