Current through Register Vol. 42, No. 11, August 30, 2024
In accordance with Act 2022- 249 the Alabama State Board of
Education (ALSBE) modifies its standards relative to teaching of numeracy,
including algebraic reasoning, cardinality, computational fluency, and
conceptual understanding, in the early childhood education, early childhood
special education, elementary education, and collaborative special education
Educator Preparation Programs (EPPs). Each program shall contain no less than
twelve Class B programs shall contain no less than 12 credit hours in numeracy,
including learning specific to dyscalculia. Number and operations, treated
algebraically, with attention to properties of operation and problem solving
should occupy 6 of those hours. With the remaining 6 hours devoted to
additional ideas: fractions The remaining 6 hours shall address algebraic
thinking, measurement, data, and geometry. Alternative Class A programs shall
have a total of 12 hours in math courses, with a minimum of 6 hours in the
aforementioned content areas and a maximum of 6 hours in accredited math
courses available to transfer. The numeracy standards in this rule are to be
implemented in coursework by August 2025.
(1)
Numeracy. Numeracy is
defined herein as the ability to understand and work with numbers. Numeracy is
the knowledge, skills, behaviors, and dispositions that students need to use
mathematics in the world and having the dispositions and capacities to use
mathematical knowledge and skills purposely.
(2)
Understand, explain, and
model are professional dispositions and practices, including
respecting and maintaining objectivity and clarity in the best interest of all
learners, including those struggling with number sense, and maintaining public
trust using current scientifically supported best practices.
(3)
A Numeracy Framework,
developed by Willis and Hogan (2000) for teachers of numeracy incorporates a
blend of three types of thinking or knowledge:
(a)
Mathematical-the skills,
concepts, and techniques for solving quantitative problems
(b)
Contextual-the awareness and
knowledge of how the context affects the mathematics being used
(c)
Strategic-the ability to
recognize the appropriate mathematics needed to solve a problem, to apply and
adapt it as necessary, and to question the use of mathematics in
context.
(4)
Curriculum. The curriculum is reflective of the recommendations of
the National Council of Teachers of Mathematics (NCTM), the Conference Board of
the Mathematics Sciences (CBMS), the United States Department of Education
(USDOE), and the Mathematics Sciences Research Institute (MSRI). These
standards have been aligned with the Alabama Course of Study (ACOS) to ensure
that candidates in programs that span grades K-5 have a deep knowledge and
understanding of all the numerical practices that students in this grade ban
should develop. Additionally, these standards reflect the efforts of the
Council for Accreditation of Educator Preparation (CAEP). They outline the
mathematical knowledge and ability statements that completers of these programs
should demonstrate to ensure that each student learns and develops to his/her
fullest potential.
(5)
Pedagogical Framework. The pedagogy undergirds the content for each of
the mathematical content areas. The teachers of numeracy will utilize these
teaching practices from NCTM to ensure that content is being delivered in a way
to optimize student understanding and application. The eight core pedagogical
principles are:
a. Establish mathematics
goals to focus on learning,
b.
Implement tasks that promote reasoning and problem solving,
c. Use and connect mathematical
representations,
d. Facilitate
meaningful mathematical discourse,
e. Pose purposeful questions,
f. Build procedural fluency from conceptual
understanding,
g. Support
productive struggle in learning mathematics, and
h. Elicit and use evidence of student
thinking.
(6)
Mathematical Practices Mathematical practices are the skills and
habits that faculty must provide opportunities for candidates to develop and
become proficient in mathematics. Teachers of mathematics will understand,
explain, and model how these mathematical practices define processes in which
students must engage in everyday as their mathematical maturity develops.
Faculty must provide opportunities for the candidate to make connections
between the mathematical practices and mathematics content within mathematics
instruction. These practices include:
a.
Making sense of problems and persevering in solving them,
b. Reasoning abstractly and
quantitatively,
c. Constructing
viable arguments and critiquing the reasoning of others,
d. Modeling with mathematics,
e. Using appropriate tools
strategically,
f. Attending to
precision,
g. Looking for and
making use of structure, and
h.
Looking for and expressing regularity in repeated reasoning.
(7)
Assessing, Planning and
Designing Contexts for Learning.
Assessing, planning, and designing contexts for learning
support the development of a coherent curriculum and an understanding of how
content topics and expectations are connected to each other throughout the
elementary grades. This connection from academic to curricular, across grade
levels requires teachers of mathematics to demonstrate understanding related to
student learning, curricular practices and standards, academic language and
assessments as they consider learning progressions within and across grade
levels.
(a)
Understand, explain,
and model how to plan sequences of instruction that includes goals,
appropriate materials, activities and assessments, and supports engagement in
learning through evidence-based practices.
(b)
Understand, explain, and
model how to administer formative and summative assessments to determine
student competencies and learning needs, and use this assessment data to
provide feedback, improve instruction and monitor learning.
(c)
Understand, explain, and
model how to differentiate instructional plans to meet the needs of
diverse students in the classroom.
(d)
Understand, explain, and
model how to develop accommodations for students with dyscalculia or a
math learning disability and provide specific strategies to assist them such
as:
1. Early warning signs, screening, and
recommendations for intervention,
2. Use of visual representations,
3. Use of instructional examples and concrete
objects,
4. Student
verbalization,
5. Use of
heuristic/multiple strategies,
6.
Provide ongoing feedback, and
7.
Review strategies and connect to previous learning.
(8)
Content
Knowledge. Effective elementary numeracy teachers understand, explain,
and model knowledge and understanding of major numeracy concepts, algorithms,
procedures, connections, and applications in varied contexts, within and among
mathematical domains.
(a)
Numerical
Practices. Numerical Practices consist of concepts within number and
operations base ten, and operations and algebraic thinking. Upon program
completion candidates shall be able to do the following:
1.
Foundations of Counting.
Understand, explain, and model the intricacy of counting, including the
distinction between counting as a list of numbers in order and counting to
determine a number of objects. (ACOS K.1, K.2, K.3, K.4, K.5,
1.10)
2.
Operations
with Numbers: Base Ten
(i) Understand,
explain, and model how the base-ten place value system relies on repeated
bundling in groups of ten and how to use varied representations including
objects, drawings, layered place value cards, and numerical expressions to help
reveal the base-ten structure. (ACOS K.14, 1.11, 1.12, 2.6, 2.7, 2.8,
2.9, 4.6, 4.7, 4.8, 4.9, 5.3, 5.4, 5.5)
(ii) Understand, explain, and model how
efficient base-ten computation methods for addition, subtraction,
multiplication, and division rely on decomposing numbers represented in base
ten according to the base-ten units represented by their digits and applying
(often informally) properties of operations, including the commutative and
associative properties of addition and multiplication and the distributive
property, to decompose a calculation into parts. (ACOS K.10, K.11,
K.12, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.13, 1.14, 1.15, 2.1, 2.2, 2.10,
2.11, 2.12, 2.13, 2.14, 3.10, 3.11, 3.12, 4.10, 4.11, 4.12, 5.6, 5.7,
5.8)
(iii) Understand,
explain, and model how to use drawings or manipulative materials to reveal,
discuss, and explain the rationale behind computation methods. COS
K.13, K.15,1.13, 2.1, 2.2, 2.3, 2.4, 2.10, 2.11, 2.12, 2.13, 2.14, 2.21, 2.22,
2.24c, 3.1, 3.2, 3.3, 3.5, 3.6, 3.8, 3.9, 3.11, 3.12, 4.2, 4.3b, 4.10, 4.11,
4.12, 5.7)
(iv)
Understand, explain, and model how to extend the base-ten system to decimals
and use number lines to represent decimals. Explain the rationale for decimal
computation methods. (ACOS 5.3, 5.4a, 5.5, 5.8)
3.
Operations and Algebraic
Thinking
(i) Understand, explain, and
model the different types of problems solved by addition, subtraction,
multiplication, and division, and meanings of the operations illustrated by
these problem types. (ACOS K.9, 1.1, 1.2, 2.1, 3.3, 3.8, 4.1, 4.2, 4.3,
5.1)
(ii) Understand,
explain, and model teaching/learning paths for single-digit addition and
associated subtraction and singledigit multiplication and associated division,
including the use of properties of operations. (ACOS K.8, K.12, 1.3,
1.4, 1.5, 1.6, 2.2, 3.1, 3.2, 3.5, 3.6, 3.7)
(iii) Understand, explain, and model
foundations of algebra within elementary mathematics, including understanding
the equal sign as meaning "the same amount as" rather than a "calculate the
answer" symbol. (ACOS 1.7, 3.4)
(iv) Understand, explain, and model numerical
and algebraic expressions by describing them in words, parsing them into their
component parts, and interpreting the components in terms of a context.
(ACOS K.10, K.11, 1.8, 2.3, 2.4, 3.8, 4.3, 5.1)
(v) Understand, explain, and model lines of
reasoning used to solve equations and systems of equations. (ACOS K.13, 1.9,
2.5, 3.9, 4.4, 4.5, 5.2)
(b)
Operations with Numbers:
Fractions1. Understand, explain, and
model fractions as numbers, which can be represented by area and set models and
by lengths on a number line. Define a/b fractions as
a part, each of size 1/b. Attend closely to
the whole (referent unit) while solving problems and explaining solutions.
(ACOS 1.23, 2.27, 3.13, 3.14)
2. Understand, explain, and model addition,
subtraction, multiplication, and division problem types and associated meanings
for the operations extend from whole numbers to fractions. (ACOS 4.15,
4.16, 5.11, 5.14, 5.15)
3.
Understand, explain, and model the rationale for defining and representing
equivalent fractions and procedures for adding, subtracting, multiplying, and
dividing fractions. (ACOS 3.15, 4.13, 4.14, 4,17, 4,18, 4.19, 5.9,
5.10, 5.12)
4. Understand,
explain, and model the connection between fractions and division, a/b =
a÷b, and how fractions, ratios, and rates are connected via unit rates.
(ACOS 5.11)
5.
Understand, explain, and model how quantities vary together in a proportional
relationship, using tables, double number lines, and tape diagrams as supports.
(ACOS 6.1, 6.2, 6.3)
6. Understand, explain, and model
proportional relationships from other relationships, such as additive
relationships and inversely proportional relationships. (ACOS 5.13,
7.2)
7. Understand,
explain, and model unit rates to solve problems and to formulate equations for
proportional relationships. (ACOS 5.13, 7.1, 7.2)
(c) Measurement, Data
Analysis and Geometry. Measurement is the process of finding a number that
shows the amount of something. It is a system to measure the height, weight,
capacity or even number of certain objects. It is the process of quantifying
something and then possibly making comparisons between two or more objects or
concepts. Typically, measurements involve 2 parts-a numeric value and the
specific unit. Data analysis is the ability to formulate questions that can be
addressed with data and collect, organize, and display relevant data to answer
them. Geometry is the study of different types of shapes, figures, and sizes in
real life. Upon program completion candidates shall be able to do the
following:
1.
Measurement.
(i) Understand, explain, and model the
general principles of measurement, the process of iterations, and the central
role of units: that measurement requires a choice of measurable attribute, that
measurement is comparison with a unit and how the size of a unit affects
measurements, and the iteration, additivity, and invariance used in determining
measurements. (ACOS K.16, K.17, 1.17, 1.18, 1.19, 1.20, 2.17, 2.18,
2.19, 2.20, 2.23, 2.24, 4.21, 5.17)
(ii) Understand, explain, and model how the
number line connects measurement with number through length. (ACOS
2.21, 2.22, 4.22)
(iii)
Understand, explain, and model what area and volume are and give rationales for
area and volume formulas that can be obtained by infinitely many compositions
and decompositions of unit squares or unit cubes, including formulas for the
areas of rectangles, triangles, and parallelograms, and volumes of rectangular
prisms. (ACOS 3.18, 3.19, 3.20, 3.21, 3.22, 3.23, 3.24, 3.25, 4.23,
5.18, 5.19, 6.26, 6.27, 6.28)
2.
Data Analysis (Statistics and
Probability)(i) Understand, explain,
and model appropriate graphs and numerical summaries to describe the
distribution of categorical and numerical data. (ACOS K.15, 1.16, 2.15,
3.16, 3.17, 5.16)
(ii)
Understand, explain, and model that responses to statistical questions should
consider variability. (ACOS 2.16, 4.20, 5.16, 6.22)
(iii) Understand, explain, and model
distributions for quantitative data are compared with respect to similarities
and differences in center, variability (spread), and shape. (ACOS 6.22,
6.23, 6.24)
(iv)
Understand, explain, and model theoretical and experimental probabilities of
simple and compound events, and why their values may differ for a given event
in a particular experimental situation. (ACOS 7.15)
(v) Understand, explain, and model how the
scope of inference to a population is based on the method used to select the
sample. (ACOS 7.10, 7.26)
3.
Geometry.
(i) Understand, explain, and model geometric
concepts of angle, parallel, and perpendicular, and use them in describing and
defining shapes; describing and reasoning about spatial locations (including
the coordinate plane). (ACOS K.18, K.19, K. 20, 4.24, 4.25, 4.26, 4.27,
4.28, 4.29, 5.20, 6.25)
(ii) Understand, explain, and model how
shapes are classified into categories, and reasoning to explain the
relationships among the categories. (ACOS K.21, K.22, K.23, 1.21, 1.22,
2.25, 2.26, 3.26, 5.21, 5.22, 5.23)
(iii) Understand, explain, and model
proportional relationships in scaling shapes up and down. (ACOS
7.17)
(9)
Unique Field Experience and/or
Practicum Requirements. Field experiences shall include placements where
candidates can observe the classroom teacher providing numeracy instruction and
participate in the teaching of numeracy in grade levels K-5.
(10)
Faculty.
(a) Undergraduate Programs. The faculty
should include at least one individual with at least a master's degree and 3
full years of professional educational work experience teaching mathematics in
grade levels K-5.
(b) Graduate
Programs. The faculty should include at least one individual with at least an
education specialist degree and 3 full years of professional educational work
experience teaching mathematics in grade levels K-5.
Author: Dr. Eric G. Mackey.
Statutory Authority: Ala. Code §§
16-3-16,
16-23-14, and 16-6H-1 through -19 (1975); Act 2022-239.
