Mathematics Common Core/TASC Teacher Leadership Institute MR. AL PFAEFFLE 1/5/15.
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Transcript of Mathematics Common Core/TASC Teacher Leadership Institute MR. AL PFAEFFLE 1/5/15.
MathematicsCommon Core/TASC
Teacher Leadership Institute
MR. AL PFAEFFLE
1/5/15
CUNY Adult Literacy &
HSE Professional Development Team
Headed by
First Institute Held March, 2014
Second Institute Held
October, 2014
Third will be Held
March, 2015
March 2014 Participants received
training in both ELA and Math Reading Writing Vocabulary Math Content Learning and
Instructional Planning Study Habits, Student
Persistence, and Informal Assessment
October 2014 More Specific! Participants focused
on either ELA or Math ELA was in a Social
Studies context In 2015 ELA will be in
a Science context Math….We will
discuss!
Albany, NY
October 27-30, 2014
NYSED Common Core/TASC
Mathematics
Teacher Learning & Leadership Institute
INTRODUCTION
As adult educators, we have entered
the Common Core era.
Standards have risen and changed!
INTRODUCTION
The GED has not changed since WWII!
The GED has been replaced in New York State by the TASC
Common Core and the Global Workforce
The TASC
(Test Assessing Secondary Completion) Developed by CTB/McGraw Hill AS of January 2014, TASC has replaced the GED
in New York State. The TASC is based on the Common Core
Standards for Mathematics. What does this mean for math instruction?
Common Core Instructional Shifts/Emphases in Mathematics
Focus Coherence Fluency Deep Conceptual Understanding Application
Common Core Instructional Shifts
FOCUSEmphasize depth over breadth. Teach less,
Learn more.
Common Core Instructional ShiftsCOHERENCE
Each lesson is not a new event, but builds on the knowledge students bring to each activity/concept/class. Make connections between topics in math.
Common Core Instructional Shifts
FLUENCYStudents develop mental strategies and
flexible thinking to build speed and accuracy in calculations.
Common Core Instructional Shifts
DEEP CONCEPTUAL UNDTERSTANDINGStudents learn more than “the trick” to get
the answer…They learn the math.
See concepts from several perspectives.
Students see math as more than a set of discrete procedures. Students can write and speak about their understanding.
Common Core Instructional Shifts
APPLICATIONStudents can use math and choose
appropriate concepts even when they are not prompted to do so.
Students apply math in real-world situations.
Students use math in other content areas to make meaning and access content.
“A mile wide and an inch deep”
…Go Deeper
Focused Instruction Focused instruction is about emphasizing depths
over breadth; teach less so students learn more.
An attempt to end the teaching practice of “A mile wide and only an inch deep”
Narrow how much content we cover and deepen the manner in which we teach
Focused Instruction
Explore content areas more fully (Deeper)
Allow students time to secure mathematical foundations and conceptual understandings
INSTRUCTORS AND STUDENTS MUST ADJUST
TO A NEW REALITY!
GUESS WHAT?
“Learning From Our Students, Learning From Each Other”
Purpose of the Institute: What’s It All About?
Deepen our conceptual understanding of selected high impact math topics applicable to the TASC
Discuss how our deepening understanding of the math content impacts our teaching
Purpose of the Institute: What’s It All About?
Share and learn from each other!
What’s It All About?
Main Focuses On: How people learn and implications for
teaching What makes math problems “problematic” Developing problem-solving skills Developing algebraic thinking Improving discourse in the classroom
Using student work
How Do Our Students Learn?
What are some preconceptions about math that you think adult education students bring with them to our classrooms?
Classroom Preconceptions
“Ideas” and “Feelings” about mathematics.Why?
Examples?“Fil in/short cut” trend (No mathematical
reasoning)
Procedural approach (non-conceptual)
Classroom Preconceptions
Preconceptions becoming misconceptionsFocus on actual mathematical content
Have been accepted as truth over the years
Implications for Teaching
Adult learners are not “blank slates”
Active inquire into students’ thinking
Building upon students initial conceptions will provide a foundation on which a more formal understanding of subject matter is built
What Makes a Problem “Problematic”
Mathematical exercise or problem?
What do you think makes a problem problematic?
What Makes a Problem “Problematic”
According to Marilyn Burns, from “Beyond Word Problems”, there is criteria for what a problem is.
1. There is a perplexing situation that the student understands
2. The student is interested in finding a solution
3. The student is unable to proceed directly toward a solution
4. The solution requires use of mathematical ideas
What Makes a Problem “Problematic”
Do you agree with the criteria?
What are implications for problem solving strategies?
Problem Solving Strategies
What are some?
Problem Solving Strategies
Pattern Organized List Table Act-It-Out Draw a Picture Use Objects
Equations Similar Problem Model Guess & Check Work Backwards
A bicycle shop has a total inventory of 36 bicycles and tricycles. There are some bicycles and some tricycles. Altogether the bicycles and tricycles have a total of 80 wheels. How many of each type are in the shop?
A bicycle shop has a total inventory of 36 bicycles and tricycles. There are some bicycles and some tricycles. Altogether the bicycles and tricycles have a total of 80 wheels. How many of each type are in the shop?
8 tricycles
28 bicycles
How many different problem solving strategies can be used with this Example?
Problem Solving Strategies
How can they be useful?
Problem Solving Strategies
Progression of scaffolding
Encourage student exploration
Reveal student thinking
Students reflect on their own thinking
Different ways to solve a problem
Correct answers are essential... but they're part of the process, they're not the product. The product is
the math the kids walk away with in their heads...
- Phil Daro
Algebraic Thinking
Not just a set of procedures!
A way of thinking about and expressing mathematical relationships
The fundamental language of mathematics
Algebraic Thinking
Key concepts of algebraic thinking include:PatternsGeneralizationsJustifying and equality
Algebraic Thinking
By recognizing unknown patterns in algebraic expressions you are ‘’thinking algebraically.”
Algebraic Thinking Through Patterns
Is there a pattern?
Can we form an equation for any figure in the pattern?
Algebraic Thinking Through Patterns
Figure 1 Figure 2
Algebraic Thinking Through Patterns
Figure 3 Figure
Algebraic Thinking
Example What is the area of the rectangle? A= L x W
Algebraic Thinking
Instead ask… How many rectangles can you make with an
area of 48 square inches?
Algebraic Thinking
How has the problem changed?
Is it a better problem?
How and why?
Algebraic Thinking
A polar bear weighs about 20 times as heavy as Billy. If Billy weighs 25 kg, how much does the polar bear weigh?
How can we make this question more “open-ended?”
Algebraic Thinking
Algebraic Thinking
Practices for Improving Discoursein the Classroom
Talk that engages students in discourse
The art of questioning
Using student thinking to propel discussions
Setting up a supportive environment
Orchestrating the discourse
Talk Moves that Engage Students in Discourse
Revoicing Asking students to restate someone else's
reasoning Ask students to apply their reason to someone
else’s Prompt students for further participation Wait time: Don’t fear the crickets
The Art of Questioning
Help students:Work togetherRely on themselves Invent and solve problemsConnect mathematics, its ideas, and
applications
Using Student Thinking to Propel Discussions
Be an active listener
Be strategic and choose ideas, methods, representations, and misconceptions in a purposeful way that enhances the quality of the discussion
Setting up a Supportive Environment
Be conscious of the physical and emotional environment
Respond neutrally to errors, but seek out novel or common misconceptions and bring them into discussion
Orchestrating the Discourse
Anticipate student responses to mathematical tasks
Monitor and engage in students’ work
Select particular students to present their work
Connect student’s responses to key mathematical ideas
Using Student Work
How can we use student work in class?
To what end?
Using Student Work
Examples of using student work.
ToolkitWhat is in the Toolkit?
Research based practices in mathematical learning and instruction
How can it benefit us as educators?Share our resources
Toolkit Resources Algebraic Thinking Big Ideas in Mathematics Maintaining Complexity in Mathematics Multiplication Proportional Reasoning The 8 Common Core Standards of Mathematical
Practice Communication in Math: Through Discussions
and Writing Lessons and Tasks
ALGEBRAIC THINKING
BIG IDEAS IN MATHEMATICS
Big Ideas cut across all the different topics we tend to study
Useful introduction to the idea of Cross Cutting Concepts in math.
MAINTAINING COGNITIVE COMPLEXITY IN MATHEMATICS “Didactic Contract”
Our students need to be engaged in productive struggle to learn and become independent problem solvers
Let our students struggle instead of doing the work for them
MULTIPLICATION
Basic computation can be can the center of frustration for many adult learners
Develop a conceptual understanding of multiplication for both low and high level students
PROPORTIONAL REASONING
Deciding when something is proportional or not and understanding what it means
Looking at different categories of proportional reasoning problems
Comparing different strategies and solution methods
THE 8 COMMON CORE STANDARDS OF MATHEMATICAL
PRACTICE The 8 Standards of M.P. represent the ideal place for teachers and programs to begin their work to align mathematics instruction with the Common Core
How can we make these practices central to our classroom instruction
The 8 Common Core Standards of Mathematical Practice
MP1. Make sense of problems and persevere in
solving them MP2. Reason abstractly and quantitatively MP3. Construct viable arguments and critique the
reasoning of others MP4. Model with mathematics MP5. Use appropriate tools strategically MP6. Attend to precision MP7. Look for and make use of structure MP8. Look for and express regularity in repeated
reasoning
COMMUNICATION IN MATH THROUGH
DISCUSSION AND WRITING Strategies and goals for filling your
classrooms with student voices
Effective math talk serves as formative assessment, draws out misconceptions, and gives insight into student thought
LESSONS AND TASKS
Understanding – by - Design model of lesson planning
Focus on student thinking, specificity in instructional goal setting, and emphasis on teacher self assessment and reflection
As we make the transition to a new set of standards we will need to exchange ideas,
materials, and experiences.
“Make Small Changes.
Do it Again.”
Questions?
Resource Website
http://cunycci.pbworks.com/