N 1 2 3
Establish mathematics goals to focus learning. Effective teaching of
mathematics establishes clear goals for the mathematics that students are
learning, situates goals within learning progressions, and uses the goals to
guide instructional decisions.
Implement tasks that promote reasoning and problem solving. Effective
teaching of mathematics engages students in solving and discussing tasks that
promote mathematical reasoning and problem solving and allow multiple entry
points and varied solution strategies.
Use and connect mathematical representations. Effective teaching of
mathematics engages students in making connections among mathematical
representations to deepen understanding of mathematics concepts and
procedures and as tools for problem solving.
Facilitate meaningful mathematical discourse. Effective teaching of
mathematics facilitates discourse among students to build shared understanding
of mathematical ideas by analyzing and comparing student approaches and
arguments.
Pose purposeful questions. Effective teaching of mathematics uses purposeful
questions to assess and advance students’ reasoning and sense making about
important mathematical ideas and relationships.
Build procedural fluency from conceptual understanding. Effective
teaching of mathematics builds fluency with procedures on a foundation of
conceptual understanding so that students, over time, become skillful in using
procedures flexibly as they solve contextual and mathematical problems.
Support productive struggle in learning mathematics. Effective teaching of
mathematics consistently provides students, individually and collectively, with
opportunities and supports to engage in productive struggle as they grapple
with mathematical ideas and relationships.
Elicit and use evidence of student thinking. Effective teaching of
mathematics uses evidence of student thinking to assess progress toward
mathematical understanding and to adjust instruction continually in ways that
support and extend learning.
UMF Teacher Education Conceptual Framework (C3TEP)
1
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring
mathematics success for all. Reston, VA: NCTM.
M.S.Ed. in Mathematics Education Recommendation Form
Applicant’s Name: _____________________________________________________________________________________________
Name of Person Providing Reference: _______________________________________ Position: _______________________________
How long have you known this person? _____ In what capacity? _________________________________________________________
Professional Knowledge and Practice:
Please indicate the applicant’s capacity across the following research-based teaching principles
1
:
(N = Not Observed/Not Enough Information to Evaluate; 1 = Area for Growth; 2 = Meets
Expectations; 3 = Area of Strength)
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