Mathematics Instructional
Strategies
In 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.
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
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.
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.
General Instructional Models
Explicit
Interactive
Implicit
Teacher serves as the Instruction includes both
provider of
explicit and implicit
knowledge
methods
Teacher facilitates students
learning by creating
situations where students
discover new knowledge
and construct own
meaning
Much direct teacher
assistance
Non-direct teacher
assistance
Balance between direct
and non-direct teacher
assistance
Teacher regulation of Shared regulation of
learning
learning
Student regulation of
learning
Directed discovery
Guided discovery
Self-discovery
Direct instruction
Strategic instruction
Self-regulated instruction
Task Analysis
Balance between part-towhole and whole-to-part
Unit approach
Behavioral
Cognitive/metacognitive
Holistic
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.
2.
3.
4.
Discourse in the Mathematics Classroom
Student Engagement Strategies
Tools for Mathematics Instruction
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
Engagement Strategies
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Appointment Clock
Museum Walk
Charades
Clues (Barrier Games)
Come to Consensus
Explores and Settlers
Find My Rule
Find your Partner
Four Corners
Give One Get One
Inside Outside Circle
Jigsaw
KWL
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
Line Up (Class Building)
Making a List
Numbered Heads Together
Partner Up
Quiz-Quiz Trade
Socratic Seminar
Talking Sticks
Teams Share Out
Think-Pair-Share
Think-Write-Pair-Share
Whip Around
Wrap Around
Y-Chart
Tools For Mathematics Instruction
• Visual Representations
• Concrete Models
• Interactive Technology
In Summary …
• General Instructional Models
• Additional Instructional Strategies
General Instructional Models
Explicit
Interactive
Implicit
Teacher serves as the Instruction includes both
provider of
explicit and implicit
knowledge
methods
Teacher facilitates students
learning by creating
situations where students
discover new knowledge
and construct own
meaning
Much direct teacher
assistance
Non-direct teacher
assistance
Balance between direct
and non-direct teacher
assistance
Teacher regulation of Shared regulation of
learning
learning
Student regulation of
learning
Directed discovery
Guided discovery
Self-discovery
Direct instruction
Strategic instruction
Self-regulated instruction
Task Analysis
Balance between part-towhole and whole-to-part
Unit approach
Behavioral
Cognitive/metacognitive
Holistic
General Instructional Models
1.
2.
3.
4.
5.
6.
7.
5 E Model (interactive)
3 Phase Model (explicit)
Singapore Model (interactive)
Concept Attainment Model (interactive)
Cooperative Learning Model (implicit)
Cognitively Guided Instruction (implicit)
Problem-Based Learning (interactive)
Additional Instructional Strategies
1.
2.
3.
4.
Discourse in the Mathematics Classroom
Student Engagement Strategies
Tools for Mathematics Instruction
Examples of Tasks Incorporating Math
Practices
5. Real World Problems