Review Mistakes
Learn
Reviewing mistakes is where the real learning happens. Students who carefully analyze their errors improve faster than those who simply move on to new material. This lesson teaches you a systematic approach to error analysis.
The Four Types of Mistakes
- Content Gap: You didn't know the concept or formula needed
- Careless Error: You knew how to solve it but made a calculation or reading mistake
- Misread/Misinterpret: You didn't understand what the question was asking
- Time Pressure: You could have solved it correctly with more time
The Error Log System
For each mistake, record:
| Field | What to Record |
|---|---|
| Date | When you did the practice |
| Source | Test name, section, question number |
| Category | Question type (algebra, geometry, etc.) |
| My Answer | What you chose and why |
| Correct Answer | The right answer and solution |
| Error Type | Content gap, careless, misread, or time |
| Takeaway | What to do differently next time |
The Review Cycle Schedule
- Same Day: Review all mistakes immediately after practice
- Day 3: Retry missed questions without looking at answers
- Day 7: Review error log entries from that week
- Day 14: Mixed review of similar question types
- Day 30: Full concept review if errors persist
Examples
Example Error Log Entry
Date: March 15
Source: SAT Practice Test 4, Section 4, Q23
Category: Problem Solving - Percentages
My Answer: B (120) - I calculated 20% of 100 and added
Correct Answer: C (125) - Need to find 100/0.80 = 125
Error Type: Content Gap - confused percentage increase vs. decrease
Takeaway: For "original price before discount" problems, divide by (1 - discount rate), don't add the discount amount
Example: Analyzing Careless Errors
Question: If 3x + 5 = 20, what is 6x + 10?
My process: Solved for x = 5, then calculated 6(5) + 10 = 40
The issue: 3x + 5 = 20 means 3x = 15, so x = 5. That's correct!
Actual error: Didn't notice that 6x + 10 = 2(3x + 5) = 2(20) = 40
Better approach: Look for shortcuts - the answer expression is just 2x the original
Practice
Analyze these student mistakes and identify the error type and takeaway:
1. Question: What is 25% of 80?
Student answered: 20 (calculated 80/4)
Correct answer: 20
Wait - the student was correct! What went wrong in this analysis?
Error Type: _____________
2. Question: Solve for x: 2(x + 3) = 14
Student answered: x = 4 (did 14/2 = 7, then 7 - 3 = 4)
Correct answer: x = 4
The student got it right. No error to log.
Lesson: Only log actual errors!
3. Question: A price increased from $40 to $50. What was the percent increase?
Student answered: 20% (calculated 10/50 = 0.20)
Correct answer: 25% (should be 10/40 = 0.25)
Error Type: _____________
Takeaway: _____________
4. Question: If f(x) = x^2 - 4, find f(-3)
Student answered: -13 (calculated (-3)^2 as -9)
Correct answer: 5 ((-3)^2 = 9, then 9 - 4 = 5)
Error Type: _____________
Takeaway: _____________
5. Question: What is the slope of the line through (2, 5) and (4, 11)?
Student answered: 8 (calculated (11-5) + (4-2) = 6 + 2 = 8)
Correct answer: 3 (slope = (11-5)/(4-2) = 6/2 = 3)
Error Type: _____________
Takeaway: _____________
6. Question: Simplify: sqrt(48)
Student answered: 4sqrt(3) (correct!)
But student ran out of time and guessed.
Error Type: _____________
Takeaway: _____________
7. Question: The sum of two consecutive integers is 47. Find the smaller integer.
Student answered: 24 (divided 47 by 2, rounded up)
Correct answer: 23 (let x + (x+1) = 47, so 2x = 46, x = 23)
Error Type: _____________
Takeaway: _____________
8. Question: If a triangle has sides 5, 12, and 13, is it a right triangle?
Student answered: No (didn't check - ran out of time)
Correct answer: Yes (5^2 + 12^2 = 25 + 144 = 169 = 13^2)
Error Type: _____________
Takeaway: _____________
Check Your Understanding
Q1: What are the four types of mistakes to categorize in your error log?
Q2: Why is recording "what you were thinking" important for error analysis?
Q3: How long should you wait before retrying a missed question?
Q4: What should your "takeaway" statement include?
Next Steps
- Create your error log template (spreadsheet or notebook)
- Log at least 10 errors from your recent practice tests
- Identify your most common error type
- Schedule review sessions based on the review cycle
- Move on to Mixed Set to apply all review cycle strategies together