Section 27.130 Mathematics

Section 27.130  Mathematics

By October 1, 2024, all candidates for an endorsement in Mathematics

will be required to complete a program aligned to the CAEP (Council for

Accreditation of Educator Preparation) Standards for Mathematics Teacher

Preparation (2012) published by the National Council of Teachers of

Mathematics, 1906 Association Drive, Reston VA 20191-1502, and available at

http://www.nctm.org/ncate/. (No later amendments to or editions of these

guidelines are incorporated.) The standards effective until September 30, 2024

are as follows:

a)         The competent teacher of mathematics communicates mathematical

content and concepts.

1)         Knowledge Indicators – The competent teacher of mathematics:

A)        understands the dynamics of working collaboratively with

others.

B)        understands learning styles and learning strategies.

2)         Performance Indicators – The competent teacher of mathematics:

A)        communicates verbally and in written, visual, and symbolic

forms using appropriate technology.

B)        creates effective learning environments where students will be

able to work collaboratively in one-to-one, small-group, and large-group

contexts.

C)        analyzes the thinking and learning strategies of all students

to extend mathematical knowledge.

b)         The competent teacher of mathematics develops and utilizes a

variety of problem-solving techniques.

1)         Knowledge Indicator – The competent teacher of mathematics

understands the many strategies for problem solving.

2)         Performance Indicators – The competent teacher of mathematics:

A)        uses problem explorations and modeling to extend mathematical

knowledge of all students.

B)        generalizes results of problems and extends them to other

problem situations.

c)         The competent teacher of mathematics recognizes a variety of

reasoning techniques and applies appropriate techniques to concepts,

procedures, and conjectures

– The competent teacher of mathematics:

A)        uses problem explorations and modeling to extend mathematical

knowledge of all students.

B)        generalizes results of problems and extends them to other

problem situations.

c)         The competent teacher of mathematics recognizes a variety of

reasoning techniques and applies appropriate techniques to concepts,

procedures, and conjectures.

1)         Knowledge Indicator – The competent teacher of mathematics

understands various ways of reasoning with respect to concepts, procedures, and

conjectures.

2)         Performance Indicators – The competent teacher of mathematics:

A)        applies mathematical reasoning and appropriate technologies in

the development of concepts, procedures, and conjectures.

B)        generalizes reasoning skills within the study of mathematics

and applies or extends them to other contexts.

d)         The competent teacher of mathematics makes connections within

and among the various branches of mathematics and other disciplines.

1)         Knowledge Indicators – The competent teacher of mathematics:

A)        understands the connections within the mathematics curriculum.

B)        understands mathematical connections to school curriculums and

to other disciplines.

C)        has knowledge of the historical development of mathematics that

includes contributions of men and women from various cultures.

2)         Performance Indicators – The competent teacher of mathematics:

A)        develops the connections within and among the various branches

of mathematics.

B)        connects mathematics to other disciplines.

e)         The competent teacher of mathematics selects, integrates and

uses appropriate technologies.

1)         Knowledge Indicators – The competent teacher of mathematics:

A)        becomes familiar with the capabilities and benefits of current

and emerging technologies.

B)        understands the selection, integration, and utilization of

appropriate technologies throughout the mathematics curriculum

The competent teacher of mathematics selects, integrates and

uses appropriate technologies.

1)         Knowledge Indicators – The competent teacher of mathematics:

A)        becomes familiar with the capabilities and benefits of current

and emerging technologies.

B)        understands the selection, integration, and utilization of

appropriate technologies throughout the mathematics curriculum.

2)         Performance Indicators – The competent teacher of mathematics:

A)        selects appropriate technologies for instruction.

B)        integrates current technology as appropriate for instruction.

f)         The competent teacher of mathematics demonstrates, applies,

and explains a knowledge and sense of number.

1)         Knowledge Indicator – The competent teacher of mathematics

knows and understands the concepts of number, number theory, and numeration

systems.

A)        The early childhood or elementary school teacher:

i)          understands number sense, including concepts of order,

magnitude, mental math, estimation, and place value, and senses the

reasonableness of results.

ii)         understands decimals, fractions, ratios, proportions, and

percents as ways to represent numbers and relationships.

iii)        knows the properties of prime and composite numbers.

B)        The middle school teacher knows and understands the content

outlined in subsection (f)(1)(A) and has knowledge of complex numbers, modular

systems, and matrices.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (f)(1)(A) and (B) and understands polar and

vector representations of complex numbers, algebraic structures, and topics

from discrete mathematics.

2)         Knowledge Indicator – The competent teacher of mathematics

knows and understands algorithms of operations

systems, and matrices.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (f)(1)(A) and (B) and understands polar and

vector representations of complex numbers, algebraic structures, and topics

from discrete mathematics.

2)         Knowledge Indicator – The competent teacher of mathematics

knows and understands algorithms of operations.

A)        The early childhood or elementary school teacher understands

composition, decomposition, and recomposition of numbers, including place value

of any base, factors and multiples, prime and composite numbers, inverses, and

the application of these concepts.

B)        The middle school teacher knows and understands the content

outlined in subsection (f)(2)(A), understands operations with algebraic

expressions, and has knowledge of symbolic manipulators.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (f)(2)(A) and (B) and has knowledge of

iterative processes as they relate to fractals and other applications.

3)         Performance Indicator – The competent teacher of mathematics

applies the concepts of number theory and numeration systems.

A)        The early childhood or elementary school teacher:

i)          uses number sense to judge the reasonableness of results.

ii)         applies proportional reasoning to solve problems.

iii)        uses the properties of prime and composite numbers to

determine greatest common factors and least common multiples to solve problems.

iv)        performs operations in any base and converts between bases.

B)        The middle school teacher demonstrates the competence outlined

in subsection (f)(3)(A) and computes and interprets the results of computation

using complex numbers, modular systems, and matrices.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (f)(3)(A) and (B) and computes using polar

and vector representations of complex numbers

)        The middle school teacher demonstrates the competence outlined

in subsection (f)(3)(A) and computes and interprets the results of computation

using complex numbers, modular systems, and matrices.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (f)(3)(A) and (B) and computes using polar

and vector representations of complex numbers.

4)         Performance Indicator – The competent teacher of mathematics

models, explains, develops, and applies algorithms of operations.

A)        The early childhood or elementary school teacher chooses

appropriately from mental math, paper and pencil, manipulative, and technology

to perform computations.

B)        The middle school teacher demonstrates the competence outlined

in subsection (f)(4)(A) and models, develops, and applies algorithms with

technology.

C)        The secondary school mathematics teacher demonstrates the competence

outlined in subsections (f)(4)(A) and (B) and uses numerical approximations as

a basis for numerical integration and numerical-based proofs.

g)         The competent teacher of mathematics understands and applies

the process of measurement.

1)         Knowledge Indicator – The competent teacher of mathematics

knows customary, metric, and non-standard measurement.

A)        The early childhood or elementary school teacher:

i)          knows how to measure length, area, volume, capacity, time,

temperature, angles, weight, and mass.

ii)         has knowledge of non-standard and emerging units such as

graphic screen pixels and font size.

B)        The middle school teacher knows and understands the content

outlined in subsection (g)(1)(A) and:

i)          understands trigonometric ratios and relationships.

ii)         understands how changing one measure of a multi-dimensional

object may affect other measures.

iii)        understands conversion factors as they apply to dimensional

analysis

graphic screen pixels and font size.

B)        The middle school teacher knows and understands the content

outlined in subsection (g)(1)(A) and:

i)          understands trigonometric ratios and relationships.

ii)         understands how changing one measure of a multi-dimensional

object may affect other measures.

iii)        understands conversion factors as they apply to dimensional

analysis.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (g)(1)(A) and (B) and understands nonlinear

scales.

2)         Performance Indicator – The competent teacher of mathematics

selects and applies appropriate units and tools for measuring, comparing, and

ordering.

A)        The early childhood or elementary school teacher:

i)          uses customary, metric, and non-standard measures.

ii)         selects and uses appropriate tools to perform various

measurements.

iii)        estimates measurement.

iv)        determines acceptable measures of accuracy and calculates

relative error.

B)        The middle school teacher demonstrates the competence outlined

in subsection (g)(2)(A) and uses trigonometric ratios and their relationships

to solve problems.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (g)(2)(A) and (B) and applies nonlinear

scales (e.g., exponential and logarithmic).

3)         Performance Indicator – The competent teacher of mathematics

uses formulas and other procedures for computing or estimating the measure of

multi-dimensional objects.

A)        The early childhood or elementary school teacher:

i)          measures objects using both direct and indirect measurement.

ii)         uses formulas to aid in indirect measurement.

iii)        applies measurements and formulas to irregular shapes,

regions, and solids.

iv)        reads and interprets scale drawings

es for computing or estimating the measure of

multi-dimensional objects.

A)        The early childhood or elementary school teacher:

i)          measures objects using both direct and indirect measurement.

ii)         uses formulas to aid in indirect measurement.

iii)        applies measurements and formulas to irregular shapes,

regions, and solids.

iv)        reads and interprets scale drawings.

B)        The middle school teacher demonstrates the competence outlined

in subsection (g)(3)(A) and:

i)          explains how changing one measure of a multi-dimensional

object affects other measurements.

ii)         reads and interprets topographical maps and architectural

drawings.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (g)(3)(A) and (B) and:

i)          applies dimensional analysis.

ii)         uses modeling and visualization to hypothesize about and

predict measurements.

h)         The competent teacher of mathematics demonstrates, applies and

explains a knowledge and sense of algebra via patterns, functions, symbols, and

models.

1)         Knowledge Indicator – The competent teacher of mathematics

knows and understands applications of concepts, representations, and

relationships of variables and patterns.

A)        The early childhood or elementary school teacher:

i)          understands the order of operations.

ii)         understands the concept of variables.

iii)        understands symbolic, numeric, and graphical representations

of mathematical situations.

iv)        understands the properties and operations of real numbers in

an algebraic context.

B)        The middle school teacher knows and understands the content

outlined in subsection (h)(1)(A) and understands a wide range of modeling

applications involving graphs, tree charts, and other visual representations of

data with multiple dimensions

cal representations

of mathematical situations.

iv)        understands the properties and operations of real numbers in

an algebraic context.

B)        The middle school teacher knows and understands the content

outlined in subsection (h)(1)(A) and understands a wide range of modeling

applications involving graphs, tree charts, and other visual representations of

data with multiple dimensions.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (h)(1)(A) and (B) and understands variable

relationships, logic, and concepts of discrete mathematics.

2)         Knowledge Indicator – The competent teacher of mathematics

knows and understands concepts and representations of relations and functions.

A)        The early childhood or elementary school teacher:

i)          understands the symbolic, numeric, graphical, and verbal representations

of relations and functions and the relationships among them.

ii)         understands polynomial and exponential functions.

B)        The middle school teacher knows and understands the content

outlined in subsection (h)(2)(A) and understands logarithmic, parametric,

trigonometric, rational, radical, and absolute value relations and their

graphs.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (h)(2)(A) and (B) and understands linear

algebra.

3)         Performance Indicator – The competent teacher of mathematics

knows and understands the development and applications of calculus.

A)        The early childhood or elementary school teacher:

i)          understands concepts of rates of change and patterns that

lead to limits.

ii)         understands concepts of distance, area, volume, and shapes

that lead to limits.

B)        The middle school teacher knows and understands the content

outlined in subsection (h)(3)(A) and:

i)          knows the historical development of calculus.

ii)         understands the concept of limits

eacher:

i)          understands concepts of rates of change and patterns that

lead to limits.

ii)         understands concepts of distance, area, volume, and shapes

that lead to limits.

B)        The middle school teacher knows and understands the content

outlined in subsection (h)(3)(A) and:

i)          knows the historical development of calculus.

ii)         understands the concept of limits.

iii)        understands the basic concepts of calculus and their

applications.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (h)(3)(A) and (B) and understands the

concepts of calculus and analytical geometry and their applications.

4)         Knowledge Indicator – The competent teacher of mathematics

knows and understands algebraic structures.

A)        The early childhood or elementary school teacher:

i)          understands the properties of the real number systems.

ii)         understands the properties of sets and Venn diagrams.

B)        The middle school teacher knows and understands the content

outlined in subsection (h)(4)(A) and understands the properties of complex and

modular systems and their applications.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (h)(4)(A) and (B) and understands groups,

rings, integral domains, and fields.

5)         Performance Indicator – The competent teacher of mathematics

applies concepts, representations, and relationships of variables and patterns.

A)        The early childhood or elementary school teacher:

i)          applies the order of operations to numerical and algebraic

expressions.

ii)         identifies, completes, and extends patterns and sequences.

iii)        represents mathematical situations symbolically, numerically,

and graphically.

iv)        applies properties and operations of real numbers in an

algebraic context.

v)         solves number sentences involving variables

l teacher:

i)          applies the order of operations to numerical and algebraic

expressions.

ii)         identifies, completes, and extends patterns and sequences.

iii)        represents mathematical situations symbolically, numerically,

and graphically.

iv)        applies properties and operations of real numbers in an

algebraic context.

v)         solves number sentences involving variables.

vi)        translates word situations to algebraic sentences and solves

them using algebra.

vii)       uses equations and inequalities as a means of solving

practical applications.

B)        The middle school teacher demonstrates the competence outlined

in subsection (h)(5)(A) and:

i)          uses a wide range of modeling applications involving graphs

and tree charts.

ii)         solves systems of linear equations graphically and algebraically

(including matrices and determinants).

iii)        solves systems of nonlinear equations and inequalities

algebraically and graphically.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (h)(5)(A) and (B) and:

i)          explains and applies symbolic logic.

ii)         explains and applies induction and recursion.

iii)        explains and applies sequences and series.

6)         Performance Indicator – The competent teacher of mathematics

uses concepts and representations of relations and functions and their

applications.

A)        The early childhood or elementary school teacher:

i)          represents functions and relations in symbolic, numeric,

graphical, and verbal forms.

ii)         finds and uses slopes and intercepts to construct, analyze,

and interpret graphs of equations and inequalities.

B)        The middle school teacher demonstrates the competence outlined

in subsection (h)(6)(A) and:

i)          finds and uses slope, symmetry, roots, intercepts, critical

points, and vertices to construct and interpret graphs of functions and

relations

nd verbal forms.

ii)         finds and uses slopes and intercepts to construct, analyze,

and interpret graphs of equations and inequalities.

B)        The middle school teacher demonstrates the competence outlined

in subsection (h)(6)(A) and:

i)          finds and uses slope, symmetry, roots, intercepts, critical

points, and vertices to construct and interpret graphs of functions and

relations.

ii)         recognizes and uses the equations of lines, hyperbolas,

parabolas, circles, ellipses, and nonlinear equations.

iii)        formulates, explains, and solves problems involving nonlinear

equations such as variation and exponential and logarithmic growth and decay.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (h)(6)(A) and (B) and applies principles and

properties of linear algebra.

7)         Performance Indicator – The competent teacher of mathematics

at the middle school or secondary level explains and uses the concepts of

calculus and applications.

A)        The middle school teacher:

i)          calculates and interprets basic limits.

ii)         illustrates the basic concepts of calculus using concrete

applications.

B)        The secondary school mathematics teacher demonstrates the

competence outlined in subsection (h)(7)(A) and uses differentiation,

integration, and other concepts of calculus to solve problems and interpret

results.

i)          The competent teacher of mathematics knows and uses geometric

methods to analyze, categorize, and draw conclusions about points, lines,

planes, and space.

1)         Knowledge Indicator – The competent teacher of mathematics

understands terminology, properties of two- and three-dimensional shapes, and

the relationships among them.

2)         Knowledge Indicator – The competent teacher of mathematics

knows Euclidean and non-Euclidean geometry, coordinate geometry, graph theory,

and transformational geometry and the relationships among them

space.

1)         Knowledge Indicator – The competent teacher of mathematics

understands terminology, properties of two- and three-dimensional shapes, and

the relationships among them.

2)         Knowledge Indicator – The competent teacher of mathematics

knows Euclidean and non-Euclidean geometry, coordinate geometry, graph theory,

and transformational geometry and the relationships among them.

3)         Knowledge Indicator – The competent teacher of mathematics

understands the process of conjecturing, justifying, and proof.

A)        The early childhood or elementary school teacher understands

inductive and deductive reasoning.

B)        The middle school teacher understands inductive and deductive

reasoning and understands the appropriate uses of different types of proof.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsection (i)(3)(B) and extends the understanding of

proof to finite and non-Euclidean settings.

4)         Performance Indicator – The competent teacher of mathematics

uses and applies the properties of geometry.

A)        The early childhood or elementary school teacher:

i)          recognizes relationships and patterns in geometric figures.

ii)         uses characteristics of geometric figures including symmetry,

congruence, and similarity to recognize, identify, build, draw, describe,

analyze, and categorize two- and three-dimensional figures and tessellation.

iii)        applies geometric concepts to solve practical applications.

iv)        explains the relationships between perimeter, area, and volume

of similar figures.

B)        The middle school teacher demonstrates the competence outlined

in subsection (i)(4)(A) and uses trigonometry to solve practical applications.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (i)(4)(A) and (B)

solve practical applications.

iv)        explains the relationships between perimeter, area, and volume

of similar figures.

B)        The middle school teacher demonstrates the competence outlined

in subsection (i)(4)(A) and uses trigonometry to solve practical applications.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (i)(4)(A) and (B).

5)         Performance Indicator – The competent teacher of mathematics

identifies, analyzes, categorizes, and applies multi-dimensional figures using

spatial visualization skills and modeling.

A)        The early childhood or elementary school teacher:

i)          translates between two- and three-dimensional representations

of the same figure including the use of coordinate geometry and graph theory.

ii)         uses manipulative, Euclidean geometry, coordinate geometry,

transformational geometry, and appropriate technology to model mathematical

concepts and solve problems.

B)        The middle school teacher demonstrates the competence outlined

in subsection (i)(5)(A) and:

i)          generates solids of revolution from two-dimensional figures.

ii)         gives examples of non-Euclidean geometry.

iii)        applies recursion and iteration geometrically.

iv)        recognizes and uses relationships that exist between algebra

and geometry.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (i)(5)(A) and (B) and:

i)          describes relationships of the planar sections of

three-dimensional objects.

ii)         explains relationships that exist between transformations

(including matrix representations) as a geometric equivalence of the function

concept.

6)         Performance Indicator – The competent teacher of mathematics

constructs convincing arguments and proofs

subsections (i)(5)(A) and (B) and:

i)          describes relationships of the planar sections of

three-dimensional objects.

ii)         explains relationships that exist between transformations

(including matrix representations) as a geometric equivalence of the function

concept.

6)         Performance Indicator – The competent teacher of mathematics

constructs convincing arguments and proofs.

A)        The early childhood or elementary school teacher makes and

identifies mathematical conjectures and provides justification to support or

refute conjectures using manipulatives; constructions; algebraic, coordinate,

and transformational methods; interactive technology; and paragraph and

two-column proofs.

B)        The middle school teacher demonstrates the competence outlined

in subsection (i)(6)(A), constructs inductive, deductive, and indirect

arguments and explains the difference among them.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (i)(6)(A) and (B) and uses a formal

axiomatic system to construct and analyze proofs.

j)          The competent teacher of mathematics demonstrates knowledge

and application of probability, descriptive and inferential statistics.

1)         Knowledge Indicator – The competent teacher of mathematics

understands how to collect, organize, and represent data to answer questions.

A)        The early childhood or elementary school teacher:

i)          understands how to create tables, graphs, charts, pictures,

and other visual representations of a set of data.

ii)         understands simple random sampling and recognizes bias.

iii)        understands line of best fit.

B)        The middle school teacher knows and understands the content

outlined in subsection (j)(1)(A) and understands data trends and curves of best

fit.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (j)(1)(A) and (B)

data.

ii)         understands simple random sampling and recognizes bias.

iii)        understands line of best fit.

B)        The middle school teacher knows and understands the content

outlined in subsection (j)(1)(A) and understands data trends and curves of best

fit.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (j)(1)(A) and (B).

2)         Knowledge Indicator – The competent teacher of mathematics

understands summary statistics.

A)        The early childhood or elementary school teacher:

i)          understands measures of central tendency, variation, and

position.

ii)         understands common distributions.

B)        The middle school teacher knows and understands the content

outlined in subsection (j)(2)(A).

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsection (j)(2)(A) and understands additional

measures of central tendency and variation.

3)         Knowledge Indicator – The competent teacher of mathematics

understands how to interpret and predict the results of data analysis.

A)        The early childhood or elementary school teacher:

i)          understands the design of observations and experiments to

answer questions.

ii)         understands the concept of reliability and validity.

B)        The middle school teacher knows and understands the content

outlined in subsection (j)(3)(A) and understands correlation and regression

techniques.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (j)(3)(A) and (B) and understands the

design of experiments used in testing hypotheses.

4)         Knowledge Indicator – The competent teacher of mathematics

understands counting techniques and probability.

A)        The early childhood or elementary school teacher:

i)          understands fundamental counting principles, combinations,

and permutations.

ii)         understands probability and odds of events

(B) and understands the

design of experiments used in testing hypotheses.

4)         Knowledge Indicator – The competent teacher of mathematics

understands counting techniques and probability.

A)        The early childhood or elementary school teacher:

i)          understands fundamental counting principles, combinations,

and permutations.

ii)         understands probability and odds of events.

iii)        understands dependent and independent events.

B)        The middle school teacher knows and understands the content

outlined in subsection (j)(4)(A) and understands the use of random variables to

solve problems.

C)        The secondary school mathematics teacher knows and understands

the content outlined in subsections (j)(4)(A) and (B) and understands the link

between probability theory and inferential statistics.

5)         Performance Indicator – The competent teacher of mathematics

poses questions and collects, organizes, and represents data to answer those

questions.

A)        The early childhood or elementary school teacher:

i)          creates tables, graphs, charts, pictures, and other visual

representations of a set of data.

ii)         collects simple random samples and recognizes sample bias.

iii)        uses visual techniques for finding, interpreting, and

applying the line of best fit.

B)        The middle school teacher demonstrates the competence outlined

in subsection (j)(5)(A) and finds and applies appropriate curves of best fit

using technology.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (j)(5)(A) and (B).

6)         Performance Indicator – The competent teacher of mathematics

calculates, explains, and interprets summary statistics.

A)        The early childhood, elementary, or middle school teacher:

i)          uses measures of central tendency and variation to describe a

set of data.

ii)         uses common distributions as appropriate to solve problems

outlined in subsections (j)(5)(A) and (B).

6)         Performance Indicator – The competent teacher of mathematics

calculates, explains, and interprets summary statistics.

A)        The early childhood, elementary, or middle school teacher:

i)          uses measures of central tendency and variation to describe a

set of data.

ii)         uses common distributions as appropriate to solve problems.

B)        The secondary school mathematics teacher demonstrates the

competence outlined in subsection (j)(6)(A) and uses additional measures of

central tendency and variation to describe a set of data.

7)         Performance Indicator – The competent teacher of mathematics

predicts, calculates, interprets, and applies the results of data analysis.

A)        The early childhood, elementary, or middle school teacher:

i)          develops a hypothesis based on a question or problem of

interest and devises a plan for the collection of data.

ii)         uses simple survey and sampling techniques.

iii)        collects, records, organizes, displays, summarizes, and

interprets data.

B)        The secondary school mathematics teacher demonstrates the

competence outlined in subsection (j)(7)(A) and chooses an appropriate

experimental design, selects and performs proper research procedures, and

interprets results.

8)         Performance Indicator – The competent teacher of mathematics

demonstrates and uses counting techniques and probability.

A)        The early childhood or elementary teacher:

i)          uses the fundamental counting principles, combinations, and

permutations.

ii)         determines the probability and odds of events.

iii)        analyzes problem situations (e.g., fairness of games,

lotteries).

iv)        creates simulations to analyze simple theoretical or

experimental probabilities.

v)         computes probabilities for dependent and independent events

ry teacher:

i)          uses the fundamental counting principles, combinations, and

permutations.

ii)         determines the probability and odds of events.

iii)        analyzes problem situations (e.g., fairness of games,

lotteries).

iv)        creates simulations to analyze simple theoretical or

experimental probabilities.

v)         computes probabilities for dependent and independent events.

B)        The middle school teacher demonstrates the competence outlined

in subsection (j)(8)(A) and:

i)          determines probabilities involving combinations and

permutations.

ii)         generates and interprets probability distributions for random

variables.

C)        The secondary school mathematics teacher demonstrates the

competence outlined in subsections (j)(8)(A) and (B) and links probability to

inferential statistics.

k)         The competent teacher of mathematics understands the process

of reading and demonstrates instructional abilities to teach reading in the

content area of mathematics.

1)         Knowledge Indicators – The competent teacher of mathematics:

A)        understands that the reading process is the construction of

meaning through the interactions of the reader's background knowledge and

experiences, the information in the text, and the purpose of the reading

situation.

B)        recognizes the relationships among the four language arts

(reading, writing, listening, and speaking), and knows how to provide

opportunities to integrate these through instruction.

C)        understands how to design, select, modify and evaluate

materials in terms of the reading needs of the learner.

D)        understands the importance of and encourages the use of

literature for adolescents in the curriculum and for independent reading.

E)        understands the relationship between oral and silent reading.

F)         understands the role of subject-area vocabulary in developing

reading comprehension

esign, select, modify and evaluate

materials in terms of the reading needs of the learner.

D)        understands the importance of and encourages the use of

literature for adolescents in the curriculum and for independent reading.

E)        understands the relationship between oral and silent reading.

F)         understands the role of subject-area vocabulary in developing

reading comprehension.

G)        understands the importance of the unique study strategies

required of the specific content area in developing reading comprehension.

H)        understands the importance of the relationship between

assessment and instruction in planning.

2)         Performance Indicators – The competent teacher of mathematics:

A)        plans and teaches lessons for students that develop

comprehension of content-area materials through instructional practices that

include analyzing critically, evaluating sources, and synthesizing and

summarizing material.

B)        plans and teaches lessons on how to monitor comprehension and

correct confusions and misunderstandings that arise during reading.

C)        plans and models the use of comprehension strategies before,

during, and after reading of text.

D)        provides opportunities for students to develop content-area

vocabulary through instructional practices that develop connections and

relationships among words, use of context clues, and understanding of

connotative and denotative meaning of words.

E)        plans and teaches lessons that encourage students to write

about the content read in order to improve understanding.

F)         plans and teaches lessons to help students develop study

strategies that include previewing and preparing to read text effectively,

recognizing organizational patterns unique to informational text, and using

graphic organizers as an aid for recalling information.

G)        plans and teaches units that require students to carry out

research or inquiry using multiple texts, including electronic resources

teaches lessons to help students develop study

strategies that include previewing and preparing to read text effectively,

recognizing organizational patterns unique to informational text, and using

graphic organizers as an aid for recalling information.

G)        plans and teaches units that require students to carry out

research or inquiry using multiple texts, including electronic resources.

H)        provides continuous monitoring of students' progress through

observations, work samples, and various informal reading assessments.

I)         analyzes and evaluates the quality and appropriateness of

instructional materials in terms of readability, content, length, format,

illustrations, and other pertinent factors.

J)         promotes the development of an environment that includes

classroom libraries that foster reading.