^{This list is adapted from }^{Principles of Instruction: }
^{Researched-Based Strategies That All Teachers Should Know}

^{1. Begin a lesson with a short review of
previous learning: Daily review can
strengthen previous learning and can lead to fluent recall. }

^{The most effective teachers ensured that students
efficiently acquired, rehearsed, and connected knowledge. Many went on to hands-on activities, but
always after, not before, the basic material was learned. }

^{2.
Limit the amount of material students receive at one time. Present new material in small steps with
student practice after each step, and assist students as they practice this
material. }

^{3.
Give clear and detailed instructions and explanations. Provide many examples.}

^{4.
Think aloud and model steps.
Providing students with models and worked examples can help them learn
to solve problems faster. }

^{Many of the skills taught in classrooms can be conveyed
by providing prompts, modeling use of the prompt, and then guiding students as
they develop independence.}

^{5.
Use more time to provide explanations.}

^{6.
Ask a large number of questions and check the responses of all
students: Questions help students
practice new information and connect new material to their prior learning.}

^{7.
Provide a high level of active practice for all students.}

^{8.
Guide students as they begin practice.
Successful teachers spend more time guiding students’ practice of new
material.}

^{9.
Check for student understanding at each point to help students learn the
material with fewer errors.}

^{The most successful teachers spent more time in guided
practice, more time asking questions, more time checking for understanding, and
more time correcting errors.}

^{10.
Ask students to explain what they have learned.}

^{11.
Obtain a high success rate: It is
important for students to achieve a high success rate during classroom
instruction. }

^{12.
Require and monitor independent practice: Students need extensive, successful,
independent practice in order to develop well-connected and automatic knowledge
and skills.}

^{13.
Provide systematic feedback and corrections, reteach material when
necessary.}

^{}

^{Common Core Standard for Mathematical Practice (see MP3)}

^{Construction viable arguments and critique the reasoning
of others. }

^{Mathematically proficient students
understand and use stated assumptions, definitions, and previously established
results in constructing arguments. They
make conjectures and build a logical progression of statements to explore the
truth of their conjectures. }^{They are able to analyze
situations by breaking them into cases, and can recognize and use
counterexamples. They justify their
conclusions, communicate them to others, and respond to the arguments of
others. They reason inductively about
data, making plausible arguments that take into account the context from which
the data arose. Mathematically
proficient students are also able to compare the effectiveness of two plausible
arguments, distinguish correct logic or reasoning from that which is flawed,
and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments
using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct,
even though they are not generalized or made formal until later grades. Later, students learn to determine domains to
which an argument applies. Students at
all grades can listen or read the arguments of others, decide whether they make
sense, and ask useful questions to clarify or improve the arguments.}