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.
  1. Demonstrate knowledge of measurement spatial sense and geometry, and proportional reasoning and percent.
  2. 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 proportionality.
  3. Develop an understanding for learning to solve problems in more than one way.
  4. Understand student misconceptions in linear, area, and volume relationships.

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.
  1. Is aware of and can classify tasks and student thinking in relation to van Hiele’s levels of geometric thought.
  2. 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.
  1. Develop an appreciation that all children can learn mathematics.
  2. 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 skills.
  1. Analyzes tasks with respect to reasoning and van Hiele levels.
  2. Can represent solutions in more than one way.
  3. 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 candidates.

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.
  1. Takes responsibility in creating a positive climate during small group activity, working collaboratively, asking questions, and engaging in purposeful learning.
  2. 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.
  1. Learn to communicate mathematical ideas symbolically, verbally, with models and diagrams, and in written form.
  2. Can share explanations to problem solutions in small- and large-group activities.
  3. 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.
  1. Understands various ways to teach elementary mathematics.

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 learner.
  1. Recognize the relationship between teaching and assessment. 
  2. Values on-going assessment as essential to the instructional process.

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 professionally.
  1. Ask meaningful questions to guide personal learning in the area of mathematics and relates those questions to teaching in a classroom. 
  2. Learn by listening to others’ responses to questions or sharing of ideas or ways of thinking during math activities.
  3. Share teaching or tutoring ideas with others including students, parents, and teachers.
  4. Participate in mathematics events that promote personal professional growth.

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.
  1. 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 community. 
  2. Recognize the contribution of the National Council of Teachers of Mathematics, and other professional organizations to the teaching profession.
  3. 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.
  1. Identify ways of appropriately integrate technology in mathematics.