Download 2-2013--Assess2-NCTM

NCTM ASSESSMENT #2: CONTENT KNOWLEDGE COURSES—GPAs
Candidates for a license to teach secondary mathematics are required to take a variety of courses to provide
them content knowledge base. These courses are consistent with the NCTM content knowledge expectations.
In addition, the liberal arts degree at Luther College includes coursework in a variety of disciplines (general
education requirements and “goals for student learning” that include three abilities that support NCTM content
knowledge:



Students who demonstrate the ability to engage in inquiry are able to: identify, gather, and use
relevant information in an ethical and legal manner; analyze sources critically and synthesize
information; devise appropriate methods to investigate a problem or issue and provide creative
solutions; use appropriate technologies to investigate a problem, analyze information, and
communicate results; identify the limitations of findings and develop questions for further inquiry.
Students who demonstrate the ability to reason are able to: critique and construct arguments while
making rational judgments about their accuracy and usefulness; construct, interpret, and evaluate
mathematical models, including various modes of data and information presentation; solve problems by
identifying and applying appropriate strategies.
Students who demonstrate the ability to communicate are able to: write with fluency, clarity, and
coherence; read, comprehend, and appreciate various types of literature; speak confidently and
coherently in both formal and informal settings; listen with objectivity and empathy; work productively
in a collaborative environment.
(Luther College Catalog, 2012-13)
The “all-college requirements” include courses that relate to CCSSM “mathematical practices,” in particular and
even more specifically than the NCTM process standards (problem solving, reasoning & proof, connections,
and communications).
C a nd id at es m us t ach i ev e a GP A o f at l ea st 2 . 5 0 fo r t h e se t o f r eq ui r ed co nt e nt a r e a
c o u rs es .
Luther
A
AB+
B
College Grading Information
4.0 grade points
B2.7 grade points
3.7 grade points
C+
2.3 grade points
3.3 grade points
C
2.0 grade points
3.0 grade points
CD+
D
DF
1.7 grade points
1.3 grade points
1.0 grade points
0.7 grade points
0.0 grade points
See below the chart of the NCTE content knowledge-related standards and the content courses in which
candidates acquire and demonstrate the content described by the standards.
NCTM Content Knowledge Standards Aligned with Required MATH Content Courses
The NCTM process standards, 1.1, 1.2, 1.3, 1.4, and 1.5, will be included in each course as part of the math learning
and math demonstration process.
1.1 Knowledge of Problem Solving. Candidates know, understand and apply the process of mathematical problem solving.
1.2 Knowledge of Reasoning and Proof, Candidates reason, construct, and evaluate mathematical arguments and develop as appreciation for
mathematical rigor and inquiry.
1.3 Knowledge of Mathematical Communication. Candidates communicate their mathematical thinking orally and in writing to peers, faculty and
others.
1.5 Knowledge of Mathematical Representation. Candidates use varied representations of mathematical ideas to support and deepen students'
mathematical understanding.
1.4 Knowledge of Mathematical Connections. Candidates recognize, use, and make connections between and among mathematical ideas and in
contexts outside mathematics to build mathematical understanding.
CS 150: Introduction to Computer Science An introduction to computer science emphasizing problem solving. Problems are selected from a variety of interesting
areas such as graphics, image processing, cryptography, data analysis, astronomy, video games, and environmental simulation. Topics include algorithm design and
object oriented programming. (4 credits)
1.6 Knowledge of Technology. Candidates embrace technology as an essential tool for teaching and learning mathematics.
ED 352 Advanced Methods I: Secondary Mathematics Advanced study of secondary teaching methods for students seeking licensure in mathematics. Study of
special methods used to teach the individual's major subject area. Teaching methods and professional participation in one's academic discipline will be covered, as
well as inclusion of special education students in a regular classroom and applications of technology. Students spend a minimum of forty contact hours in cooperating
school classrooms in addition to on-campus meetings. (2 credits)
EDUC 367 Advanced Teaching Methods II Continued study of advanced teaching methods for students seeking licensure in mathematics, science, social science,
with special emphasis on analysis of best practice, methodological research and curriculum design within the respective content area. (2 credits)
CS 150: Introduction to Computer Science An introduction to computer science emphasizing problem solving. Problems are selected from a variety of interesting
areas such as graphics, image processing, cryptography, data analysis, astronomy, video games, and environmental simulation. Topics include algorithm design and
object oriented programming. (4 credits)
1.7 Dispositions. Candidates support a positive disposition toward mathematical processes and mathematical learning.
If there is a concern about a candidate’s disposition, appropriate professors will work with the head of the Education Department to work with the
candidate.
ED 352 Advanced Methods I: Secondary Mathematics Advanced study of secondary teaching methods for students seeking licensure in mathematics. Study of
special methods used to teach the individual's major subject area. Teaching methods and professional participation in one's academic discipline will be covered, as
well as inclusion of special education students in a regular classroom and applications of technology. Students spend a minimum of forty contact hours in cooperating
school classrooms in addition to on-campus meetings. (2 credits)
EDUC 367 Advanced Teaching Methods II Continued study of advanced teaching methods for students seeking licensure in mathematics, science, social science,
with special emphasis on analysis of best practice, methodological research and curriculum design within the respective content area. (2 credits)
1.9 Knowledge of Number and Operations. Candidates demonstrate computational proficiency, including a conceptual understanding of numbers,
ways of representing number, relationships among number and number systems, and the meaning of operations.
NCTM standard 1.9 represents learning that is the foundation for many content areas, particularly for the algebra 1.10.
1.10 Knowledge of Different Perspectives on Algebra. Candidates emphasize relationships among quantities including functions, ways of
representing mathematical relationships, and the analysis of change.
Math 140 Pre-Calculus with Derivatives I and II Algebraic and graphical representations of functions including: polynomial, rational, exponential, logarithmic, and
trigonometric; techniques of solving equations and inequalities; modeling; introduction to instantaneous rates of change: limits, derivatives; continuity; applications of
derivatives. (4 credits)
MATH 471 Abstract Algebra I Real numbers and integers satisfy many nice properties under addition and multiplication, but other sets behave differently: matrix
multiplication and composition of functions are noncommutative operations. Which properties (associativity, commutativity, identity, inverses) are satisfied by
operations on sets determine the basic algebraic structure: group, ring, or field. The internal structure, (subgroups, cosets, factor groups, ideals), and operationpreserving mappings between sets, (isomorphisms, homomorphisms), are examined. Emphasis is on theory and proof, although important applications in symmetry
groups, cryptography, and error-correcting codes may also be covered. Prerequisites: MATH 220, 240. (Quant) (4 credits)
1.11 Knowledge of Geometries. Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures,
and their properties.
Math 365 Geometry Elements of Euclidean and non-Euclidean geometries: incidence, betweenness, separation, congruence, and parallel postulates. Geometry of
physical space. Historical development. A proof oriented course. Prerequisites: MATH 220, 240 (4 credits)
1.12 Knowledge of Calculus, Candidates demonstrate a conceptual understanding of limit, continuity, differentiation, and integration and a
thorough background in techniques and application of the calculus.
Math 151 Calculus I Topics related to instantaneous rates of change: functions, limits, continuity, derivatives, mean value theorem and applications; antiderivatives
and definite integrals. Graphing calculator use is required. (Students who earn credit for MATH 151 may not earn credit for MATH 140, or MATH 141.) Prerequisites:
a minimum of one and one-half years of algebra, one-half year of trigonometry, and one year of geometry.
OR
Math 140 (see above) & Math 141 Continuation of topics of MATH 140: functions and their derivatives, chain rule, the mean value theorem, Riemann sum
approximation for integrals, definite integrals, antiderivatives, and applications. Graphing calculator use is required. (Students who earn credit for MATH 141 may not
earn credit for MATH 151.) (4 credits)
Math 152 Calculus II Applications of the definite integral, techniques of integration, differential equations, power series, Taylor series, and an introduction to
computer algebra systems. Prerequisite: MATH 141 or MATH 151 (4 credits)
1.13 Knowledge of Discrete Mathematics. Candidates apply the fundamental ideas of discrete mathematics in the formulation and solution of
problems.
Math 220 Discrete Structures Applications of the definite integral, techniques of integration, differential equations, power series, Taylor series, and an introduction
to computer algebra systems. Prerequisite: MATH 141 or MATH 151 (4 credits)
1.14 Knowledge of Data Analysis, Statistics and Probability. Candidates demonstrate an understanding of concepts and practices related to
data analysis, statistics, and probability.
Math 321 Probability and Statistics I Axioms and laws of probability, independence, conditional probability, combinatorics, discrete and continuous random
variables, mathematical expectation, central limit theorem, descriptive statistics, confidence intervals. Only two of MATH 321, 322, 327, and MATH 328 may apply
toward the math major. Prerequisite: MATH 152. (4 credits)
Knowledge of Measurement. Candidates apply and use measurement concepts and tools.
Electives: Candidates Choose One (1) of the four (4) courses listed below
1.4 Knowledge of Mathematical Connections. Candidates recognize, use, and make connections between and among mathematical ideas and in
contexts outside mathematics to build mathematical understanding.
Math 235: Operations Research Model building. Analytic tools useful to management chosen from linear programming, simplex algorithm, sensitivity analysis,
duality; integer linear programming; goal programming; dynamic programming; networks, PERT-CPM, maximum flow, shortest path; simulation; nonlinear
programming. Offered alternate years. Prerequisite: MATH 140 or MATH 151. (4 credits)
1.14 Knowledge of Data Analysis, Statistics and Probability. Candidates demonstrate an understanding of concepts and practices related to
data analysis, statistics, and probability.
Math 322: Probability and Statistics II Sampling distribution theory, theory of estimation and hypothesis testing, confidence intervals, inferences for means and
proportions, correlation and regression, chi-square tests. Only two of MATH 321, 322, 327, and MATH 328 may apply toward the math major. Prerequisite: MATH
321. (4 credits)
1.12 Knowledge of Calculus, Candidates demonstrate a conceptual understanding of limit, continuity, differentiation, and integration and a
thorough background in techniques and application of the calculus.
1.4 Knowledge of Mathematical Connections. Candidates recognize, use, and make connections between and among mathematical ideas and in
contexts outside mathematics to build mathematical understanding.
Math 352: Ordinary Differential Equations An introduction to first and second order differential equations, existence and uniqueness theorems, higher order linear
differential equations, Laplace transforms, power series solutions, boundary value problems, systems of linear differential equations, and applications in the physical,
biological, and social sciences. Prerequisite: MATH 240. (4 credits)
Candidates are expected to achieve a content knowledge GPA of at least 2.50.
2012-2013: 2 candidates
NCTM Standard
Range of
Content Knowledge
Course Grades
2.0 to 4.0
MEAN GPA
2.881
GPA RANGE
2.667-3.095
%--#
 2.50
100%--2
There are just two candidates in the 2012-2013 cohort. It is not possible to draw a conclusion about
the efficacy of the Math Education program with data points from just two candidates.
The two candidates met the expectations: GPA > 2.50.
No candidate achieved below 2.0 for a course grade.