# Ala. Admin. Code r. 290-3-3-.26 - Mathematics (Grades 6-12)

(1)

**Rationale.**All secondary mathematics teachers should be prepared with depth and breadth in the mathematical domains identified in Rule 290-3-3-.26(2)(a) and should know, understand, teach, and be able to communicate their mathematical knowledge with the breadth of understanding reflecting competencies for each of these domains. These standards are consistent with the 2020 standards of the National Council of Teachers of Mathematics (NCTM). The standards build upon the Alabama Core Teaching Standards.(2)

**Program Curriculum.**In addition to meeting Rules 290-3-3-.03(6)(a)1. -4., 290-3-3-.03(6)(e)1.(i) -(iii) and 2.(i)-(iii), 290-3-3-.04, 290-3-3-.05, and 290-3-3-.14, the teaching field shall require an academic major of at least 30 semester hours of credit with at least 18 semester hours of upper-division credit. Additional information is provided in the definition for academic major in Rule 290-3-3-.01(2).(a)

**Knowing and Understanding Mathematics.**Candidates demonstrate and apply understandings of major mathematics concepts, procedures, knowledge, and applications within and among mathematical domains of Number; Algebra and Functions; Calculus; Statistics and Probability; Geometry, Trigonometry, and Measurement.1. Essential Concepts in Number. Candidates
demonstrate and apply understandings of major mathematics concepts, procedures,
knowledge, and applications of number including flexibly applying procedures,
using real and rational numbers in contexts, developing solution strategies,
and evaluating the correctness of conclusions.

*Major mathematical concepts in Number include number theory; ratio, rate, and proportion; and structure, relationships, operations, and representations.*2. Essential Concepts in Algebra and
Functions. Candidates demonstrate and apply understandings of major mathematics
concepts, procedures, knowledge, and applications of algebra and functions
including how mathematics can be used systematically to represent patterns and
relationships including proportional reasoning, to analyze change, and to model
everyday events and problems of life and society.

*Essential Concepts in Algebra and Functions include algebra that connects mathematical structure to symbolic, graphical, and tabular descriptions; connecting algebra to functions; and developing families of functions as a fundamental concept of mathematics. Additional Concepts should include algebra from a more theoretical approach including relationship between structures (e.g., groups, rings, and fields) as well as formal structures for number systems and numerical and symbolic calculations.*3.
Essential Concepts in Calculus. Candidates demonstrate and apply understandings
of major mathematics concepts, procedures, knowledge, and applications of
calculus including the mathematical study of the calculation of instantaneous
rates of change and the summation of infinitely many small factors to determine
some whole.

*Essential Concepts in Calculus include limits, continuity, the Fundamental Theorem of Calculus, and the meaning and techniques of differentiation and integration.*4. Essential Concepts in Statistics and
Probability. Candidates demonstrate and apply understandings of statistical
thinking and the major concepts, procedures, knowledge, and applications of
statistics and probability, including how statistical problem solving and
decision making depend on understanding, explaining, and quantifying the
variability in a set of data to make decisions. They understand the role of
randomization and chance in determining the probability of events.

*Essential Concepts in Statistics and Probability include quantitative literacy, visualizing and summarizing data, statistical inference, probability, and applied problems.*5.
Essential Concepts in Geometry, Trigonometry, and Measurement. Candidates
demonstrate and apply understandings of major mathematics concepts, procedures,
knowledge, and applications of geometry including using visual representations
for numerical functions and relations, data and statistics, and networks, to
provide a lens for solving problems in the physical world.

*Essential Concepts in Geometry, Trigonometry, and Measurement include transformations, geometric arguments, reasoning and proof, applied problems, and non-Euclidean geometries.*(b)

**Knowing and Using Mathematical Processes**. Candidates demonstrate, within or across mathematical domains, their knowledge of and ability to apply the mathematical processes of problem solving; reason and communicate mathematically; and engage in mathematical modeling. Candidates apply technology appropriately within these mathematical processes.1. Problem Solving. Candidates demonstrate a
range of mathematical problem-solving strategies to make sense of and solve
nonroutine problems (both contextual and noncontextual) across mathematical
domains.

2. Reasoning and
Communicating. Candidates organize their mathematical reasoning and use the
language of mathematics to express their mathematical reasoning precisely, both
orally and in writing to multiple audiences.

3. Mathematical Modeling and Use of
Mathematical Models. Candidates understand the difference between the
mathematical modeling process and models in mathematics. Candidates engage in
the mathematical modeling process and demonstrate their ability to model
mathematics.

(c)

**Knowing Students and Planning for Mathematical Learning.**Candidates use knowledge of students and mathematics to plan rigorous and engaging mathematics instruction supporting students' access and learning. The mathematics instruction developed provides equitable, culturally responsive opportunities for all students to learn and apply mathematics concepts, skills, and practices.1. Student Diversity.
Candidates identify and use students' individual and group differences to plan
rigorous and engaging mathematics instruction that supports students'
meaningful participation and learning.

2. Students' Mathematical Strengths.
Candidates identify and use students' mathematical strengths to plan rigorous
and engaging mathematics instruction that supports students' meaningful
participation and learning.

3.
Positive Mathematical Identities. Candidates understand that teachers'
interactions impact individual students by influencing and reinforcing
students' mathematical identities, positive or negative, and plan experiences
and instruction to develop and foster positive mathematical
identities.

(d)

**Teaching Meaningful Mathematics.**Candidates implement effective and equitable teaching practices to support rigorous mathematical learning for a full range of students. Candidates establish rigorous mathematics learning goals, engage students in high cognitive demand learning, use mathematics specific tools and representations, elicit and use student responses, develop conceptual understanding and procedural fluency, and pose purposeful questions to facilitate student discourse.1. Establish
Rigorous Mathematics Learning Goals. Candidates establish rigorous mathematics
learning goals for students based on mathematics standards and practices.

2. Engage Students in High
Cognitive Demand Learning. Candidates select or develop and implement high
cognitive demand tasks to engage students in mathematical learning experiences
that promote reasoning and sense making.

3. Incorporate Mathematics-Specific Tools.
Candidates select mathematics-specific tools, including technology, to support
students' learning, understanding, and application of mathematics and to
integrate tools into instruction.

4. Use Mathematical Representations.
Candidates select and use mathematical representations to engage students in
examining understandings of mathematics concepts and the connections to other
representations.

5. Elicit and Use
Student Responses. Candidates use multiple student responses, potential
challenges, and misconceptions, and they highlight students' thinking as a
central aspect of mathematics teaching and learning.

6. Develop Conceptual Understanding and
Procedural Fluency. Candidates use conceptual understanding to build procedural
fluency for students through instruction that includes explicit connections
between concepts and procedures.

7.
Facilitate Discourse. Candidates pose purposeful questions to facilitate
discourse among students that ensures that each student learns rigorous
mathematics and builds a shared understanding of mathematical ideas.

(e)

**Assessing Impact on Student Learning.**Candidates assess and use evidence of students' learning of rigorous mathematics to improve instruction and subsequent student learning. Candidates analyze learning gains from formal and informal assessments for individual students, the class as a whole, and subgroups of students disaggregated by demographic categories, and they use this information to inform planning and teaching.1. Assessing
for Learning. Candidates select, modify, or create both informal and formal
assessments to elicit information on students' progress toward rigorous
mathematics learning goals.

2.
Analyze Assessment Data. Candidates collect information on students' progress
and use data from informal and formal assessments to analyze progress of
individual students, the class as a whole, and subgroups of students
disaggregated by demographic categories toward rigorous mathematics learning
goals.

3. Modify Instruction.
Candidates use the evidence of student learning of individual students, the
class as a whole, and subgroups of students disaggregated by demographic
categories to analyze the effectiveness of their instruction with respect to
these groups. Candidates propose adjustments to instruction to improve student
learning for each and every student based on the analysis.

(e)

**Social and Professional Context of Mathematics Teaching and Learning.**Candidates are reflective mathematics educators who collaborate with colleagues and other stakeholders to grow professionally, to support student learning, and to create more equitable mathematics learning environments.1. Promote
Equitable Learning Environments. Candidates seek to create more equitable
learning environments by identifying beliefs about teaching and learning
mathematics, and associated classroom practices that produce equitable or
inequitable mathematical learning for students.

2. Promote Mathematical Identities.
Candidates reflect on their impact on students' mathematical identities and
develop professional learning goals that promote students' positive
mathematical identities.

3. Engage
Families and Communities. Candidates communicate with families to share and
discuss strategies for ensuring the mathematical success of their
children.

4. Collaborate with
Colleagues. Candidates collaborate with colleagues to grow professionally and
support student learning of mathematics.

## Notes

Previous Rule.09 was renumbered.20 per certification published August 31, 2021; effective October 15, 2021.

**Author:** Dr. Eric G. Mackey

**Statutory Authority:**
Code of Ala.
1975, ยงยง
16-3-16,
16-23-14.

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