Two Works in Progress:

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• Two Works in Progress
• Aligning 4-8 Degree Program With State Standards
  Filling the Gaps
• Impact of Teacher Knowledge on Student
  Performance Revealing Patterns

Mourat Tchoshanov Departments of Mathematical
Sciences and Teacher Education University of
Texas at El Paso
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• Work in Progress - 1
• Aligning 4-8 Pre-service Mathematics Teachers
  Education Program
• With State Standards
• Filling the Gaps
• __________________________________________________
  ____________
• The study was conducted by Matthew Winsor
  through TNE mini-grant

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Outline

• Motivation for the Study
• Research Plan
• Content on TExES Exam
• Coursework Deficiencies
• Findings Recommendations

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Some Definitions

• Grades 4-8 Generalist A future teacher who will
  be certified to teach every subject in grades
  4-8.
• Grade 4-8 Mathematics Specialist A future
  teacher who is certified to teach mathematics in
  grades 4-8, i.e. has specialized in mathematics.
• TExES state certification exam.

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Motivation for Study

• Teachers for a New Era (TNE) Mathematics Working
  Group focused on the mathematical education of
  future middle school (grades 4-8) mathematics
  teachers.
• Is a capstone course for future middle school
  teachers feasible?

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Research Plan

• Determine the mathematics future middle school
  teachers are required to know (TExES).
• Determine if the mathematics is being taught in
  required UTEP mathematics courses (Survey).
• Material not being covered could be included in a
  capstone course for middle school teachers.

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Content on TExES Exam

• Standard I. Number Concepts The mathematics
  teacher understands and uses numbers, number
  systems and their structure, operations and
  algorithms, quantitative reasoning, and
  technology
• Standard II. Patterns and Algebra The
  mathematics teacher understands and uses
  patterns, relations, functions, algebraic
  reasoning, analysis, and technology
• Standard III. Geometry and Measurement The
  mathematics teacher understands and uses
  geometry, spatial reasoning, measurement concepts
  and principles, and technology
• Standard IV. Probability and Statistics The
  mathematics teacher understands and uses
  probability and statistics, their applications,
  and technology
• Standard V. Mathematical Processes The
  mathematics teacher understands and uses
  mathematical processes to reason mathematically,
  to solve mathematical problems, to make
  mathematical connections within and outside of
  mathematics, and to communicate mathematically.
• Standard VI. Mathematical Perspectives The
  mathematics teacher understands the historical
  development of mathematical ideas, the
  interrelationship between society and
  mathematics, the structure of mathematics, and
  the evolving nature of mathematics and
  mathematical knowledge.

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Courses Where Content is Covered
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Mathematics Course of Study for Middle School
Degree Programs
Grades 4-8 generalist Grades 4-8 mathematics specialist
Math 1320 Mathematics for Social Scientist Math 2303 Properties of the real numbers I Math 3308 Conceptual Algebra Math 3309 Conceptual mathematics II Stat 1380 Basics of Descriptive and Inferential Statistics Math 1508 Pre-Calculus Math 2303 Properties of the Real Numbers I Math 3308 Conceptual Algebra Math 3309 Conceptual Mathematics II Stat 1380 Basics of Descriptive and Inferential Statistics Math 1411 Calculus I Math 2300 Discrete Mathematics Math 2325 Introduction to Higher math Math 3300 History of Mathematics Math 3303 Properties of Real Numbers II Math 3304 Fundamentals of Geometry from an Advanced Standpoint Math 3323 Matrix Algebra
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Areas of Deficiency (fragment)
Mathematics Topics Areas of Deficiency in 4-8 Generalist coursework Areas of deficiency in 4-8 Mathematics Specialist coursework
Algebra Mapping representation of functions Parent functions Effect of changing coefficients of parent functions on graph Finding intersections of functions Trigonometric functions Solving systems of inequalities Parent functions Effect of changing coefficients of parent functions on graph Finding intersections of functions Solving systems of inequalities

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Findings Recommendations

• Mathematics 4-8 specialist degree plan
• Had some minor gaps in their mathematical
  preparation. Most notably missing from the
  specialist degree plan is the opportunity for
  students to closely examine families of functions
  and their properties.
• Another deficiency in the mathematics 4-8
  specialist degree plan is examining complex
  numbers.
• Both deficiencies found in the mathematics 4-8
  specialist degree plan could be addressed in a
  capstone course.

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Findings Recommendations (continued)

• Generalist 4-8 degree plan
• On the other hand, the Generalist 4-8 degree plan
  had several glaring deficiencies in the area of
  mathematics. Notably absent from the generalist
  4-8 degree plan is an entire calculus course and
  an entire geometry course. The generalists are
  still responsible for calculus and geometry
  questions on their TExES exam.
• As with the mathematics 4-8 Specialist degree
  plan, the Generalist 4-8 degree plan lacks the
  opportunity to examine families of functions and
  complex numbers. Moreover, the generalist 4-8
  degree plan lacks the opportunity to study graph
  theory, a topic that is become more prevalent in
  the grades 4-8 mathematics curriculum.
• Furthermore, the Generalist 4-8 degree plan does
  not give students the opportunity to become
  fluent in proof. Although pupils in grades 4-8
  do not formally prove mathematics theorems, they
  are required to reason about mathematics and
  defend their reasoning to their peers. If the
  teacher has not had the opportunity to prove
  theorems, they may be weak at mathematical
  reasoning.
• It does not seem reasonable to believe that the
  implementation of a capstone course could address
  all of the deficiencies found in the generalist
  4-8 degree plan. Other measures have to be taken
  in order to prepare our students more effectively.

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Work in Progress 2 (TNE Pilot Study) Impact of
Teacher Knowledge on Student Performance Reveali
ng Patterns ____________________________________
________________________________________________
This study was supported by TEA grant on
Improving Student Achievement through
Professional Development Partnership (Co-PIs
Mourat Tchoshanov and Larry Lesser)
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Overview

• What does TAKS Data Tell Us?
• Research Question
• Sample and Methodology
• Teacher Knowledge and Student Achievement
• Cognitive Demand and Mathematical Tasks
• Results and Interpretation

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Students TAKS Performance(All Students, Percent
Met Standard)

• 2003 2004 2005 2006
• Elementary Grades
• 3rd grade - 74 83 83 82
• 4th grade - 70 78 81 83
• 5th grade - 65 73 79 81
• Middle Grades
• 6th grade - 60 67 72 79
• 7th grade - 51 60 64 70
• 8th grade - 51 57 61 67
• High School Grades
• 9th grade - 44 50 56 56
• 10th grade - 48 52 58 60
• 11th grade - 44 67 72 77

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6th Grade Students Passing Scores by TAKS
Objectives (4 local MS campuses)
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Research Questions What kind of teacher
knowledge is essential for student
achievement? Does a cognitive demand level of
teacher knowledge affect student achievement?
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• Research Sample
• Study sample consisted of 22 in-service teachers
  from
• low-SES schools (based on percentage of students
  participating in free or reduced-price lunch
  programs)
• student population is 80-90 Latino/ Hispanic.

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• Methodology
• In order to assess the impact of teacher
  knowledge on student achievement, we used the
  following measures
• Texas Assessment of Knowledge and Skills (TAKS)
  scores for two consecutive years of the test
  administration (2005 and 2006). TAKS scores were
  collected to assess teacher impact on student
  achievement.
• Teacher Observation Protocol. The protocol was
  used for documenting observations of teacher
  practice with focus on the TAKS objectives and
  strategies (protocol analysis is in-progress).
• Teacher Knowledge Survey. The survey was used to
  assess teacher knowledge and consisted of 33
  multiple choice problems addressing corresponding
  TAKS objectives. Survey items were designed using
  different levels of cognitive demand.

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• Teacher Knowledge and Student Performance
• A body of existing research claims that U.S.
  teachers lack essential knowledge for teaching
  mathematics and that teachers intellectual
  resources affect student achievement (Coleman et
  al., 1966, Ball, 1991 Stigler Hiebert, 1999,
  Ma, 1999, Hill et al., 2005).
• The pilot study supports this claim and shows
  that teacher knowledge and student achievement
  parallel each other.

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6th Grade Student TAKS Passing Scores (by Campus,
District, and State) vs. Teacher Knowledge (N22)
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• Why tasks are important?
• Students learn from the kind of work they do
  during class, and the tasks they are asked to
  complete determines the kind of work they do
  (Doyle, 1988).
• Mathematical tasks are critical to students
  learning and understanding because tasks convey
  messages about what mathematics is and what doing
  mathematics entails (NCTM, 1991, p. 24).
• The tasks make all the difference (Hiebert et
  al., 1997, p. 17).
• Tasks provide the context in which students
  think about mathematics and different tasks place
  different cognitive demands on students learning
  (Doyle, 1983 Henningsen Stein, 1997 Porter,
  2004).

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• Cognitive Demand Mathematical Tasks
• Cognitive demand can be defined as the kind and
  level of thinking required of students in order
  to successfully engage with and solve the task
  (Stein et al., 2000, p. 11).
• Such thinking processes range from memorization
  to the use of procedures and algorithms (with or
  without attention to concepts, understanding, or
  meaning), to complex thinking and reasoning
  strategies that would be typical of doing
  mathematics (e.g., conjecturing, justifying, or
  interpreting) (Henningsen Stein, 1997, p. 529).
  
• Given the importance of tasks, the next issue
  is What do teachers need to know to select or
  make up appropriate individual tasks and coherent
  sequences of tasks? The simple answer is that
  they need to have a good grasp of the important
  mathematical ideas and they need to be familiar
  with their students thinking (Hiebert et al.,
  1997, p. 34).
• Similarly, Grossman, Schoenfeld, Lee (2005)
  posed a critical question What do teachers need
  to know about the subject they teach? (p. 201),
  and provided a fairly straightforward answer
  Teachers should possess deep knowledge of the
  subject they teach (ibid, p.201).

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Levels of Cognitive Demand

• Level 1 Facts and Procedures
• Memorize Facts, Definitions, Formulas,
  Properties, and Rules
• Perform Computations
• Make Observations
• Measure
• Solve Routine Problems
• Level 2 Concepts and Connections
• Justify and explain solutions to problems
• Use and select multiple representations to model
  mathematical ideas
• Transfer knowledge
• Connect two or more concepts to solve
  non-routine problems
• Communicate Big Ideas
• Explain findings and results from analysis of
  data
• Level 3 Models and Generalizations
• Generalize
• Make and test conjectures

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Example of Increasing Cognitive Demand
Level 1. What is a rule for fraction division?
Level 2. Solve the same problem in more than one
way, for example, draw a model or illustrate
the problem with manipulatives
Make up a story for the fraction division
problem
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Teacher Knowledge Survey Results by Cognitive
Demand Levels
High Cognitive Level
Low Cognitive Level
75
48
52
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Question-in-Progress How strong is the
connection between Teacher Knowledge and Student
Performance?
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Assumption-in-Progress Level of Teacher
Knowledge has a Potential to Impact Student Gain
Knowledge Survey Score
N22 r .486 plt.01
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Conclusion

• There is a connection between teacher knowledge
  and student achievement - in general, and there
  are revealing patterns in the connection with
  regard to specific mathematical domains,
  processes and levels of cognitive demand - in
  particular.
• The Teacher Knowledge Survey showed the lowest
  performance on the patterns, relationships, and
  algebraic reasoning and measurement
  objectives, which are precisely the lowest
  performing two out of the six TAKS objectives for
  students!
• Within each objective, items on the 33-problem
  Teacher Knowledge Survey were also sorted by
  levels of cognitive demand. Not surprisingly,
  teachers did the best on problems involving the
  lowest level of cognitive demand.

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Conclusion (cont.)

• Surprisingly, teachers did slightly better on
  problems at the highest level of cognitive demand
  than on problems at the middle level. The same
  pattern was observed in student performance on
  the state standardized test (TAKS).
• Considering the limitations of the study (small
  sample of teachers and short intervention
  period), we intended only to present what appears
  to be a promising model for identifying
  performance patterns and potentially impacting
  some of the teacher variables on student
  achievement.

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Current Stage of the Instrument Development

• Test bank was developed by the TNE Math Working
  Group team (faculty of UT-El Paso Colleges of
  Science and Education and EPCC mathematics
  faculty)
• The test-bank consists of 300 problems aligned
  with TExES standards
• Test items were designed at different levels of
  cognitive demand
• Currently, test bank is being revised and
  converted into computer system
• Based on the pilot study results, the Math
  Working Group anticipates that the instrument
  might play a role of a predictor of pre-service
  teacher readiness to challenge the state exam
• The Group also plans to use the instrument (with
  in-service teachers) as an indicator of a
  potential student success.

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Can you imagine!?
Im DONE.
Gracias!