kitchen table math, the sequel: Middle School Math Pre Tests

Thursday, August 20, 2009

Middle School Math Pre Tests

Any math teachers here use pre tests? PaulB, are you around? I think your school required you to use them, but I can't find the thread where you talked about how it was (not) working.

I am wondering what the stated purpose is of the pre tests.

I can see someone offering the following explanation:

A pre test is a useful way to determine the current knowledge level/ability/readiness for the material about to be taught.

But then what? Once you determine that, how is that knowledge to be used? Are teachers who are required to pretest allowed to change their content? Slow down? Reteach? Repeat prior material? If an individual student were to ace the pre test would they be exempted?

Is this to help the teacher know where the "differentiated" in the classroom are in skill set (as if he didn't know already?)?

I heard some anecdotes about the use of pre tests in middle school math here, but didn't understand the constraints under which the teacher performed. In that teacher's case, implementation issues were a problem.

The main issue was that the teacher sent the pre tests home. At least some of the students and parents didn't understand that this was a pre test, and thought their children were performing poorly. The students too seemed to internalize that doing badly on the pre test meant they were bad at math. No protestations to the contrary by the teacher mattered. (proposed solution: grade but do not return pre tests to children or parents, though unclear if that was within the teacher's purview to control.)

Even without the pre test being sent home, the student internalization seems a real issue. Constantly giving tests to kids where they know they can't do the work seems to be the definition of negative reinforcement.

To me, pre tests seem valuable only to very mature students who can use them to tailor their -own- preparation for the course material. To me, this smacks of the case of those twin ideas "kids need to be prepared for college so they must act like college students now" and "experts do this so we need to teach the novices to do it the same way". That is, someone saw that college professors use pre tests on their students, so middle school teachers should do the same.

One thing seems clear: if you didn't have a spiral curriculum, then with awfully few exceptions, the prior ending unit test would BE a pre test, voila!

UPDATE: Mark Roulo's comment made clear that my post was unclear. I meant giving pre tests at the beginning of every chapter/unit/thread in the math class, not just at the beginning and end of a semester or year. So students are getting a "pre test" every 2-3 weeks, and say, the day after the get an end test on the material they've just been shown, but the pre test is on material they have not yet seen, or supposedly on the prereqs for the material they are about to see.


Cheryl van Tilburg said...

Hi Allison,

Dave Suarez, a really talented math and science teacher at the Jakarta International School, uses pre-tests extensively with his middle-school students. Here's a website that describes how it works: Challenge By Choice.

In my children's experience, the pre-tests weren't a downer at all; Suarez positions them carefully with students, and maintains a drumbeat of positivity in the classroom that's appropriate with pre-teens.


G Johnson said...

It is heartening to hear that pre-tests can help. Thanks for the link. I've seen two kinds of pre-tests; one of pre-requisites, and one which was mostly on the upcoming course content. The latter mandated pre-test torpedoed my hopes to make an engaging first impression. The students who took the test seriously were frustrated, and since it was not part of the grade and not preceeded by study or followed by discussion, many mistakenly saw it as representative of tests to come. How are such tests framed in your schools? As coupled with a similar test in May to measure student achievement?

SteveH said...

Challenge By Choice seems to be more about assessment and not pre-testing of material they haven't seen yet. They break kids into tiers, but it appears to be done in the same classroom - kind of like flexible, in-class tracking. The pre-tests I've seen seem to be a tool for differentiation by unit. It seems like you either separate kids or you don't. Some curricula like to pretend that they can do both in one big, happy learning environment.

Anonymous said...

My former sister-in-law taught math for two years as a TFA teacher. She gave a pre-test at the beginning of each year for two reasons:

(1) To see where the class was, both in terms of average and in terms of spread, and
(2) So that she could give the same test at the end of the year and see how much the class learned.

I don't know if she used the results in any specific way to change *how* or *what* she taught.

-Mark Roulo

Anonymous said...

"... if you didn't have a spiral curriculum, then with awfully few exceptions, the prior ending unit test would BE a pre test ..."


Even without spiraling, kids can (and DO) "forget" a lot of math over the summer. One can easily imagine a cramming push at the end of the year for the test (and a non-spiraling cram at that) where the kids learned enough to pass the test, but not deeply enough to remember the material 3 months later.

Plus, sometimes people move. It isn't unreasonable to expect 5%-10% of the kids in a classroom to have been at some other school (with its own curriculum) the year before.

You could certainly *use* the end-of-year test from the year before as your own pre-test, but I'd be very wary of using the *results* from the previous year's end-of-year test as my pre-test results.

-Mark Roulo

Allison said...

Maybe I was unclear, but I meant unit testing for a reason.

This is not about beginning of the year testing, this is about testing on "pre test" every 3 weeks or so as the students go through units in math. The students are being given these pre tests not once, but every time they change thread/unit/subject.

In a sanely structured math curriculum, the previous chapter really is everything you need for the next chapter for most of the material. Special sections on measurements or some geometry work, maybe. But moving through multiplication, division, fractions, decimals?

Anonymous said...

Sane structure???? What's that?

We had the following unit transition assessments (about every 5 weeks);

* 'On Demand' task (usually a single demanding question to sum up the unit we were exiting)

* 'Unit Project' (just like the previous but results sent to district to be trashed)

* Unit Test

* Post Test (for the unit just completed)

* Pre Test (for the upcoming unit)

The structure was spiral so unit progressions had no connection to each other. You could have a probability unit following a scaling unit, for example.

This series of assessments was just nuts so I never did them all. Sometimes I would just incorporate one of them into my unit test. Pre and post tests were not scored for grades they were intended as formative assessment only. Unfortunately kids don't perceive them that way and they get really ugly after a few hours of this garbage.

Sadly, as with all things formative, there was no infrastructure to support any effective adjustments you might have made based on the things you learned from it. All this has since been scrapped; another magic brew consumed and expelled.

Susie can't add??? Dig out the geometry unit.

Crimson Wife said...

I've heard of teachers allowing students who score above a certain threshold on chapter pre-tests to skip the assigned problem sets. Though if a child is consistently doing this, my question is why isn't the teacher accelerating him/her to the next grade level for that subject?

palisadesk said...

Though if a child is consistently doing this, my question is why isn't the teacher accelerating him/her to the next grade level for that subject?

Not allowed. Enrichment is permitted, but advancement, no.

Your circumstances may vary.

KathyIggy said...

I know our middle school uses pre-tests in the SPED "instructional" math class. My daughter is in this class. The pretest is given at the beginning of each chapter and the teacher than tailors the problem sets given to each student. Then a chapter post-test is given to measure understanding. The results of these tests were discussed at yearly IEP meetings when the next grade's math teacher would be present and were used to come up with goals for the next year. I'd imagine there's a lot less flexibility in the regular ed classes. At the elementary level our district gave the same assessment at the very beginning of the year and then at the end to see whether district goals were met.

Anonymous said...

Hi Paul! Glad to see you've returned. Had a nice vacation?

re: your school's implementation before they trashed this silliness, what was the stated rationale of the pre test? What is "formative assessment" supposed to mean? If you weren't allowed to change anything based on it, did anyone who required it of you know what it was for?

"Unfortunately kids don't perceive them that way"

Was there any way to mitigate this that you found?

In your experience with the spiral method, would there have been any other initial assessment method that would have been helpful to a young teacher to understand what his students didn't understand?

LynnG said...

Are you using pre-test and formative assessment interchangeably?

Theoretically, a teacher is supposed to adjust the curriculum according to the results of a formative assessment, which can be just 2 or 3 problems done without much fanfare.

In practice, acing the pre-test has rarely resulted in the student skipping the unit. Instead, they are given additional work (on top of what is assigned for everyone in the class) as "enrichment." My daughter quickly figured out that doing well on the pre-test meant more work.

Cheryl van Tilburg said...

Hi all,

In response to SteveH's comment on the Challenge by Choice approach ("They break kids into tiers, but it appears to be done in the same classroom - kind of like flexible, in-class tracking.") -- the pretesting actually happens at the beginning of each unit.

To some extent, the kids have already been tracked into Dave's class (the school has two math levels in 7th grade). The pretest divides students into three different groups for each unit (green, blue, and black -- like ski trails). Each student's color level can (and usually does) change during the course of the year depending on the topic. And the kids have a certain amount of choice regarding their color group.

Dave admits that differentiating instruction for the three groups is the tricky part (the differentiated assessments are easy). He describes several approaches in the comments for the "Tiered Instruction and Assessments" section of the website.

Hope this clarifies the approach a little. I'm an English teacher, so I claim no special knowledge on teaching math. But Dave's thinking on this subject seemed thoughtful. And based on feedback from the kids (including mine), it was motivating.


palisadesk said...

My district has several middle school programs that are not exactly "magnet" schools but are an alternative program for seventh-eighth grade and which offer a very  academically demanding course of study. They follow the required curricula but in unconventional ways, emphasizing organizational skills, a combination of group work and individual in-depth study, simulations and service learning, integration of the arts into curriculum topics in social studies and literature.
I've visited and admired three of these programs and had the opportunity to sit down with a couple of the teachers who went over the specifics of how they taught the math curricula to a diverse group of students who were not separated for discrete classes by grade.  They made extensive use of pre-tests.
My recollections are not detailed but I recall the general thrust of what they told (and showed) me.  The math requirements for 7th & 8th grade, being a spiral, overlap significantly. They have the year planned into units which cover the required components of both 7th & 8th grade math, with sequential skills  and specific required knowledge specified.  Before they begin a new unit all students take the same pre-test.

The purpose is to determine the focus of the student's study for the unit, and where s/he will start in the continuum.  They have assignments, projects, resources, lessons prepared for several possible groupings; the results of the pretest suggest which grouping is appropriate for each student, who then meets with one of the teachers to develop a plan for the unit -- what work s/he will do, what  skills must be mastered, what resources will be used, what assignments will be competed (some are done with others, some independently), what specific direct-teaching classes s/he will attend, and so on.  Student and teacher sign a contract for the unit, stipulating what each will do, with timelines indicated.  Some students are exempted from much of the unit (most of the eighth grade students would be exempted from all the earlier parts of the unit, while the seventh graders would not be expected to master all the material but merely a designated minimum). 

Advanced students develop a plan to expand on their current level of knowledge -- either through independent study, special research or investigations, work with a mentor (some liaison occurs with secondary or college faculty, with professionals in occupations related to the student's interests, etc.). If the student can demonstrate mastery of all the required curriculum goals s/he can develop a unique area of study for the upcoming period of time. Examples given were students who wished to learn more about designing computer graphics or investigating artificial intelligence, working with scientists in fields like limnology, astronomy or meteorology, researching "enrichment" type topics like the history of number systems or topology, which are not included in the regular curriculum.
Students who show many unmastered skills must cover more and complete more assignments  to meet expectations for their grade.  These schools  don't offer "remedial" work (they emphasize the program is for students with average achievement, not students with exceptionalities or severe academic delays), but of course some students enter with weaker skill sets than others. Those students are required to work harder and do more in order to catch up.
They also use post-tests and evaluation of student work to determine whether students have met their goals at the end of a unit.  I was impressed with how well-organized the program was and how it resembled what I've heard described in business terms as a "tight-loose" structure: tight on expectations and outcomes, but flexible (loose) in processes and methods.
These programs have been in operation for more than 20 years and have a very good track record of success with children of varying backgrounds. It seemed a good example of effective use of pre-tests.

Anonymous said...

I have never heard of "formative assessment", and can't define it. It sounds like gobbledygook to me. A formative experience is one that forms you. A formative assessment is one that forms assessment? assesses your formation?

I use pre test to mean a test given to see if you have the pre requisites needed to do the next step. What do others mean by it?

In engineering, a validation test could be given pre and post to some event. It would be the same test, and it would evaluate the change of state between pre and post event.

are pre and post tests literally the same tests in any of these cases?
If pre tests aren't testing that, what are they?

kcab said...

At least in elementary, pre-tests cover the same material as post, though the problems will not be *exactly* the same. Students do sometimes know the material without having seen it in the classroom setting. It would be great if they could be accelerated, but at least enrichment is better than eating their brains.

See, for example, "Developing Math Talent" by Assouline and Lupkowski-Shoplik.

ChemProf said...

One problem, Allison, is that there are a bunch of things that can be called "pre-tests." One is what you'd think -- test students on the material they are about to cover, then test again to see the improvement. Done right, it can be helpful to know what you can cover quickly, because they already know it, and what is new. Another is a placement test, to divide students into tracks or assign classes. A last one is a formative assessment, where you do a quick test in class to see if students understand what they have been taught. If formative assessment is used properly, the teacher adapts what he/she is doing based on student understanding. However, a lot of the time, teachers are trying to get through the material and don't have the time or inclination to actually make use of the information from the pretest or formative assessment, in which case it is basically useless.

Again, as we've talked about so many times, these can be useful, but often they aren't used well.

ChrisA said...


Thanks for clearing it up, I had no idea you were talkinb about pre-tests every 2 - 3 weeks. That seems stoopid.

ChemProf said...

I could see the point of that kind of test if it really covers pre-requisite material for the new unit, especially if they were short (like 10 minutes) and especially for a spiral curriculum, where you might want to know what prior material students really knew.

However, handing them back graded to the students seems like a recipe for disaster. Something like PaulB's whiteboards seems like a better way to quiz the class and get that same information for the teacher without making some students decide they aren't good at math because they aren't psychic!

Anonymous said...

Formative assessment is used to adjust teaching. Summative assessment is used to measure learning. At least that's how we use it in my district.

If you are minimally aware of what is going on in your classroom (at least IMO), formative assessment is something that is ongoing and doesn't need to be formal. The real deal here is that the pre-post thing is dual purpose, in theory.

You could use it to adjust teaching (formative) or you could use it to measure teaching effectiveness (summative). Which paradigm, depends upon your point of view or intended purpose.

To my kids though, a test is a test. I found that nobody did anything with the results of the pre-post thing so my mitigation was to scrap it.

Anonymous said...

Well, I'm with the kids.

A test is a test.

The idea that there's a difference in whether a "pre test" is a formative assessment or a tracking/placement device or a "what did you learn" test is, personally, nonsense.

The test is the test. How you USE the test results shouldn't confuse anyone into thinking that these are different tests, or that anyone has said anything important by differentiating formative assessment from placement, because the idea that formative assessment and placement are bifurcated in the first place is already nuts.

ChemProf said...

"a test is a test."

Sure. That's why even in college, we usually give our placement tests before students are in the class, to put them in the right course. That way there's no confusion about "does this count". If it is an issue for college students, I wouldn't expect it to work any better for middle school kids. And every couple of weeks just sounds like a mess (plus, frankly, probably a waste of class time).

I know some colleagues have had luck with "pre-tests" given online and for credit that test whether students have read the material, but that is a whole different deal.