Strategies for Teaching, Supporting and Assessing Students’ Understanding and Development of Algebra and Function

Concepts, Operations and Skills Leading to Conceptual Fluency, Proficiency in varied Applications, and Entry to Algebra (6-12)

WEI Math AcademyDecember 6, 2014

Mike WeidnerBridget Schock

Learning Objectives

• Understand the progression of mathematics content focused on algebra and functions

• Identify instructional strategies that develop students’ mathematical habits of mind that enhance student algebraic and functional competence and their application

• Engage in activities that model appropriate instructional strategies that support students’ behaviors in mathematical sense-making, conjecturing, reasoning, and communicating

Marshmallow Tower

The task is simple: in eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top.

http://www.online-stopwatch.com/countdown-timer/

Making Connections

• As you were working on the marshmallow task, did your team exhibit evidence of "productive struggle"? Was communication important on your team? How so?

• How does this task fit in the big picture of the Common Core State Standards?

CCSSM: Wisconsin

• Adopted CCSSM on June 2, 2010

• Governing member of the Smarter Balanced Assessment Consortium (SBAC), with assessments to be rolled out in the 2014-2015 school year

1.5

• Make sense of problems

• Reason quantitatively

• Viable arguments & critique

• Model with mathematics

• Strategic use of tools

• Attend to precision

• Look for and use structure

• Look for regularity in reasoning

K–8 Standards by Grade Level

High School Standards by Conceptual Categories

________________________

– Domains

– Clusters

– Standards

Standards for Mathematical Practice

Standards for Mathematics Content

CCSSM New Structure & New Terminology

1.6

K-8 Domains & HS Conceptual Categories

Standards for Mathematical Practice1

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.2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Reasoning and

Explaining

Modeling and

Using Tools

Seeing Structure and Generalizing

William McCallum, The University of Arizona 1.8

Focus: Unifying themes and guidance on “ways of knowing” the mathematics.

Coherence: Progressions based on mathematics and student learning.

Rigor: Deep, genuine understanding of mathematics and ability to use that knowledge in real-world situations.

CCSSM Design Principles

Productive Struggle

http://www.npr.org/blogs/health/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning

Task #1: The Bus ProblemThere are three different busing companies that the Algebra Academy works with. Which company will provide the best deal for the field trips?

number of passengers

cost

10 $125

20 $145

30 $165

40 $185

50 $205

60 $225

70 $245

80 $265

90 $285

$1.25 per person, plus a $250 administrative fee

per trip

Carrie’s Cartage CompanyBest Bus Business

Able Transport

Task #1: The Bus Problem

• What were the big math ideas of this task?

• What standards does this task align to?

• How did you experience productive struggle?

Standards for Mathematical Practice

• Read the Math Practice Standard that you are least familiar with.

• What are some student behaviors when engaged in a task with the Math Practice Standard?

• What are some teacher moves that need to happen in order for the students to become engaged with the standard?

Growth Mindset

https://www.khanacademy.org/youcanlearnanything

Task #2: Toothpick Problem

In your group, determine a mathematical model that gives the total number of toothpicks required to construct a square of any size that is subdivided into 1x1 squares of toothpicks. The 1x1 square and the 2x2 square are shown.

Task #2: Toothpick Problem

• What were the big math ideas of this task?

• What standards does this task align to?

• How did you experience productive struggle?

Making Connections

• How do you see productive struggle in the Bus and Toothpick problems with your own students?

• How did you experience the Math Practice Standard when engaged with the tasks?

Thank You!!!

• Survey and Evaluations• Resources

http://www.nicolet.us/faculty/mweidner/2014weialgfunsworkshop.cfm