Deliberate Practice for Algebra 1 with the TI-Nspire® Calculator: Electronic Supplemental Resources.

A PROJECT in MATHEMATICS

Steven Mendoza

Proposal Summary•Motivation

• Incoming barriers• Number concept• Number facts

• Outgoing barriers• Computation• Procedural automaticity

•Intended outcome• Develop automaticity through deliberate practice

• Goal: schema automation• Support: Cognitive Load Theory

Intended Outcome: Schema Automation

• Cognitive Load Theory– Working memory is limited– Intrinsic, germane, and extraneous loads– Cognitive overload– Automated schemas– Early versus later stages of learning

Why is schema automation desirable?

Deliberate Practice

• Students’ practice has actually improved their performance.

• Practice is within the student’s ability level.• Timely and descriptive feedback.• Repeated opportunities to practice a task

through practicing other tasks like it

Brabeck, M., & Jeffrey, J. (2011). Practice for Knowledge Acquisition (Not Drill and Kill).

•Content choice: Linear equations in one and two variables• TEKS• Common Core State Standards

•Justification• Current district resources• Electronic resources

Proposal Summary

Existing Resources Has this been done before? Are we reinventing the wheel?

Holt 2-3 (2007) Practice Problems reproduced with permission from HMH Publishing

Existing Resources (continued)

Carnegie Learning’s Algebra 1, based on cognitive tutor.

coolmath.com

MethodologyCreation Cycle

1. Coded a usable version2. Implemented in classroom3. Revised code based on usage data

Updates for Usability• Accessible from any Nspire document• Parsing user input for flexiblity

Changes to Program Structures• Narrowed focus of ysolver()• Created separate programs for linear forms

Additional Features• Generators

•3 programs with levels• 1-variable linear equations• 2-variable linear equations• Systems of 2-variable linear equations• Teacher documentation for usage

•3 programs for linear forms• Slope-intercept form• Point-slope form• Standard form• Worksheets for student usage

•Generator for most programs

Products

Program Details: eqpractice()

Program Details: eqpractice()

Program Details: ysolver()

Program Details: ysolver()

Program Details: addeq()

Program Details: slopeint()

Program Details: slopeint()

Program Details: practicegen()

ImplementationInstallation•Approximately 15 minutes for class set•One-time installation

Teacher Documentation•Instruction for installation and usage•flowcharts

Student Documents•Instructions for usage•Worksheets to accompany programs•Sample work

Handouts

•Sample problems•Description paragraphs•Teacher instructions•Student work

Thanks for your time.

Choice Of Content Focus

• State and National Standards– Texas Essential Knowledge and Skills– National Council Teachers of Mathematics– Common Core State Standards Initiative

Why focus on linear equations, functions, and systems?

4 Readiness Standards and 7 Supporting Standards for Algebra 139 TOTAL

•Algebraic Thinking (Driscoll) -Doing/undoing -Symbol sense -Multiple representations

Motivation: Classroom Needs

Student Needs– Incoming barriers

• Number concept• Number facts

– Outgoing barriers• Computation• Procedural

Teacher Response– Quantity of practice– Quality of practice– Feedback– Individualization

PRACTICE!!! Shift focus to GERMANE load.