800:131 Mathematical Reasoning for Teaching II
Alignment with INTASC Professional Standards
Principle #1: CONTENT KNOWLEDGE--The candidate
understands the central concepts, tools of inquiry, and structures of the
discipline(s) he or she teaches and can create learning experiences that make
these aspects of subject matter meaningful for students.
- Demonstrate knowledge of measurement spatial sense and
geometry, and proportional reasoning and percent.
- Understand the educational value of revisiting elementary
school mathematics curriculum regarding measurement concepts and systems,
benchmarks and estimation strategies, 2- and 3-dimensional shapes and
- Develop an understanding for learning to solve problems
in more than one way.
- Understand student misconceptions in linear, area, and
Principle #2: LEARNING AND DEVELOPMENT--The candidate
understands how children learn and develop, and can provide learning
opportunities that support their intellectual, social and personal development.
- Is aware of and can classify tasks and student thinking
in relation to van Hiele’s levels of geometric thought.
- Through video cases, course
readings, and class discussions, students will develop an awareness that
student errors are an opportunity for learning.
Principle #3: DIVERSE LEARNERS--The candidate
understands how students differ in their approaches to learning and creates
instructional opportunities that are adapted to diverse learners.
- Develop an appreciation that all children can learn
- Can identify the need for a
variety of approaches to learning, in that, there are more than one way to
solve a problem most math problems and it is the role of the teacher to be
prepared to represent mathematical ideas in more than one way in order to reach
as many students as possible.
Principle #4: INSTRUCTIONAL STRATEGIES--The candidate
understands and uses a variety of instructional strategies to encourage
students' development of critical thinking, problem solving, and performance
- Analyzes tasks with respect to reasoning and van Hiele
- Can represent solutions in more than one way.
- Experiences the learning of
measurement, spatial sense and geometry, and proportional reasoning and percent
through various instructional strategies deemed as effective instructional
approaches for the elementary grades and made explicit for the teacher
Principle #5: CLASSROOM MANAGEMENT--The candidate
uses an understanding of individual and group motivation and behavior to create
a learning environment that encourages positive social interaction, active
engagement in learning, and self-motivation.
- Takes responsibility in creating a positive climate
during small group activity, working collaboratively, asking questions,
and engaging in purposeful learning.
- Recognizes the value of
intrinsic motivation to students’ life-long growth and learning and models
strategies for themselves that are likely to encourage this development in students.
Principle #6: COMMUNICATION--The candidate
uses knowledge of effective verbal, nonverbal, and media communication
techniques to foster active inquiry, collaboration, and supportive interaction
in the classroom.
- Learn to communicate mathematical ideas symbolically,
verbally, with models and diagrams, and in written form.
- Can share explanations to problem solutions in small-
and large-group activities.
- Recognizes the importance
of learning to explain your thinking so that children may understand.
Principle #7: PLANNING INSTRUCTION--The candidate
plans instruction based upon knowledge of subject matter, students, the
community, and curriculum goals.
- Understands various ways to teach elementary
Principle #8: ASSESSMENT--The candidate
understands and uses formal and informal assessment strategies to evaluate and
ensure the continuous intellectual, social and physical development of the
- Recognize the relationship between teaching and
- Values on-going assessment as essential to the
Principle #9: REFLECTION AND PROFESSIONAL DEVELOPMENT--The candidate
is a reflective practitioner who continually evaluates the effects of his/her
choices and actions on others (students, parents, and other professionals in
the learning community) and who actively seeks out opportunities to grow
- Ask meaningful questions to guide personal learning in
the area of mathematics and relates those questions to teaching in a
- Learn by listening to others’ responses to questions or
sharing of ideas or ways of thinking during math activities.
- Share teaching or tutoring ideas with others including
students, parents, and teachers.
- Participate in mathematics events that promote personal
Principle #10: SCHOOL-COMMUNITY RELATIONS--The candidate
fosters relationships with school colleagues, parents, and agencies in the
larger community to support students' learning and well-being.
- Be aware of and begin to participate in parent/teacher
groups, local and state professional mathematics organizations, and local
community organizations that promote mathematics development in school and
- Recognize the contribution of the National Council of
Teachers of Mathematics, and other professional organizations to the
- Be knowledgeable of standards written by various
professional groups in the area of mathematics studies and use these
guidelines in preparing to teach.
Principle #11: USE OF TECHNOLOGY--The candidate integrates the computer
and other high and low technology into classroom teaching activities,
assessment and/or documentation.
- Identify ways of appropriately integrate technology in mathematics.