6.2 Error-Log Patterns and Redo Sets
Key Takeaways
- A useful error log names the cause of a miss, not just the topic label.
- Redo sets should include wrong answers, slow correct answers, and guessed correct answers because all three expose score risk.
- The best correction writes the first correct setup and the prevention rule that would have stopped the miss.
- Review patterns should drive the next practice set: if scale factors, medians, or function composition keep recurring, those become targeted drills.
The Error Log Is a Diagnostic Tool
A missed ACT Math question is rarely just an algebra miss or a geometry miss. It has a cause: a domain gap, a translation mistake, a formula recall problem, a unit error, a timing decision, or an answer-choice trap. The purpose of an error log is to separate those causes so your next drill is not random.
Log more than wrong answers. Include any question you guessed, any question that took more than about 90 seconds, and any question you solved by a method you would not trust under test pressure. A slow correct answer can become a wrong answer on test day if it steals time from two easier items.
A High-Value Log Format
Use five columns. Keep each entry short enough that you will actually maintain it.
| Column | What to write | Example |
|---|---|---|
| Problem signal | The cue you should have noticed | Similar triangles with scale factor 3 |
| Tested skill | The math idea | Area scales by k^2 |
| Actual error | What happened | Multiplied area by 3 instead of 9 |
| Correct first move | The setup that should start the redo | New area = old area x 3^2 |
| Prevention rule | One future instruction | Length, area, and volume do not share the same scale |
Avoid vague labels such as careless. Careless is a mood, not a fix. If you used diameter in an area formula, the prevention rule is check radius before any circle formula. If you found the mean when the question asked for median, the prevention rule is sort first and identify the requested statistic before adding.
Common Pattern Families
Translation errors happen when the words are converted into the wrong model. Percent of the original, dollars per item, at least one, no replacement, and greater than versus at least are frequent triggers. The redo should begin by rewriting the relationship in symbols or units before any computation.
Formula-selection errors happen when two formulas feel related. Circumference versus area, mean versus median, permutation versus combination, and sine versus cosine are classic pairs. The redo should include a contrast statement: circumference is boundary length; area is inside region.
Order errors happen in function composition, matrix multiplication, operation order, and conditional probability. For f(g(2)), do g first. For a conditional probability, restrict the sample space first. For a matrix product, check the inner dimensions before multiplying.
Scale errors happen in geometry and unit conversions. Similar lengths scale by k, areas by k^2, and volumes by k^3. Rates require a per-one unit before multiplying to a new total.
Execution errors happen after a correct setup: sign slips, distribution mistakes, inequality flips, calculator entry problems, or failure to check an extraneous radical solution. The prevention rule should name the exact checkpoint, such as flip only when multiplying or dividing by a negative.
Redo Sets That Actually Change Behavior
A redo set is not re-reading the explanation and nodding. It is a small mixed set built from old risk. The first redo should happen within 24 hours with the original problem hidden as much as possible. The second redo should happen three to five days later with nearby problems added. The final redo should appear inside a timed mixed set so the skill has to compete with other topics.
Build redo sets in groups of six to ten. Use about half direct misses, a quarter slow correct questions, and a quarter new look-alikes. Keep topics mixed: two algebra/function items, two geometry/trig items, one statistics/probability item, and one essential-skills word problem. That mix prevents the false comfort that comes from knowing every item in a drill uses the same rule.
Worked Error-Log Entries
Suppose a question asks for the median of 12, 18, 18, 23, and 79, and you calculate the mean. The topic is statistics, but the cause is statistic selection. The correction is median = middle after sorting, so 18; the prevention rule is identify mean, median, mode, or range before touching the calculator.
Suppose a radical equation produces x = 9, but substituting 9 into the original creates a false statement. The topic is radicals, but the cause is not checking after squaring. The correction is check proposed roots in the original equation; the prevention rule is squaring can add solutions.
Suppose a probability item asks for at least one success in three tries, and you try to add three separate success probabilities with overlap. The cause is sample-space overlap. The correction is use the complement: 1 minus the probability of no successes.
Weekly Review Metrics
At the end of each week, count misses by cause, not just by chapter. If six of twelve misses are translation errors, another formula sheet will not solve the main problem; you need word-problem setup drills. If four misses are calculator entry errors, write more intermediate expressions before typing. If late-section questions are mostly skipped, practice triage and elimination rather than adding more untimed content review.
The goal is a shrinking error pattern. You do not need a perfect log. You need enough evidence to choose the next best drill.
Redo Set Rule
A redo is complete only when you can solve the problem cold and explain why the original wrong path was tempting. If the same trap still feels plausible, keep the item in the active stack and pair it with a near miss from a different topic.
Which error-log entry is most actionable after a student misses a similar-figures area question?
A student got a question right by guessing after two minutes of work. How should it be treated in review?
A probability question asks for at least one success in several independent trials. Which review note is most useful?