Goals for Today

What are the Process Standards?

How can I embed them into my curriculum?

How are good tasks created?

Examples, please!

Let's do this!

Process Standard 5

Process Standard 6

Geometry Example

What about ISTEP+ and ECA???

The 3 P's ...

Algebra 2 Example

Resources

See Resource page provided

**Problem Solving with the 8 Indiana Math Process Standards: 9 - 12**

Process Standard 1

Process Standard 2

Process Standard 3

Process Standard 4

Process Standard 7

Process Standard 8

The Math Process Standards do not stand alone and are not intended to be taught as stand alone lessons.

They are an integral part of learning and doing mathematics.

You can estimate the temperature by counting the number of chirps of the snowy tree cricket. The outdoor temperature is about 40°F more than one fourth the number of chirps the cricket makes in one minute.

1.) What is a function that represents this situation?

How many chirps do you think Sheldon heard in 1 minute?

For how long did Sheldon time the chirps?

What would the temperature be in Sheldon’s apartment?

2.) So, can you determine who won the bet? Was Sheldon right? Was it a snowy tree cricket? Or was Howard right that it was just an ordinary field cricket? Why do you think this? Support your answer with math.

Algebra 1 Example

Problem Solving

Perseverance

Precision

http://blog.mrmeyer.com/2012/ten-design-principles-for-engaging-math-tasks/

How can I make a pre-existing task better?

"Opportunities for student learning are not

created simply by putting students into

groups, by placing manipulatives in front

of them, or by handing them a calculator.

Rather it is the level and kind of thinking

in which students engage that determines

what they will learn."

NCTM PSFTM 1991

Martha was re-carpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

Stein, Smith, Henningsen, & Silver, 2000, p. 1

Martha's Carpeting Task

Ms. Brown’s class will raise rabbits for their spring science fair.

They have 24 feet of fencing with which to build a rectangular rabbit

pen in which to keep the rabbits.

The Fencing Task

1.) If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?

2.) How long would each of the sides of the pen be if they had only 16 feet of fencing?

3.) How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

SpringBoard Mathematics, Algebra 2, Unit 4, Pg. 378

2012 Pearson Education, Algebra 1 Common Core, Pg. 262

Celebrities!!!

How good are you at guessing ages?

Our task is to predict the ages of the celebrities. Enter your guess or prediction in the data table provided.

After we make our predictions, we will see their actual ages!

Celebrities Task

How did you do?

Mathalicious

Buck Institute

Emergent Math

Edutopia

Dan Meyer

Julie Evans

Bloomfield Jr/Sr High School

I teach Algebra 1, Algebra 1 Enrichment, ISTEP+ 8 Lab, and Calculus.

I am married and have an 8 year old daughter, Reagan, and 5 year old daughter, Adalyn.

Fun Fact: I am still listening to Christmas music (Pentatonix) in my car because the CD is stuck in the CD player. I secretly don't mind though!

What are the Process Standards?

How can I embed them into my curriculum?

How are good tasks created?

Examples, please!

Let's do this!

Today's Goals - Did we meet them?

Let's continue to share and communicate!

Julie Evans

jevans@bsd.k12.in.us

Process Standards are behaviors we want

students

to exhibit.

Rigor - Pursue with equal intensity:

Conceptual Understanding

Procedural Skill & Fluency

Application

The 3 Legged Stool - RIGOR

Conceptual

Understanding

Procedural Skill

& Fluency

More than one

entry point

Application

K-6 Fluency

Standards

Math Facts

Real world application

Process Standards

1 & 6

2 & 3

4 & 5

7 & 8

Every day

Critical

Reasoning/

Explaining

Modeling/

Tools

Reasoning/

Structure

Make sense of

problems

and

persevere

in solving them

Proficient students ...

explain the meaning of a problem and look for entry points

monitor and evaluate their progress and change course if necessary

check their answers to problems using a different method

analyze given, constraints, relationships, goals

use concrete objects, pictures to conceptualize and solve

understand approaches of others and identify correspondences between different approaches (communication with others)

Testing

Open ended questions ...

If it's worth 4 points, only 1 point is for the answer.

The other 3 points are for reasoning.

Evidence of student initiated problem solving strategies:

Students

self-identify entry

points to the solution

Students

plan a solution

pathway and

discuss with their peers

Students determine the

reasonableness

of their solution

Let them struggle! Just when you're ready to jump in, give them 1 more minute.

Precise Communication

Strategies for Communication

Modeling

"I'm not good at being precise. Help me."

Math Vocabulary

Precision should be a daily word.

Attention to Detail

Precise Solutions, Symbols & Units

Precise Solutions

How precise is your solution? How did you know how precise the solution should be?

Units

What units did you use? How did you know to use those units?

Symbols

Were there any symbols necessary and embedded in your solution? How did you know?

Decontextualize Problems

Students are problem solving or making sense of problems. It is the process of taking words in a problem and analyzing them so that they can be represented as a symbol or model for students to solve.

A lesson should never be about the strategy ... It should always be about the math!

The Process Standards should lend themselves to the math.

The Content Standard is the anchor.

The Process Standard supports.

Concrete

Pictorial

Symbolic

Steps to solve

Understand

Plan

Solve

Check

The "Math" Scientific Method

Step 1 - Present a Problem

Step 2 - Analyze What's Given

Step 3 - Decide a Solution Path

Step 4 - Test your Solution Path

Step 5 - Come to an Answer

Step 6 - Define Your Results (Justify)

While doing Step 6, students should site evidence from Steps 1 - 5.

Students must become comfortable with making conjectures, justifying and communicating their conclusions and responding to the arguments of others.

Conjectures - Does the student have an opportunity to present what they know without teacher influence?

Critique - Does the student have an opportunity to critique and respond to the critique of his peers?

Testing

Process Standards 2 & 3 are important because of testing ... They will be assessed on ISTEP+!

Also, they tie in well with Process Standard 1.

Mathematical modeling problems are big, messy, real, and open-ended.

In modeling, students need to make genuine choices about what is important, decide what mathematics to apply and determine whether their solution is useful.

Modeling provides opportunities for students to develop and practice mathematics-related skills, then communicate their understanding and interpretation of the problem.

Model with Mathematics

Model with Mathematics

Crucially important ... Brings meaning to the math!

We don't want the model to come at the end! We want the model to drive the math.

Testing

Process Standards 1 & 4 will likely be tied together.

Use Tools Strategically

Tools - Physical or Technology

Think about the tools available to students during testing.

Students choose the tools ... Not the teacher.

Students should know the strength and limitations of each tool.

Structure helps students learn what to expect in mathematics.

If middle school students learn how mathematics works and why it works the way it does, they begin to notice, look for, and make use of structure to solve problems as they become engaged in what it means to do mathematics.

Big Idea

Do the students seem to have an understanding of the Big Idea as opposed to a procedural understanding of the Math content?

Decomposition

Is there evidence of the students decomposing the math into simpler problems to derive solutions to a more specific problem?

Structure

Do the students display knowledge of an overall structure that allows them to navigate through the math in a meaningful manner?

Problem with shortcuts ...

Students think if it works once or twice, it always works.

"Let's find a situation where this doesn't work."