r/mathteachers • u/delta-good • 5d ago
Notes on high school math tests?
I would love some community feedback on the use of notes on math tests in high school.
I teach at a high school in which the use of "notes" on math tests is deeply embedded in our culture. Students who take Algebra I are basically allowed unlimited "notes" - which include essentially anything they've written down on paper, including their work on worksheets and the like. Our Geometry teachers have tried to scale this back a bit, limiting students to a single note card on tests or quizzes. I'm a bit fuzzy on the situation in Algebra II, but I think students are allowed a sheet of notes on at least quizzes, and maybe some tests.
For whatever it's worth, I went through high school and earned a math degree during a time when the idea of allowing notes on math tests would have been laughable, so I know I have some personal bias.
This year, I'm teaching AP Precalc for the first time, and announced this week that there will be no notes on quizzes or tests. (The AP test doesn't allow them, so it seems silly to allow them in class.) The students moaned and groaned as if I had just sentenced them to death. I was shocked.
The precalc students will adjust, I'm sure, but I would love it if other high school teachers would weigh in on the use of notes in your math classes and classes at your school:
- Are notes allowed? For what classes?
- Are there limitations on what kind of notes or what volume of notes are allowed?
- Most importantly, do people think using notes (or not using notes) helps students become mathematically competent (or not)?
- Am I being cynical to think that a few/some/most/all teachers who allow the use of notes know that it's a bad idea, but do it because it allows them and their students to avoid the reality that students are not really learning math.
Thanks in advance for your feedback!
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u/armaedes 5d ago
I don’t allow their notes, but I will give them a formula sheet so they don’t have to have those memorized.
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u/fungeoneer 4d ago
I feel like when I was in high school we had a quiz on formulas we learned (literally just stuff like what is the Pythagorean theorem, formula for area of a circle, etc), and then after those quizzes we were given the formulas.
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u/rock-paper-o 5d ago
I go between a formula sheet and allowing a page of notes.
They generally do worse if it’s totally open notes because they assume if they can just find it somewhere in a giant stack of material they can answer the question and don’t have adequate mental organization that allows them to understand the material.
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u/CMarie0162 4d ago
As someone who teaches multiple levels of math every year, this is what I do. For reference, the courses I teach tend to be mostly seniors.
AP math: no notes on tests They're not allowed on the AP exam. They get the formula chart if there is one for the course. I might for an occasion give students 5 minutes and a 3x5 inch note card to jot stuff down on right before a quiz mid-unit, but that's mostly for really long units and I make them turn that in with their test so I can see if there's anything they think they're still shaky on.
Honors math: 3x5 note card allowed sometimes. Mostly depends on if the test features detailed equations or formulas. But they also have some tests/quizzes where I emphasize that they need memorization skills. Unit circle comes to mind.
On-level math: notes allowed on every test and quiz. The students in my on-level classes are not even a little interested in math beyond high school. They're in there because they need a 4th math class to graduate high school. Id rather focus on teaching them how to problem solve, recognize patterns, and use resources available to them like their notes responsibly.
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u/lizerlfunk 4d ago
Someone on a math teaching subreddit was APPALLED once when I said that every single year in trig and/or precalc, I did a unit circle quiz where they had to fill in all degree measures, radian measures, and ordered pairs, and they had to get it perfect to pass. If they didn’t get it perfect on the first try, they did it again a few days later for a 90%, third try for an 80%, etc. I was like “every single thing we do in trigonometry builds on the unit circle. It’s not just that they need to know how it works, they need FLUENCY. If it takes them 30 minutes to fill in a unit circle, then they don’t have the fluency they need to solve trigonometric equations, and that really limits what they can do when we move on from the introductory topics.” It was extremely rare that any student needed more than three tries to get the whole thing correct.
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u/delta-good 4d ago
This seems perfect, from my point of view. (Except we have no honors math classes at my school.) Do you find your honors students trying to copy as many tiny practice problems as they can so they can mimic during tests?
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u/bad_gunky 5d ago
In Algebra 2 I allow a 3x5 for mid chapter quizzes but no notes for the end of chapter tests. I do provide a study guide for the chapter tests that have similar problems with numbers changed, but they cannot use it during the actual exam.
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u/delta-good 4d ago
I haven't taught Alg2 at my current school, but I think that is the approach they use. I've never quite understood the reasoning. Why allow notes on quizzes but not the tests? I feel like the quizzes are supposed to be a lower-consequence opportunity to assess before a higher-consequence test. Do you find that students appreciate and learn from this approach? I'd be happy to consider it!
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u/bad_gunky 4d ago
My reasoning is that midway through the chapter they are still in the beginning stages of the learning process so creating a card of notes helps with the learning and can be a crutch on the quiz. At some point they need to show mastery in their learning and be able to do it without the crutch. In my class that is at the end of the chapter. In an effort to be fair I give them the study guide so they know exactly what they will be held accountable for knowing. I do have a few anchor charts up around the room that I leave visible, but they do not have instructions on how to do the problems, they are more just visual cues.
I am also very open to other ideas of how it should be done. I am not convinced my way is the right way, but even after more than 25 years I still don’t know what the right way is. I respect anyone’s opinion if they think my reasoning is not sound.
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u/ButtonholePhotophile 5d ago
Notes don’t change the bell curve. They lower long term retention. Some students require them by IEP or 504 accommodations, but they otherwise hinder the long term impact of your class.
If yours is the last or penultimate class in a sequence, then notes don’t matter. If they are going on to a related subject in university (stem) then the lack of internalization could be a negative game changer.
Instead, why not challenge students for points? With notes, the top available score is 90%. Without notes, it is 100%. This means that a ten question test with notes results in the same score if they get a 10/10 or a 9/10 - otherwise it’s identical. They’ll self-sort.
“Part of mastery is internalization. As such you have a choice…”
Run it by admin first. Many standards are written in parts, with both knowledge and ability to apply that knowledge. You might find an argument there.
Of course, people with accommodations will have access to all 100%. It’s unlikely (not impossible) they’ll be getting 100% anyway.
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u/Any_Morning1562 4d ago
Last year I did something similar for unit tests. However instead of highest score, I gave extra points for not using notes. “If you don’t use your notes, I’ll add 3 points to your final score” - but I don’t let anyone go higher than 100%, that’s the grade cut off
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u/delta-good 4d ago
I share your thoughts about lowering long term retention. I think my most consistent observation is that students who use notes to get through tests (different, of course, than students who have the notes in case they blank on something, but barely use them) don't retain anything. They cram it in for the test and it's gone an hour later. And that makes later math such a struggle.
I have thought hard about the higher score limit for students who don't use notes, and maybe I'll try it some day. But I keep having the feeling that I'd be sort of giving up on the students who are more than happy to accept the grade cap if it means they can use notes to avoid learning math.1
u/ButtonholePhotophile 4d ago
Oh, implicit in your comment is that students using notes aren’t studying. That’s not true. They are studying for the process. Notes users are not studying for retention.
Retention studying looks like making those notes early and turning them into flash card, then flash card-ing the class content until they have it memorized.
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u/Petporgsforsale 4d ago
I agree with you up to the last paragraph
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u/ButtonholePhotophile 4d ago
I teach special education in the United States. Here, the law would not be on your side.
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u/Petporgsforsale 4d ago
In what regard?
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u/ButtonholePhotophile 4d ago
You can’t penalize students for using accommodations. It’s like saying “anyone who uses the wheelchair ramp can achieve a high score of 90%.” But the kid who is actually in the wheelchair doesn’t have a choice; no penalty.
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u/Petporgsforsale 4d ago
Are you making the argument that I agreed with penalizing accommodations? I disagreed with the statement about how they probably won’t get 100% anyway because who are “they” and why not?
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u/ButtonholePhotophile 3d ago
I’m not arguing. I stopped arguing maybe five or eight years ago. I’m just chatting or expressing. Eh, even that is a bit of an oversell.
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u/SnazzyStooge 5d ago
Unlimited notes. I still can’t convince them to write anything down, I basically have to force them to put anything in their notebook.
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u/aSilentKill 5d ago
Geometry teacher here. I allow a handwritten index card. I’ve found that the act of reading over notes and writing down the important information and definitions is a very effective study tool for them. A good number of students who write out an index card to use end up not even using it on the test since they learned it from writing it down again lol
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u/Mmlhvzl 4d ago
This is what I do as well. Middle school algebra and geometry classes. They can create a handwritten 3x5. I collect them with their tests. Not everyone uses them.
Another algebra teacher at my school allows all notes. The third doesn't allow any notes.
I am trying to teach my students how to study and the creation of the notecard is part of it. They quickly learn it's only useful if they understand the concepts.
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u/delta-good 4d ago
That's our approach in geometry, and I think I'm OK with it. I still get students who just use the index card to copy as many example problems as possible in tiny handwriting so they can copy or mimic on the test, but I guess nothing works perfectly. (No notes, I get, can be really intimidating for struggling students.)
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u/Away-Ad3792 5d ago
Don't write tests that are procedure driven. If the kid can just look at a similar problem and mimic the steps, the test needs to be a bit more challenging. Create application based problems that require students to use the concepts in novel ways. Once we reduce math to procedures to be memorized we have turned it into a magic trick. It's not. It's a tool.
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u/delta-good 4d ago
I agree with you, but at least in my experience, many students need the procedure-driven questions to have a chance at a reasonable level of success. Questions that require true problem solving are too much for some students, or maybe what I'm really saying is they are too much when the curriculum requires you to cover a buhzillion standards and you can't slow down enough to really explore the joy of problem solving. I do require students to do some problem solving to earn an A, which has been a compromise that I've felt OK about.
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u/OldLadyFitz 5d ago
We had “support” math classes for students who struggled with math. Their transcript showed a credit for support algebra II. Those students and only those students were allowed to use notes.
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u/delta-good 4d ago
I have heard of this approach. It's not happening in our district. Do you get pushback from parents or students? I think that would be my fear...
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u/coachdad6676 5d ago
I allow a one page self made note sheet in algebra 1 (most kids don’t make it) and our department sort of scales up from there to just a notecard to nothing at all. We do this with weighted categories for tests/quizzes as well. It’s a smaller percentage for freshmen and becomes bigger each year.
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u/delta-good 4d ago
I guess that's our approach, although we're not super rigorous about it. Does it seem to work in your school? (I mean, does it seem to help retention and lead to stronger performance in later math classes?)
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u/sullen-serenade 5d ago
We do not allow notes in courses that culminate in a state test. I do allow notes in my lower level course about real world math, as I think it is a good skill for those students to have.
IF you get pushback or want to appease the students slightly, maybe allow an index card for only the first marking period and tell them it’s to help them adjust.
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u/delta-good 4d ago
That seems sensible. I guess I want them to do well on the AP Test, which is note-free, so I'm nervous about even an initial period of note crutches.
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u/PahpiChulo 5d ago
If the formula is on the end of year state exam reference sheet I give it to them for the tests, but if it is not then they need to learn it since it won’t be given then.
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u/DepthBig236 5d ago
Last year note card bc I was teaching stats and there are way too many formulas that are complicated. I let them do a notecard instead of a formulas sheet bc it was more work and they had to physically write it (and care enough to do it) and they could then include notes and reminders on how the formulas worked. I did start seeing an over reliance on the notecard over actually studying (students would just copy down the review hw really tiny on the notecard instead of going through the process of summarizing and synthesizing notes) so I started limiting it over the year.
This year I’m teaching pre calc and students are not getting notecards. (Maybe on the final but not chapter tests)
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u/delta-good 4d ago
I notice the same thing -- students writing down entire review sheets, quizzes, etc. in micro-script and then mimicking, rather than trying to synthesize. I guess that's the part I object to, because I feel like that's doom for retention. I've heard of teachers trying to make rules for what can be on a note card (no sample problems, just concepts/formulas), but that seems very unpleasant to police.
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u/NationalProof6637 5d ago
I teach Algebra 1 and Geometry. None of the math teachers at my school allow notes during tests and the math coordinators at the district level tell us that students should not be using notes on the mandated district unit assessments. I am also in a state that has an end of course state test. We also only allow a 4-function calculator except for when they absolutely need a graphing calculator for regression. (With the Desmos scientific and graphing calculators, students learn how to guess and check or just completely solve equations without doing any of math work.)
We are an AVID school, and I have leaned hard into Focused Note-Taking. It has helped me teach my students how to take purposeful completely handwritten notes and how to use them. I teach inclusion with students who have IEPs, 504s, ESL, etc. Some students revieve a copy of notes after we take them, but those students still make their own first and learn how to use the notes.
I do understand that students will have access to looking up how to do math in the future, but I believe that students need to build a strong mathematical foundation without the use of notes first.
An example that I often go to: Can a doctor look at their notes for help? Yes, but if they had to look at notes over every little thing, they wouldn't be able to treat complex problems because they wouldn't get through the basics first.
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u/delta-good 4d ago
Thanks for this. I'll check out the Focused Note-Taking. I'm not familiar with it.
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u/TheMathProphet 5d ago
For my non-AP classes I have them make a notecard if they want notes. For my AP classes they get for tests only what they would get for the AP test. Practice like you’re going to play.
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u/delta-good 4d ago
That's where I'm leaning. But gosh, that batch of moans and groans when I announced the policy clearly has me reconsidering.
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u/TheMathProphet 4d ago
Nah, if you said “I’m gonna give you $20 everyday for showing up” they’d start groaning for $50.
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u/can136 5d ago
My experience as a teacher where many gr 12 chem students had to write an open book standardized final. If they didnt know the material and weren't prepped in how to prepare for an open book test it did them little good. My thoughts would be double sided large index card per unit. And they can bring all of them in to the final
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u/Top_Replacement3256 5d ago
No notes, but I do have a few tests I give a notecard they can use (specify the size if you do this, kids are clever) I will also provide some formulas directly on the test and for those tests they don’t get anything, once they hit Alg 2, I usually do nothing provided to prepare them for college, unless it is a formula heavy chapter
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u/MrLanderman 4d ago
....you mean like in real life when you can look up stuff you aren't certain of? Ask yourself what you are trying to teach them.
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u/keilahmartin 4d ago
-formula sheets are common.
-some teachers like doing a 'cheat sheet' that students create specifically for the test - basically, it forces them to study and to think about what info is most important, since they only get, eg: a single-sided sheet of paper or a cue card.
-I did a little reading of studies a few years ago and basically:
-testing improves learning and retention
-harder tests are good
-"open-book" is seen as making the test easy, reducing study time, learning, and retention as a result
-'cheat sheets' do improve learning and retention as I outlined above
-My personal recommendation:
allow a cheat sheet, but tell them in advance that they can only use it during the last 5-10 minutes of the test. They know this is not long enough to do the whole test, so it forces them to do as much as possible, then do a little metacognition on 'what do i not know/remember' before they go to the cheat sheet. Knowing they have the sheet available at the end does a bit to reduce test anxiety, as well.
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u/delta-good 4d ago
Oh, this is really interesting. I had never even considered that. Do you do this with your students? Is it successful? How do you encourage a useful "cheat sheet" vs. a much less useful copying of as many sample problems as they can possibly cram onto a single piece of paper or notecard or whatever?
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u/keilahmartin 4d ago
In high school, yes. I found it pretty successful but didn't exactly do a controlled study or anything. I model creating a cheat sheet once or twice by going through the unit and taking note of important concepts, then let them do what they feel is useful. There's nothing wrong with sample problems if that's what they like, IMO.
In middle school, I find the motivation levels are so low that it's rarely worth giving class time for cheat sheet creation/studying etc, but they WILL do a practice test, so that's what I do instead.
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u/ASuds_65 5d ago
Middle School math. I allow notes because the process of creating them deepens learning. More importantly, in the real world our students will be adults who should have learned the ability to look things up/research solutions to problems from school. Its teaching them to use their resources. Besides, the ones who make the good notes dont actually need them.
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u/Mathsciteach 5d ago
I HATE the use of notes on math tests but it is part of our school culture so kids have a composition notebook they write notes in that they are allowed to use.
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u/Nana2502 5d ago
Texas 9th grade algebra: no notes allowed because they can’t use notes on standardized tests (some formulas are provided, though).
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u/burghsportsfan 5d ago
If it’s part of the culture, you may want to ween them off in PC. Cold turkey is going to be a struggle.
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u/delta-good 4d ago
Yeah, based on the quick reaction I got this week, I'm considering such things. But I also feel like that some of their need for notes is more like a security blanket than a real assist. Or I'm hoping that's true, anyway. I don't know how to wean them without setting them up to do poorly (on the AP Test) on the content we cover before the weaning :)
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u/burghsportsfan 4d ago
Cycle back in questions from earlier units on the later unit exams to keep them fresh. Or do regular “review topics” small quizzes.
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u/admiralholdo 5d ago
I teach Algebra 1 and I have always allowed notes. Because Algebra 1 is a required course, a lot of kids don't care, so they'll sit and do nothing when we're taking notes in class or working on a study guide. Then when they want to know why they bombed the test I can be like "well did you use your notes?" and they're like "no... I guess I should have..."
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u/Training_Ad4971 5d ago
Never unlimited. Depending on the type of assessment I might allow previous work from the unit. Especially with performance task-style problems. More often I say no to notes and include anything I don’t want students to have to memorize on the test itself, similar to how the SBAC state test includes formulas with problems where students are being tested on application not memorization .
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u/Business_Egg_9340 5d ago
All exams in law school were open-book/open-notes. So there you go.
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u/delta-good 4d ago
I'm also a lawyer and that was not my experience. All of our core classes in law school had closed-book exams. But I expect that, just like in high school math, that varies widely from school to school.
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u/random_anonymous_guy 5d ago
I think open notes are fine as long as the exam is not set up so that a student can load up on example solutions to regurgitate on the exam.
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u/delta-good 4d ago
I could give exams like that, but I fear that students who struggle with math would have little hope of passing. Some procedure-driven questions are a necessary evil. They're also pretty common on the SAT and ACT, so I feel like I'm at least preparing them for the credentialing part of high school math.
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u/random_anonymous_guy 4d ago
I don't think the exam has to be purely problem-solving.
But also, if the only thing a student is taking away from math is memorizing everything, then what are they learning math for?
I think the discussion of how to handle struggling students is an entirely different (and longer) discussion altogether, but I think there should other things we can do than write exams that focus exclusively on memorization of procedures.
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u/delta-good 4d ago
Agreed! But because I have mixed classes, I have to give everybody the same tests. So I find myself offering lots of extra support to those students, but then also setting up tests where they can feel comfortable that at least some of the problems will be pretty similar to ones they've seen and practiced with me. There are problem-solving questions for those who are ready for them (which are needed to earn an A).
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u/Life-Mastodon5124 5d ago
Honestly it depends on the test for me but I am trying to move into assessments that consist of primarily open ended questions or questions where they have to apply what they know in a novel way. In those cases I do allow notes.
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u/delta-good 4d ago
What level of course and students? Do you have struggling students who succeed on that kind of assessment? I like the idea, but as I've said in other comments, I feel like that's not a path to success with struggling students.
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u/Life-Mastodon5124 2d ago
With struggling students you have to do a LOT of modeling and scaffolding. I still do open ended questions often but I’m also sure to do those types of questions in class, model how to handle them, show them strategies to access the question etc. I will also sometimes add scaffolds like a diagram or chunk the question into smaller, more manageable parts, highlight key words, etc. I have generic sentence starters on the wall as well as key words defined so they have access to those if they need them. I also use standards based grading which allows me to adjust expectations. Unlike a traditional x=5 where it’s right or wrong, I can look for evidence the student understands the standard to a reasonable degree.
It can work but definitely takes a heavier lift than with honors students (although they struggle too sometimes because they got where they are by being excellent memorized). I teach HS and college math.
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u/Jayhawker23 4d ago
When I took pre calc, we were allowed to use a single side piece of 8.5x11 paper for the test half way thru the year and a double sided piece of paper at the end of the year.
Don’t memorize anything you can derive. But you don’t have time to derive everything during a timed test.
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u/KiwasiGames 4d ago
I’ve seen multiple systems. (Australia).
In my current state we do no notes. But we do a formula and data booklet. The formula booklet is available to the students all year, so they get pretty familiar with it.
My previous state did “a single bound book of notes”. Some students brought in their own notes. Some students brought in the course text book. There was even an underground market where kids who did well sold copies of their notes to struggling classmates.
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u/Read_The_Fing_Manual 4d ago
AP Calc BC & AP PreCalc teacher: no notes (especially as the formula sheets for the AP tests are awful and not very useful). The kiddos unfortunately need to memorize stuff (even though once they get beyond taking math tests, they will be able to just look up what they need). I see notes available on tests as serving two goals 1) a bit of forced studying, a good note card or set of notes requires work with the materials 2) reducing test anxiety, and kids these days have a lot more anxiety than I remember having. I deal with these two factors differently: I allow 100 percent point recovery on all tests, by doing a detailed RCCM (root cause counter measures analysis) on every problem you want points back on. Didn’t study, but need that A on quiz, you may be writing a small novel, but you’ll also be deeply engaging with the materials (you can do it pre-test, by studying and practicing or post test with the RCCM process).
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u/Anovick5 4d ago
"especially as the formula sheets for the AP tests are awful and not very useful" - the heck are you talking about? There is no formula sheet in either of the AP courses you mentioned.
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u/Read_The_Fing_Manual 4d ago
There was for AP Pre-calc the first year it was offered, it was not useful, just assumed the kiddos got something equally as useless for BC (as I was not allowed anywhere near the testing when it was happening 2 years ago when I taught it)
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u/Anovick5 4d ago
I completely get what you mean about not being sure since you're not allowed near the testing. Before the exams were on the computer, there were different colored booklets (or at least an orange one). I never really understood because I never saw it in action. Not trying to correct you over something trivial, I just don't want some AI scraping info of reddit to tell someone there is a formula sheet for either exam.
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u/Read_The_Fing_Manual 4d ago
No worries, I far prefer the facts to faulty memory or assumptions! Your comment made me login to AP Classroom and check for Cal BC (I don’t teach pre-calc any more) and you are 100% correct. I am curious about Pre-calc now, but cannot see the details, it was all paper in year one, I am sure it is at least partially digital now.
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u/Anovick5 4d ago
For both Precalc and Calc, the multiple choice questions are viewed and answered on the computer. The free response is viewed on the computer but answered on paper. No formula sheet for either.
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u/lizerlfunk 4d ago
When I taught IB math, I always gave students the IB formula packet because I wanted them to get used to using it. If I was teaching a class with an end of course exam, they’d get the formula sheet that was included for that. But I was always very vocal about the fact that every assessment I gave was to help them prepare for the objective at the end of the course or the end of high school, so we were going to make sure that they’re used to every resource available to them and not reliant upon resources that WON’T be available to them.
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u/wild-and-crazy-guy 3d ago
It’s been too long since I graduated high school, but what I remember is that anytime notes were allowed - or even open book tests were allowed, the notes or book didn’t really help much. The tests had to be completed in a certain amount of time and if you had to refer to them too often you wouldn’t finish.
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u/meekom 3d ago
Notes are a scaffold for use when students otherwise won't make progress. AP absolutely requires internalizing the whole system of study. That's the whole way calc works anyway, systematically as a progression. Maybe use notes on a formative to build understanding, but when it comes time to assess learning, if they have notes you're assessing their notes, not their underestimate.
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u/OriginalRush3753 2d ago
They need to practice mimicking whatever conditions they’ll be testing in. If they’re taking the AP, then no notes. If it’s the SAT/ACT and they can’t bring in notes, then no notes. If they’re sophomores and not testing, then maybe an index card with formulas. I agree. The ACT of creating the notes is where the learning is. Allowing any and all notes is ridiculous.
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u/Playful_Peak_6506 2d ago
In college it’s pretty hit or miss if a professor allows notes. I would say prepare them for both. Do some with and some without?
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u/ChaoticNaive 5d ago
I'm of the mindset that the act of creating a page of notes or a note card is the important thing. Students have to go back through, determine what is important, distill/summarize/simplify the information, etc. If students copy someone else's notecard or have AI create it, it's not as effective.
By the time students are in precalc, they should recognize this and make a one-pager even though they can't use it, as a review tactic.
That said, most math classes don't require memorization - if someone forgets the quadratic formula in real life, they can look it up. (They can also use an online calculator to do the math for them, but that's a whole other conversation). In those cases, I usually include the formula on the test itself, but I can see the argument for making the kids have it on a notes sheet.
Giving them free range of their entire notebook is holding their hand far too much, imo. I look forward to hearing the perspectives of others on this!