Training Teachers in the Effective Mathematical and Pedagogical Uses of Software Zhonghong Jiang, Texas State University, San Marcos Daniel Scher, KCP.

Training Teachers in the EffectiveMathematical and Pedagogical

Uses of Software

Zhonghong Jiang, Texas State University, San MarcosDaniel Scher, KCP Technologies

Scott Steketee, KCP Technologies

Perspectives from the Dynamic Number and Dynamic Geometry in Classrooms Projects

The Dynamic Number Project

• Builds on the paradigm of Dynamic Geometry®

• Dynamic Number: The direct manipulation of number representations and numerical constructions

• Goal: The development of software tools to deepen students' conceptions of integers, fractions, decimals, real numbers, and early algebra in grades 2–8 mathematics

The Dynamic Geometry in Classrooms Project

• Randomized controlled trial of an approach to high-school geometry that utilizes Dynamic Geometry software and supporting instructional materials to supplement ordinary instructional practices.

• Goal: Test the hypothesis that the use of Dynamic Geometry software to engage students in constructing mathematical ideas through experimentation, observation, data recording, conjecturing, and proof results in better geometry learning for most students.

The Dynamic Number Project

The Dynamic Number Project

The Dynamic Geometry in Classrooms Project

The Dynamic Geometry in Classrooms Project

curriculum & software innovation

field testing

number lines

dynamic number grids

geometric functions

fraction representations

professional development

teachers develop technical skills

teachers improve instructional

strategies

randomized controlled trial

76 classrooms

students experiment...

...observe...

...conjecture...

...and prove.

do students learn geometry better?

Shared Aspects of Our Two Projects

• The Geometer’s Sketchpad®• A belief that technology, when properly

used, can foster mathematical growth in both teachers and students

• The need for professional development so that teachers can learn the technology and use it well to promote the goals of the project

Goals of Technology-Centered PD

Participants learn the nuts and bolts of the software

Participants see how the software can help them accomplish exactly what they already do when teaching mathematics

Low-End GoalsLow-End Goals

Goals of Technology-Centered PD

• Make the mathematics primary: Teachers learn the software in the context of exploring meaningful mathematics. How the software works is viewed as secondary to what it allows them do.

• Deepen teachers’ mathematical understanding: Teachers gain a deeper understanding of the mathematics they already know — and even learn some new mathematics — as a result of using the software.

High-End Mathematical GoalsHigh-End Mathematical Goals

Goals of Technology-Centered PD

Teachers emphasize high-order thinking.Teachers consider how use of the software can engage students in higher-order thinking than was possible without the software.

Teachers modify instructional strategies.Teachers observe, consider, and adopt new strategies known to be appropriate to and effective with the technology.

High-End Pedagogical GoalsHigh-End Pedagogical Goals

Professional Development Issues

• Teacher satisfaction with PD is often low. “I have a colleague who calls professional development ‘drive-by trainings’ —it’s a good way of describing what we get.”

• PD is often ineffective. For instance, the recent Middle School Mathematics Professional Development Impact Study showed very little change in teacher behavior, even for a putatively well-designed PD intervention.

Today’s Session

• Provide an overview of the professional development aspects of our respective projects.

• Consider how to conduct technology PD to maximize teacher satisfaction and classroom effectiveness.

• Engage you in thinking and sharing your thoughts on how PD that focuses on technology can set its sights on the “high-end” mathematical and pedagogical goals we’ve described.

The Dynamic Number Project

Five elementary schools and one middle school in New York, Pennsylvania, Georgia, and California

Field test and critique new Sketchpad activities

Collaborate with us to develop Sketchpad activities

Role of the teachersRole of the teachers

18 teachers

The field test populationThe field test population

Goals of the Online Course

• Provide an intensive introduction to Sketchpad• Focus on elementary number and early algebra concepts,

but not to the exclusion of geometry• Promote discussions of the barriers to introducing

technology and ways to overcome them• Ask teachers to reflect on the pedagogical and

mathematical implications of using Sketchpad• Develop teachers' confidence in breaking out of a

lockstep approach to implementing Sketchpad-based activities

Details of the Course:

Details of the Course:

Six weeks in length

Six weeks in length

Grades based on projects and participation

Grades based on projects and participation

Two moderators: Scott and Daniel

Two moderators: Scott and Daniel

The Dynamic Geometry in Classrooms Project

• The professional development component of this project, for project years 1 and 2, consists of a summer institute (5 full-day sessions) and the academic year follow-up (6 Saturday half-day sessions).

• An approach of integrating technology, mathematics, and pedagogy in the professional development training

• A support system needed to help the participating teachers in applying what they have learned from the PD into their classrooms

Teachers Learn Software in the Context of Exploring Meaningful Mathematics

• The nature of the PD sessions is interactive and emphasizing participants’ active involvement and the conceptual understanding of mathematics.

• Important mathematics concepts, processes, and relationships are presented or revisited through conjecturing-investigating-proving tasks, usually challenging problem situations.

• These tasks/situations are explored with the dynamic geometry (DG) software as a tool. Teachers learn DG skills in the process of using them to tackle the tasks/problems.

• Through their learning experiences, teachers clearly see how DG environment encourages and facilitates mathematical investigations.

• The sessions were designed to accommodate some participants who were novice users and others who were more experienced.

Teachers Explore the Pedagogy Needed To Use the Software Well in Their Classrooms• The participant-centered, inquiry-based training method

models the instructional ideas and strategies we’d like teachers to use.

• To further help teachers to consider changes in their instructional strategies, in the relation between them and their students, and in how they facilitate student learning, mathematical explorations are always followed by discussions on questions such as “How will you teach this content in your classrooms using DG software?” and “How will you lead your students in conjecturing and proving using DG software?”

• All participants in groups of 3 or 4 prepare lesson plans to present to the entire group.

Classroom Observations for Selected Teachers

• The project staff members visit the participating teachers’ classrooms regularly to monitor the implementation of the DG treatment, get to know whether the teachers need help, and are able to provide timely assistance.

• Eighteen teachers were randomly selected through stratified sampling (stratified at the number of years teaching geometry and the types of classes they are teaching).

• Each of the selected teachers is observed five times. The five observations are evenly distributed throughout the entire school year.

• The observers use the Classroom Observation Protocol that the project has developed to score each class observed or to be observed.

The power of the DG

approach itself

The power of the DG

approach itself

StipendsStipendsGraduate credit

(3) for successful completion of the

professional development

Graduate credit (3) for successful completion of the

professional development

Personal copy of the

Geometer’s Sketchpad software

Personal copy of the

Geometer’s Sketchpad software

Instructional materials from

Key Curriculum Press

Instructional materials from

Key Curriculum Press

The GSP software for the school

computer lab(s)

The GSP software for the school

computer lab(s)

G. Travel funds for selected teachers to attend

state mathematics conferences and make

group presentations

G. Travel funds for selected teachers to attend

state mathematics conferences and make

group presentations

IncentivesIncentives

Campus Level Team Work

• Organize learning communities among teachers at the same school or conveniently nearby schools.

• Teachers cooperate with each other by offering and requesting help and deal collaboratively with instructional/learning issues that result as part of the DG implementation.

• Each team has a leader and he/she interacts with the project staff members frequently.

An On-line Help Component

The project uses the university TRACS system to include an on-line Help component to provide teachers with on-going support by sharing success stories, giving DG instructional suggestions that are frequently updated, providing links to various DG resources, etc.

Specifically the Key Curriculum Press is very supportive, and provides each DG group teacher with free access to Key Online Sketchpad LessonLink which contains hundreds of Dynamic Mathematics activities aligned to the textbooks and state standards.

Build Stronger Collaborative Relationships with School

Districts • The project research team makes great efforts to

build stronger collaborative relationships with the participating school districts so that the school/district administration is always supportive for the participating teachers to both continue their own professional development effort and implement the DG approach in their classrooms.

• Examples of such efforts include constant discussions with school/district administrators/masters teachers on important issues such as how to encourage teachers' active participation and avoid attrition, and collaborative presentations at professional meetings.