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The Power of Progressions: Untangling the Knotty Areas of Teaching - - PowerPoint PPT Presentation

May 31, 2023 204 likes •966 views

The Power of Progressions: Untangling the Knotty Areas of Teaching and Learning Mathematics Graham Fletcher gfletchy@gmail.com @gfletchy www.gfletchy.com Procedural Conceptual Fluency Understanding Application

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Graham Fletcher gfletchy@gmail.com @gfletchy www.gfletchy.com

The Power of Progressions: Untangling the Knotty Areas of Teaching and Learning Mathematics

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Procedural Fluency Application Conceptual Understanding

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
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Procedural Fluency

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Procedural Fluency Application Conceptual Understanding

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
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Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

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Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

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Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

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Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

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Demetrius has 17 Skittles which is 12 fewer than Alicia. How many Skittles does Alicia have?

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17 12 fewer

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17 12

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17 12

W T F ?

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17 12

W T F ?

hat’s he ive

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Current Research

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65%

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“65% of children entering primary school today will ultimately end up working in completely new job types that don’t yet exist.”

http://reports.weforum.org/future-of-jobs-2016/chapter-1-the-future-of-jobs-and-skills/
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“Early mathematics competency predicts later reading achievement better than early literacy skills.”

  • A. Szekely. Unlocking Young Children’s Potential: Governors’ Role in Strengthening
Early Mathematics Learning (Washington, D.C.: National Governors Association Center for Best Practices, October 28, 2014).
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You little plucker!

John SanGovanni, NCTM ‘16
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number

John SanGovanni, NCTM ‘16

You little plucker!

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?

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The Big Reveal

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Graham had some Skittles. He had 19 yellow, 15

  • range, 19 green, 17 purple, and 21 red. How many

Skittles did Graham have?

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3-Act Tasks

Act 1:

  • Real world problem or scenario presented
  • What do you notice? What do you wonder?
  • Make estimates

Act 2:

  • Identify missing variables and missing variables to solve
  • Define solution path using variables

Act 3:

  • Solve and interpret results of the solution
  • Validate answer
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Most asked questions:

  • How often should we use 3-Act Tasks?
  • When should we use 3-Act tasks? How do they fit

into the scope of a unit?

  • How long does one task usually take?
  • What if we don’t have the time?
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  • 1. Anticipating student responses to challenging mathematical tasks;
  • 2. Monitoring students’ work on and engagement with the tasks;
  • 3. Selecting particular students to present their mathematical work;
  • 4. Sequencing the student responses that will be displayed in a
specific order and;
  • 5. Connecting different students’ responses and connecting the
responses to key mathematical ideas.

5

The practices are:

MTMS: Vol. 14, No. 9, May 2009-5 Practices for Orchestrating Productive Mathematics Discussions
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Identify and name the strategy used, then place the student work in order in terms of efficiency (least to greatest)

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Identify and name the strategy used, then place the student work in order in terms of efficiency (least to greatest)

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19+15+19+17+21

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1-counting all 1-counting all

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1-counting all 2-counting all with skip counting 1-counting all

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1-counting all 2-counting all with skip counting 1-counting all 3-making tens from ones

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1-counting all 2-counting all with skip counting 1-counting all 3-making tens from ones 4-making tens from ones

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1-counting all 2-counting all with skip counting 1-counting all 3-making tens from ones 5-Place value partitioning 4-making tens from ones

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1-counting all 2-counting all with skip counting 1-counting all 3-making tens from ones 5-Place value partitioning 4-making tens from ones 6-Partial Sums

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1-counting all 2-counting all with skip counting 1-counting all 3-making tens from ones 5-Place value partitioning 4-making tens from ones 7-Landmark Numbers 6-Partial Sums

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1-counting all 2-counting all with skip counting 1-counting all 3-making tens from ones 5-Place value partitioning 4-making tens from ones 7-Landmark Numbers 6-Partial Sums

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1-counting all 2-counting all with skip counting 1-counting all 3-making tens from ones 5-Place value partitioning 4-making tens from ones 7-Landmark Numbers 6-Partial Sums

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3-Act Tasks 5 Practices Progressions

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= 91 + + +

Using the digits 1-9 at most one time each, create 4 numbers that have a sum of 91. You can use the 9 & 1 from the cards

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Kindergarten?

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