Okay, this is actually related to my algebra/pacing thread from earlier this week, but is really a discrete issue/question by itself as well.

What is the appropriate or normal or common or ideal percentage that you would want a student to score on a unit pretest for math in general and algebra in particular?

I realized that part of the pacing issue (speeding through online algebra curriculum) that DS is having may be due to the fact that he already scores mid 80's to mid 90's on the chapter pretests. DS' teacher mentioned to him that another student scored below 50% on a pretest. Is that the normal and/or ideal?

However, regardless of the pretest percentage, it is clear to me that DS needs to take the Algebra course and that he has things to learn in the course. He has never taken Algebra and I certainly would not want him to skip something so foundatinal so this is not an issue of accelerating him further.

Part of it is that I am a bit surprised, then I realized I have no idea what is the normal/expected percentage for math in general and Algebra in particular since the only pretesting done was always in spelling. Both DS and DD always got 17 to 20 correct out of 20 spelling words from K to 4th grade, but many of their classmates routinely got many of the spelling words correct as well. That was no big deal since the spelling homework worked on other skills (like phonics, roots, etc.) and that just meant they didn't have to bother studying. Thank God that spelling is no more starting 5th grade this year.

As I was thinking this through, I realized that I would probably consider K-6 math a little differently than Algebra as well. Pre-algebra is somewhere in between but I would probably group it closer to Algebra. DS was able to get his first acceleration from 2nd grade math to 4th grade math partly because he scored highly on the year-end tests for 2nd-5th grade without being taught any curiculum beyond 2nd grade. I think this was possible because elementary math involves a lot of spiraling, is very common sense based, and could be absorbed in the process of daily living (grocery store, baking, etc.). Thus, I was very comfortable accelerating him the first time, especially since the district did an aptitude test as well. Actually, I was comfortable accelerating him the second time as well from 5th grade math to Pre-algebra (skipping 6th grade math).

As I mentioned above, there is no question of accelerating DS, but perhaps the high speed pace makes sense in view of the high pretest percentages? What is the ideal or expected percentage on chapter pretests?

Well, I would consider 80% or higher to be considered mastery of the material... so scoring that on a pre-test would indicate to me that they don't need to go through that material at all. I'd venture a guess that the average is probably closer to 50-70%, but I'm not a teacher, so that's total guesswork.

If they are working at the right level I'd probably want my kid to be scoring around 60% or so. To me, that would indicate at least a passing familiarity with the material, but with some clear areas they need to work on/learn about. That material, at that point, should be a little challenging, but not frustrating.

I would think if you are getting 80 to 90 % on pretests you would still study the chapter, but on concepts you have you only do one to three sample problems and concepts that are new you do a more thorough study and more problems. Like you said you don't want gaps in algebra it is foundational.

This is how my son did all of 2nd grade math in one nine weeks. He took each chapter pre test. On the 100% chapters he skipped and less than 100% he only did what he needed to learn and then moved on.

Thanks for your input. The 60% ideal makes sense in general. Now you have jogged my memory . . . ALEKS actually permits moving onto the next math course based on 85% mastery although by default, they have you working/testing through 100% since it's assessed by topics represented as pie slices.

It may partly be that my standards are too high based on my own level of mastery, but it seems to me that DS hasn't achieved complete mastery.

On my son's pretests the pages where the topic was taught was right next to the problem. So if you missed 5 problems you turned to those pages and did those lessons only.

That is a reasonable approach. You know, I should ask him how many problems he actually does for each section in the chapter. He has told me that he does go through each lesson and do practice problems before each section assessment. However, the only things that are recorded/graded are the assessments. In other words, "homework" doesn't count.

That's very convenient. Actually, no one would know whether DS did the lesson and practice problems but he would still have to do the assessments (maybe a half dozen problems) for each section.

I don't think there can be a general answer to this question, because it depends entirely on the kind of pre-test and the nature of the mistakes being made. On the one hand, you might not want a silly slip e.g. an arithmetic error to be a reason not to study something higher than arithmetic. At the other extreme, you might not want failing to see a clever application of a technique to be a reason to restudy material that was going to introduce the technique. If your aim is to make sure that the student doesn't skip something such that they end up weaker than the students who don't skip it, the data you need is "what marks do students who have just studied the material get on this test?" and then you want to be towards the upper end of that distribution.

FWIW, EPGY considers the placement to be correct correct if the student gets (only) 70%-80% of the problems correct.

Hmm. I have a somewhat different perspective. My overall message is that if you think your son is ready for algebra and he's getting high scores on PRE-tests, you should seriously consider putting him in algebra.

Here's why.

Personally, I'm not convinced about the need for pre-algebra with gifted kids. My son is taking pre-algebra and I've looked through his textbook. It adheres to California standards and so is a fair description of pre-algebra in this entire populous state.

Roughly a third of the book reviews late elementary-level math (fractions, decimals) and does some middle school math. The rest of the book deals mostly with basic non-rigorous algebra, with a chapter on triangles.

So anyone who does this course will end up repeating ~2/3 of it during algebra 1, with slightly harder problems. This is why I think pre-algebra isn't a good choice for gifties.

Way back when I was in school, pre-algebra was mainly aimed at students who weren't super-strong in math. It made sense: they got a review of important stuff from late elementary (5th/6th then) and junior high. Then they went through some basic algebra slowly. This approach helped them build a foundation for algebra 1 and beyond. Alternatively, the stronger students took algebra in 9th grade and the gifties took it in 8th (because 8th grade math was a mostly a basic version of pre-algebra).

These days, schools seem to have forgotten all this stuff and push pre-algebra on 7th graders in an effort to get everyone into algebra at an age that used to be the target for gifted students. The weaker students miss out on a lot of extra practice that they need. The gifties presumably get bored in algebra 1 until they hit the new stuff sometime in January or so.

So while people have made good points about not wanting to miss important concepts, it's highly likely that your son WON'T miss them if he takes algebra 1, because it just repeats pre-algebra anyway. Ergo, my advice is to look through his current textbook carefully and compare it to the school's algebra 1 textbook. You may find a lot of repeated topics. After you've looked at both books, you'll be able to make an informed decision about which course to put him in.

Bingo.

I think it's a bad idea, too.

It led my DD to completely TUNE OUT of most Algebra 1.

Seriously-- she engaged in such procrastination in BOTH courses that she literally completed a full year in what amounted to about 2 weeks of more-or-less intensive (read, 3-4 hr daily) study, and earned 90-100% on everything.

I wouldn't say that her pre-algebra foundation had been all that strong going into 6th grade math, truthfully. She stopped doing Singapore in roughly 3rd grade, and had done Calvert for most of 3rd/4th, then Prentice Hall courses 1 and 2. Well, part of each. It was an odd year.

The only material that she was weak on in that body was manipulating fractions, which she knew conceptually, but had trouble with in terms of accuracy because she wasn't writing things down.

She seriously coasted until Algebra II, which then proceeded to ROUNDLY kick her butt because she hadn't developed any real resilience or study skills.

I don't even know what pre-algebra is, actually. I never had anything called that. It's possible that 7th grade math might have encompassed what they call pre-algebra now, or, come to think of it, it may have been an 8th grade class in junior high but I went to a church school in 8th grade and missed it. I know we started with algebra in 9th grade.

I guess it didn't hurt me any.

I don't think they have a class called pre-algebra in DS's middle school or high school, either. A rose by any other name....

I suspect Pre-Algebra is a name and that actual curriculum varies from state to state and school district to school district. As Val mentioned, back when I was in school the "Pre-Algebra" class was specifically for the students who (in 9th grade) weren't ready to take Algebra. In my kids' school, Pre-Algebra was a good prep for Algebra I, and really didn't contain any rehash of things already covered. The repetition in our school seems to occur more with the 5th/6th/7th grade math - - and I think this is true for much of our school district, which is why it's easy for gifted kids to skip 6th/7th grade math (which is typically what is done) and move on into pre-Algebra right after the 5th grade math course.

polarbear

I'm not sure I understood correctly --- do you mean that the upper 50% of the class is considered to be GT?

If so, they've bundled a lot of average students into their GT group and it's not really surprising (to me at least) that a lot of them are struggling. Students with solidly average ability shouldn't be taking algebra until much later than 7th grade.

That's a good point. I am trying to mostly stay out of it and let the school do their job so I haven't actually looked at the problems or check any of his assessments before or after the fact. According to DS, the pretest questions are similar to the questions on the end of chapter practice test and real test.

That's why I love this forum - it helps me clarify what I am thinking! I suppose my goal is to ensure that DS is always at the 99 percentile at the end of each course for that course.

Wow - 70% seems rather low to me!

Actually, DS already aced the Pre-algebra course and a national Algebra readiness assessment last year. This year he is enrolled in an online Algebra course arranged by the District office, who also provides a live instructor one day a week.

DS decided to implement a single skip to Pre-algebra last year rather than a double skip to Algebra. He wanted to make sure that he had a super strong foundation. So you may have an excellent point regarding the overlap. It makes sense that he is able to score mid-80's to mid-90's on the Algebra chapter pretests by extending what he learned last year in Pre-algebra.

However, I don't regret having DS take Pre-algebra last year because he is not as strong in Geometry and about 40% of his Pre-algebra course covered geometry and trigonometry topics. Of course, the trignometry topics were cursory and focused on sine, cosine, tangent, secant, cosecant, cotangent and basic real world applications.

It is a pretest. Presumably it is a lot harder after doing the study.

According to the Diagnostic Testing / Prescriptive Instruction model (DT-PI) discussed in the book "Developing Math Talent" and summarized at http://www.win.tue.nl/~wstomv/quotes/developing-math-talent.html , a student should take tests at progessively more difficult levels until he or she scores below the 85th percentile.

From going through it with my older child, I see Algebra II as a natural extension of Algebra I (i.e., higher order equations and more emphasis on systems of equations). That's why I would not consider advocating skipping Algebra I. It is important to my thinking that the Algebra foundation be super strong and automatic.

As an example of why I don't think he should skip Algebra I notwithstanding chapter pretest scores of mid-80's to mid-90's: I have seen him solve an equation in five steps instead of 4. While I always emphasize that there is a number of ways to solve a problem and it is good to see multiple ways, it is equally important as he progresses to higher mathematics to be able to immediately see the most elegant and efficient approach.

LOL about the birds! That's reminds me that proper use of the correct vocabulary/terminology is another reason that I would not consider skipping Algebra I .

I suppose that Pre-algebra can be whatever the school elects to include. Unlike Val's description of California math curriculum, about 40% of DS' Pre-algebra curriculum would be more properly label Pre-geometry & Pre-trigonometry. In fact, I think the course may finally be relabeled. Probably something like passport to algebra and geometry.

Interestingly, I took Pre-algebra over three decades ago and while we covered geometry topics there were no coverage of basic trigonometry. Come to think of it, I am not sure if the non-GT Pre-algebra covers exactly the same topics.

Polarbear, I think you are exactly on point. Interestingly, in my day (well over 3 decades ago), the Pre-algebra course was to get the advanced kids out of 7th grade math and onto more advanced concepts.

LOL. DS scored a 96% on the last chapter pretest. It would be really sad if he scores lower on the end of chapter test.

Thanks for reminding me of that book. I have a copy and read it a couple of years ago but didn't remember about the 85% guideline discussed in the book. I do wonder though if the model should apply equally as you move higher in math since that book seem more geared toward elementary and middle school.

The idea is that he fills the 'gaps' as he encounters them. Too much repetition => boredom and decrease in motivation. (Much discussed in this forum.)

Example (an actual Alcumus AOPS problem): "Represent 39/2500 as a decimal.". DC does long division, then sees a shorter solution (multiplying both parts by 4) - he'll know in the future to look at the particulars of the numbers first.

(I'm actually not trying to sway you one way or the other, because your final decision may be driven by very practical considerations - e. g., whether he'll have to work completely on his own, without outside help.)

I am glad to read an opinion different from my own. That's why this forum is so useful. It actually isn't a question of DS skipping Algebra I, but rather an issue of how comfortable I am in allowing him to zoom through the Algebra I course. If he does zoom through it, then there is the question of what to do with him the rest of the year.

Quantum2003, I misread your original post. Sorry! I thought your DS was in pre-algebra now.

No problem. Your input was still relevant.

Wow am I glad that I read through this thread I had no idea that pre-algebra (no such thing in the UK 30+ years ago) means basic algebra and trig and geometry I the country!

Starting about a decade back (of which I am aware), our district included "elementary" algebra and "elementary" geometry in the elementary math curriculum. I used to refer to it as "kiddie" algebra because it was very basic algebraic concepts in an elementary friendly approach. Compared to 30 years ago, more than half of the current elementary math curriculum are new. In addition to "algebra" and "geometry", there are units on probability and statistics (the three measures of central tendency), graphing and measurements that go far beyond what used to be covered in elementary math.

The "algebra" and "geometry" in pre-algebra naturally extend beyond the basics covered in elementary math. Regarding the trigonometry, I am not sure that it is covered in the other pre-algebra textbooks as that certainly was not covered when I studied pre-algebra.