Gifted Issues Discussion homepage Forums Parenting and Advocacy Appropriate % on chapter pre-tests (math/algebra)?

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.