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/