Mathematics RtI: One Program's Efforts to Enhance Teacher Candidates' Knowledge and

Skills

David Allsopp, David Hoppey,

Stacy Hahn, Aimee Frier,

Scot RademakerUniversity of South Florida

Presentation Outline

• Program Structure & Sequence• Summer Institute Description• Individual Math Intervention Project (IMIP)

Description• Research Questions• Research Design• Findings• Implications

Structure of the Program

Competency based program of study that:• Focuses on developing teachers as problem solver • Integrates content across a logical developmental

sequence• Scaffolds expectations for learning from an acquisition to

generalization framework• Emphasizes collaborative teaching structures and situates

the program to engage in interdisciplinary partnerships• Provides graduates with supported opportunities to gain

the necessary knowledge, skills, and dispositions to meet the needs of students with disabilities

TE

Program Sequence

Semester 1

•7 hour instructional block

•Linked field experiences

•Partner schools

Semester 2

•6 hour instructional block

•Linked field experience

•Partner schools

•Content emphasis

Semester 3

•3 hour instructional block

•Linked field experience (Summer Institute)

•Partner district

•Content emphasis

Semester 4

•5 hour instructional block

•Linked field experience (year long placement)

•Partner schools

•Content emphasis

Semester 5

•3 hour instructional block

•Final internship

•Content emphasis

•Professional seminar

•PPPs•Reading Endorsement

•ESOL Endorsement

Team Teaching Approach

Continuous Progress Monitoring: Knowledge, Skills, and Dispositions

Purposes of the Summer Institute

1) Work with a partnership school to provide students with learning/cognitive based disabilities extended school learning experiences in reading and mathematics

2) Provide special education pre-service teacher candidates opportunities to implement and receive feedback on the use of research supported reading and mathematics instructional practices for students with disabilities.

3) Provide special education pre-service teacher candidates with opportunities to plan, implement and manage classroom instruction responsibilities and experience the realities of this with high levels of support.

4) Provide special education pre-service teacher candidates with opportunities to teach collaboratively and reflect on and learn from both the benefits and challenges of effective collaboration.

5) Provide special education pre-service teacher candidates opportunities to experience interacting with school personnel and students’ families in professional ways.

Summer Institute Logistics

• Third semester of program• 2 week seminar (occurs before beginning of practicum)– 3 days per week/4 hours per day

• 5 week practicum – 3 days per week/4 hours per day

• Partnership with a Charter School for Students with Disabilities (K-12/Transition)

• Assigned to classrooms of 4-8 students with a co-teach partner

• Supervised by program faculty/doctoral students

Individual Math Intervention Project (IMIP)

This assignment has 3 parts. • Part 1: Student Selection/description of needs, strengths, and interests• Part 2: Intervention Development (See handouts)

– A. Pre-Assessment– B. Hypothesis/Intervention Design– C. Progress Monitoring Plan

• Part 3: Intervention Implementation, Evaluation, and Final Analysis– A. Session Notes/Ongoing data based decision making– B. Instructional Timeline including strategies and progress monitoring

tools used– C. Post-Assessment– D. Student Performance Reflective Summary and Future

Recommendations– E. Weekly and Final Reflections on what the pre-service teacher

learned

Structure for TC Daily Intervention Sessions

Instructional Phases - (see handout)

1. Measure Progress & Make Instructional Decisions

2. Problem Solve the New

3. Build Proficiency

Mathematics Literacy Initiative

Overall Research Questions

1. What is the nature of pre-service special education teacher candidates’ implementation of individualized mathematics interventions that utilize research supported practices (IMIP)?

2. How does the analysis of students’ IMIP projects inform faculty about teacher candidates’ thinking related to data based instructional decision-making in mathematics?

Research Design• Qualitative analysis of teacher candidate performance artifacts

(Individualized Mathematics Instruction Project – IMIP).• Sampling – random sample of 13 teacher candidates’ IMIP from

the same cohort (N=36)– Pilot – 5 teacher candidates’ IMIP representing a range of overall

performance (lowest-highest)• Instrumentation – IMIP Evaluation Form (see example)• Analysis – Open coding process

– Individual researchers evaluated one of 5 IMIP– Researchers met to compare evaluations of first two areas of IMIP

Evaluation Form– One researcher reviewed all completed evaluation forms and

generated initial codes– All five researchers met to review codes, discuss, and reach

consensus including themes/families/examples

Sample: IMIP Analysis Form

Preliminary Findings

Areas of Analysis

– Student Needs– Assessment– Intervention Design– Planning– Instructional Practices– NCTM Processes

Research Question #1:

What is the nature of preservice special education teacher candidates’ implementation of individualized mathematics interventions that utilize research supported effective practices?

Assessment

Use of a Continuous Cycle of Assessment

Use of particular assessment techniques over others

Connection/comparison of data across assessment cycle (pre, ongoing, post)

Instructional decisions apparent at particular points and not others

Focus on certain components (pre, ongoing, post) rather than all

Number Knowledge Test; Student Interests; CRA Assessment OVER error pattern analysis and flexible

interview

Limited

Parallel to which assessment component TC completed

Themes

Intervention Design

Difficulty with isolating scope and sequence of target concept/Skill

Difficulty articulating the function (“because”) of the mathematics difficulty the student is demonstrating

Connection between initial intervention design and subsequent intervention sessions

Consistent completion of data/planning forms

Level of clarity/specificity of intervention across sessions

Lack of complete understanding of the targeted math concept & relationships to

other concepts (Number Sense, Operations, Algebraic Thinking)

Lack of complete understanding of the targeted math concept & relationships to

other concepts (Number Sense, Operations, Algebraic Thinking)

Limited in some cases; Evident in others

Limited in some cases; Evident in other cases

Level of clarity/specificity increases across sessions for most cases

Themes

Planning

Instructional decision-making/real-time planning within lessons

Connection between pre-intervention planning (daily planning guides) and data/information recorded on daily session notes

Clarity/specificity in describing thinking from session to session

Limited in a few; Evident in most

Limited but somewhat improved across sessions

Improves across sessions for all but one case

Themes

Instructional PracticesRS Instructional Practice

Evident? Demonstrates Reflective Practice?

C-R-A Sequence Yes - 2No - 3

Yes - 1No - 4

Advance Organizers Yes - 3No - 2

Yes - 0No - 5

Explicit Modeling Yes - 4No - 1

Yes - 3No - 2

Language Experiences Yes - 0No - 5

Yes - 0No - 5

Scaffolding/Guided Practice

Yes - 2No - 3

Yes - 1No - 4

Multiple Opportunities to Respond

Yes - 3No - 2

Yes - 2No - 3

Research Supported Instructional Practices: Themes

• Evidence of use more apparent than reflection about use of RSP– Example: Weekly Reflections

• Lack direct connections between use of a specific practice to student learning

• General descriptions/examples of RSP– Example: Explicit Modeling

• Lack references to/examples of specific EM technqiues such as “think alouds,” examples/non-examples, cueing, visuals, etc.

• Little variation in how RSP were applied across sessions– Example: Advance Organizers/Graphic Organizers

• Same LIP procedures and GO used across sessions

Preliminary Findings

Assessment

Intervention Design

Daily Lessons

Instructional Decisions

Research Question #2:

How does the analysis students’ IMIP projects inform faculty about teacher candidates’ data based instructional decision-making in mathematics?

Logical Progression of DBDM

Intervention Design• Hypothesis• Pre-assessment data • Instructional Practices• Progress Monitoring

Plan

Daily Lessons• Planning Guide• Session Notes• Summary Notes

Instructional Decisions• Uses DBDM to plan

for the next days lesson

Assessment

DBDM Discussion Points• How well students designed the project did not necessarily

correspond to the way the project was implemented and monitored.– Some students’ intervention design was appropriate but they had

difficulty effectively adapting instruction using ongoing data.– On the other hand, other students did not effectively design an

appropriate intervention but used ongoing data effectively to meet students needs.

– 1 of the 5 students was able to do both. • In this analysis a lack of understanding of the math concepts

that the pre-service teachers were teaching was apparent which subsequently influenced the effectiveness of DBDM.

How Can this Research Inform Teacher Education Programs?

• Need to embed Pedagogical Content Knowledge (PCK) throughout the program

• Developmental nature of learning to teaching – especially for learning to teach students with disabilities or students

who struggle with mathematics• Need engaged scholars who find opportunities to provide

targeted field experiences, ongoing instruction, and continuous feedback for pre-service teachers on providing effective mathematics interventions

• Need for faculty across SPED and mathematics education to become knowledgeable about the needs of mathematical and disability related learning needs for students with exceptionalities

Next Steps

• Revise instrumentation & analysis procedures as appropriate based on pilot

• Complete analysis of remaining eight IMIP from sample; determine if saturation is apparent

• Finalize interpretations• Target areas in program for enhancement/change

(e.g., incorporate fidelity checks)• Dissemination

Contact Information

• David Allsopp - dallsopp@usf.edu • David Hoppey – dth@usf.edu • Stacy Hahn – shahn@usf.edu • Aimee Frier - adfrier@usf.edu • Scot Rademaker - srademaker@usf.edu