1. Content Knowledge of Elementary Pre-service Teachers
Presentation slide for courses, classes, lectures et al.
Ryan Nivens East Tennessee State University

2. Background Dr. Witherspoon’s Concerns
RODP (online) vs. On-campus teaching of 1410/1420
Dr. Vogel’s research on content knowledge
My own Concerns
Letters of Recommendation
Lack of knowledge of content strength
Introductory notes.

3. Background (cont.) Ready2Teach Modular format of coursework
“The Ready2Teach program will meet the standards of content knowledge requirements as well as any other teacher education program.”
Introductory notes.

4. Background (cont.) InTASC Content Knowledge Standards
Standard #4: Content Knowledge
The teacher understands the central concepts, tools of inquiry, and structures of the discipline(s) he or she teaches and creates learning experiences that make these aspects of the discipline accessible and meaningful for learners to assure mastery of the content.
Standard #5: Application of Content
The teacher understands how to connect concepts and use differing perspectives to engage learners in critical thinking, creativity, and collaborative problem solving related to authentic local and global issues.
Introductory notes.

5. Background National Council on Quality Teaching
Standard 6: Elementary Content.
The institution prepares teacher candidates with content understanding necessary to teach to the Common Core Standards as well as the full elementary curriculum, and have expertise in a single subject.
A program will earn a "strong design" designation if adequate elementary mathematics content is combined with elementary mathematics methods instruction in a coordinated set or sequence of courses that satisfies indicators
Common Core Standards – Math
TCAP testing in public schools
Introductory notes.

6. Combining Influences
Content Knowledge Test
MATH 1410 Drs. Witherspoon & Vogel
Math Methods - Nivens
Ready2Teach
InTASC
NCQT
CCSS
TCAP
Content knowledge tests for my Math Methods courses mirroring CCSS
Probability & Data;
Num. & Ops in Base 10;
Num. & Ops – fractions, ratio, proportions
Geometry
Expressions & Equations

7. New Modular Format for K-6 Math Methods
Module 3: Assessment (InTASC #4,5,6)
Designing an assessment (evidence-based best practices)
Content Areas: Ratio & Fractions, Geometry
(Common Core Domains: Number and Operations – Fractions, Geometry, Ratios and Proportional relationships)
(Common Core “Mathematical Practices” #1-8) 
Module 4: Reflective Teaching practices (InTASC #4,5,7,8,9,10)
Performance-based Assessment teaching project
Content Areas: Algebra
(Common Core Domains: Expressions and Equations)
(Common Core “Mathematical Practices” #1-8)
Module 1: Student Learning (InTASC #1,2,3,4,5)
Analysis of Student Work (PBL part 1)
Content Areas: Probability, Data analysis
(Common Core Domains: Statistics and Probability)
(Common Core “Mathematical Practices” #1-8)
Module 2: Instructional Strategies (InTASC #4,5,7,8)
Remediation Plan (PBL part 2)
Content Areas: Number & Operation
(Common Core Domains: Number and Operations in Base 10)

8. Comparisons of Math requirements
All three licensure programs
Interdisciplinary Studies K-6 licensure
Special Ed K-12
Early Childhood pK-3
Require 3-4 Hours of math from this list
MATH 1530 Probability and Statistics Non-Calculus (3 hrs.)
MATH 1840 Analytical Geometry and Diff Calculus (4 hrs.)
MATH 1910 Calculus I (4 hrs.)
Beginning course details and/or books/materials needed for a class/project.

9. Comparisons of Math requirements
Interdisciplinary Studies K-6 licensure
6 additional hours in Math
Math 1410 Number Concepts & Algebraic Structures (3 hrs.)
Math 1420 Logic & Problem Solving (3 hrs.)
Special Ed K-12
No additional hours in Math (currently planning to change that)
CUAI 3430 Methods in Teaching Math K-8 (3 hrs.)
Early Childhood pK-3
3 additional hours in Math
Beginning course details and/or books/materials needed for a class/project.

10. The Idea that Formed
Math 1410
Pre-Admission
CUAI 3420
Special Education K-8
CUAI 4310
Teacher Education K-6
CUAI 4517
Early Childhood Education PK-4
Using the state Practice TCAP tests in grades 3-8, a battery of D2L assessments were created to assess the content knowledge of my teacher candidates.
Beginning course details and/or books/materials needed for a class/project.

11. Research Questions
What is the level of content knowledge of my pre- service math teachers?
Is there a difference between pre-service teachers from programs with differing math requirements?
Are items from the TCAP practice tests useful in answering these questions?

12. Pilot Testing Fall 2011 One section CUAI 3430 Math Methods K-8
Two sections
CUAI 4310 Math Methods K-6
These courses were chosen because the tests fit the description of the course requirements. CUAI 4517, EC math methods, was not used because the test does not fit the scope of the course.

13. Pilot test Fall 2011 Probability (content grades 3, 5, 6)
Class
Program
Class Average
Range σ n
3430
Spec. Ed
89.21%
62 – 100%
9.8 18
4310 – 1
ISED
91.18%
76 – 100
7.1 24
4310 – 2
89.75%
77 – 100
5.5 25
A schedule design for optional periods of time/objectives.

14. Pilot test Fall 2011 Num&Ops Base 10 (content grades 3, 5, 6)
Class
Program
Class Average
Range σ n
3430
Spec. Ed
85.34%
66 – 100%
9.1 18
4310 – 1
ISED
91.71%
68 – 100
8.4 25
4310 – 2
89.75%
80 – 100
5.8 24
A schedule design for optional periods of time/objectives.

15. Pilot test Fall 2011: Num&Ops Fractions, Ratios & Geometry (content grades 3, 5, 6)
Class
Program
Class Average
Range σ n
3430
Spec. Ed
86.54%
43 – 100%
14.6 18
4310 – 1
ISED
92.65%
77 – 100
5.5 26
4310 – 2
89.58%
76 – 100
7.5 25
A schedule design for optional periods of time/objectives.

16. Pilot test Fall 2011 Algebra (content grades 3, 5, 6)
Class
Program
Class Average
Range σ n
3430
Spec. Ed
89.91%
51 – 100%
12.3 18
4310 – 1
ISED
94.22%
77 – 100
6.2 25
4310 – 2
93%
76 – 100
6.0
A schedule design for optional periods of time/objectives.

17. Average Scores on All Tests
Example graph/chart.

18. Analysis In all sections on all tests, at least one person scored 100%
The section with the least amount of mathematics course requirements always had the lowest score and the largest standard deviation
The scores on the probability test may be higher due to all courses studying probability concepts in my course in the first weeks
Introductory notes.

19. Discussion
The entire TCAP practice sets of questions are now available in a D2L question library and as assessments,
Available now or at the Math/Science for Elem. Teachers Conference (Roane State).
Validity of the TCAP practice tests in assessing Common Core math.
Currently I am analyzing the TCAP practice tests in relation to the CCSS-math. (poster session at CSMC Research Conference in March).
Introductory notes.

20. Implications and Suggestions
Thoughts on the tests
Ideas
Suggestions

21. Thank you for your time.
Ryan Nivens, Ph.D Past-President, Appalachian Association of Mathematics Teacher Educators President, Upper East Tennessee Council of Teachers of Mathematics Assistant Professor | Center of Excellence in Mathematics and Science Education Department of Curriculum and Instruction | Clemmer College of Education East Tennessee State University PO Box Johnson City, TN phone