Student Detail / Individual detail report · 4 weeks

Sarah Park

Grade 9 · Algebra 1 — radicals, special products, factoring, quadratics Action needed · Priority 1
48 problems
Solved · 4 weeks
145 problems cumulative
60% ▼ 8pp
Accuracy
Previous 4 weeks 68% → 60%
41%
Independent solve rate
Hint dependence 59%
7 days
Study streak
Restarted after 6-day gap, Jul 13–18
18 min
Daily average
62% of study after 11 PM
1:42
Time per problem
Same-grade average 3:10 — quick-give-up pattern

Learning Profile — 6 areas, scaled

All axes scaled 0–100 · derivations in the footnotes
25 50 75 100 Concept understanding 601 Procedural fluency 382 Calculation accuracy 503 Application 444 Consistency 305 Independent solving 416
Sarah Park Same-grade median 72% — common baseline for all axes (Grade 9, n=18,900)
  1. 1 Concept understanding 60 — scaled from the 4-week overall accuracy of 60%
  2. 2 Procedural fluency 38 — scaled from Factoring accuracy 38% (5/13)
  3. 3 Calculation accuracy 50 — scaled reflecting 4 sign-handling errors (50%) among the 8 factoring misses
  4. 4 Application 44 — scaled from Quadratic Equations accuracy 44% (4/9)
  5. 5 Consistency 30 — combined from the 7-day streak · 6-day gap · 18-minute daily average
  6. 6 Independent solving 41 — taken directly from the 41% independent solve rate

Last 6 weeks — weekly accuracy, weeks of 6/15 – 7/20

Shaded area = this report period (4 weeks) · hatched chip = the week with the 6-day gap
Report period (4 weeks) 40 60 80 100 Week with 6-day gap Median 72 Week of 6/15: 70% Week of 6/22: 68% Week of 6/29: 66% Week of 7/6: 60% Week of 7/13: 55% (includes 6-day gap) Week of 7/20: 60% 70 55 60 6/15 6/22 6/29 7/6 7/13 7/20
Sarah Park weekly accuracy Same-grade median 72% (Grade 9, n=18,900)
6/15
70%
—
6/22
68%
▼ 2
6/29
66%
▼ 2
7/6
60%
▼ 6
7/13 · 6-day gap
55%
▼ 5
7/20
60%
▲ 5

Practice Record — results by unit, this 4 weeks

Unit Correct/Incorrect (● correct · ○ incorrect) Accuracy · Sample Stage
Radicals & Real Numbers ●●●●●●●●●●●●○○○ 80% · 12/15 Proficient
Polynomial Multiplication & Special Products ●●●●●●●●○○○ 73% · 8/11 Developing
Factoring ●●●●●○○○○○○○○ 38% · 5/13 Beginning · Action needed
Quadratic Equations ●●●●○○○○○ 44% · 4/9 Beginning · prerequisite gap effect
Symbols show each unit's correct/incorrect makeup, not the order solved. Mastery stages: Beginning <60% · Developing 60–79% · Proficient 80–92% · Mastered >92%.

Teaching Notes

Teaching Notes

Diagnosis · Root cause — prerequisite concept chain

The decline is not driven by new material but by fundamentals (factoring). Sarah uses the special-product formulas in the forward direction (expanding) but not in reverse (factoring) — a pattern observed across her work. Most misses arise from reversing the special products learned earlier and from sign handling — the Quadratic Equations slump (44% · 4/9) reads as a downstream effect of the factoring gap (38% · 5/13). All 3 mid-session Socratic drop-offs happened in factoring.

Error breakdown · 8 factoring misses

Sign-handling errors4 · 50%
Wrong formula choice3 · 38%
Factor concept not formed1 · 13%

Wrong formula choices cluster on the difference-of-squares vs. perfect-square decision.

Error Review · 3 representative misses (actual answers)

Case 01 · Factoring
ProblemFactor x²−x−6
Student(x+3)(x−2)
Correct(x−3)(x+2)
Checked that the product is −6 but skipped checking that the sum is −1 — sign correspondence missed.
Case 02 · Factoring
ProblemFactor 4x²−9
Student(2x−3)²
Correct(2x+3)(2x−3)
Wrong formula choice — applied the perfect-square formula to a difference-of-squares case, a²−b².
Case 03 · Quadratic Equations
Problemx²+6x+9=0
Student(x+3)² correct → solution x=3
Correctx=−3
Factored correctly — the sign of the solution flipped at the very last step.

Session log · Socratic excerpt — Jul 25, Factoring

AI"For x²−x−6, shall we start by finding two numbers that multiply to −6?"
Sarah"3 and −2? Or −3 and 2…"
AI"Both pairs multiply to −6. Now, which pair adds up to −1?"
Sarah"−3 and 2! Oh… so that's why it's (x−3)(x+2)."

8 sessions in 4 weeks · 9 min average · 19 hint requests in total · 3 mid-session drop-offs (all in factoring). She gets there when guided — turning that into independent solving is the task.

Strength signals · Positive signs

  • Corrected her own misses 4 times in the radicals unit — the seed of a self-checking habit.
  • Answers in the Socratic dialogue stay earnest — this is not an attitude problem.
  • Came back on her own after the 6-day gap — a rebound is likely once the rhythm returns.

This Week's Action Plan

Action Plan
1
Pause the Quadratic Equations progression for now
Resuming after factoring stabilizes is the efficient path — the current slump is a downstream effect of the prerequisite gap.
2
Prescription set: 12 problems reversing the special products
Difficulty easy → medium · sent as a DoubleDive homework pack. Focus on practicing the reverse direction (factoring).
3
5 minutes in class — review the sign correspondence rule
Just one thing: "check the product and the sum together." 4 of the 8 misses came from sign handling.
4
Re-assess factoring in 2 weeks
Re-rate the mastery stage. Decide when to resume Quadratic Equations based on the result.
This report is generated automatically from DoubleDive learning records and does not replace teacher judgment. Students and data are illustrative samples.
Generated Jul 27 (Mon), 6:00 AM · Report period Jun 29 – Jul 26, 2026 (4 weeks) · Next report Aug 3 (Mon) · Westfield Math Academy · Teacher Ms. Susan Lee · ← All students