Central Bucks Schools Teaching Authentic Mathematics in the 21st Century

Central Bucks Schools

Teaching Authentic Mathematics in the 21st Century

Contact: Tara Schmucker tschmucker@cbsd.org

Throughout this course you will demonstrate an understanding of the course content and practice the skills discussed. There will be activities requiring planning, applying, reflecting, metacognition, and sharing.

Note that some activities will require that you submit responses electronically. All work can be created in a word processing program and then be copied and pasted into the collection fields on screen.

As you progress through the course, be sure to:

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  Read and listen to the information presented.
  
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  Print and read additional materials as directed.
  
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  Follow the Learning Guide closely as you progress through the multimedia portions of the course. It contains step-by-step instructions for all activities.
  
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  Complete all activities, some of which require application in your building/district.
  
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  Participate actively and frequently in all discussion activities.
  
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  Add information to your Learning Log as directed and at any other time you choose.
  
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  Visit the "Links" section and navigate through the additional web resource links.
  
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  Create a course resource binder for future reference by collecting all printed course materials and activities that will help you successfully complete the culminating activity.
  

This course is divided into five units. The first unit is an introduction to the objectives and materials of the course. The second unit focuses on authentic intellectual work, teaching, learning, and authentic assessment. In the third unit, you will learn how to analyze lessons to determine if they are authentic, and you will explore the standards of authentic instruction. The fourth unit requires that you engage in the action research cycle, including guided practice in each cycle step. In the last unit, the completion of the culminating activity based on the collection of reflections and results from course activities will occur.

The following is an estimate of the time it will take to complete each unit.

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

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  Analyze and adapt current instructional practices to reflect appropriate elements of authentic instruction incorporating technology and to create an authentic learning environment.
  
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  Incorporate authentic instruction with technology while focusing on the achievement of academic standards by all students.
  
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  Implement authentic instruction as a means of increasing student engagement.
  
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  Utilize technology effectively in authentic instruction to promote higher level thinking skills.
  
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  Develop and implement appropriate assessment strategies for an authentic learning environment.
  

Course Objectives

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.
   

As explored in the course Teaching in the 21^st Century: The Need for Change, 21^st Century students require critical thinking, problem solving, communication, and technological skills to integrate successfully into today's advancing society. Twenty-first Century students will need to master emerging content in global awareness, civic literacy, and financial and economic literacy. In order to communicate this knowledge, innovate, and collaborate, students must also be able to master technology. The Teaching Authentic Mathematics in the 21^st Century course meets the goal of the 21^st Century Teaching and Learning Series by helping to transform high school instruction from the 20^th Century to 21^st Century teaching and learning.

During this course teachers develop the skills they will need for creating dynamic, technology-rich, authentic classroom environments where students engage in real-world application of key concepts. In this course teachers will progress through a pedagogical transformation that builds the instructional foundation for real change in classroom practice and ensures the change is being implemented through action research and classroom observations. Teachers will review recent research by industry experts explaining the core components of authentic learning, instruction, and assessment. Teachers will engage in guided practice activities enabling them to connect theory to practice and transform their traditional classrooms into authentic learning environments.

This course explores the four standards of authentic instruction identified by Dr. Fred Newmann, a leading expert on authentic instruction. Newmann's standards: higher order thinking, depth of knowledge, substantive conversation, and connectedness to the world are essential building blocks for attaining the 21^st Century skills students need to be effective in the 21^st Century workplace. Through authentic instruction teachers offer individualized, meaningful, and relevant educational experiences for all students resulting in increased student engagement and improved student achievement. In authentic classrooms, teachers act as facilitators or coaches supporting students as they take ownership of their learning and begin their journey to becoming life-long learners.

To keep pace with the 21^st Century's technology and information revolution, effective, targeted mathematical instruction is critical. Mathematics teachers must provide students multiple opportunities to investigate critical questions, weigh different points of view in light of discoveries, form positions, and present and defend their work while collaborating with peers. Mathematical literacy is essential to the application of numerical information in order to make informed choices about life, community, the nation, world, and universe. Mathematics education provides teachers a rich venue for engaging students in authentic intellectual work. Teaching authentically in the Mathematics classroom encourages students to investigate, research, and collaborate to solve real-world issues. By teaching mathematics authentically, teachers will become agents of educational change and their students will be prepared for the 21^st Century workplace. --Copyright 2007 Learning Sciences International. All Rights Reserved.

Range of Instructional Practice

Adapted from Indicator: Range of Use by Learning Point Associates, available online at

The following look-fors, or evidence based behaviors that positively impact student learning, can be used as guidelines for determining whether instruction is truly authentic. At the conclusion of this course, the following look-fors will be evidenced in your instruction:

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  Teacher engages students in higher order thinking using technology.
  
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  Teacher provides opportunities for students to develop and demonstrate a depth of knowledge and understanding of central and significant concepts.
  
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  Teacher encourages substantive conversation and/or elaborated writing that extends student understanding of the subject.
  
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  Teacher designs instruction that enables students to connect subject matter to personal or public issues or concerns they have faced or are likely to face in the world beyond the classroom.
  
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  Teacher creates a classroom environment that incorporates strong social support mechanisms for academic achievement.
  
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  Teacher supports student use of 21st Century skills and technology.
  

Look for: Higher Order Thinking: Teacher engages students in higher order thinking using technology.

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  Plans for students to organize, interpret, analyze, evaluate or use information and ideas in ways that transform their meaning instead of just repeating or reporting information.
  
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  Provides opportunities for students to pose and solve complex problems.
  
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  Encourages students to discover new meanings and understandings.
  
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  Allows students to experience levels of uncertainty, ambiguity and/or conflicting views in thinking through questions and solutions.
  
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  Provides opportunities for student thinking to become visible.
  
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  Plans appropriate levels of academic tasks to maintain student engagement.
  
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  Uses technology appropriately to promote higher order thinking.
  

Look for: Depth of Knowledge: Teacher provides opportunities for students to develop and demonstrate a depth of knowledge and understanding of central and significant concepts.

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  Encourages students to construct explanations, develop arguments, and consider alternative perspectives on the meaning of ideas and events.
  
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  Presents fewer topics in a systematic and connected way so students spend more time learning about ideas and events instead of rushing through the content.
  
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  Promotes in-depth understanding of complexity in subject matter instead of providing superficial exposure and awareness.
  
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  Designs student tasks that involve applying discipline-specific concepts to different situations.
  
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  Allows students the opportunity to revise and improve their thinking.
  
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  Uses technology appropriately to promote depth of knowledge.