Central Bucks Schools Teaching Authentic Mathematics in the 21st Century



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Technology Used:
Calculator
Geometer's Sketchpad

Assessment Tool:
Baseball field task and report

4 Standards

Higher Order Thinking: Generalizing the chart for the n-gon. Using the knowledge of regular polygons to design a regular polygon for the baseball field.

Depth of Knowledge: Differences between regular and non-regular polygons. Knowing how to complete the chart for the regular polygons using mathematical skills and patterns.

Substantive Conversation: Students discussing differences between shapes and real objects. Students discussing in pairs the differences between regular and non-regular polygons. Students discussions as they constructed the baseball field using Geometer's Sketchpad.

Value Beyond the School: Determining the measure of interior and exterior angles for construction or design purposes. Building a model using technology and measurements. Generating a table or chart to find values from a pattern beginning with a simpler problem.

© Copyright 2007 Learning Sciences International.


All Rights Reserved. 

Lesson Plan Location

Evidence/Specific Adaptation Ideas

 

 

 

 

 

 




 

 

 

 

 

 

 

 

 

 




  1. Now review Dr. Newmann's feedback on the same lesson.
     

Dr. Fred Newmann's Expert Feedback

Lesson Plan Location

Evidence/Specific Adaptation Ideas

Higher Order Thinking Skills

This lesson is a good example of Higher Order Thinking Skills.

Depth of Knowledge

Effectiveness in this area could be increased by more explicit consideration of advantages/uses of regular vs. non regular polygons. For example, why is the distinction important to learn? Also, are there some situations when it may be unclear what type it is. This would add to understanding of complexity of the concepts.

The baseball diamond activity could build more depth if students had to evaluate or give feedback on the accuracy of different student proposals. This suggestions should illustrate that when you have students working in groups it can be useful to specify in more detail what kind of intellectual work you want them to do. E.g., Brainstorming is different from developing and defending a proposal or product.






Substantive Conversation

Students would be conversing about disciplinary content, but the plan gives no assurance that their conversations will be structured so that students respond to one another and build upon statements of prior speakers to develop collective understanding. Can you include some prompts or anticipated moves of the teacher to make the conversations systematic in this way?

Value Beyond the School

Finding objects in the world that conform to the geometric definitions is not a mathematical problem that students are likely to confront beyond school—just telling them to use mathematical definitions to label things beyond school. That can be valuable for learning the definitions, but wouldn't score very high.

In contrast, trying to design a baseball diamond might be a problem requiring mathematics that students confront, especially if they worked in landscape architecture for a baseball club.

Could you think of a real world situation where making a choice between a regular vs. non regular polygon would be important, or perhaps a controversy in a remodeling project or other design venture about what kind of a polygon (how many sides, how regular) would be most efficient etc.


Assessment Plan Rubric

Design a baseball diamond or golf course or a project that would require a decision between using a regular vs. non regular polygon.




  1. Please respond to the following questions:

    1. What similarities and differences did you identify between your analysis and Dr. Fred Newmann's?

 

 


    1. What did you learn?

 

 


    1. Briefly summarize how you would adapt the lesson to improve its authenticity. Please include your thoughts on how and where higher order technology tools might be used effectively to enhance instructions. (Please refer to the "Range of Instructional Practice" chart and the "Technology: Productivity Use vs. Higher-Level Thinking Use" chart.)

 

 


  1. Summarize your responses in the space provided. Be prepared to add the summary to your Learning Log.

 

 


  1. Enter your summary in your Learning Log by clicking on "Resources" and then "Learning Log." (Label your entry "Lesson Analysis")

  2. Close the Learning Log window to return to the course.

  3. Return to the course.

Personal Notes for Implementation:
 

 

 



 
Sync Point Discussion Activity

In this activity you will participate in a discussion with the other members of your study group regarding the key concepts considered in this unit.



    1. The Sync Point Discussion will take place in a document in Google (www.docs.google.com).

    2. Please log into your Google account.

    3. Locate the file labeled “Sync Point Discussion 3: Teaching Authentic.”

As you reflect upon the four standards of authentic intellectual work, which standard will be the most difficult to implement? Discuss why it will be a challenge, and solutions or techniques that will help master meeting all four standards. How will higher order technology tools help you keep your instruction authentic?

    1. Respond to the members of the group.

    2. Please complete this assignment by Friday, December 19, 2008.

Personal Notes for Implementation:

 

 



 
UNIT 4: TEACHER ACTION RESEARCH

Unit Overview:

In this unit you will define and incorporate the cycle of action research and its benefits. Next, you will identify a pressing question of concern in the classroom and collect the necessary assessment data needed to explore the concern. Then, you will analyze and synthesize the data to develop a plan of action. Instruction will be planned and delivered, and progress monitoring will ongoing. Information from the progress monitoring will provide insight on instructional implications. The final step of the cycle involves the collaboration and sharing of research with peers. As a result of the action research you will identify areas to improve instructional outcomes.


Unit 4 Activity Time Breakdown

 

Course Objectives



As a result of this course, you will be able to:

  1. analyze and adapt current instructional practices to reflect appropriate elements of authentic instruction and to create an authentic learning environment.

  2. incorporate authentic instruction while focusing on the achievement of academic standards by all students.

  3. implement authentic instruction as a means of increasing student engagement.

  4. utilize technology effectively in authentic instruction to promote higher level thinking skills, and

  5. develop and implement appropriate assessment strategies for an authentic learning environment.

*For each activity/experience the relevant objectives are identified in the third column of the chart.

Unit 4:  Teacher Action Research

Section 4.1:  Teacher Action Research

Topic 4.1.1: What Is Action Research?

Title

Estimated Time

Objectives Identified

Complete Course Activity: Teacher Action Research K-L-D Chart

5 minutes

NA

View Multimedia Segment

1 minute

1

Optional: View Resource Multimedia Segment

4 minutes

1

Topic 4.1.2:  How Do I Develop an Action Research Question?

View Multimedia Segment

5 minutes

1,2,3,5

Optional: View Resource Multimedia Segment

5 minutes

1,2,3,5

Optional: Read article titled A Passion for Inquiry in an Era of 'Right Answers': Inquiring about Teachers Inquiring about Their Practice

20 minutes

1,2,3,5

Complete Course Activity: Research Inquiry Topic

30 minutes

1,2,3,5

Topic 4.1.3:  What Student Assessment Data Should I Collect and How Should I Analyze It?

View Multimedia Segment

1 minute

1,2,3,4,5




Optional: View Resource Multimedia Segment

3 minutes

1,2,3,4,5

Optional: View Resource Multimedia Segment

1 minute

1,2,3,5

Optional: Read article titled Effective Use of Assessment Data in Action Research

15 minutes

1,2,3,4,5

Optional: Read article titled Instructional Implications of Student Data Assessment

20 minutes

1,2,3,5

Job-embedded Activity: Assessment Data Collection

25 minutes

1,2,3,4,5

Job-embedded Activity: Identify Instructional Needs

75 minutes

1,2,3,4,5

Topic 4.1.4:  How Do I Plan and Deliver Instruction Based on Individual Student Needs?

View Multimedia Segment

2.5 minutes

1,2,3,5

Optional: View Resource Multimedia Segment

2.5 minutes

1,2,3,5

Optional: Read article titled Connecting Action Research to Individual Student Needs

5 minutes

1,2,3,5

Prediscussion Activity: Individual Student Needs

10 minutes

1,2,3,5

Discussion Activity: Individual Student Needs

20 minutes

1,2,3,5

Topic 4.1.5:  How Do I Progress Monitor and Post Assess?

View Multimedia Segment

1 minute

1,2,3,5

Optional: View Resource Multimedia Segment

2 minutes

1,2,3,5

Optional: Read article titled Progress Monitoring and Post Assessment

7 minutes

1,2,3,5

Job-embedded Activity: Progress Monitoring and Post Assessment

50 minutes

1,2,3,5

Topic 4.1.6:  How Do I Determine Instructional Implications?

View Multimedia Segment

1 minute

1,2,3,5

Optional: View Resource Multimedia Segment

2 minutes

1,2,3,5

Optional: View Resource Multimedia Segment

2 minutes

1,2,3,5

Optional: Read article titled How Do I Determine Instructional Implications?

15 minutes

1,2,3,5

Optional: Read article titled Action Research Case Studies

15 minutes

1,2,3,5

Job-embedded Activity: Identifying Instructional Implications

35 minutes

1,2,3,4,5

Topic 4.1.7:  How Can I Collaborate With Peers to Share the Results and What I Learned From My Action Research?

View Multimedia Segment

1 minutes

1,2,3,5




Optional: View Resource Multimedia Segment

2 minutes

1,2,3,5

Optional: Read article titled Study Group Protocols for Sharing Action Research

7 minutes

1,2,3,5

Job-embedded Activity: Sharing with Peers

30 minutes

1,2,3,4,5

Complete Course Activity: Classroom Look-Fors End of Course Self Assessment

30 minutes

1,2,3,4,5

Participate in Sync Point Discussion (Non-Blended Graduate Version & CPE Version only)

60 minutes

1,2,3,4,5

Participate in Sync Point Discussion (Blended Study Group/Graduate Version only)

180 minutes

1,2,3,4,5

Unit 4 Essay Question (excluding Self-study Version)

35 minutes

1,2,3,4,5

Unit 4 Time Totals

Blended Study Group Version

11 hours & 6 minutes

 

© Copyright 2007 Learning Sciences International.


All Rights Reserved.
Section 4.1: Teacher Action Research

Topic 4.1.1: What Is Action Research?

Course Activity: Teacher Action Research K-L-D Chart

In this activity you will reflect on the teacher action research cycle.



  1. Locate the "Teacher Action Research K-L-D Chart” on the following page and complete the "K" column of the chart, recording what you already know about the topic.

  2. Save the chart for later use. You will be directed when to fill in the "L" and "D" columns. This information will be used to complete the culminating activity.

  3. Return to the course to continue.

Personal Notes for Implementation:
 

 

 



 
Teacher Action Research K-L-D Chart

Teacher ___________________ Date ____________ District/School__________________

What I Already Know (K)

What I Learned (L)

What I Will Do (D)

What is your current knowledge (K) of this topic?  Consider:

  • college courses

  • professional reading

  • peer conversations

 

List key points or phrases below.

What new or extended learning (L) have you gained from this unit?

What knowledge, strategies, and/or practices have you experienced or extended with this content?

List key words or phrases. (You may refer to the prior screens to review the content.)

How will what you learned impact what you do (D) in your building?

Think about your authentic instructional practices and reflect on how they may be changed or revised based on data collection and interpretation, course content knowledge, and research-based practices that were present in this course.

List key points and phrases below.

 

 

Learning into Doing

 

 



Data Collection and Analysis

 

 



 

 

 



Based on a document developed and written by the CAIU Writing Team:
A. Morton, C. Eisenhart, M. Bigelow, P. Conahan, M.K. Justice (2004)

© Copyright 2007 Learning Sciences International


All Rights Reserved.

 

Teacher Action Research K-L-D Chart



Teacher ___________________ Date ____________ District/School__________________

What I Already Know (K)

What I Learned (L)

What I Will Do (D)

What is your current knowledge (K) of this topic?  Consider:

  • college courses

  • professional reading

  • peer conversations

 

List key points or phrases below.

What new or extended learning (L) have you gained from this unit?

What knowledge, strategies, and/or practices have you experienced or extended with this content?

List key words or phrases. (You may refer to the prior screens to review the content.)

How will what you learned impact what you do (D) in your building?

Think about your authentic instructional practices and reflect on how they may be changed or revised based on data collection and interpretation, course content knowledge, and research-based practices that were present in this course.

List key points and phrases below.

 

 

Learning into Doing

 

 



Data Collection and Analysis

 

 



 

 

 




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