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Department of Mathematical Sciences School of Science and Technology B.A. in Mathematics Education CIP Code: 13.1311 Program Code: 155 Program Quality Improvement Report 2009-2010 1
Student Learning Outcomes The following standards, as designated by the NCTM, are used for the Mathematics Education program: Standard 1: Knowledge of Mathematical Problem Solving Standard 2: Knowledge of Reasoning and Proof Standard 3: Knowledge of Mathematical Communication Standard 4: Knowledge of Mathematical Connections Standard 5: Knowledge of Mathematical Representation 2 Program Quality Improvement Report 2009-2010
Standard 6: Knowledge of Technology Standard 7: Dispositions Standard 8: Knowledge of Mathematics Pedagogy Standard 9: Knowledge of Number and Operation Standard 10: Knowledge of Different Perspectives on Algebra Standard 11: Knowledge of Geometries 3 Program Quality Improvement Report 2009-2010
Standard 12: Knowledge of Calculus Standard 13: Knowledge of Discrete Mathematics Standard 14: Knowledge of Data Analysis, Statistics, and Probability Standard 15: Knowledge of Measurement Standard 16: Field-Based Experiences * All sixteen standards are mandated student-learning outcomes. 4 4 Program Quality Improvement Report 2009-2010
Alignment with Cameron Universitys Mission Statements framework which students can acquire the skills and knowledge that will enable them to become highly qualified mathematics secondary teachers promote and establish excellent working relations with all departments in the university optimizes the goals from all the mission statements including the University, School of Science and Technology, and the Department of Mathematical Sciences highest quality of education possible enhances the opportunities for students to make meaningful contributions to the community 5 Program Quality Improvement Report 2009-2010
Alignment with Cameron Universitys Strategic Plan 2013 Candidates will: receive the highest quality education become fully qualified to teach mathematics in the secondary schools interact with the community in the form of field-based experiences become effective teachers of mathematics strengthen connections with the community 6 Program Quality Improvement Report 2009-2010
Program Direct Measures of Student Learning Assessment # 1 Oklahoma Subject Area Test (OSAT) for Advanced Mathematics Assessment # 2 Major Field Achievement Test (MFT) in Mathematics Assessment # 3 Lesson Plans Assessment # 4 Student Teaching Evaluations Assessment # 5 Teacher Work Sample (TWS) Assessment # 6 Mid-level Assessment Exam Assessment # 7 Mathematical Proof Portfolio Assessment # 8 Technology Portfolio 7 Program Quality Improvement Report 2009-2010
Shortfalls in Student Learning When It Occurs During MATH 2613 Foundations of Mathematics Major Assessments Recommended Remediation Retake after completing additional math classes Mid-level Assessment Exam (passing score required) After completing at least 30 of 39 hours of required core mathematics courses OSAT (Advanced Mathematics) (passing score required) Retake after completing additional math classes During EDUC 4313 Practicum in Assessment and Instruction Teacher Work Sample (passing the class required) Retake class Before completion of MATH 4772 Teaching of Secondary Mathematics Major Field Test (Mathematics) (passing score required) Meet with assigned mathematics instructor for tutoring and guidance. Retake. During Math 4772 Lesson Plans (passing score required on all lesson plans) Meet with mathematics instructor for tutoring and guidance. Rework lesson plans and resubmit to instructor. Meet with mathematics faculty member who graded the proofs. Rework and resubmit. Meet with mathematics faculty member who graded the portfolio. Rework and resubmit. During Math 4772 Mathematical Proof Portfolio (score of Meets Standards or higher required) During Math 4772 Technology Portfolio (score of Meets Standards or higher required) During Student Teaching Student Teaching Evaluation (passing scores required on both student teaching evaluation forms) Meet with math education faculty committee for career counseling and guidance. Possibly repeat student teaching. 8 Program Quality Improvement Report 2009-2010
Midway Check Check candidates progress on the following: Mid-level Assessment Grade Point Average (at least 2.5) Grades of C or better in math courses Oklahoma General Education Test (OGET) Teacher education admission 9 Program Quality Improvement Report 2009-2010
Program Actions Since Fall 2009 Last year s action plan: Develop a technology portfolio Add an induction proof of a recursive relation to the mathematical proof portfolio Realign the lesson plan format Develop a pretest for MATH 2215 Calculus I Collect more data Last year s PQIR presentation focused on three standards: Standard 2: Knowledge of Reasoning and Proof Standard 6: Knowledge of Technology Standard 13: Knowledge of Discrete Mathematics 10 Program Quality Improvement Report 2009-2010
Standard 2: Knowledge of Reasoning and Proof Learning Outcomes 2.1 Recognize reasoning and proof as fundamental aspects of mathematics. 2.2 Make and investigate mathematical conjectures. 2.3 Develop and evaluate mathematical arguments and proofs. 2.4 Select and use various types of reasoning and methods of proof. 11 Program Quality Improvement Report 2009-2010
Standard 2: Knowledge of Reasoning and Proof Assessments Oklahoma Subject Area Test in Advanced Mathematics Mid-level Assessment Exam Mathematical Proof Portfolio Technology Portfolio 12 Program Quality Improvement Report 2009-2010
TABLE 1 Oklahoma Subject Area Test (OSAT) scores, Advanced Mathematics NCTM Standard 2 Total number of OSATs scored: n=2 Academic Year Mean State Score on Mathematical Processes and Number Sense Mean Score on Mathematical Processes and Number Sense (NCTM Standard 2) 2008-2009 (n=2) 260* 280.5 2009-2010 (n=0) NA NA * Weighted Mean for tests given on 4/18/2009 and 5/30/2009. Total state tests given = 59 13 Program Quality Improvement Report 2009-2010
TABLE 2 Results of Oklahoma Subject Area Test NCTM Standard 2 Total Number of OSATs scored: n = 2 Does Not Meet Standards 0-239 Meets Standards 240-269 Exceeds Standards 270-300 Total* Total Mathematical Processes and Number Sense 0% 0% 100% 100% 14 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data OSAT Two mathematics education majors took the OSAT during the AY 2008-2009. There were no mathematics education candidates who took the OSAT during the AY 2009-2010. Both candidates exceeded standards in Mathematical Processes and Number Sense. No Trend Analysis can be done at this time. 15 Program Quality Improvement Report 2009-2010
TABLE 3 Results of Mid-level Assessment Exam NCTM Standard 2 Total Number of Mid-level Assessment Exams Scored: n = 5 Does Not Meet Standards 1 Meets Standards - 3 Exceeds Standards 5 Total NCTM Standard 2 Fall 2007 (n=2) Fall 2008 (n=1) Fall 2009 (n=2) Total (n=5) 50% 0% 0% 20% 0% 100% 50% 40% 50% 0% 50% 40% 100% 100% 100% 100% 16 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Mid-level Assessment Exam During the Fall semesters of 2007-2009, the Mid-level Assessment Exam was administered to five mathematics education candidates. For Standard 2, one candidate did not meet standards while the other candidate exceeded standards in the Fall 2007. The mathematics education candidate taking the exam in the Fall semester of 2008 met only Standard 2. For Standard 2, one mathematics education candidate met standards and one candidate exceeded standards in the Fall 2009. Due to the small number (n = 5) of mathematics education candidates taking the Mid-level Assessment Exam, a definitive conclusion cannot be drawn at this time nor can trend analysis be conducted. 17 Program Quality Improvement Report 2009-2010
TABLE 4 Results of Mathematical Proof Portfolio NCTM Standard 2 Total Number of Proof Portfolios Scored: n = 2 Does Not Meet Standards 1 Meets Standards - 3 Exceeds Standards 5 Total* Proof by Contradiction 2008-2009 (n=2) 2009-2010 (n=0) Total (n=2) Direct Proof 2008-2009 (n=2) 2009-2010 (n=0) Total (n=2) Proof by Induction 2008-2009 (n=2) 2009-2010 (n=0) Total (n=2) Proof by Induction (Recursive Relation) added Fall 2009 2009-2010 (n=0) Proof Evaluation 2008-2009 (n=2) 2009-2010 (n=0) Total (n=2) All Proofs 2008-2009 (n=2) 2009-2010 (n=0) Total (n=2) 0% NA 0% 0% NA 0% 100% NA 100% 100% NA 100% 0% NA 0% 50% NA 50% 50% NA 50% 100% NA 100% 0% NA 0% 100% NA 100% 0% NA 0% 100% NA 100% NA NA NA NA 0% NA 0% 0% NA 0% 100% NA 100% 100% NA 100% 0% NA 0% 38% NA 38% 63% NA 63% 100% NA 100% * percentages may not add up to 100 due to rounding 18 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Mathematical Proof Portfolio Two mathematics education candidates submitted mathematical proof portfolios for evaluation during the Spring 2009 semester. In the proof by Contradiction and Proof Evaluation categories both candidates exceeded standards. In the Proof by Induction category both candidates met standards In the Direct Proof category one candidate exceeded standards and the other met standards. There were no mathematics education candidates who completed the proof portfolio during the AY 2009-2010. The sample (n=2) is statistically insignificant, and a definite conclusion cannot be drawn nor can a trend analysis be completed. 19 Program Quality Improvement Report 2009-2010
TABLE 5 Results of Technology Portfolio NCTM Standard 2 Total Number of Technology Portfolios Scored: n = 0 Does Not Meet Standards 1 Meets Standards - 3 Exceeds Standards 5 Total Triangle Worksheet (College Geometry) 2009-2010 (n=0) Total Recursive Worksheet (Discrete Mathematical Structures) 2009-2010 (n=0) Total NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 20 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Technology Portfolio The technology portfolio replaced the upper-level assessment during AY 2009-2010. No students were enrolled in MATH 4772 (Teaching of Secondary Mathematics) during AY 2009-2010 thus no data was collected. 21 Program Quality Improvement Report 2009-2010
Standard 6: Knowledge of Technology Learning Outcomes 6.1 Use knowledge of mathematics to select and use appropriate technological tools, such as, but not limited to, spreadsheets, dynamic graphic tools, computer algebra systems, dynamic statistical packages, graphing calculators, data-collection devices, and presentation software. 22 Program Quality Improvement Report 2009-2010
Standard 6: Knowledge of Technology Assessments Lesson Plans Student Teaching Evaluation Teacher Work Sample Technology Portfolio 23 Program Quality Improvement Report 2009-2010
TABLE 6 Results of Lesson Plans NCTM Standard 6 Total Number of Lesson Plans Scored: n = 6 (two for each of the three assigned lesson plans) Does Not Meet Standards - 1 Meets Standards - 3 Exceeds Standards - 5 Total* NCTM Indicator 6.1 2008-2009 (n=6) 2009-2010 (n=0) 0% NA 83% NA 17% NA 100% NA * percentages may not add up to 100 due to rounding 24 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Lesson Plans There were no mathematics education candidates who completed lesson plans during AY 2009-2010. The sample (n=2) is statistically insignificant, and a definite conclusion cannot be drawn nor can a trend analysis be completed. 25 Program Quality Improvement Report 2009-2010
TABLE 7 Results of Student Teaching Assessment, Education Portion NCTM Standard 6 Total Number of Assessments: n = 12 Total Number of Candidates: N=2 Does Not Meet Standards 1* Meets Exceeds Standards 3* Observed # of Not Standards - 2* Mean Max Min E3 NCTM Indicator 6.1 2009-2010 (n=4) 2.75 2 3 0 0% 25% 75% M10 NCTM Indicator 6.1 2009-2010(n=8) Total (n=12) 2.7 2.72 2 2 3 3 1 1 0% 0% 29% 27% 71% 73% * percentages may not add up to 100 due to rounding 26 Program Quality Improvement Report 2009-2010
Table 21 Results of Student Teaching Assessment, Mathematics Addendum NCTM Standard 6 Total Number of Assessments: n = 8 Total Number of Candidates: N=2 Does Not Meet Standards 1 Meets Standards - 2 Exceeds Standards 3 Obser Mean # of Not Max Min ved M10 (NCTM 6.1) Fall 2009 (n=4) 2.5 2 3 0 0% 50% 50% Spring 2010 (n=4) 3.0 3 3 1 0% 0% 100% Total (n=8) 2.7 2 3 1 0% 29% 71% *Percentages may not add up to 100 due to rounding. 27 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Student Teaching Evaluation Two mathematics education candidates completed student teaching during AY 2009-2010 . For Standards 6, candidates met standards approximately 28% of the time and exceeded standards approximately 72% of the time. The sample (n=2) is statistically insignificant, and a definite conclusion cannot be drawn nor can a trend analysis be completed. 28 Program Quality Improvement Report 2009-2010
TABLE 8 Results of Teacher Work Sample NCTM Standard 6 Total Number of Teacher Work Samples Scored: n = 2 Does Not Meet Standards - 1 0-10 0% 0% 0% Meets Standards - 3 11-28 0% 0% 0% Exceeds Standards - 5 29-36 100% 100% 100% Total Factor 4 (36 points) 2008-2009 (n=1) 2009-2010 (n=1) Total (n=2) 100% 100% 100% 29 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data TWS One mathematics education candidate completed a Teacher Work Sample during AY 2009-2010. The one mathematics education candidate who completed Standard 6 exceeded standards. The sample (n=2) is statistically insignificant, and a definite conclusion cannot be drawn nor can a trend analysis be completed. 30 Program Quality Improvement Report 2009-2010
TABLE 9 Results of Technology Portfolio NCTM Standard 6 Total Number of Technology Portfolios Scored: n = 0 Does Not Meet Standards 1 Meets Standards - 3 Exceeds Standards 5 Total* Real-World problem worksheet (Graphing Calculator) 2009-2010 (n=0) Total Statistics worksheet (Graphing Calculator) NA NA NA NA NA NA NA NA 2009-2010 (n=0) Total NA NA NA NA NA NA NA NA Triangle Worksheet (College Geometry) 2009-2010 (n=0) Total Recursive Worksheet (Discrete Mathematical Structures) 2009-2010 (n=0) Total NLVM Worksheet (Teaching of Secondary Mathematics) 2009-2010 (n=0) Total All Items 2009-2010 Total NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 31 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Technology Portfolio The technology portfolio replaced the upper-level assessment during AY 2009-2010. No students were enrolled in MATH 4772 (Teaching of Secondary Mathematics) during AY 2009-2010 thus no data was collected. 32 Program Quality Improvement Report 2009-2010
Standard 13: Knowledge of Discrete Mathematics Learning Outcomes 13.1 Demonstrate knowledge of basic elements of discrete mathematics such as graph theory, recurrence relations, finite difference approaches, linear programming, and combinatorics. 13.2 Apply the fundamental ideas of discrete mathematics in the formulation and solution of problems arising from real-world situations. 13.3 Use technological tools to solve problems involving the use of discrete structures and the application of algorithms. 13.4 Demonstrate knowledge of the historical development of discrete mathematics including contributions from diverse cultures. 33 Program Quality Improvement Report 2009-2010
Standard 13: Knowledge of Discrete Mathematics Assessments Oklahoma Subject Area Test for Advanced Mathematics Major Field Achievement Test in Mathematics Mathematical Proof Portfolio Technology Portfolio 34 Program Quality Improvement Report 2009-2010
TABLE 10 Results of Oklahoma Subject Area Test (OSAT) scores, Advanced Mathematics NCTM Standard 13 Total number of OSATs scored: n=2 Academic Year Statistics, and Discrete Mathematics 2008-2009 (n=2) 2009-2010 (n=0) Mean State Score on Probability, Mean Score on Probability, Statistics, and Discrete Mathematics (NCTM Standard 13) 252 259* NA NA *Weighted Mean for tests given on 4/18/2009 and 5/30/2009. Total state tests given = 59 35 Program Quality Improvement Report 2009-2010
TABLE 11 Results of Oklahoma Subject Area Test NCTM Standard 13 Total Number of OSATs scored: n = 2 Does Not Meet Standards Meets Standards Exceeds Standards Total 0-239 240-269 270-300 Total Probability, Statistics, and Discrete Mathematics 50% 0% 50% 100% 36 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data OSAT Two mathematics education majors took the OSAT during the AY 2008-2009. One candidate exceeded standards in Probability, Statistics, and Discrete mathematics. One candidate did not meet standards in Probability, Statistics, and Discrete mathematics. There were no mathematics education candidates who took the OSAT during the AY 2009-2010. No Trend Analysis can be done at this time. 37 Program Quality Improvement Report 2009-2010
TABLE 12 Results of Major Field Achievement Test NCTM Standard 13 Total Number of Major Field Achievement Tests Scored: n = 3 Does Not Meet Standards - 1 Meets Standards - 3 Exceeds Standards - 5 Total 120-135 0% 0% NA 0% 136-170 100% 50% NA 67% 171-200 0% 50% NA 33% Total 100% 100% NA 100% 2007-2008 (n=1) 2008-2009 (n=2) 2009-2010 (n=0) Total (n=3) * percentage may not add up to 100 due to rounding 38 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Major Field Achievement Test There were no candidates who took the Major Field Achievement Test during AY 2009-2010. The sample (n=3) is statistically insignificant, and a definite conclusion cannot be drawn nor can a trend analysis be completed. 39 Program Quality Improvement Report 2009-2010
TABLE 13 Results of Mathematical Proof Portfolio NCTM Standard 13 Total Number of Proof Portfolios Scored: n = 0 Does Not Meet Standards 1 Meets Standards - 3 Exceeds Standards 5 Total Proof by Induction (Recursive Relation) added Fall 2009 2009-2010 (n=0) Total (n=0) NA NA NA NA NA NA NA NA * percentage may not add up to 100 due to rounding 40 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Mathematical Proof Portfolio No data has been collected for Standard 13 for Proof by Induction (recursive relation was added Fall 2009). There were no mathematics education candidates who completed the proof portfolio during the AY 2009-2010. 41 Program Quality Improvement Report 2009-2010
TABLE 14 Results of Technology Portfolio NCTM Standard 13 Total Number of Technology Portfolios Scored: n = 0 Does Not Meet Standards 1 Meets Standards - 3 Exceeds Standards 5 Total Recursive Worksheet (Discrete Mathematical Structures) 2009-2010 (n=0) Total NA NA NA NA NA NA NA NA * percentage may not add up to 100 due to rounding 42 Program Quality Improvement Report 2009-2010
Trend Analysis of Assessment Data Technology Portfolio The technology portfolio replaced the upper-level assessment during AY 2009-2010. No students were enrolled in MATH 4772 (Teaching of Secondary Mathematics) during AY 2009-2010 thus no data was collected. 43 Program Quality Improvement Report 2009-2010
Program Priority Learning Outcomes for Current Year Standard 1: Knowledge of Mathematical Problem Solving Standard 3: Knowledge of Mathematical Communication Standard 6: Knowledge of Technology 44 Program Quality Improvement Report 2009-2010
Standard 1: Knowledge of Mathematical Problem Solving 45 Program Quality Improvement Report 2009-2010
Program objective and measurement (Create separate chart or table for each priority objective) PROGRAM GOAL: Standard 1: Knowledge of Mathematical Problem Solving MEASUREMENT OF PROGRAM OBJECTIVE Methods used to determine validity of measurement instruments Methods used to determine reliability of measurements CURRICULUM AREA OR TARGET AUDIENCE PROGRAM OBJECTIVE Schedule for measurements Measurements 1.1 Apply and adapt a variety of appropriate strategies to solve problems. Required Courses: MATH 1001 MATH 2215 MATH 2235 MATH 3013 MATH 3302 MATH 3333 MATH 3413 MATH 4423 MATH 4772 STAT 3013 EDUC 4313 EDUC 4965 EDUC 4975 OSAT (direct) State wide test Determined by Oklahoma Commission for Teacher Preparation (OCTP) Recommended that students take after completing 30 or more hours of their mathematical course work 1.2 Solve problems that arise in mathematics and those involving mathematics and other contexts. MFT (direct) National norm Norm reference scores Every Spring semester Student Teaching Evaluation (direct) Developed by Department of Education Developed by Department of Education Assessed in EDUC 4965 and EDUC 4975 46 46 Program Quality Improvement Report 2009-2010
Program objective and measurement (Create separate chart or table for each priority objective) PROGRAM GOAL: Standard 1: Knowledge of Mathematical Problem Solving MEASUREMENT OF PROGRAM OBJECTIVE Methods used to determine validity of measurement instruments Methods used to determine reliability of measurements CURRICULUM AREA OR TARGET AUDIENCE PROGRAM OBJECTIVE Schedule for measurements Measurements 1.3 Build new mathematical knowledge through problem solving. Elective Courses: MATH 2244 MATH 3213 MATH 3253 MATH 4113 MATH 4483 TWS (direct) Developed by Department of Education Developed by Department of Education Assessed in EDUC 4313 Technology Portfolio (direct) Portfolio graded using standardized rubric Faculty using rubric discuss rubric before grading begins Collected during MATH 4772 1.4 Monitor and reflect on the process of mathematical problem solving. 47 47 Program Quality Improvement Report 2009-2010
Display of Assessment Data OSAT TABLE 16 OSAT scores NCTM Standard 1 Total number of OSATs scored: n=2 Academic Year OSAT score Mean Mean Score on Mathemati- cal Processes and Number Sense Mean Score on Relations, Functions, and Algebra Mean score on Measure- ment and Geometry Mean score on Trigonome- try and Calculus Mean score on Probability, Statistics, and Discrete Mathema- tics Mean Score on Con- structed Res- ponse 2008-2009 (n=2) 269.5 280.5 253.5 271 268 252 281.5 State Mean* 260 260 267 257 256 259 267 2009-2010 (n=0) NA NA NA NA NA NA NA *Weighted Mean for tests given on 4/18/2009 and 5/30/2009. Total state tests given = 5 48 Program Quality Improvement Report 2009-2010
Display of Assessment Data OSAT (continued) TABLE 17 Results of OSAT NCTM Standard 1 Total Number of OSATs Scored: n = 2 Meets Standards 240-269 Exceeds Standards 270-300 Does Not Meet Standards Total* 0-239 Total OSAT Advanced Mathematics 2008-2009 (n=2) 2009-2010 (n=0) Mathematical Processes and Number Sense 2008-2009 (n=2) 2009-2010 (n=0) Relations, Functions, and Algebra 2008-2009 (n=2) 2009-2010 (n=0) Measurement and Geometry 2008-2009 (n=2) 2009-2010 (n=0) Trigonometry and Calculus 0% 50% 50% 100% NA NA NA NA 0% 0% 100% 100% NA NA NA NA 50% 0% 50% 100% NA NA NA NA 0% 0% 100% 100% NA NA NA NA 2008-2009 (n=2) 2009-2010 (n=0) Probability, Statistics, and Discrete Mathematics 0% 50% 50% 100% NA NA NA NA 2008-2009 (n=2) 2009-2010 (n=0) Constructed Response 50% 0% 50% 100% NA NA NA NA 2008-2009 (n=2) 2009-2010 (n=0) 0% 50% 50% 100% NA NA NA NA *Percentages may not total 100% due to rounding. 49 Program Quality Improvement Report 2009-2010
Display of Assessment Data MFT TABLE 18 Results of Major Field Achievement Test NCTM Standard 1 Total Number of Major Field Achievement Tests Scored: n = 3 Does Not Meet Standards - 1 Meets Standards - 3 Exceeds Standards - 5 Total* 120-135 0% 0% NA 0% 136-170 100% 50% NA 67% 171-200 0% 50% NA 33% Total 100% 100% NA 100% 2007-2008 (n=1) 2008-2009 (n=2) 2009-2010 (n=0) Total (n=3) *Percentages may not add up to 100 due to rounding. 50 Program Quality Improvement Report 2009-2010
