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Assessment Report for Exam - College Algebra | MATH 1340, Exams of Algebra

Material Type: Exam; Class: College Algebra; Subject: MATH; University: University of Texas - Pan American; Term: Fall 2003;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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The University of Texas – Pan American
Mathematics Assessment Report
October 21, 2003
Introduction
The purpose of this document is to report on the results of an assessment that was
conducted during the spring of 2003 to determine the degree to which students achieve
desired learning outcomes in mathematics as a result of their completing the University's
core curriculum. In May 2003, an assessment test was designed with questions aligned
with predetermined objectives and administered to students in 18 sections of Math 1340 –
College Algebra. Math 1340 is the predominant course used by students at UTPA to
satisfy the mathematics requirement of the core curriculum: approximately 68% of all
students take Math 1340 as their core class.
Described in this report is a brief overview of the objectives for mathematics in the
core curriculum, the method in which these objectives were assessed in the spring 2003
semester, a summary of the assessment results, and conclusions and recommendations
based on these results. Results of the assessment will be used to improve student learning
by providing feedback to departments and programs on campus to enable them to identify
ways in which they may improve pedagogical practices and curriculum.
Exemplary Objectives
According to the Texas Higher Education Coordinating Board, the purpose of the
mathematics component of the core curriculum is to develop a quantitatively literate
college graduate (THECB Core Curriculum: Assumptions and Defining Characteristics,
April 1998.) Every graduate from UTPA should be able to apply basic mathematical
tools to solve real-world problems and make well-informed decisions aided by
mathematical analysis. The THECB goes on to list the following seven Exemplary
Objectives in support of this goal:
1. To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical
methods to modeling and solving real-world situations.
2. To represent and evaluate basic mathematical information verbally,
numerically, graphically, and symbolically.
3. To expand mathematical reasoning skills and formal logic to develop
convincing mathematical arguments.
4. To use appropriate technology to enhance mathematical thinking and
understanding and to solve mathematical problems and judge the
reasonableness of the results.
5. To interpret mathematical models such as formulas, graphs, tables, and
schematics, and draw inferences from them.
6. To recognize the limitations of mathematical and statistical models.
7. To develop the view that mathematics is an evolving discipline, interrelated
with human culture, and understand its connections to other disciplines.
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The University of Texas – Pan American

Mathematics Assessment Report

October 21, 2003

Introduction

The purpose of this document is to report on the results of an assessment that was conducted during the spring of 2003 to determine the degree to which students achieve desired learning outcomes in mathematics as a result of their completing the University's core curriculum. In May 2003, an assessment test was designed with questions aligned with predetermined objectives and administered to students in 18 sections of Math 1340 – College Algebra. Math 1340 is the predominant course used by students at UTPA to satisfy the mathematics requirement of the core curriculum: approximately 68% of all students take Math 1340 as their core class. Described in this report is a brief overview of the objectives for mathematics in the core curriculum, the method in which these objectives were assessed in the spring 2003 semester, a summary of the assessment results, and conclusions and recommendations based on these results. Results of the assessment will be used to improve student learning by providing feedback to departments and programs on campus to enable them to identify ways in which they may improve pedagogical practices and curriculum.

Exemplary Objectives

According to the Texas Higher Education Coordinating Board, the purpose of the mathematics component of the core curriculum is to develop a quantitatively literate college graduate (THECB Core Curriculum: Assumptions and Defining Characteristics , April 1998.) Every graduate from UTPA should be able to apply basic mathematical tools to solve real-world problems and make well-informed decisions aided by mathematical analysis. The THECB goes on to list the following seven E xemplary Objectives in support of this goal:

  1. To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations.
  2. To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically.
  3. To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.
  4. To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results.
  5. To interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.
  6. To recognize the limitations of mathematical and statistical models.
  7. To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.

The purpose of this assessment is to document the degree to which students achieve these objectives by completing the University’s core curriculum.

Method of Assessment

Overview of the Assessment Plan

The assessment method implemented here was developed in the 2002-2003 academic year with the help of the Task Force on Mathematics and Computer Science in the Core Curriculum, the Department of Mathematics College Algebra Project, the Core Implementation and Assessment Committee, and the Division of Academic Affairs. Under this plan, local tests are composed and administered to students in those classes that meet the University’s core requirement in mathematics. The tests are composed in such a way that each Exemplary Objective is addressed by several test questions using a combination of multiple choice, short answer, and free response problems. The assessment plan describes a phased process in which classes in the College Algebra Project were to be assessed in the spring of 2003. A copy of the plan may be obtained from the Assistant Vice President for Undergraduate Studies.

Sample Population

Assessment of mathematics in the core curriculum for year 2002-2003 is based on the results of a local test administered to students in 18 sections of Math 1340 – College Algebra (sections 01-17, 24). A random sample of 30% of the approximately 500 students was selected for the mathematics assessment based on the last four digits of the students’ student number and course section number. The names of the 148 selected student names were provided by the Research Analyst of the Office of the Provost.

Composition of the Assessment Test

The assessment test was developed by members of the College Algebra Project. The 20 item test was composed in such a way that each Exemplary Objective was addressed by several test questions using a combination of multiple choice, short answer, and free response problems. A copy of the test items can be found in Appendix A. Prior to the spring 2003 semester, instructors of these sections included in their syllabus the stipulation that students may use their score on this test to replace one other test score from their class. Along with the test, scoring rubrics (see Appendix B) for free-response questions were designed to conform to a scale of

(0) Unacceptable, (1) Below Satisfactory, (2) Meets Expectations, (3) Exceeds Expectations.

The rubric for multiple choice problems was set to be

(0) Unacceptable (incorrect response), (2) Meets Expectations (correct response).

  1. Understand the connection with mathematics to other disciplines. 57.1%

Conclusions and Recommendations

Conclusions The overall results indicate that students taking Math 1340 through the College Algebra Project have relative strengths in achieving Objectives 1-4, with the number of responses meeting or exceeding expectations ranging from 71.6% to 82.0%. Students, however, are comparatively weak in achieving Objectives 5-7. Some tentative conclusions about the mathematical and quantitative reasoning abilities of these students can be made based on the results of this assessment test. The results reflect both students who passed Math 1340 and those who did not. The students’ best performance was on several test questions aligned with Objective 1 (applying algebraic and higher order thinking) and Objective 3 (developing convincing mathematical arguments). In these questions, student success was predicated on their ability to know and apply basic formulas, algorithms, and algebra techniques. Students did well in representing basic mathematical information graphically and symbolically (Objective 2), but were relatively weak in interpreting and drawing inferences from these representations (Objective 5). Questions pertaining to the use of appropriate technology (Objective 4) centered on the use of a calculator. Two questions required a calculator to obtain meaningful results; in these problems, students identified the need for a calculator and obtained the correct result 70% of the time. Objective 6, the ability to recognize limitations of mathematical models, is admittedly difficult to achieve. In this assessment, questions were composed which required students to check their results to eliminate spurious solutions arising from seemingly convincing mathematical arguments. From the scoring rubric, however, it is not possible to distinguish those students who failed to check the reasonableness of their results from those students who had an incorrect problem solving strategy. Nevertheless, only 43.9% of the responses demonstrated both a correct problem solving strategy and the understanding that the reasonableness of the results must be checked. Finally, the students’ ability to connect mathematics with other disciplines (Objective

  1. was tested through two free response application problems. Compared with other areas, the students’ performance was relatively weak on these problems as well with approximately 57% of the responses meeting or exceeding expectations.

Department of Mathematics Recommendations The following recommendations are based on input from the Department of Mathematics Curriculum Committee. Recommendations regarding program improvement include:

  • Review the syllabus and book used in Math 1340 in order to strengthen the alignment between learning outcomes of the course and the objectives of the mathematics component of the core curriculum. This may include, for example,

identifying topics from that need to be emphasized more or to be presented in different ways.

  • Developing learning and teaching strategies that will improve the students’ abilities to meet Objectives 5-7 regarding interpreting and drawing inferences from mathematical models, recognizing limitations of mathematical models, and understanding the connection between mathematics and other disciplines.
  • Meet periodically with all instructors in the College Algebra Project to review the objectives and discuss learning and teaching strategies. This activity will be particularly important as the assessment expands to include courses taught by one-year instructors, part-time teachers, and teaching assistants. Recommendations regarding the assessment process and its long-term implementation include:
  • Separate those students from the data analysis who ultimately fail the core course since these students did not complete the core curriculum requirement.
  • Obtain assessment tests and final exams from other institutions in courses used to satisfy their core curriculum requirement in mathematics. Reviewing other tests may facilitate the improvement of the local assessment test, as well as help develop a test bank of questions for future assessments.
  • Review and revise, as appropriate, the student learning outcomes developed in the Mathematics Assessment Plan (Core Implementation and Assessment Committee, May 2003) for the purpose of improving their alignment with the Exemplary Objectives.
  • Create a standing committee on Assessment in the Department of Mathematics in order to facilitate long-term implementation and planning of assessment activities. The duties of the committee should include oversight of the development, administration, and evaluation of the assessment test. This entails working closely with the appropriate departmental subcommittees which oversee areas such as College Algebra, Statistics, and Business Mathematics.

Core Implementation and Assessment Committee Recommendations

The following recommendations are based on input from the University’s Core Implementation and Assessment Committee.

  • Include a formal measure of inter-rater reliability as part of the calibration session among the assessment test readers
  • Increase the sample size to facilitate additional data analysis.