Knowledge, Skills and Abilities for Basic Math Endorsement
(1) In addition to passing the required Commission-approved
subject-matter, examinations for basic math and completing the required
practicum experience, the following requirements must be met to add a basic
math endorsement onto any Initial or Continuing Teaching License. The
requirements to add a basic math endorsement onto a Basic or Standard Teaching
License can be found at
(2) Demonstrated Content
Knowledge:
(a) For knowledge of numbers, operations, candidates will:
(A) Demonstrate conceptual
understanding of complex numbers and real numbers particularly rational numbers
and integers; ways of representing numbers; relationships among numbers and
number systems; and the meaning of operations; and
(B) Be computationally proficient and choose the appropriate
computational format such as exact or approximate; and method, such as mental, paper
and pencil, or electronic.
(b) For knowledge of Algebra and functions,
candidates will:
(A) Understand the various roles of algebra and demonstrate conceptual
understanding of variables and functions including linear, quadratic and
exponential functions and their inverses;
(B) Use a variety of representations including verbal, pictorial,
tabular, symbolic and graphic to emphasize relationships among quantities; and
(C) Demonstrate conceptual understanding of and skill in appropriate
use of symbols.
(c) For knowledge of Geometry, candidates
will:
(A) Use spatial visualization
and geometric modeling and constructions to explore and analyze geometric
shapes, structures, and their properties;
(B) Make conjectures about two-
and three-dimensional shapes and offer justifications for conjectures; and
(C) Apply coordinates geometry and transformations including the use of
congruence, similarity, and symmetry to analyze mathematical situations.
(d) For knowledge of measurement,
candidates will:
(A) Understand measurement processes including estimation, accuracy and
choice of measurement tool for both
(B) Understand and use direct and indirect measurement techniques and
formulas for both two- and three-dimensional figures.
(e) For knowledge of data analysis and probability
and statistic, candidates will:
(A) Design investigations, collect data, use a variety of ways to
display the data and critically interpret data representations;
(B) Make predictions and draw conclusions involving uncertainty by
applying basic concepts of probability; and
(C) Use appropriate statistical methods to analyze and describe shape,
spread, and center data; then they use that information to make inferences.
(f) For knowledge of Calculus, candidates
will:
(A) Demonstrate a conceptual understanding of limits, particularly in
relation to understanding series, repetitive processes and non-terminating
decimals; and
(B) Demonstrate a conceptual understanding of rate of change and the
relationship to minimums, maximums and area of a region.
(3) Demonstrated
Competency in Following Process Standards.
(a) For competency in problem solving,
candidates will engage in mathematical inquiry through understanding a problem,
exploring, conjecturing, experimenting and justifying.
(b) For competency in reasoning and proof,
candidates will:
(A) Select and use various types of reasoning including categorizing
based on numeric and geometric properties, and using Venn diagrams, set
notation and operations; and
(B) Develop and evaluate mathematical arguments such as informal proofs,
and the foundations on which arguments are built.
(c) For competency in communication,
candidates will:
(A) Organize and consolidate their mathematical thinking through
communication;
(B) Communicate coherently and use the language of mathematics, such as
symbols and terminology, to express ideas precisely; and
(C) Analyze the mathematical thinking of others.
(d) For competency in representation,
candidates will:
(A) Use multiple forms of representation including concrete models,
pictures, diagrams, tables and graphs; and
(B) Use invented and conventional terms and symbols to communicate
reasoning and solve problems.
(e) For competency in connections,
candidates will:
(A) Understand how mathematical
ideas interconnect and build on one another to produce a coherent whole; and
(B) Recognize and apply mathematics in contexts outside of mathematics.
(4) Demonstrated
knowledge and skill in mathematics pedagogy
(a) For demonstrated knowledge and skill in the principles equity candidates
will demonstrate high expectations and strong support for all students to learn
mathematics.
(b) For demonstrated knowledge and skill
in developing curriculum, candidates will:
(A) Map curriculum that is coherent, focused on important mathematics
and carefully sequenced;
(B) Be familiar with curriculum both preceding and following the middle
level; and
(C) Be able to discern the quality of learning opportunities for
students when given a particular task, activity, educational software, etc.,
and are able to make adaptations to assure quality.
(c) Le For demonstrated knowledge and
skill in developing quality learning environment candidates will foster a
classroom environment conducive to mathematical learning through
(A) Providing and structuring the
time necessary to explore sound mathematics and grapple with significant ideas
and problems;
(B) Using the physical space and
materials in ways that facilitate students' learning of mathematics;
(C) Providing a context that
encourages the development of mathematical skill and proficiency; and
(D) Respecting and valuing students'
ideas, ways of thinking and mathematical dispositions.
(d) For demonstrated knowledge and skill
in teaching, candidates will:
(A) Understand what mathematics students know and need to learn and
then challenge and support them to learn it well; and
(B) Orchestrate discourse by:
(i) Posing questions and tasks that elicit,
engage and challenge each student's thinking;
(ii) Listening carefully to students' ideas; asking students to clarify
and justify their ideas orally and in writing;
(iii) Deciding what to pursue in depth from among the ideas that
students bring up during a discussion;
(iv) Deciding when and how to attach mathematical notation and language
to students' ideas;
(v) Deciding when to provide information, when to clarify an issue,
when to model, when to lead, and when to let a student struggle with a
difficulty; and
(vi) Monitoring students' participation in discussions and deciding
when and how to encourage each student to participate.
(e) For demonstrated knowledge and skill
in learning, candidates will:
(A) Know that students must learn mathematics with understanding,
actively building new knowledge from experience and prior knowledge; and
(B) Have the ability to recognize and move students from concrete to
abstract levels of understanding.
(f) For demonstrated knowledge and skill
in assessment, candidates will:
(A) Use a variety of formal and informal, formative and summative
assessment techniques to support the learning of important mathematics;
(B) Understand how, why, and when to use various assessment techniques
and tools; as well as how these tools inform their understanding about student
thinking and understanding; and
(C) Plan instruction based upon the information obtained through
classroom and external assessments of each student’s developmental level.
(g) For demonstrated knowledge and skill
in technology, candidates will:
(A) Understand that technology is an integral part of teaching and
learning mathematics both influencing what is taught and enhancing how it is
learned.
(B) Demonstrate effective and appropriate use of technology.
(h) For demonstrated knowledge and skill
in mathematic historical development candidates will demonstrate knowledge of
historical and cultural influences in mathematics including contributions of
underrepresented groups.
(5)
This endorsement is valid to teach any course at or below Algebra I including:
(a) Remedial Math;
(b) Mathematics;
(c) Basic Math;
(d) Math Concepts (grades 6-8);
(e) Pre-Algebra;
(f) Introductory Algebra;
(g) Basic Algebra;
(h) Algebra I;
(i) Competency Mathematics;
(j) Consumer Mathematics;
(k) General Math I & II;
(l) Mathematics Fundamentals;
(m) Math Lab;
(n) Middle Mathematics Skills;
(o) Problem Solving; and
(i) Other math-related courses at or below
the Algebra I level.
(6) This endorsement is required for teaching any subject in subsection
(4) above:
(a)
More than 51% of a full teaching
assignment on a Basic or Standard Teaching License with an elementary
endorsement issued after 1987 with the licensure code of (016); or
(b)
More than 10 hours per week or if conditionally assigned in more than one
subject, (See,
(A) Any Basic or
Standard Teaching License with other than an elementary endorsement; or
(B) An Initial or
Continuing Teaching License with a high school authorization.
Stat.
Auth.: ORS 342
Stats.
Implemented: ORS 342.120 - ORS 342.143, ORS 342.153, ORS 342.165, & ORS
342.223 - ORS 342.232
Hist.: