Spring 2008
Geometer’s Sketchpad Workshop
Denise K. Henry
EDTEC 544 Instructional Design SDSU
Instructional Opportunity
Supplementing the mathematics curriculum with activities that make abstract concepts more concrete is necessary to deliver instruction that is relevant and comprehensible to the students representing varied learning styles and levels present in Aptos High School’s (AHS) mathematics classrooms. Current AHS mathematics students receive instruction and demonstrate learning in traditional ways that do not capitalize on available technological resources. Construction, modeling, application and analysis of concepts in Algebra, Geometry, Trigonometry, Precalculus, and Calculus can be achieved through the use of the Geometer’s Sketchpad (GSP) software. AHS mathematics teachers have access to the GSP software and computer laboratories yet do not integrate the software into their instructional delivery or as a tool to allow students an alternative method to demonstrate mastery of learning objectives. This study centers on: Identification of barriers to use of GSP software Discovery of training needs Derivation of an instructional system
Audience Analysis
AHS employs seven mathematics teachers who instruct sections of Algebra Support, Algebra I, Geometry, Advanced Algebra/Trigonometry, Pre-Calculus, AP Calculus AB, and AP Statistics courses. Seventy percent of the teachers responded to an online survey designed to gather data regarding technical expertise, familiarity with GSP software, and comments relating previous experiences with GSP. Informal interviews of staff who maintain computer lab usage calendars yielded logistical information required to plan for use of the computer lab.
2
Survey Questions and Results (N = 7)
1. How many years have you taught math at AHS? Mean = 8 Median = 7 Range = 9 2. Please indicate your level of familiarity with the GSP software. Never tried it = 60% Used occasionally = 40% 3. If you have used it, please share the details. Successes? Failures? Frustrations? “VERY engaging, but difficult when the lab is finicky. I was one of the few teachers willing to try the software and as a result felt alone. When I "lost" a day and fell behind in the pacing compared to other teachers I also felt pressure (mostly on myself) to catch up. While I feel that the gains in going out-weighed the potential losses of not getting quite a much done, it was hard to be alone in that position.” “I know how to use it, but I haven't taught geometry here for 10 years.” “The lab was out of date, so it was painfully time consuming. It took a lot of preparation, which was frustrating. The kids thought it was okay, but weren't very enthusiastic. I may need to try different activities.” “I used it once or twice in my teacher credential program but never as a teacher.”
4. Are you familiar with: Application or Process Email MS Word Drawing Tools Reserving a Computer Lab Managing student network folders Managing students in a computer lab setting % Unfamiliar % Somewhat Familiar 20 40 60 80 0 40 % I’m a Pro 80 60 20 0 20 20
0 0 20 20 80 40
5. When do you prefer to attend trainings? Please check all that apply. Training Preferences Face to Face, During School Hours Face to Face, After School Hours Online, on My Own Time Response Frequency (%) Response Count
40 60 60
2 3 3
It appears that teachers misconceive the functionality of GSP to be limited to geometry course content. Eighty percent of teachers do not feel they are experts in student management in a computer lab setting and an equal percentage is unfamiliar with electronic submissions of student deliverables. Face to face or computer-based sessions are appropriate delivery methods for training of this audience. Teachers should not perceive
their attendance at the workshop as an inconvenience. Their attendance will enable each to meet the monthly professional development directive issued by their principal.
Interview Summary
Information surrounding procedures to reserve the computer laboratories was gathered through personal interviews. AHS librarians maintain two computer labs in the media center. An online calendar on the library’s web page displays availability. Reservations are made via email and accepted on a first-come, first-serve basis; however, English/Language Arts class reservations may take priority. Labs typically book up one week prior to the intended date of use. The Career Center houses the third computer lab at AHS. The reservation process mirrors the process for reserving media center lab space; reservations are submitted via email to the principal’s secretary. Teachers tend to reserve at this location close to the intended date of use as well.
Function Analysis
Analysis and practice of the steps a teacher will perform to facilitate a mathematics lesson that incorporates a GSP activity and receive an electronic deliverable surfaced the functions listed below. Reserve a computer lab Select a GSP activity Incorporate a GSP activity in a mathematics lesson Create and list student expectations and processes Write performance objective for a GSP activity Receive electronic student deliverables Resolve or escalate technical issues
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Recommendations
Analysis on the audience, content, and tasks the learners will perform support the creation and delivery of a GSP professional development workshop for AHS math teachers. The teachers, subject-matter experts in their fields, possess the level of technical knowledge and ubiquitous access to the technologies required to develop and facilitate instructional activities using the GSP software. A hands-on training event accompanied by take-home resources including reference sheets, sample lesson plans, troubleshooting outlines, activity response sheets, and blank pages to record personally relevant notes for future reference encourage transfer and retention of training topics.
Content Maps
The steps illustrated in the following content maps emerged through research of the software publisher’s online and hard-copy resources, interview with staff members who have a key role in the process, and first-hand practice. Each content map communicates the instructional goal, one corresponding objective, and tasks associated with a specific objective.
Goal Statement: Aptos High School (AHS) mathematics teachers will be able to create or modify a lesson to incorporate a Geometer’s Sketchpad (GSP) activity.
Given a computer with Internet access and email capabilities AHS mathematics teachers will be able to reserve a computer lab on a specific day and class period. 1
Library
Library or Career Center? 1.1
Career Center
Go Aptos High School home page. 1.2 Email reservation request to Vicki Silva. Include date and class period. 1.3
Click Library button. 1.2.1
Click view library calendar. 1.2.2
Is the period you want to reserve available? 1.4
N
Choose alternative location or date. 1.3.1
Y
Library Email request to library staff. Include date and class period. 1.5
Career Center Process Complete. 1.6
Goal Statement: AHS mathematics teachers will be able to create or modify a lesson to incorporate a GSP activity.
Teachers will be able to locate instructional activities using GSP software.
Given URLs of publisher- and user-created activities, a computer with Internet access and a teacher’s resource book, AHS mathematics teachers will be able to select and describe a GSP activity that models specific concepts within a specific mathematics course. 2
PublisherCreated? 2.2
Which resource do I prefer? 2.1
UserCreated? 2.2
Refer to teacher’s resource workbook. 2.3
Go to The GSP online Resource Center. 2.4
Click Find links to others' sketches and related resources. 2.5
Click the Resources button in the menu bar. 2.4.1
General Resources > Classroom Activities 2.4.2
Perform Internet search to locate GSP activities 2.2.1
Download activity 2.4.3
Goal Statement: AHS mathematics teachers will be able to create or modify a lesson to incorporate a GSP activity. Given a list of instructional events and access to a collection of GSP activities, Aptos High School mathematics teachers will be able to select and match one GSP activity to one instructional event and explain how the event is supported by the activity. 3
Y
Do you have a lesson plan? 3.1
N
Does it include an activity? 3.2
N
Determine activity event * 3.2.1 Contact department chair 3.3.1
Y
Replace with GSP activity for event* 3.2.1
Y
Are you concerned that activity will negatively impact pacing? 3.3
* Instructional Events 1. Gain Attention 2. Communicate objective to learner 3. Stimulate prior knowledge 4. Present distinctive features of content 5. Guide learner’s practice 6. Facilitate learner’s performance 7. Assess learner’s performance 8. Enhance learner’s retention and transfer
N
Facilitate activity. 3.4
Goal Statement: AHS mathematics teachers will be able to create or modify a lesson to incorporate a GSP activity. Given a collection of GSP activities, AHS mathematics teachers will be able to write a performance objective that includes an overt performance, measurable condition, and criterion used to measure a student deliverable for the activity. 4
Write objective 4.1
Student will be able to…
Synthesize components to create a one sentence objective 4.5
Describe overt performance 4.2
Construct a right triangle and label the right angle Explain condition under which activity is completed 4.3
Using GSP drawing tools
Express criterion used to measure deliverable 4.4
The labeled right angle measures exactly 90 degrees
Goal Statement: AHS mathematics teachers will be able to create or modify a lesson to incorporate a GSP activity.
Teachers will be able to locate instructional activities using GSP software.
Given examples of differences between procedures that students follow when working in a classroom versus a computer lab, AHS mathematics teachers will be able to list three procedures for students to follow when working in a computer lab. 5 Where will students meet? 5.1
Identify target behaviors 5.2
Embed behavior in procedure 5.2.1
Classroom 5.1.1
Computer Lab 5.1.2
List procedures 5.2.2
Add logistical procedure 5.2.3
Deliver to students 5.3
Goal Statement: AHS mathematics teachers will be able to create or modify a lesson to incorporate a GSP activity.
Given a lesson plan detailing potential technical issues, AHS mathematics teachers will be able to list the steps to resolve or escalate technical issues. 6
Review troubleshooting steps for students 6.1
A
Deliver troubleshooting documentation to students 6.1.1
A. Refer to “Student troubleshooting documentation”
Review troubleshooting steps for teachers 6.2
B A
B. Refer to “Teacher troubleshooting documentation”
Review steps to submit online tech help ticket to site and district 6.3
C
C. Refer to “Submitting help ticket documentation”
Retain troubleshooting documentation for use in lab 6.4
Goal Statement: AHS mathematics teachers will be able to create or modify a lesson to incorporate a GSP activity.
Given a computer, network storage space, and an email account, AHS mathematics teachers will be able to locate a self-created storage space created to receive electronic student deliverables. 7
Determine location to receive electronic submissions 7.1
Create network folder 7.1.1
Create email folder and filter 7.1.2
Communicate method to student 7.2
Instructional Objectives, Strategies, and Assessment
Motivational Strategy:
Participants are invited to attend the workshop via email. The email contains a hyperlink to a video montage on the TeacherTube website depicting highly engaged students working through GSP activities. Students are pictured completing individual and cooperative activities to support varied instructional events. Teachers are encouraged to post comments about the video to begin a dialogue about the software prior to the training event.
Objective 1:
Given a computer with Internet access and email capabilities, Aptos High School mathematics teachers will be able to reserve a computer lab on a specific day and class period.
Instructional Strategy:
Each participant is seated at a computer terminal. The facilitator gives an overview of section in reference binder corresponding with the procedures, and then models performance as learners carry out the steps to reserve computer labs. Since lab reservation is initiated via email, learners copy facilitator on emails sent to request reservations.
Assessment Item:
Reserve the computer lab located in the library during 5th period on May 20, 2008. CC the facilitator on any electronic communications you complete during this process.
Objective 2:
Given URLs of publisher- and user-created activities, a computer with Internet access and a teacher’s resource book, AHS mathematics teachers will be able to select and describe a GSP activity that models specific concepts within a specific mathematics course.
Instructional Strategy:
Facilitator leads brainstorming session to generate list of 5-10 instructional concepts teachers feel are the “big ideas” in the course each currently teaches. Responses are listed on a whiteboard or flip chart. The facilitator adds the proof of the Pythagorean Theorem if not already mentioned. Participants, seated at computer terminals, follow along with the facilitator’s explanation and demonstration of the procedure to locate a GSP activity modeling a proof of the Pythagorean Theorem. Teachers will work in the same break-out group all session. Each group is directed to select, note the location, and describe key features for at least one activity corresponding to a concept listed during the brainstorm session. Each group records findings on a flip chart page then shares their selections and descriptions when time is called. Pages are taped to the wall and are revisited throughout the workshop for use in subsequent activities. The pages are referred to as FCP (Flip Chart Page) when included in instructional strategies that follow.
Assessment Item:
Write one concept that you feel is important for your students to master then select and describe a GSP activity that models the concept.
Objective 3:
Given a list of instructional events and access to a collection of GSP activities, Aptos High School mathematics teachers will be able to select and match one GSP activity to one instructional event and explain how the event is supported by the activity.
Instructional Strategy:
Participants locate the list of instructional events in resource binder. The facilitator leads a discussion to stimulate thought about the ways that GSP activities can support varied instructional events. The facilitator refers break-out groups to their FCP and directs each group to reach consensus on the instructional event that is supported by the activity listed. Each group writes the name of the instructional event and a justification for the choice on its FCP.
Assessment Item:
Select one GSP activity from the collection of activities, match it to an instructional event, and then explain how the event is supported by the activity.
Instructional Events Gain Attention Communicate objective to learner Stimulate prior knowledge Present distinctive features of content Guide learner’s practice Facilitate learner’s performance Assess learner’s performance Enhance learner’s retention and transfer
Objective 4:
Given a collection of GSP activities, AHS mathematics teachers will be able to write a performance objective that includes an overt performance, measurable condition, and criterion used to measure a student deliverable for the activity.
Instructional Strategy:
The facilitator guides participants through the process of writing performance objectives that include an overt performance, condition, and criterion used to measure a student deliverable for a GSP activity. The facilitator provides examples and non-examples of performance objectives. Groups write an objective for the activity selected on its FCP. Groups share objectives and give feedback to strengthen objective writing skills.
Assessment Item:
Select a GSP activity from the collection then write a performance objective for the activity.
Objective 5:
Given examples of differences between procedures that students follow when working in a classroom versus a computer lab, AHS mathematics teachers will be able to list three procedures for students to follow when working in a computer lab.
Instructional Strategy:
Participants refer to matrix in reference binder that compares and contrasts procedures students follow when working in a computer lab with procedures students follow when working in a classroom. Group members discuss modifications they feel are necessary to the matrix, make individual notes, then share modifications with the whole group.
Assessment Item:
Use the Classroom vs. Computer Lab Procedure matrix in your reference binder to write three procedures for students to follow when working in a computer lab.
Objective 6:
Given a lesson plan detailing potential technical issues, AHS mathematics teachers will be able to list the steps to resolve or escalate technical issues.
Instructional Strategy:
Participants refer to the troubleshooting documentation in their reference binder as the facilitator gives an overview of frequently occurring technical issues and troubleshooting steps. Groups refer to the sample lesson plan detailing potential technical issues then list steps to resolve each potential issue. Groups share lists with whole group and give feedback to strengthen individual resolution skills.
Assessment Item:
Explain the steps to resolve or escalate the following issues: A student cannot find the GSP activity file you created for today’s investigation. The GSP software is not found on the student’s desktop when she logs in. A student cannot remember his Aptos High School network login and password.
Objective 7:
Given a computer, network storage space, and an email account, AHS mathematics teachers will be able to locate a self-created storage space created to receive electronic student deliverables.
Instructional Strategy:
Participants are seated at computer terminals with reference binders open to the page explaining methods to receive electronic student deliverables. The facilitator provides an overview of the methods. Participants decide which method they prefer to use then follow the facilitator as she projects a step-by-step demonstration to set up each location. Upon completion, participants are asked to return to the computer desktop then locate the storage space each created.
Assessment Item:
Locate the storage space you created to receive electronic student deliverables. If you created a network folder, print the screen displaying the folder and write the path on the page. If you created an email folder with a filter, print the screen displaying the email folder in the main view of your email application and the screen displaying the filter dialog box.