There are two critical components for student success in standardized tests:
Working through the corresponding Math Academy course will provide students with mastery of the curriculum.
However, students must then engage in an active process of test preparation, which takes place mostly outside the Math Academy platform. Guidance on how to do this successfully is provided here.
If a student wants to earn a high test score, then they must have extensive and solid knowledge of the underlying content.
Yes, many standardized tests include non-standard problem types that go beyond typical course content.
But to have any chance of solving a non-standard problem, a student must be able to solve standard problems that are similar, or at least, that exercise the component skills being pulled together in the non-standard problem.
Yes, non-standard problems often require some sort of “mental leap.”
But the longer a “mental bridge” a student has built outwards in that direction, the shorter the distance they'll have to leap, and the higher the chance that they'll make the leap fully across. And the way that a student builds this mental bridge is by having a complete knowledge base of all the standard problem types.
IMPORTANT: Students must complete the entire course at least six weeks before the test date to leave sufficient time for test preparation.
Extensive content knowledge does not automatically guarantee a high test score! In other words, mastery of course content is a vital component of test success, but it is not sufficient on its own.
Earning a high test score requires plenty of practice with the following things, which are specific to the particular test being taken:
In the six weeks leading up to the test, students must do the following:
In the six weeks before the test, students should take at least six different practice tests, all of which should be completed under timed conditions.
It is important to use practice tests that most accurately represent the types of problems that a student could expect to see on the real test.
For this reason, students should obtain practice tests directly from the organization that administers the particular standardized test that they plan to take.
The entire practice testing process should reflect the conditions that the student can expect to experience on test day. In particular, when taking practice tests, students should work in a comfortable, quiet environment under timed conditions.
Note that while practice tests must be timed, they can be broken up into smaller increments. For instance, if the whole practice test is 2 hours long, then a 30-minute segment could be constructed by doing every problem number that is a multiple of 4.
(The test must be broken up longitudinally like this because the end of the test is typically more difficult and will take more time than the beginning of the test.)
Time management is essential when taking standardized tests. If a student is really struggling with a particular question, they shouldn't dwell on it too much. Instead, they should fill in their best guess and move on. They should also write down the question number on a sheet of scrap paper so they can return to it later if there's time.
To be clear: students should refrain from guessing as much as possible! Guessing the answer to a question is a last resort.
However, most standardized tests do not penalize incorrect answers, meaning that students should take their best guess on any questions they do not know how to answer. (If a test does penalize incorrect answers, then students should only guess if they are able to eliminate most of the incorrect answer choices.)
Whenever a student guesses on a problem or is otherwise not completely confident in their answer, they must note the question number on a sheet of scrap paper. It is essential that these questions are reviewed again. Every time a student learns how to solve a question that stumped them previously, they increase their expected score on the real test.
Once a student has finished a practice test, they should grade it using the official scoring guide for that test. On a separate piece of paper or spreadsheet, they should record the following information:
Some tests like AP Calculus have Free Response sections. While students can easily grade a Multiple Choice section on their own using an answer key, it's important to grade Free Response sections very carefully, paying close attention to the rubric.
Even with a detailed rubric, it is not uncommon for students to mistakenly gloss over areas where they would have missed points. For instance, even if a student's answer is “almost” correct, they may lose significant points for not including units, not rounding to the correct number of decimal places, not checking the conditions of a theorem that they are applying, etc.
To be completely sure that a student's Free Response section is graded accurately, it is ideal to have the grading done by a tutor who has experience preparing students for the test. While tutors can be expensive by the hour, it is sometimes possible to arrange a discounted flat-rate price where
At the very least, if no tutor is unavailable, then the student should grade their Free Response section together with an adult. The adult must check to make sure that the student carefully follows the grading rubric when determining how many points are earned by each of their responses.
After taking a practice test and recording their performance, a student should immediately review the list of questions they missed or didn't feel completely confident on.
It is important that this review takes place immediately after the practice test, or at least on the same day. The longer a student waits before the review, the less they will remember about their areas of confusion, the longer the review will take, and the less they will learn from it.
When reviewing areas of weakness, it is critical to minimize reliance on reference material as much as possible. Each question should be reviewed according to the following procedure:
IMPORTANT: If a student peeks at the solution when solving a problem, they should wait a few minutes and then re-attempt the problem without any assistance. The student should continue this process until they are able to solve every problem completely unassisted, without peeking back at any reference material.
After a student reviews the list of questions they missed or guessed, they should work through these problems again the next day following the same procedure outlined above: attempt to solve the problems unassisted, peeking at reference material only if completely stuck.
The student should continue working through the problems every day until they are able to confidently solve all the problems without assistance.
After a student has worked through the problem set correctly and confidently without relying on any reference material, they should work through the same problem set again a few days later, and once more after a week. The goal is for students to first learn how to solve the problems correctly, and then engage in spaced review to maximize their retention of what they've learned.
During these spaced reviews, if a student ever answers a problem incorrectly, they should repeat the same procedure of reviewing the solution and re-attempting the problem until they are able to work it out correctly unassisted.
IMPORTANT: It is essential to always attempt to recall the correct solution strategy from memory! Successfully recalling fuzzy information is what extends the duration of that memory. Simply re-reading information may refresh it in one's mind, but it will not actually slow down the rate of forgetting.
Once a student has completed a week of spaced review on the list of missed questions, they can repeat the entire test a week later under timed conditions.
This will give them additional practice in time management with the confidence they have the knowledge and experience to score highly on that test.
Once done, they should grade it and record the new score next to their previous score. They should find their score has improved considerably.
We stress that the highest priority is working through at least six practice tests, followed by a targeted review of the questions they get wrong. This is preferable to retaking one or two tests multiple times. But doing both is best.
Students must prioritize practice tests in the six weeks before the test. However, they should also continually review content knowledge.
Once a student completes the corresponding course in the Math Academy system, they should enter “test-prep mode.” This happens automatically for test-specific courses like SAT Math Fundamentals, but test prep mode can also be triggered manually in the user settings for any courses in the system.
When a student completes a course in test-prep mode, they will not be given more advanced content to learn - instead, our task-selection algorithms will prioritize review tasks that optimally remediate weaknesses and strengthen the student's existing knowledge.
Normally, we strike a balance between teaching new content and reviewing previously-learned content, providing “just enough” review that students do not forget what they've learned. But in test-prep mode, students focus entirely on reviewing previously-learned content so that they can be 100% fresh on every single topic on the day of the test.
During the six weeks leading up to the test, students should spend around 90 minutes on preparation per day:
In the last week or two before the test, students should increase their preparation time to at least two hours per day, spending extra time on practice tests.
We emphasize that it is absolutely crucial to spend adequate time on both practice tests and standard course content – in particular, every single day in the final week leading up to the test.
At the time that a student takes the test, they need to be 100% solid and 100% fresh on all their standard course content and all the non-standard problem types covered in the practice tests.
Students who have mastered the course content are often surprised at how low their initial practice test scores are.
Rest assured, this is perfectly normal. It takes some exposure to get used to the time limit, question types, and phrasing of the test questions.
Students who master their content knowledge and follow our guidance for practice tests will find that their test scores improve dramatically during the first few practice tests.
IMPORTANT: Even if a student's practice test score reaches maximum level during the first few practice tests, it is critical to continue taking practice tests in accordance with this test preparation guide.
Students need to consistently achieve high scores on practice tests, and they do this continually all the way up to the day of the test. If they do not, then they will become rusty and perform worse than anticipated on the day of the test.
This is especially important on tests like AP Calculus, where score ranges are grouped into high-level categories. On the AP Calculus test scores range from 1 to 5, with 5 being the highest. If a student “just barely” scores a 5 on the practice test, that is not enough to expect a 5 on the real test. The student needs to continue taking practice tests until they are scoring deep into the territory of a 5, and they need to do this continually all the way up until the day of the test.
Students should complete their entire Math Academy course at least six weeks prior to the test date.
Then, they should enable test-prep mode so that their learning tasks focus entirely on strengthening existing knowledge. They should continue completing 30-45 XP on Math Academy every day so that they are 100% fresh on every single topic on the day of the test.
At the same time, students should take at least six different practice tests under timed conditions. They should spend 60 minutes taking / grading / re-attempting practice tests every day, increasing to 90 minutes per day in the week leading up to the day of the test.