NHA Algebra 1 Unit 1: Three-Lesson Comparative Analysis
Comprehensive Summary of Lessons 1-3
This document synthesizes findings from individual lesson analyses to identify patterns in "the NHA way".
Executive Summary
After analyzing the first three lessons of NHA's Algebra 1 curriculum, clear patterns emerge that define "the NHA way":
- Problem-based learning where students construct understanding before procedures are formalized
- Orchestrated classroom discourse using the 5 Practices (Anticipate, Monitor, Select, Sequence, Connect)
- Multiple representations valued equally, with explicit connections made across all forms
- Progressive scaffolding from concrete to abstract with intentional preparation
- Productive struggle embraced as learning, not avoided
- Timing evolution from unrealistic (Lesson 1) to realistic two-day structure (Lesson 3)
Quality progression: Lessons improve from B+ (90%) → A- (91%) → A (94%), showing curriculum refinement and responsiveness to implementation realities.
Part 1: Comparative Overview
Lesson Basics
| Aspect | Lesson 1 | Lesson 2 | Lesson 3 |
|---|---|---|---|
| Lesson Type | Develop Understanding | Develop Understanding | Develop Understanding |
| Time Structure | Single 55-min (actually 74 min) | Single 55-min (actually 56-61 min) | TWO 55-min periods |
| Main Concept | Variables represent patterns, seeing structure | Arithmetic sequences, function notation | Geometric sequences, exponential growth |
| Overall Grade | B+ (90%) | A- (91%) | A (94%) |
The 5 Practices Across Lessons
All three lessons implement the 5 Practices, but with increasing sophistication:
| Practice | Lesson 1 | Lesson 2 | Lesson 3 |
|---|---|---|---|
| Anticipate | 4+ strategies anticipated | 2 visual methods, recursive thinking issue | 2 visual methods, common difference failure, exponent difficulty |
| Monitor | Press for visual connections | Help stuck students make table/graph | Watch for common difference attempt (productive failure) |
| Select | 2-4 different grouping methods | Visual, table, graph, recursive | Visual methods, failed common difference, doubling pattern |
| Sequence | Color → Groups → Constants → Area | Visuals → Equations → Table → Graph | Visuals → Contrast with arithmetic → Ratio → Recursive → Explicit |
| Connect | Focus on "ways of seeing" | Show 4t+1 from different perspectives | Show multiplying vs adding, exponents from repeated multiplication |
Pattern: Sequencing becomes more sophisticated. Lesson 3 intentionally includes productive failure in the sequence.
Part 5: "The NHA Way" - Defining Characteristics
1. Multiple Representations Valued Equally
Evidence from Lessons:
- L1: Tiles → Groupings → Expressions (multiple equivalent forms valued)
- L2: Visual → Table → Graph → Recursive → Explicit (all four labeled with same features)
- L3: All representations + contrast between types (arithmetic vs geometric)
2. Vocabulary After Experience
What This Looks Like:
- Terms introduced at END of lesson, after conceptual work
- Students need language to describe what they've done
- Vocabulary is motivated, not arbitrary
Evidence from Lessons:
- L1: "Variable," "expression," "equivalent" after 64 minutes of pattern work
- L2: "Arithmetic sequence," "recursive/explicit" after experiencing both equation types
- L3: "Geometric sequence," "common ratio" after discovering adding doesn't work
3. Productive Struggle in Community
What This Looks Like:
- Problems designed to require reasoning (not just procedure application)
- Discussion builds on varied student approaches
- Teacher facilitates, doesn't lecture
- Class learns from each other's methods
Part 6: Conclusion
Summary of Findings
"The NHA Way" is defined by:
- Orchestrated classroom discourse (5 Practices)
- Multiple representations with explicit connections
- Sense-making over procedures
- Vocabulary after conceptual experience
- Productive struggle in community
- Rich, accessible tasks with multiple entry points
- Progressive scaffolding from concrete to abstract
- Realistic implementation (by Lesson 3's two-day model)
Quality improves across lessons:
- B+ (90%) → A- (91%) → A (94%)
- Implementation practicality improves dramatically (78% → 88% → 96%)
- Two-day structure in Lesson 3 solves timing problems from Lessons 1-2
Critical decision for stakeholders:
Self-paced AI can deliver high-quality instruction, but it will be philosophically different from "the NHA way." The question is whether the benefits of AI (adaptive pacing, personalized practice, interactive visualizations) compensate for the loss of peer discourse and community-based learning.