Mathematics Instructional Strategies

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Mathematics Instructional Strategies

• In the Age of Common Core State Standards

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After School Job(4th/5th Grade)

• Leonard needed to earn some money so he offered
  to do some extra chores for his mother after
  school for two weeks. His mother was trying to
  decide how much to pay him when Leonard suggested
  the idea
• Either you pay me 1.00 every day for the two
  weeks, or you can pay me 1 for the first day, 2
  for the second day, 4 for the third day, and so
  on, doubling my pay every day.

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After School Job(4th/5th Grade)

• Which option does Leonard want his mother to
  choose? Write a letter to Leonards mother
  suggesting the option that she should take. Be
  sure to include drawings that explain that will
  explain your mathematical thinking.

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After School Job(4th/5th Grade)
Day Start with 1 Start with 1
1 1 1
2 1 2
3 1 4
4 1 8
5 1 16
6 1 32
7 1 64
8 1 1.28
9 1 2.56
10 1 5.12
11 1 10.24
12 1 20.48
13 1 40.96
14 1 81.92
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Instructional Strategies Chapter

• The purpose of this chapter is not to prescribe
  the usage of any particular instructional
  strategy, but to enhance teachers repertoire.
• Teachers have a wide choice of instructional
  strategies for any given instructional goal, and
  effective teachers look for a fit between the
  material to be taught and strategies to teach it.
  
• Ultimately, teachers and administrators must
  decide which instructional strategies are most
  effective in addressing the unique needs of
  individual students.

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The Teaching of Mathematics

• must be carefully sequenced and organized to
  ensure that all standards are taught at some
  point and that prerequisite skills form the
  foundation for more advanced learning.
• However, it should not proceed in a strictly
  linear order, requiring students to master each
  standard completely before being introduced to
  another.
• Practice leading toward mastery can be embedded
  in new and challenging problems that promote
  conceptual understanding and fluency in
  mathematics.

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Instructional Strategies Chapter

• Before discussing the many and varied
  instructional strategies that are at the disposal
  of teachers, three important topics for CA CCSSM
  instruction will be discussed
• the Key Instructional Shifts of the CA CCSSM,
• the Standards for Mathematical Practice,
• the Critical Areas of Instruction at each grade
  level.

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Key Instructional Shifts

• The Mathematical Content standards emphasize key
  content, skills, and practices at each grade
  level and support three major principles
• Focus Instruction is focused on grade level
  standards.
• Coherence Instruction should be attentive to
  learning across grades and should link major
  topics within grades.
• Rigor Instruction should develop conceptual
  understanding, procedural skill and fluency, and
  application.

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General Instructional Models
Explicit Interactive Implicit
Teacher serves as the provider of knowledge Instruction includes both explicit and implicit methods Teacher facilitates students learning by creating situations where students discover new knowledge and construct own meaning
Much direct teacher assistance Balance between direct and non-direct teacher assistance Non-direct teacher assistance
Teacher regulation of learning Shared regulation of learning Student regulation of learning
Directed discovery Guided discovery Self-discovery
Direct instruction Strategic instruction Self-regulated instruction
Task Analysis Balance between part-to-whole and whole-to-part Unit approach
Behavioral Cognitive/metacognitive Holistic
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General Instructional Models

• 5 E Model (interactive)
• Engage-Explore-Explain-Elaborate-Evaluate
• 3 Phase Model (explicit)
• I do we d0 you do
• Singapore Model (interactive)
• Concept Attainment Model (interactive)
• Cooperative Learning Model (implicit)
• Students work together to solve a problem and
  provide input
• Cognitively Guided Instruction (implicit)
• Problem-Based Learning (interactive)

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Additional Instructional Strategies

1. Discourse in the Mathematics Classroom
2. Student Engagement Strategies
3. Tools for Mathematics Instruction
4. Examples of Tasks Incorporating Math Practices
5. Real World Problems

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Discourse in the Mathematics Classroom

• Students will be expected to communicate their
  understanding of mathematical concepts, receive
  feedback, and progress to deeper understanding.
• When students communicate their mathematical
  learning through discussions and writing,
• they are able to relate the everyday language
  of their world to math language and to math
  symbols.
• The process of writing enhances the thinking
  process by requiring students to collect and
  organize their ideas. Furthermore, as an
  assessment tool, student writing provides a
  unique window to students thoughts and the way a
  student is thinking about an idea.

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Discourse Strategies

• Number Talks
• 5 Practices for Orchestrating Discussions
• Anticipating
• Monitoring
• Selecting
• Sequencing
• Connecting

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Engagement Strategies
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Engagement Strategies

1. Appointment Clock
2. Museum Walk
3. Charades
4. Clues (Barrier Games)
5. Come to Consensus
6. Explores and Settlers
7. Find My Rule
8. Find your Partner
9. Four Corners
10. Give One Get One
11. Inside Outside Circle
12. Jigsaw
13. KWL

1. Line Up (Class Building)
2. Making a List
3. Numbered Heads Together
4. Partner Up
5. Quiz-Quiz Trade
6. Socratic Seminar
7. Talking Sticks
8. Teams Share Out
9. Think-Pair-Share
10. Think-Write-Pair-Share
11. Whip Around
12. Wrap Around
13. Y-Chart

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Tools For Mathematics Instruction

• Visual Representations
• Concrete Models
• Interactive Technology

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In Summary

• General Instructional Models
• Additional Instructional Strategies

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General Instructional Models
Explicit Interactive Implicit
Teacher serves as the provider of knowledge Instruction includes both explicit and implicit methods Teacher facilitates students learning by creating situations where students discover new knowledge and construct own meaning
Much direct teacher assistance Balance between direct and non-direct teacher assistance Non-direct teacher assistance
Teacher regulation of learning Shared regulation of learning Student regulation of learning
Directed discovery Guided discovery Self-discovery
Direct instruction Strategic instruction Self-regulated instruction
Task Analysis Balance between part-to-whole and whole-to-part Unit approach
Behavioral Cognitive/metacognitive Holistic
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General Instructional Models

1. 5 E Model (interactive)
2. 3 Phase Model (explicit)
3. Singapore Model (interactive)
4. Concept Attainment Model (interactive)
5. Cooperative Learning Model (implicit)
6. Cognitively Guided Instruction (implicit)
7. Problem-Based Learning (interactive)

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Additional Instructional Strategies

1. Discourse in the Mathematics Classroom
2. Student Engagement Strategies
3. Tools for Mathematics Instruction
4. Examples of Tasks Incorporating Math Practices
5. Real World Problems