High Yield Instructional Strategies- Math
Component of Math
Proficiency
Conceptual
understanding
Strategic competence
Definition
Instructional Strategies (Sample)
Video Clips and more
information
Comprehension of mathematical
concepts, operations, and relations.
It is the functional grasp of
mathematical ideas. It enables
students to learn new ideas by
connecting to ideas they already
know.
Connect current content to students’
previous experiences directly and explicitly to
help them build connections.
http://www.coedu.usf.edu/main/
departments/sped/mathvids/strat
egies/tubi.html
The ability to formulate, represent,
and solve mathematical problems in
efficient, effective, and flexible ways.
Ideas:
 Work within your PLC to uncover the flow
of the SEs through the grade levels. Have
frequent conversations in PLCs about
how topics were introduced, taught, and
discussed in earlier grade levels so that
you can draw explicit connections to
remind students. (“[this] is what you did
last year. [this] is the new aspect we are
adding this year in x grade.”)
 Ask the students to make these
connections for themselves through class
conversation, journaling, etc.
 Introduce a new concept by giving the
students a very brief directly related
question or activity from each grade level
preceding your own.
Use a single problem solving system or
graphic organizer. Collaborate at your grade
level or school to adopt a single system or
graphic organizer used in every math
classroom.
Ideas:
 UPS : Understand, Plan, Solve,
Check
 Understand, See (draw a
representational model of the

problem situation), Solve, Reflect (“I
know my solution is reasonable
because…”)
Find (write a restatement of the
problem that starts with the word
Find), Know (write what you know
from the problem), Solve, Check (use
a different procedure or
understanding to find the solution
another way.)
Adaptive reasoning
The capacity for logical thought,
reflection, explanation, and
justification.
Give students ample opportunity to engage
in authentic problem solving including
justifying their responses and responding to
other students work.
http://www.ted.com/talks/dan_m
eyer_math_curriculum_makeover
.html
Procedural fluency
Skill in carrying out procedures
flexibly, accurately, efficiently, and
appropriately.
Provide regular time to reinforce grade level
operations and procedures. Ensure that
students have multiple opportunities to
respond, a way to show mastery and
advance, and teachers have an efficient way
to evaluate progress. Understand that
procedural fluency follows conceptual
understanding in cognitive development.
Self correcting materials:
http://www.coedu.usf.edu/main/
departments/sped/mathvids/str
ategies/scm.html
Ideas:
 Computer aided instruction.
 Self correcting materials.
 Instructional games.
Productive
disposition
The habitual inclination to see
mathematics as sensible, useful, and
worthwhile, coupled with a belief in
diligence and one’s own efficacy.
Make development and improvement of
students’ productive disposition an explicit
priority rather than a side effect.
Ideas:
 Use a productive disposition inventory
(see Tiered Academic Plan)at regular
Instructional games:
http://www.coedu.usf.edu/main/
departments/sped/mathvids/str
ategies/ig.html




Critical Features of
Effective Instruction
Provide high-quality
constructive learning
experiences
intervals to help students see their
baseline and growth in this area.
Ensure student regularly experiences
success.
Develop a motivational system that
contains rewards at all three levels-engagement-contingent, completioncontingent, and achievementcontingent.
Conference with student regularly—help
student identify successes, acknowledge
role of effort in achievement, and set
short-term goals.
Access school-based services to assign
student a mentor who can help bolster
positive disposition, lunch clubs, etc.
Definition
Instructional Strategy (Sample)
Video Clip
When students are allowed to
explore a problem or mathematical
situation, they analyze, predict, and
make decisions. These skills are
critical for success in the 21st century
world of work.
Use the 5E model for lesson planning/design.
(Engage, Explore, Explain, Elaborate,
Evaluate.)
http://www.ted.com/talks/dan_m
eyer_math_curriculum_makeover
.html
Ideas:
 Ensure the students have had an
opportunity to Engage, Explore, and
Explain for themselves before the
teacher provides a procedure or direct
teach. Teacher explanations of math
concepts, procedures, and skills should
be for clarification and consolidation, not
introduction.
 The 5Es do not need to be present in
every single class period, but each new
concept/skill should incorporate the 5Es.
Provide
mathematically
rigorous learning
experiences
Mathematically rigorous learning
experiences involve problems that
have multiple solution methods and
possibly multiple solutions. They
require students to think and reason
about mathematics and
communicate their understanding
verbally.
Find the rigor in the materials.
Move between
concrete, pictorial,
and abstract at all
levels of curriculum
Concrete mathematical tools provide
support for understanding and
thinking about mathematics. Use of
these tools is critical to help students
construct meaning.
As learning continues, students may
be ready to move to pictorial models
that grow from their understanding
of the concrete model.
Through further instruction, they
may be ready to leave the concrete
and pictorial models behind in favor
of the speed of abstract
understanding. Students must use
the concrete and pictorial to explain
the abstract. Additionally some
students may never understand the
abstract without sufficient
understanding of the concrete and
pictorial.
Real-world problem solving takes
mathematics out of the theoretical
world and connects it to the lives of
Normalize manipulative use in the classroom.
Emphasize real-world
problem solving
Ideas:
 When planning, look at the suggested
resources and choose a learning plan that
incorporates rigorous, open ended
activities.
 Do not dilute the rigor by breaking things
down too far for the students. Avoid
over-directing and over-explaining.
Ideas:
 Reuse the same manipulatives for many
concepts, helping students generalize.
For example, two color chips can be used
for any counting, grouping, array,
organizing, etc.
 Keep the manipulatives easily accessible
in the classroom for students to use at
their discretion.
 Do not rush students past manipulatives
and pictorial modeling.
 When addressing a student question, the
teacher should reach for manipulatives
before a pencil.
Use the Engage and Explore parts of the
lesson cycle to give students the real world
context for the mathematics. Choose
http://www.ted.com/talks/dan_m
eyer_math_curriculum_makeover
.html
http://www.coedu.usf.edu/main/
departments/sped/mathvids/strat
egies/cra.html
http://www.ted.com/talks/dan_m
eyer_math_curriculum_makeover
.html
students. It increases enthusiasm for
mathematics and provides a means
for remembering the mathematics.
National Council of Teachers of
Mathematics (2000). Changing faces
of mathematics: Perspectives on
African Americans. National Council
of Teachers of Mathematics: Reston,
VA.
Incorporate frequent
formative and
summative
assessment
Formative Assessment helps teachers
understand what students know and
are able to do while the unit
instruction continues. It is the
assessment that lets the teacher
know who understands and who
needs reteaching or extension. It is
done during the teaching cycle.
Summative Assessment happens at
the end of the unit and tests to see if
the students mastered the content in
the unit. A unit test or performance
assessment at the end of the unit
gives summative assessment
information.
Stiggins (2008). An introduction to
student-involved assessment FOR
learning. Pearson: Upper Saddle
River, NJ.
learning activities that emphasize real world
connections. Help students see the
progression from real world to a
mathematical model of the real world.
Ideas:
 Have students write their own problems
in context that has meaning for them.
 Have students explore the difference
between the “messy” real world and the
“clean” mathematic model through
discussion and journaling.
 Give students opportunities to choose
between activities or in how they will
present their learning.
Involve students in assessment efforts.
Ideas:
Use sticker chart (individual or whole
class posters) to track mastery of skills
and SEs.
 Have students graph pre-, during, and
post- assessment data during a unit.
 Have students keep a year long record of
SEs and progress toward mastery.
