Teaching Authentic Mathematics in the 21st Century
Contact: Tara Schmucker email@example.com
Teaching Authentic Mathematics in the 21st Century
Learning Guide—Blended Study Group Version Use this guide as you progress through the course to organize your thoughts and to help you plan ways to apply the content you have learned in your building/district. At times, you may be prompted to refer to the learning guide for specific directions or activities. This course is structured using units, sections, and topics. For further explanation, please refer back to the online orientation.
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:
Read and listen to the information presented.
Print and read additional materials as directed.
Follow the Learning Guide closely as you progress through the multimedia portions of the course. It contains step-by-step instructions for all activities.
Complete all activities, some of which require application in your building/district.
Participate actively and frequently in all discussion activities.
Add information to your Learning Log as directed and at any other time you choose.
Visit the "Links" section and navigate through the additional web resource links.
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.
*Many articles are provided in podcast format for increased portability and to provide flexibility for different learning styles. However, learners are also encouraged to print out the articles to add to their resource binder for future reference. UNIT 1: INTRODUCTION
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.
Teaching Authentic Mathematics in the 21st Century
As explored in the course Teaching in the 21st Century: The Need for Change, 21st 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 21st Century course meets the goal of the 21st Century Teaching and Learning Series by helping to transform high school instruction from the 20th Century to 21st 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 21st Century skills students need to be effective in the 21st 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 21st 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 21st 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
Artificial Context: Level of authenticity where students are exposed to instruction that contains drill and practice and results are self-contained within the classroom
Real World Context: Level of authenticity where students use processes of inquiry to solve real problems and create knowledge that is valued by persons or communities outside the school environment
Basic Skills: Lower complexity of learning that includes the use of knowledge and comprehension thinking skills
Higher Order Thinking Skills: Higher complexity of learning that includes the use of application, analysis, synthesis, and evaluation thinking skills
Didactic: Instruction involving lecture and the textbook rather than demonstration and laboratory study
Constructivist: Individuals are active agents, they engage in their own knowledge construction by integrating new information into their schema, and by associating and representing it into a meaningful way
Drill and Practice: Instruction designed to build a student’s fluency with a specific skill
Integrated Learning Systems: A curriculum bundle that provides instructional content as well assessment and management tools
Productivity Tools: Student use of software for processing, storing, analyzing, and/or communicating data
Expression and Visualization Tools: Student use of software such as graphics, charting, or video editing packages that enables the use to express ideas primarily using images
Communications and Virtual Collaboration: Students participate in systems that enable users to communicate face-to-face as well as electronically
Simulations: Recreates real world phenomenon in the classroom experience, enabling the student to have an experience often times not possible any other way
Problem Solving with Real Data Sets: Students using technology to access, process, analyze, and communicate solutions to problems using relevant, real-world situations/data
Topic 1.1.4 Classroom Look-fors
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:
Teacher engages students in higher order thinking using technology.
Teacher provides opportunities for students to develop and demonstrate a depth of knowledge and understanding of central and significant concepts.
Teacher encourages substantive conversation and/or elaborated writing that extends student understanding of the subject.
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.
Teacher creates a classroom environment that incorporates strong social support mechanisms for academic achievement.
Teacher supports student use of 21st Century skills and technology.
Teaching Authentic Classroom Look-fors Rubric
Look for: Higher Order Thinking: Teacher engages students in higher order thinking using technology.
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.
Provides opportunities for students to pose and solve complex problems.
Encourages students to discover new meanings and understandings.
Allows students to experience levels of uncertainty, ambiguity and/or conflicting views in thinking through questions and solutions.
Provides opportunities for student thinking to become visible.
Plans appropriate levels of academic tasks to maintain student engagement.
Uses technology appropriately to promote higher order thinking.
Higher Order Thinking
The teacher provides a lesson that continuously engages almost all students in higher order thinking.
Students apply, analyze, synthesize, or evaluate information throughout the lesson. The problem(s) or question(s) posed by the teacher have multiple answers and press students to construct new knowledge rather than recall or report information. To score advanced, each student does not necessarily have to demonstrate their thinking, but it is clear that almost all students are engaged in complex thinking. In-depth understanding of the subject matter is not necessary to score advanced.
The teacher provides a lesson that often engages most students in higher order thinking.
The majority of students in the class applies, analyzes, synthesizes, or evaluates information. The teacher poses problems or questions that result in most students manipulating information and ideas in ways that transform meaning. For example, students brainstorm, explain, hypothesize, or arrive at a conclusion or interpretation.
The teacher provides a lesson that occasionally engages some students in higher order thinking.
Students are primarily engaged in lower order thinking (recall, reporting, and routine practice) for most of the lesson. There is at least one important question or activity in which some students manipulate information and ideas in ways that transform meaning.
The teacher provides a lesson that does not engage students in higher order thinking.
Students are engaged in lower order thinking; i.e., they either receive or recite pre-specified information, or participate in routine practice and drill. A few students may analyze, synthesize, or evaluate information but this is only a minor diversion within the lesson.
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.
Encourages students to construct explanations, develop arguments, and consider alternative perspectives on the meaning of ideas and events.
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.
Promotes in-depth understanding of complexity in subject matter instead of providing superficial exposure and awareness.
Designs student tasks that involve applying discipline-specific concepts to different situations.
Allows students the opportunity to revise and improve their thinking.
Uses technology appropriately to promote depth of knowledge.
Depth of Knowledge
The teacher continuously provides extensive opportunities for almost all students to develop and demonstrate depth of knowledge and understanding of central and significant concepts.
The teacher successfully structures the lesson to sustain a focus on a significant topic, issue or theme. Almost all students demonstrate complex understanding of the topic by clarifying the problematic nature of information and/or ideas; arriving at a reasoned and well-supported conclusion; or explaining how they solved a complex problem. In general, students' reasoning, explanations, and arguments demonstrate fullness and complexity of understanding.
The teacher often provides opportunities for most students to develop and demonstrate depth of knowledge and understanding of central and significant concepts.
The teacher successfully structures the lesson to sustain a focus on a significant topic, issue or theme. Many students provide information, arguments, or reasoning that demonstrates the complexity of an important topic, issue, or theme. Some students, however, show only superficial understanding or struggle to master more complicated ideas.
The teacher occasionally provides opportunities for some students to develop and demonstrate depth of knowledge and understanding of central and significant concepts.
The teacher provides limited opportunities for in-depth understanding. Most students are not asked to, or cannot, use knowledge to make distinctions, construct arguments, or solve problems.
The teacher does not provide opportunities for students to develop and demonstrate depth of knowledge and understanding of central and significant concepts.
The lesson is unstructured, covers large amounts of content or students review or practice basic information and skills. Key concepts and ideas may be mentioned or covered, but students show only a superficial acquaintance or trivialized understanding of these complex ideas.