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Indiana Math Process Standards: 9 - 12

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Julie Evans

on 3 November 2016

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Transcript of Indiana Math Process Standards: 9 - 12

Algebra 1 Example
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."
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