Mathematics Instructional StrategiesIn the Age of Common Core State Standards

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.”

After School Job(4th/5th Grade)

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

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

After School Job(4th/5th Grade)

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.

Instructional Strategies Chapter

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.

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.

Key Instructional ShiftsThe 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.

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

General Instructional Models

General Instructional Models1. 5 E Model (interactive)

▫ Engage-Explore-Explain-Elaborate-Evaluate2. 3 Phase Model (explicit)

▫ I do – we d0 – you do3. Singapore Model (interactive)4. Concept Attainment Model (interactive)5. Cooperative Learning Model (implicit)

▫ Students work together to solve a problem and provide input

6. Cognitively Guided Instruction (implicit)7. Problem-Based Learning (interactive)

Additional Instructional Strategies1. Discourse in the Mathematics Classroom2. Student Engagement Strategies3. Tools for Mathematics Instruction4. Examples of Tasks Incorporating Math

Practices5. Real World Problems

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”.

Discourse Strategies

•Number Talks•5 Practices for Orchestrating Discussions

▫Anticipating ▫Monitoring ▫Selecting ▫Sequencing ▫Connecting

Engagement Strategies

Engagement Strategies1. Appointment Clock 2. Museum Walk3. Charades4. Clues (Barrier Games)5. Come to Consensus 6. Explores and Settlers7. Find My Rule8. Find your Partner9. Four Corners10. Give One Get One11. Inside Outside Circle12. Jigsaw13. KWL

14. Line Up (Class Building) 15. Making a List16. Numbered Heads

Together 17. Partner Up18. Quiz-Quiz Trade19. Socratic Seminar20. Talking Sticks21. Teams Share Out22. Think-Pair-Share23. Think-Write-Pair-Share24. Whip Around25. Wrap Around26. Y-Chart

Tools For Mathematics Instruction•Visual Representations•Concrete Models•Interactive Technology

In Summary …

•General Instructional Models•Additional Instructional Strategies

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

General Instructional Models

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)

Additional Instructional Strategies1. Discourse in the Mathematics Classroom2. Student Engagement Strategies3. Tools for Mathematics Instruction4. Examples of Tasks Incorporating Math

Practices5. Real World Problems