Academic Rigor in Mathematics

1
Academic Rigor in Mathematics

• Leadership Team Meeting
• January 2005

2
Begin Working on the Following Task

• Turkey Task
• Several turkey dinners are being prepared for
  families. Some weigh as little as 6 pounds and
  others as much as 24 pounds or more. A turkey
  requires 15 minutes per pound to cook. How can
  we figure out the amount of time needed for any
  size turkey?

3
Instructions

• In your table group, discuss what makes this task
  rigorous. (5 minutes)
  

4
Characteristics of Academically Rigorous Tasks

• Use procedures for the purpose of developing
  deeper levels of understanding.
  
• Suggest broad general procedures (multiple
  solution pathways)
  
• Begin with where students are. Have multiple
  entry points.
  
• Allow for multiple representations
• Are complex and non-algorithmic thinking (there
  is not a predictable, well-rehearsed approach or
  pathway explicitly suggested by the task)

5
Characteristics of Academically Rigorous Tasks
(contd)

• Allow for exploration of mathematics to build
  understanding.
  
• Demand self monitoring of ones own cognitive
  processes
  
• Require appropriate use of students relevant
  knowledge
  
• Require students to analyze the task and evaluate
  the reasonableness of answers.
  
• Require considerable cognitive effort

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Categories of Mathematical Tasks

• LOWER-LEVEL COGNITIVE DEMANDS
• Memorization Tasks
• Procedures Without Connections Tasks
• HIGHER -LEVEL COGNITIVE DEMANDS
• Procedures With Connections Tasks
• Doing Mathematics Tasks

7
Planning for Learning(Standards-Based
Instruction)
8
The Mathematical Tasks Framework
Student Learning
TASKS as they appear in curricular/ Instructi
onal
materials
TASKS as set up by the teachers
TASKS as implemented by students
9
Linking To Research Why Academic Rigor?

• Set Up Implementation Learning
• High High High
• Low Low Low
• High Low Moderate

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Session Objectives

• Reviewing the general features of academic rigor
  in a standards-based mathematics curriculum
  
• Discuss how culturally relevant and responsive
  teaching supports academic rigor for all
  students
  
• Identify teacher moves that maintain academic
  rigor by using the Thinking Through A Lesson
  Protocol.
  
• Plan the next steps for your school in
  implementing an academically rigorous mathematics
  curriculum.

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5 Principles of Culturally Relevant and
Responsive Teaching

• Principle I Learning is optimized when students
  are able to make connections between what they
  already know and what they are expected to
  learn.
• Principle II The meaning or significance that
  learners impose on an experience shapes how and
  whether knowledge is stored long term memory.
  
• Principle III. Learners can demonstrate
  competence in non-traditional ways.
  
• Principle IV Ability is not static or finite,
  as human beings we build our brains through our
  engagement with experience.
  
• Principle V Through effort, monitoring and
  adjusting our strategies when we do not
  understand, we exert influence over what and how
  we learn These strategies and habits of mind
  are teachable.

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Professional Literature

• Steins Chapter 2, Using Cognitively Complex
  Tasks in the Classroom and Chapters 1-4 of
  Dreamkeepers.
  
• Work in pairs to prepare the response to one of
  the 5 questions at your tables. (10
  minutes)
  
• Each pair shares their response to the rest of
  the table group. (2 minutes per pair)
  
• Whole group wrap-up. (5 minutes)

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Making Sense Teaching and Learning Mathematics
With Understanding (James Hiebert,
T. Carpenter, et. al)

• We understand something if we see how it is
  related or connected to other things we
  knowReflection and communication play an
  important role in making connections
• Dimensions of Classrooms That Promote
  Understanding
  
• Nature of Classroom Tasks
• Role of the Teacher
• Social Culture of the Classroom
• Mathematical Tools as Learning Supports
• Equity and Accessibility

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The Turkey Task

• 4th Grade Class at Hooper Avenue Elementary
  School
  
• Standards
• Algebra and Functions 1.0 Students use and
  interpret variables, mathematical symbols, and
  properties to write and simplify expressions and
  sentences
• AF1.1 Use letters, boxes, or other symbols to
  stand for any number in simple expressions or
  equations.
  
• Number Sense 3.0 Students solve problems
  involving addition, subtraction, multiplication,
  and division of whole numbers and understand the
  relationships among the operations.
• Mathematical Reasoning 1.0 Students make
  decisions about how to approach problems.
  
• Mathematical Reasoning 2.3 Use a variety of
  methods, such as words, numbers, symbols, charts,
  graphs, tables, diagrams, and models to explain
  mathematical reasoning.

15
Video Vignette

• Write down what you expect to see in the video
  with regards to teacher moves and the role of the
  students (3 minutes)
  
• Use the graphic organizer to take note of
  observable teacher moves and student actions that
  maintain rigor and/or are culturally relevant and
  responsive. (12 minutes)
• Table discussion Share your observations. Take
  note of 3 moves that all or the majority of your
  table observed and finds significant. (10
  minutes)
• Whole group wrap-up. (5 minutes)

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The StaircaseToothpick Lesson

• From LUCIMath
• 4th Grade Standards
• AF 1.1 Use letters, boxes, or other symbols to
  stand for any number in simple expressions or
  equations
  
• AF 1.4 Use and interpret formulas to answer
  questions about quantities and their
  relationships
  
• AF1.5 Understand than an equation such as
  y3x5 is a prescription for determining a second
  number when a first number is given.
  
• MG 2.1 Draw the points corresponding to linear
  relationships on graph paper.
  
• MR 1.0 Students make decisions about how to
  approach problems.
  
• MR 2.3 Use a variety of methods, such as words,
  numbers, symbols, charts, graphs, tables,
  diagrams, and models to explain mathematical
  reasoning.

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Enacting a Rigorous LessonThe
StaircaseToothpick Lesson

• Use the graphic organizer to describe the teacher
  moves that would maintain the rigor in this task
  and the expected student actions/responses. 20
  minutes
• Divide into 2 groups at your table
• Each group will describe the enactment of the
  entire lesson Opening, work period, closing
  
• Incorporate culturally relevant and responsive
  teaching strategies.
  
• Use the Teaching Through A Lesson Protocol in
  planning the enactment.
  
• The groups at each table will share with each
  other. (3 min each)
  
• Whole group wrap-up

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Final Reflection

• In your leadership team meeting, review your
  Three Commitments.
  
• Turn in the form. We will send a copy to your
  school.