Texas Register, Volume 38, Number 21, Pages 3215-3396, May 24, 2013 Page: 3,252
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1701 North Congress Avenue, Austin, Texas 78701, (512)
475-1497. Comments may also be submitted electronically to
rules@tea.state.tx.us or faxed to (512) 463-5337. A request
for a public hearing on the proposed new section submitted
under the Administrative Procedure Act must be received by
the commissioner of education not more than 14 calendar days
after notice of the proposal has been published in the Texas
Register
The new section is proposed under the Texas Education Code,
7.102(c)(4), which authorizes the SBOE to establish curricu-
lum and graduation requirements; 28.002, which authorizes the
SBOE to identify by rule the essential knowledge and skills of
each subject of the required curriculum that all students should
be able to demonstrate and that will be used in evaluating in-
structional materials; and 28.025, which authorizes the SBOE
to determine by rule curriculum requirements for the minimum,
recommended, and advanced high school programs that are
consistent with the required curriculum under 28.002.
The new section implements the Texas Education Code,
7.102(c)(4), 28.002, and 28.025.
111.46. Discrete Mathematics, Adopted 2013 (One-Half to One
Credit).
(a) General requirements. Students shall be awarded one-half
to one credit for successful completion of this course. Prerequisite:
Algebra II.
(b) Introduction.
(1) The desire to achieve educational excellence is the driv-
ing force behind the Texas essential knowledge and skills for mathe-
matics, guided by the college and career readiness standards. By em-
bedding statistics, probability, and finance, while focusing on fluency
and solid understanding, Texas will lead the way in mathematics edu-
cation and prepare all Texas students for the challenges they will face
in the 21st century.
(2) The process standards describe ways in which students
are expected to engage in the content. The placement of the process
standards at the beginning of the knowledge and skills listed for each
grade and course is intentional. The process standards weave the other
knowledge and skills together so that students may be successful prob-
lem solvers and use mathematics efficiently and effectively in daily
life. The process standards are integrated at every grade level and
course. When possible, students will apply mathematics to problems
arising in everyday life, society, and the workplace. Students will use
a problem-solving model that incorporates analyzing given informa-
tion, formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problem-solving process and the rea-
sonableness of the solution. Students will select appropriate tools such
as real objects, manipulatives, paper and pencil, and technology and
techniques such as mental math, estimation, and number sense to solve
problems. Students will effectively communicate mathematical ideas,
reasoning, and their implications using multiple representations such as
symbols, diagrams, graphs, and language. Students will use mathemat-
ical relationships to generate solutions and make connections and pre-
dictions. Students will analyze mathematical relationships to connect
and communicate mathematical ideas. Students will display, explain,
or justify mathematical ideas and arguments using precise mathemati-
cal language in written or oral communication.
(3) In Discrete Mathematics, students are introduced to the
improved efficiency of mathematical analysis and quantitative tech-
niques over trial-and-error approaches to management problems in-
volving organization, scheduling, project planning, strategy, and de-
cision making. Students will learn how mathematical topics such asgraph theory, planning and scheduling, group decision making, fair di-
vision, game theory, and theory of moves can be applied to manage-
ment and decision making. Students will research mathematicians of
the past whose work is relevant to these topics today and read articles
about current mathematicians who either teach and conduct research at
major universities or work in business and industry solving real-world
logistical problems. Through the study of the applications of math-
ematics to society's problems today, students will become better pre-
pared for and gain an appreciation for the value of a career in mathe-
matics.
(4) Statements that contain the word "including" reference
content that must be mastered, while those containing the phrase "such
as" are intended as possible illustrative examples.
(c) Knowledge and skills.
(1) Mathematical process standards. The student uses
mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday
life, society, and the workplace;
(B) use a problem-solving model that incorporates an-
alyzing given information, formulating a plan or strategy, determining
a solution, justifying the solution, and evaluating the problem-solving
process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives,
paper and pencil, and technology as appropriate, and techniques, in-
cluding mental math, estimation, and number sense as appropriate, to
solve problems;
(D) communicate mathematical ideas, reasoning, and
their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record,
and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and
communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and
arguments using precise mathematical language in written or oral com-
munication.
(2) Graph theory. The student applies the concept of graphs
to determine possible solutions to real-world problems. The student is
expected to:
(A) explain the concept of graphs;
(B) use graph models for simple problems in manage-
ment science;
(C) find the valences of the vertices of a graph;
(D) identify Euler circuits in a graph;
(E) solve route inspection problems by Eulerizing agraph;
graph;(F) determine solutions modeled by edge traversal in a
(G) compare the results of solving the traveling sales-
man problem (TSP) using the nearest neighbor algorithm and using a
greedy algorithm;
(H) distinguish between real-world problems modeled
by Euler circuits and those modeled by Hamiltonian circuits;38 TexReg 3252 May 24, 2013 Texas Register
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Texas. Secretary of State. Texas Register, Volume 38, Number 21, Pages 3215-3396, May 24, 2013, periodical, May 24, 2013; Austin, Texas. (https://texashistory.unt.edu/ark:/67531/metapth313174/m1/36/: accessed April 26, 2024), University of North Texas Libraries, The Portal to Texas History, https://texashistory.unt.edu; crediting UNT Libraries Government Documents Department.