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TUTOR FOR UNDERSTANDING:

ELEMENTARY MATH

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OUR ESSENTIAL QUESTION

How do children learn math most effectively?

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How do children learn math most effectively?

CONCRETE

PICTORIAL

ABSTRACT

JEROME BRUNER

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Jerome Bruer

How do children learn math most effectively?

concrete

experience

visual/pictorial

representations of concrete experience

abstract/symbolic

representations

1

JEROME BRUNER

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concrete

experience

visual/pictorial

representations of concrete experience

abstract/symbolic

representations

How do children learn math most effectively?

JEROME BRUNER

How can I connect this to what students already know?

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Physical objects are used to represent and solve math problems.

Addition and Subtraction

Place Value

Multiplication and Division

Fractions

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CONCRETE

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Pictures are used to approach and solve math problems.

CONCRETE → PICTORIAL

Addition and Subtraction

Place Value

Multiplication and Division

Fractions

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Addition and Subtraction

Place Value

Multiplication and Division

Fractions

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​

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1 3

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Pictures are used to approach and solve math problems.

CONCRETE → PICTORIAL → ABSTRACT

Addition and Subtraction

Place Value

Multiplication and Division

Fractions

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​

​

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Addition and Subtraction

Place Value

Multiplication and Division

Fractions

​

​

​

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THINK

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SHARE

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How might you leverage the CPA continuum during tutoring sessions?

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Teaching math how you learned it.

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Read about the Common Core standards and get to know your school’s curriculum.

Focusing on the PRODUCT over the PROCESS.

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After students solve, ask them to explain and justify their answers.

Teaching tips and tricks.

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If there’s a “smart-cut,” ask students why the shortcut makes sense.

Reinforcing harmful math myths.

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Familiarize yourself with the math myths, reflect on your own math learning experiences.

COMMON MISTAKES TO AVOID

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Teaching math how you learned it.

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Read about the Common Core standards and get to know your school’s curriculum.

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COMMON MISTAKES TO AVOID

The rapid changes and increased complexity of today’s world present new challenges and put new demands on our education system.

-Miriam Bar-Yam, Kathleen Rhoades, Linda Booth Sweeney, Jim Kaput, and Yaneer Bar-Yam, Complex Systems Perspectives on Education and the Education System, New England Complex Systems Institute (2002).

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Focusing on the PRODUCT over the PROCESS.

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After students solve, ask them to explain and justify their answers.

COMMON MISTAKES TO AVOID

“The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students mathematics learning.”

  • Orchestrating Mathematical Discourse to Enhance Student Learning

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Teaching tips and tricks.

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If there’s a “smart-cut,” ask students why the shortcut makes sense.

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COMMON MISTAKES TO AVOID

“Students who learn to articulate and justify their own mathematical ideas, reason through their own and others’ mathematical explanations, and provide a rationale for their answers develop a deep understanding that is critical to their future success in mathematics and related fields.”

  • Carpenter, Thomas P., Meagan Loef Franke and Linda Levi. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary Schools

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Reinforcing harmful math myths.

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Familiarize yourself with the math myths, reflect on your own math learning experiences.

COMMON MISTAKES TO AVOID

“...we have stereotyped ideas about who can be good at maths. So if you’re a woman or a person of color, you’re dealing with that pressure. If you have fixed ideas about who can do maths, a fixed mindset, then that stereotype can really take root.”

  • Gonser, Sarah.. “Are we teaching the math kids need?”. Edutopia, 2021

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THINK

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What is your key takeaway from this learning?

What is your charge as an elementary math tutor?

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COMMON TOOL: ZEARN

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ZOOMING IN: WORD PROBLEM

Whole Group Word Problems:

  • Provides students with the opportunity to apply mathematical concepts and skills to new contexts
  • Engages learners in productive math dialogue
  • Supports students in building positive math identities

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PUT ON YOUR STUDENT HAT

Engage in this word problem as a learner!

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Consider:

  • How does it feel to engage in this tutoring session as a learner?
  • What tutor moves (words/actions) made your student experience most meaningful?

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FIRST READ

What’s happening?

______ children play a game.

There are ❓❓children on each team. How many teams play the game?

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Write a division sentence to represent the problem.

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SECOND READ

How could you solve the problem?

Twenty children play a game.

There are 5 children on each team. How many teams play the game?

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Write a division sentence to represent the problem.

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THIRD READ

Solve:

Twenty children play a game.

There are 5 children on each team. How many teams play the game?

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Write a division sentence to represent the problem.

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WRAPPING UP THE DISCUSSION

Think:

  • What is similar about these models?
  • How are these models different?

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THINK

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SHARE

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How did it feel to engage in the tutoring session as a learner?

What tutor moves (words/actions) made your student experience most meaningful?

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Key Point: Word Problem

Word Problems:

Word problems are connected to the mission (unit) and can be solved using a variety of approaches

Purpose:

  • Supports students in problem solving and applying the concepts learned to a real-world situation
  • Teachers & tutors should support students in visualizing what’s happening, encouraging multiple representations, and having students talk about their strategies

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ADDITIONAL RESOURCES

HERE

www.help.zearn.org