Ed 507.25 and Ed 507.26 COMPETENCY ASSESSMENT CROSSWALK FOR
Middle Level Mathematics Teacher (12 Noncredit Bearing Units)
General Overview The Middle Level Mathematics Track contains twelve, two-part units. Each unit is comprised of 4 content modules, which include various learning materials such as readings, interactions, and videos. Each unit includes a competency crosswalk delineating the competencies addressed within the unit and their associated learning tasks and assessments. Similarly, each of the 4 learning modules within the unit begins with a summary of the module’s key concepts and understandings and describes the activities within. Modules’ learning activities and assessments range in format to include (but are not limited to) essays, quizzes, meetings with school personnel, notes, and various forms of assessments. Each unit includes collaborative discussions with various members of an on-site Professional Learning Community (PLC), in which the participant can discuss key topics, solidify the content from unit readings, media, and assignments, and experience the application of unit concepts. Examining the learning concepts in the context of a school community provides opportunity for the content to come to life in practice.
Units in the Middle Level Mathematics Track Include: • • • • • •
• • • • • •
Precalculus Probability & Statistics Aspects of Mathematics Learning Mathematical Proof for Educators Number Systems Geometric Structures Page 1 of 17
Calculus 1 History of Mathematics Reading & Writing in the Mathematics Content Area Discrete Mathematics Algebra Theory for Middle Level Teachers Middle Level Mathematics Methodology
Competencies Acquired Through the UNH College of Professional Studies The following crosswalk depicts the Ed 507.25 and Ed 507.26 competencies acquired through the units within the UNH College of Professional Studies’ Middle Level Mathematics Track.
Ed 507.25 Competencies COMPETENCY (a)
HOW ACQUIRED
A candidate for certification as a mathematics teacher shall have skills, competencies, and knowledge in the following areas: (1)
In the area of knowledge of pedagogy, the candidate shall have the ability to: a.
Plan and conduct units and lessons, appropriate for the grade range, and which:
1.
Competency
Unit
Enable students to construct new concepts through active participation in mathematical modeling, investigations, and problem- solving;
Aspects of Mathematical Learning - Parts 1 & 2 Reading & Writing in the Mathematics Content Area– Parts 1 & 2 Middle Level Mathematics Methodology- Parts 1 & 2
2.
Include multiple explanations and representations, including, but not limited to informal and formal arguments or proofs;
Aspects of Mathematical Learning - Parts 1 & 2 Middle Level Mathematics Methodology - Parts 1 & 2
3.
Incorporate literacy strategies that assist students in reading and understanding mathematics;
Reading & Writing in the Mathematics Content Area – Parts 1 & 2
4.
Provide opportunities for students to use written, oral, and other creative expressions to demonstrate their understanding of mathematical concepts to a variety of audiences;
Aspects of Mathematical Learning - Parts 1 & 2 Reading & Writing in the Mathematics Content Area – Parts 1 & 2 Middle Level Mathematics Methodology – Parts 1 & 2
5.
Emphasize connections within and between mathematics and other disciplines;
Middle Level Mathematics Methodology – Parts 1 & 2
6.
Select and use instructional tools, including, but not limited to, manipulatives and physical models, drawings, virtual
Aspects of Mathematical Learning- Parts 1 & 2
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environments, spreadsheets, presentation tools, and mathematics-specific technologies such as graphing tools and interactive geometry software, computer algebra systems, and statistical packages;
Middle Level Mathematics Methodology – Parts 1 & 2
7.
Make sound decisions about when instructional tools enhance teaching and learning, recognizing both the insights to be gained and possible limitations of such tools; and
Aspects of Mathematical Learning-Parts 1 & 2 Reading & Writing in the Mathematics Content Area– Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
8.
Model and develop the following 8 standards of mathematical practices: (i)
Make sense of problems and persevere in solving them;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
b.
(ii)
Reason abstractly and quantitatively;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
(iii)
Construct viable arguments and critique the reasoning of others;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
(iv)
Model with mathematics;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
(v)
Use appropriate tools strategically;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
(vi)
Attend to precision;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
(vii)
Look for and make use of structure; and
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
(viii)
Look for an express regularity in repeated reasoning;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
Apply an understanding of learning theories and equitable teaching practices to the teaching of mathematics appropriate for students within the grade range which articulate: 1.
Why conceptual knowledge of mathematics is needed in conjunction with the teaching of procedures or algorithms; and
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Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
2.
c.
(2)
Foundations of pedagogical knowledge, effective and equitable mathematics teaching practices, and positive and productive dispositions toward teaching mathematics to support students’ sense making, understanding, and reasoning; and
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology- Parts 1 & 2
Plan and conduct a variety of assessments and evaluations appropriate for the grade range that: 1.
Diagnose students’ preconceptions, misconceptions, and understandings of mathematics and continuously monitor students’ understandings; and
Aspects of Mathematical Learning-Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
2.
Evaluate procedural and conceptual understanding, and interpret students’ mathematical processes and communication skills.
Aspects of Mathematical Learning– Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
In the area of knowledge of mathematical processes and habits of mind, the candidate shall have the ability to: a.
Use problem-solving to investigate and understand increasingly complex mathematical content, including, but not limited to, the ability to: 1.
Apply and adapt a problem-solving process using a variety of heuristics or strategies to solve problems that arise in mathematics and other contexts;
Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2 Geometric Structures- Parts 1 & 2 Probability & Statistics- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof for Educators- Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete Mathematics- Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2
2.
Use problem-solving to develop one’s own mathematical knowledge;
Precalculus- Parts 1 and 2 Probability & Statistics – Parts 1 & 2 Calculus 1- Parts 1 and 2 Geometric Structures- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof for Educators- Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete Mathematics – Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2
3.
Reflect upon one’s own and others’ solutions and the problemsolving process; and
Precalculus- Part 1 & 2 Calculus 1- Parts 1 & 2
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Geometric Structures- Parts 1 & 2 Probability & Statistics- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof for Educators- Parts 1 & 2 Number Systems-Parts 1 & 2 Discrete Mathematics-Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2
4.
b.
c.
Refine problem-solving strategies, as needed;
Precalculus- Parts 1 & 2 Calculus- Parts 1 & 2 Geometric Structures- Parts 1 & 2 Probability & Statistics - Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof for Educators – Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete Mathematics- Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2
Use mathematical reasoning and proof, including, but not limited to, the ability to: 1.
Develop and evaluate mathematical conjectures;
Geometric Structures- Parts 1 & 2 Mathematical Proof- Parts 1 & 2
2.
Construct and evaluate proofs and logical arguments to verify conjectures;
Geometric Structures- Parts 1 & 2 Mathematical Proof- Parts 1 & 2
3.
Select and use various types of reasoning and methods of proof; and
Geometric Structures- Parts 1 & 2 Mathematical Proof- Parts 1 & 2
4.
Demonstrate the capacity to articulate an understanding of how reasoning and proof are integral components of mathematics;
Geometric Structures- Parts 1 & 2 Mathematical Proof- Parts 1 & 2
Communicate an understanding of mathematics, including, but not limited to, the ability to: 1.
Demonstrate the capacity to communicate clearly about mathematics and mathematics education in both written and
Page 5 of 17
Aspects of Mathematical Learning- Parts 1 & 2 Reading & Writing in the Mathematics Content Area - Parts 1 & 2
oral forms using accurate and appropriate mathematical language and notation;
Middle Level Math Methodology- Parts 1 & 2 Calculus 1- Parts 1 & 2 Probability & Statistics- Parts 1 & 2 Geometric Structures – Parts 1 & 2 Mathematical Proof- Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete MathematicsParts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2 History of Mathematics – Parts 1 & 2
2.
Interpret and explain mathematical ideas acquired through reading mathematics in professional publications; and
Aspects of Mathematical Learning-Parts 1 & 2 Middle Level Math Methodology- Parts 1 & 2 Probability & Statistics- Parts 1 & 2
1.
Illustrate learning progression from concrete to abstract representations;
Aspects of Mathematical Learning- Parts 1 & 2 Middle Level Math Methodology- Parts 1 & 2
2.
Articulate how the use of formal language and notation increases in importance as mathematical concepts are developed in the mathematics curriculum;
Aspects of Mathematical Learning- Parts 1 & 2 Reading & Writing in the Mathematics Content Area - Parts 1 & 2 Middle Level Math Methodology- Parts 1 & 2
3.
Select, apply, and translate among mathematical representations to investigate mathematical concepts and solve mathematical problems; and
Aspects of Mathematical Learning – Parts 1 & 2 Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2 Mathematical Proof- Parts 1 & 2 Geometric Structures – Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete Mathematics- Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2 Probability & Statistics – Parts 1 & 2 History of Mathematics – Parts 1 & 2 Middle Level Mathematics Methodology – Parts 1 & 2
4.
Develop and use models to explain mathematical concepts;
Aspects of Mathematical Learning – Parts 1 & 2 Precalculus- Parts 1 & 2 Calculus1- Parts 1 & 2 Probability & Statistics- Parts 1 & 2
d.
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Geometric Structures – Parts 1 & 2 History of Mathematics – Parts 1 & 2 Middle Level Mathematics Methodology – Parts 1 &2
e.
f.
Recognize, explore, and develop mathematical connections, both within mathematics and across disciplines, including, but not limited to, the ability to: 1.
Provide examples of how mathematics is practiced in various fields; and
History of Mathematics- Parts 1 & 2 Number Systems- Part 2 Discrete Mathematics - Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2 Probability & Statistics – Parts 1 & 2
2.
Build mathematical understanding by showing how ideas build on one another across grade levels to form a coherent discipline; and
Aspects of Mathematical Learning – Parts 1 & 2 Middle Level Math Methodology – Parts 1 & 2 Probability & Statistics – Parts 1 & 2
Develop additional habits of the mind related to mathematics, including, but not limited to, the ability to: 1.
Learn mathematics independently;
Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2 Geometric Structures – Parts 1 & 2 Probability & Statistics- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof- Parts 1 & 2 Number Systems- Parts 1& 2 Discrete Mathematics- Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2
2.
Exhibit a curiosity for mathematics;
Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2 Geometric Structures – Parts 1 & 2 Probability & Statistics- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof- Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete Mathematics- Parts 1 & 2 Algebra Theory for Middle Level Teachers – Parts 1 & 2
3.
Recognize that learning from mistakes is an essential component when working mathematically;
Aspects of Mathematical Learning – Parts 1 & 2 Middle Level Math Methodology- Parts 1 & 2
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Precalculus- Parts 1 & 2 Calculus I- Parts 1 & 2 Geometric Structures- Parts 1 & 2 Probability & Statistics – Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof- Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete Mathematics- Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2 4.
Recognize the power and value of estimation and mental computation when working mathematically;
Precalculus- Parts 1 & 2 Calculus1- Parts 1 & 2 Geometric Structures- Parts 1 & 2 Probability & Statistics- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof- Parts 1 & 2 Number Systems- Parts 1 & 2 Discrete Mathematics- Parts 1 & 2 Algebra Theory for Middle Level Teachers – Parts 1 & 2
5.
Understand the value and power of strategic use of technology when solving mathematical problems;
Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2 Geometric Structures- Parts 1 & 2 Probability & Statistics - Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof, Parts 1 & 2 Number Systems, Parts 1 & 2 Discrete Mathematics, Parts 1 & 2 Algebra Theory for Middle Level Teachers, Parts 1 & 2
6.
Recognize that mathematics is the language of science and nature; and
Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2 Geometric Structures- Parts 1 & 2 Probability & Statistics- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof, Parts 1 & 2 Number Systems, Parts 1 & 2 Discrete Mathematics, Parts 1 & 2 Algebra Theory for Middle Level Teachers, Parts 1 & 2
7.
Recognize that mathematics is a tool for quantitative reasoning;
Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2
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Geometric Structures- Parts 1 & 2 Probability & Statistics- Parts 1 & 2 History of Mathematics- Parts 1 & 2 Mathematical Proof, Parts 1 & 2 Number Systems, Parts 1 & 2 Discrete Mathematics, Parts 1 & 2 Algebra Theory for Middle Level Teachers, Parts 1 & 2 (3)
In the area of knowledge of the learner, including developmental and environmental characteristics appropriate for the grade range, the candidate shall have the ability to: a.
(4)
Demonstrate appropriate strategies for supporting students to: 1.
Move from concrete to abstract representations of mathematical concepts; and
Aspects of Mathematical Learning-Parts 1 & 2 Middle Level Math Methodology- Parts 1 & 2
2.
Connect conceptual and procedural knowledge;
Aspects of Mathematical Learning-Parts 1 & 2 Middle Level Math Methodology– Parts 1 & 2
b.
Communicate understanding of mathematics anxiety, including signs of it, issues related to it, and supporting students to respond to and overcome it;
Aspects of Mathematical Learning- Parts 1 & 2
c.
Recognize that attitudes about mathematics can change across a lifespan and therefore teachers need to address the affective domain; and
Aspects of Mathematical Learning- Parts 1 & 2
d.
Demonstrate knowledge of how exceptional students learn mathematics and strategies to use with exceptional students;
Aspects of Mathematical Learning-Parts 1 & 2 Middle Level Math Methodology – Parts 1 & 2
b.
Communicate understanding of mathematics anxiety, including signs of it, issues related to it, and supporting students to respond to and overcome it;
Aspects of Mathematical Learning- Parts 1 & 2
In the area of number and operations, the candidate shall have the ability to: a.
Demonstrate a capacity to use models to explore and explain relationships, including magnitude, among fractions, decimals, percents, ratios, and proportions;
Discrete Mathematics- Parts 1 & 2 Number Systems- Parts 1 & 2
b.
Apply, explain, and justify concepts in number and number theory;
Number Systems- Parts 1 & 2 Algebra Theory for Middle Level Teachers- Parts 1 & 2
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(5)
c.
Demonstrate computational proficiency and fluency, including the use of a variety of algorithms, estimation strategies, and mental mathematics techniques to judge the reasonableness of answers or approximate solutions;
Precalculus- Part 1 Calculus 1- Parts 1 & 2 Geometric Structures- Parts 1 & 2 History of Mathematics – Parts 1 & 2
d.
Demonstrate knowledge of concepts and applications of limits and infinity;
Calculus 1- Part 1
e.
Demonstrate a capacity to apply the concepts of proportional reasoning;
Precalculus- Part 1
f.
Demonstrate a capacity to make sense of large and small numbers and use scientific notation in mathematical and scientific modeling;
Precalculus- Part 1
g.
Demonstrate a capacity to use physical materials and models to explore and explain the operations and properties of real and complex numbers with extensions to matrices and vectors; and
Number Systems- Part 1
h.
Demonstrate a capacity to apply the concepts of exponents, including integer and rational, through modeling and applications;
Precalculus- Part 1 Calculus 1- Parts 1 & 2
In the area of geometry and measurement, the candidate shall have the ability to: a.
Build and manipulate representations of 2-and 3-dimensional objects and perceive an object from different perspectives;
Geometric Structures – Parts 1 & 2
b.
Analyze properties of and relationships among geometric shapes and structures;
Geometric Structures– Parts 1 & 2
c.
Apply transformations with connections to congruency and similarity;
Geometric Structures– Part 1
d.
Demonstrate knowledge of non-Euclidean geometries;
Geometric Structures– Part 2
e.
Connect the ideas of algebra and geometry through the use of coordinate geometry, graphing, vectors, and motion geometry;
Geometric Structures– Part 1
f.
Recognize measurement attributes and their effect on the choice of
Geometric Structures– Parts 1 & 2
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appropriate tools and units;
(6)
g.
Apply strategies, techniques, tools, and formulas to determine measurements and their application in a variety of contexts;
Geometric Structures – Part 1
h.
Employ estimation as a way of understanding measurement processes and units;
Geometric Structures– Part 1
i.
Complete error analysis through determination of the reliability of numbers obtained from measurement;
Geometric Structures– Part 1
j.
Understand and apply measurement conversion strategies;
Geometric Structures– Part 1
k.
Apply geometric ideas and tools relating to the Pythagorean theorem, similar triangles, and trigonometry to solve problems;
Geometric Structures– Part 1
l.
Use constructions, models, and dynamic geometric software to explore geometric relationships;
Geometric Structures– Part 1
m .
Derive and explain formulas found in Euclidean geometry; and
Geometric Structures– Part 1
n.
Construct proofs using the axioms of Euclidean and non-Euclidean geometries;
Geometric Structures– Parts 1 & 2
In the area of functions and algebra, the candidate shall have the ability to: a.
Model and analyze change and rates of change in various contexts;
Precalculus- Part 1 Calculus 1- Part 1
b.
Use mathematical models to understand, represent, and communicate quantitative relationships, including, but not limited to equality, equations, inequalities, and proportional relationships;
Precalculus- Parts 1 & 2
c.
Explore, analyze, and generalize a wide variety of patterns and functions using multiple representations including, but not limited to, tables, graphs, written word, and symbolic rules;
Precalculus- Parts 1 & 2
d.
Represent information and solve problems using matrices;
Discrete Math -Part 1 Algebra Theory for Middle Level Teachers- Part 2
e.
Use graphing utilities and other technological tools to represent,
Precalculus- Parts 1 & 2
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(7)
explain, and explore algebraic ideas including functions, equations, and expressions;
Calculus 1- Parts 1 & 2
f.
Generalize patterns and functions using recursive and explicit representations;
Precalculus- Parts 1 & 2 Calculus 1- Parts 1 & 2 Algebra Theory for Middle Level Teachers- Part 1
g.
Articulate the meaning of functions and their inverse relationships, both formally and informally, with the use of concrete materials and graphing utilities; and
Calculus 1- Part 1 Algebra Theory for Middle Level Teachers - Part 1
h.
Understand and compare the properties of classes of functions and their inverses, including exponential, polynomial, rational, step, absolute value, root, logarithmic, and periodic, including trigonometric;
Precalculus- Parts 1 & 2 Calculus 1 – Parts 1 & 2 Algebra Theory for Middle Level Teachers- Part 1
In the area of data, statistics, and probability, the candidate shall have the ability to: a.
Design investigations, collect data, display data in a variety of ways, and interpret data representations including bivariate data, conditional probability and geometric probability;
Probability & Statistics- Parts 1 & 2
b.
Use appropriate methods to estimate population characteristics, test conjectured relationships among variables, and analyze data;
Probability & Statistics - Parts 1 & 2
c.
Use appropriate statistical methods and technology to analyze data and describe shape, spread, and center;
Probability & Statistics- Part 1
d.
Use both descriptive and inferential statistics to analyze data, make predictions, test hypotheses, and make decisions;
Probability & Statistics- Parts 1 & 2
e.
Apply probability concepts in identifying odds, fair games, mathematical expectation, and invalid conclusions;
Probability & Statistics- Part 1
f.
Judge the validity of a statistical argument, including evaluating the sample from which the statistics were developed and identify misuses of statistics;
Probability & Statistics- Parts 1 & 2
g.
Determine and compare experimental, theoretical, and conditional probabilities; and
Probability & Statistics- Part 1
h.
Use statistical models to explore the connections between statistics and probability including correlation, regression, and analysis of variance;
Probability & Statistics- Parts 1 & 2
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(8)
(9)
(10)
In the area of calculus, the candidate shall have the ability to: a.
Use mathematical modeling and the concepts of calculus to represent and solve problems from real-world contexts;
Calculus 1- Parts 1 & 2
b.
Use technology to explore and represent fundamental concepts of calculus; and
Calculus 1- Parts 1 & 2
c.
Understand and describe the connection of calculus to middle and high school mathematics topics;
Middle Level Mathematics Methodology – Parts 1 & 2
In the area of discrete mathematics, the candidate shall have the ability to: a.
Apply the fundamental ideas of discrete mathematics in the formulation and solution of problems arising from real-world situations; and
Discrete Mathematics- Parts 1 & 2
b.
Use technology to solve problems involving the use of discrete structures; and
Discrete Mathematics- Parts 1 & 2
In the area of history of mathematics, demonstrate a knowledge of the historical development of numbers and number systems, measurement and measurement systems, geometry, including non-Euclidean geometry, algebra, probability and statistics, calculus, and discrete mathematics.
History of Mathematics- Parts 1 & 2
Ed 507.26 Competencies COMPETENCY (a)
HOW ACQUIRED
A candidate for certification as a middle level mathematics teacher shall have skills, competencies, and knowledge in the following areas: (1)
In the area of number and number operations the candidate shall have the ability to:
Competency a.
Unit
Represent, use, and apply introductory concepts and properties of complex numbers;
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Precalculus – Part 1 Algebra Theory for Middle Level Teachers- Part 1
(2)
(3)
b.
Identify and illustrate the mathematics that underlies the procedures and operations involving real numbers and their subsets; and
Number Systems –Part 1 Algebra Theory for Middle Level Teachers- Parts 1 & 2
c.
Explain the distinctions among real numbers and their subsets with connection to field axioms;
Algebra Theory for Middle Level Teachers- Part 2 Number Systems –Part 1
In the area of functions and algebra the candidate shall have the ability to: a.
Understand, identify, and apply arithmetic and geometric sequences; and
b.
Represent and analyze group and field properties of real numbers and other mathematical structures;
In the area of calculus the candidate shall have the ability to: demonstrate an understanding of calculus concepts including limits, continuity, differentiation, and integration; and
(4)
Algebra Theory for Middle Level Teachers - Parts 1 & 2
Calculus 1 – Parts 1 & 2
In the area of discrete mathematics demonstrate a conceptual understanding of the fundamental ideas of discrete mathematics, including, but not limited to: a.
Finite graphs;
Discrete Math – Part 2
b.
Trees;
Discrete Math – Part 2
c.
Networks;
Discrete Math – Part 2
d.
Propositional logic; and
Discrete Math – Part 1
e.
Combinatorics.
Discrete Math – Part 1
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To Learn More, Contact: UNH College of Professional Studies 88 Commercial St, Manchester, NH 03101 855-472-4255 cps.unh.edu/online Carolyn Cormier, Ed.D. Academic Center Director carolyn.cormier@unh.edu 603-513-1155 Kate Shumway-Pitt, M.Ed. Educator Preparation Program Director kathleen.shumway-pitt@unh.edu 603-822-5431 Tammy Carnevale, M.Ed. & C.A.G.S Administrative Assistant tammy.carnevale@unh.edu 603-573-6430
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About UNH College of Professional Studies The University of New Hampshire brings together students, faculty, and private and public partners to create life-changing opportunities and innovative solutions in our neighborhoods and across the world.
Exclusively Focused on Adult Students With associate, bachelor’s, and master’s degrees, post-baccalaureate programs for teachers, credit for prior learning, and a variety of transfer opportunities, UNH College of Professional Studies focuses on areas of study that are responsive to the needs of employers. Our degree programs and certificates align with the schedules of working professionals, parents, and others with full lives and busy routines. Our faculty and staff specialize in supporting adult learners. We understand that you’re balancing many responsibilities and that going to college is only one part of what makes you, you.
Top Ranked & Trusted We’re proud to be top ranked by U.S. News & World Report for “Best Online Bachelor’s Programs” and “Best Online Bachelor’s for Veterans”.
100% Online, Accredited, and Affordable We are a public, nonprofit college regionally accredited by the New England Commission of Higher Education, and we annually achieve top honors from U.S. News & World Report for Best Online Programs.
Credit for What You Know Students can choose from among several options for demonstrating college-level learning acquired from many types of life experiences, including workplace training, on-the-job learning, volunteer training, or self-study.
Learn More! Visit: https://cps.unh.edu/online
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Professional Development Units: FAQ Who should participate in these Professional Development Units? The units were designed for teachers currently employed by NH school districts under Statements of Eligibility and are working toward earning certification by completing NHDOE approved Site Based Licensure Plans. Certified teachers might also be interested in participating in the units for professional development purposes. Can I use these units toward a teacher certification program at UNH CPS? No, these units are for professional development only and will not earn college credit. These units specifically target certification competencies in each content area track and have been reviewed by the NH Department of Education for use on Site Based Licensure Plans. They do not fully equate to any courses offered at UNH College of Professional Studies. How do these units differ from regular UNH CPS program courses? These professional development units are entirely self-paced. Unlike traditional courses (which include peer interaction and continuous instructor presence and engagement), Professional Development units do not include any peer or instructor interaction and are entirely self-facilitated. Traditional CPS courses are 8 weeks long and have predetermined start and end dates. These professional development units consist of 4 learning modules, which participants have 8 weeks to complete. How can these units help me get certified as a teacher? These units are designed to meet specific certification competencies present on teachers’ Site Based Licensure Plans. A Site Based Licensure Plan is an agreement between the NH Department of Education and a ‘not yet certified’ teacher hired by a school district under a NHDOE issued Statement of Eligibility. Can I take these units if I’m already a certified teacher? Yes! Current certified teachers may take these units for professional development based on interest and/or recertification purposes. How much do they cost? Professional Development units cost $250 per unit. Is there scholarship funding available? Yes! Limited scholarship funds are available in each content area track. Inquire for more information (see page 15-16).
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