Mathematics Instructional Strategies In the Age of Common Core State Standards

After School Job(4 th /5 th 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(4 th /5 th 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.

DayStart with $1 Start with 1¢ 1$11¢ 2$12¢ 3$14¢ 4$18¢ 5$116¢ 6$132¢ 7$164¢ 8$1$1.28 9$1$ $1$ $1$ $1$ $1$ $1$81.92 After School Job(4 th /5 th 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 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.

ExplicitInteractiveImplicit 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 discoveryGuided discoverySelf-discovery Direct instructionStrategic instructionSelf-regulated instruction Task AnalysisBalance between part-to- whole and whole-to-part Unit approach BehavioralCognitive/metacognitiveHolistic General Instructional Models

1.5 E Model (interactive) ▫Engage-Explore-Explain-Elaborate-Evaluate 2.3 Phase Model (explicit) ▫I do – we d0 – you do 3.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 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

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

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 14.Line Up (Class Building) 15.Making a List 16.Numbered Heads Together 17.Partner Up 18.Quiz-Quiz Trade 19.Socratic Seminar 20.Talking Sticks 21.Teams Share Out 22.Think-Pair-Share 23.Think-Write-Pair-Share 24.Whip Around 25.Wrap Around 26.Y-Chart

Tools For Mathematics Instruction Visual Representations Concrete Models Interactive Technology

In Summary … General Instructional Models Additional Instructional Strategies

ExplicitInteractiveImplicit 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 discoveryGuided discoverySelf-discovery Direct instructionStrategic instructionSelf-regulated instruction Task AnalysisBalance between part-to- whole and whole-to-part Unit approach BehavioralCognitive/metacognitiveHolistic 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 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