DOCSLIB.ORG

An Analysis of Grades and Placement in the Transition from Pre-Calculus To

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
An Analysis of Grades and Placement in the Transition from Pre-Calculus To An Analysis of Grades and Placement in the Transition from Pre-Calculus to Calculus at the University of Manitoba by Darja Barr A Thesis submitted to the Faculty of Graduate Studies of The University of Manitoba in partial fulfillment of the requirements of the degree of DOCTOR OF PHILOSOPHY Faculty of Education University of Manitoba Winnipeg Copyright © 2019 by Darja Barr ii Declaration I, Darja Barr, declare this document to be my own unaided work, and where published sources are used, they are acknowledged. ______________________________ Darja Barr iii Abstract Recently, first-year mathematics instructors at universities across North America and around the globe have been noticing a decline in the mathematics skills and preparation of the incoming student body, and these students have been failing out of first-year mathematics courses at alarming rates (Crowther, Thompson & Cullingford, 2007; Hourigan & O’Donaghue, 2007; Kajander & Lovric, 2005; Rylands & Coady, 2009). Though some universities have implemented placement or diagnostic tests to measure the preparedness of their incoming students, many still use high school grades as the only indicator of students’ readiness for university mathematics. However, researchers have found mixed results in terms of the effectiveness of high school grades at predicting success in university mathematics courses (Finnie et. al, 2010; Geiser, 2007; Salim & Al-Zarooni, 2009) due to factors such as the miss-alignment of teaching methods, students’ entering knowledge, and skills, the curricula in high school and university, and high school grade inflation. This dissertation includes two studies. The first study analyzed the relationship between grade 12 Pre-Calculus grades and first-year university Calculus grades at a large Canadian university over the period from 2001-2015. The results show that the disconnect between high school grades in mathematics and university grades in mathematics has been growing over time, and is significant for students who are not performing well in university Calculus. Recommendations include the implementation of placement examination, and increased communication and collaboration between K-12 and university mathematics educators and administrators. iv The second study looked at the effectiveness of the ALEKS placement test at predicting students’ readiness for first-year Calculus. Results show that including this mathematics placement test along with high school grades and some demographic variables can help predict the students’ success in Calculus more validly. Recommendations include the implementation of the ALEKS placement test for entry into university Calculus courses, as well as some additional measures that could aid in placing underrepresented minority students more appropriately. Furthermore, the sharing of information between university and high school mathematics teachers is recommended. v Acknowledgements I would like to acknowledge the support of my Advisor, Dr. Robert Renaud, and committee members, Dr. Xikui Wang and Dr. Rodney Clifton. Their time, effort, and encouragement were critical to the completion of this work. I would also like to thank my colleagues Dr. Anna Stokke, Dr. Robert Craigen, and once again Dr. Rodney Clifton, who stood by my side through the difficult times in this doctoral process. Without their support, this work would never have come to fruition. In addition, I thank the teachers and administrators of the Winnipeg School Division, who not only listened to these research results, but also because they have been working for the past two years to implement the recommendations based on this research. This has truly been one of the most valuable parts of the doctoral process. Finally, I thank the never wavering support and encouragement of my parents and friends. Most of all my number one teammate, Myles Barr. Thank you for the many hours of help with reading, writing, and emotional support through the past years! vi Table of Contents Declaration ...................................................................................................................... ii Abstract.......................................................................................................................... iii Acknowledgements ......................................................................................................... v List of Tables .................................................................................................................. x List of Figures ................................................................................................................ xi Chapter 1: Introduction ................................................................................................... 1 Challenges in University Education ............................................................................. 3 Mathematics Achievement in University ..................................................................... 8 The Two Studies ....................................................................................................... 10 Study 1: An Analysis of the Relationship Between Pre-Calculus and Calculus Grades ................................................................................................................... 11 Study 2: Analyzing the Effectiveness of the ALEKS Mathematics Placement Test 12 Significance of the Studies ........................................................................................ 13 Contributions to the Field ...................................................................................... 13 Contributions to University Instructors and Students ............................................. 14 Limitations of the Studies .......................................................................................... 16 Overview of the Dissertation ..................................................................................... 18 References ................................................................................................................. 20 Connecting Section ....................................................................................................... 25 Chapter 2: An Analysis of the Relationship Between Pre-Calculus and Calculus Grades26 Predictors of University Achievement ....................................................................... 28 Grade Inflation in High School .............................................................................. 30 vii The “Mathematics Problem” ..................................................................................... 32 Predictors of University Mathematics Achievement .................................................. 38 Grade Inflation in Mathematics Courses ................................................................ 39 Factors Associated with Predictability ................................................................... 42 Pre-Calculus and Calculus in the Manitoba Context .................................................. 45 The Research Questions ............................................................................................ 46 Method ...................................................................................................................... 47 The Students .......................................................................................................... 47 The Courses........................................................................................................... 50 Variables ............................................................................................................... 51 Results ...................................................................................................................... 51 Research Question 1 .............................................................................................. 51 Research Question 2 .............................................................................................. 59 Research Question 3 .............................................................................................. 61 Research Question 4 .............................................................................................. 69 Discussion ................................................................................................................. 71 Limitations ............................................................................................................ 75 Conclusion ................................................................................................................ 76 References ................................................................................................................. 78 Connecting Section ....................................................................................................... 84 Chapter 3: Analyzing the Effectiveness of the ALEKS Mathematics Placement Test..... 85 Why Use Mathematics Placement Testing? ............................................................... 87 What is Mathematics Placement Testing? .................................................................. 89 viii Institutional Tests .................................................................................................. 92 ACCUPLACER .................................................................................................... 93 COMPASS ...........................................................................................................
Load more

Recommended publications
  • The Long-Term Consequences of Teacher Discretion in Grading of High-Stakes Tests∗
    The Long-term Consequences of Teacher Discretion in Grading of High-stakes Tests∗ Rebecca Diamond† Petra Persson‡ This Draft: October 2, 2017 First Draft: February 28, 2016 Abstract We examine the long-term consequences of teacher discretion in grading of high- stakes tests. Bunching in Swedish math test score distributions reveal that teachers inflate students who have “a bad test day,” but do not to discriminate based on im- migrant status or gender. By developing a new estimator, we show that receiving a higher grade leads to far-reaching educational and earnings benefits. Because grades do not directly raise human capital, these results emphasize that grades can signal to students and teachers within the educational system, and suggest important dynamic complementarities between students’ effort and their perception of their own ability. ∗A previous version of this paper was circulated under the title “The Long-term Consequences of Grade Inflation." We are grateful to Raj Chetty, John Friedman, Matt Gentzkow, Caroline Hoxby, Guido Imbens, Eddie Lazear, Paul Oyer, Luigi Pistaferri, Kathryn Shaw, Alan Sorensen, Chris Taber, and seminar and conference participants at Boston College, Brown, Cornell, Gothenburg, Houston, Michigan, the Minneapo- lis Fed, NYU, Oslo, Santa Clara, Stanford, UC Berkeley, UC Davis, UC San Diego, UC Santa Cruz, SIEPR, Stockholm, the Swedish Institute for Social Research, Uppsala, Wisconsin, Yale, the 2016 Applied Microe- conomics Jamboree at Duke, the 2015 All California Labor Conference at UCLA, the 2016 Utah Winter Business Economics Conference, and the 2015 Western Economic Association International for helpful com- ments. We are especially grateful to Bjorn Ockert, Jonas Vlachos, and Olof Aslund.
    [Show full text]
  • Degraded Currency: the Problem of Grade Inflation
    Degraded Currency: THE PROBLEM OF GRADE INFLATION American Council of Trustees and Alumni The American Council of Trustees and Alumni (ACTA) is a 501(c)(3) nonprofit educational organization committed to academic freedom, excellence, and accountability. Founded by Lynne Cheney and former Colorado Governor Richard Lamm in 1995, ACTA has members from over 400 colleges and universities. Its quarterly publication, Inside Academe, goes to over 12,000 readers, including 3,500+ college and university trustees. Degraded Currency: THE PROBLEM OF GRADE INFLATION American Council of Trustees and Alumni “Students tend to select courses with teachers who grade leniently, often learning less along the way. Uneven grading practices allow students to manipulate their grade point averages and honors status by selecting certain courses, and discourage them from taking courses that would benefit them. By rewarding mediocrity, excel- lence is discouraged.” – VALEN E. JOHNSON, PROFESSOR OF STATISTICS DUKE UNIVERSITY By George C. Leef October 2003 Degraded Currency: The Problem of Grade Inflation People are quite familiar with the problem of monetary inflation. As prices rise higher and higher, the value of the dollar shrinks. The problem of grade inflation is similar: as student grade averages rise, the value to a student of earning a high grade average shrinks. Having an A average when only 10% of the student body has an A average is indicative of strong academic achievement, but having an A average when half of the student body has 1 one is far less so. If grades are heavily clustered at the top, it is not possible to know which students have done outstanding work and which are just average.
    [Show full text]
  • High School Profile 2015-2016
    CEEB Code 052971 High School Profile 2015-2016 Ortega Campus Ashbury Campus Sausalito Campus Upper School San Francisco Lower School Marin Lower School Grades 6-12 PreS – Grade 5 PreS– Grade 5 1201 Ortega Avenue 755 Ashbury Street 610 Coloma San Francisco, CA 94122 San Francisco, CA 94117 Sausalito CA 94965 phone: 415-661-5232 x1100 phone: 415-661-5232 x2100 phone: 415-661-5232 x3100 fax: 415-564-6677 fax: 415-661-0945 fax: 415-924-2849 Management Headmaster Director of College Counseling Counseling Assistant Direction Proviseur Directrice d’Orientation Assistante d’Orientation Philippe Legendre Natalie Bitton Andrea Feeney Ext. 1704 Ext. 1751 Ext. 1201 [email protected] [email protected] [email protected] The Lycée Français de San Francisco (LFSF), established in 1967, is the only Course Load: During the final three years of secondary education, LFSF exclusively French immersion school in the San Francisco Bay Area. We students often carry a course load of between 37-40 hours per week, with a welcome students in Pre-School to Grade 12. Our program is designed to corresponding amount of homework. LFSF is a commuter school, and so provide students with a structured, well-assimilated body of general students do often travel an hour or more to and from school. As a result, knowledge while encouraging the development of analytical and critical students often seek extracurricular opportunities outside of school which thinking skills. Our unique curriculum fosters autonomy, initiative, self-esteem impacts the number of teams, activities and clubs that LFSF offers on site. and the respect of others through cooperation and responsibility.
    [Show full text]
  • The Declining Work Ethic of the American Engineering Student S
    The Declining Work Ethic of the American Engineering Student S. Michael Wells 1 Abstract – The work ethic of our American engineering freshmen has been declining consistently for decades. The Cooperative Institutional Research Program (CIRP) survey and other sources document the many negative trends in our students—trends that set habits and continue into the students’ college experience. The survey shows that High School grade inflation is steadily on the rise and students are studying less. Adding to the problem is the practice of social promotion in our public school systems, and the unconstructive interference from parents. Because our nation’s high schools are requiring less of students, incoming engineering freshmen are ill prepared to perform well at our universities, working to the detriment of the students and putting the future of our nation at risk. Keywords: declining, work, ethic, grade, inflation EVIDENCE THERE IS A PROBLEM Many of us who have been engineering educators for many years have observed the decline in the quality and attitude of students. The Cooperative Institutional Research Program (CIRP) survey, generally regarded as the most authoritative source on the state of the American college student, has been gathering information on college freshmen since the 1960s. One of the findings is that from 1987 to 2003, the percent of students saying they had studied six or more hours per week in high school fell from 47% to 34.9% [1]. That trend is even more disturbing when it is considered that in 2003, 44.1% of the students stated they had had an “A” average in high school—up from 17.6% in 1968.
    [Show full text]
  • International High School of the French American International
    International High School of the French American International School School Profile 2018-2019 CEEB Code: 052943 School website: www.internationalsf.org College Counselors: Ashley Rochman [email protected] (415) 558-2073 Alex Trempus [email protected] (415) 558-2072 Head of School: Melinda Bihn [email protected] High School Principal: Joel Cohen [email protected] __________________________________________________________________________________________________ Our School The International High School of the French American International School (often referred to as International, IHS, or FAIS) was established in 1962 as an independent, coeducational prekindergarten-12thgrade school located in the heart of urban San Francisco. A belief in the value of diversity is a keystone of our mission statement, and we consequently serve a richly diverse student population from San Francisco and the wider Bay Area, including international students. Enrollment: 382 students enrolled in the high school 93 students in the Class of 2019 69 students in the International Baccalaureate program, 24 in the French Baccalaureate program 1100 students enrolled school wide 98 percent of the Class of 2018 enrolled in a four-year college Accreditation: Western Association of Schools and Colleges (WASC), the French Ministry of Education, the California Association of Independent Schools, the International Baccalaureate Organization, and the Council of International Schools. Our Programs and Faculty Our school offers the full International Baccalaureate diploma program, including the bilingual option, as well as the French Baccalaureate S (Science and Math emphasis), ES (Economics and Social Sciences emphasis), and the International Option (OIB). Please refer to the charts below for an overview of these programs. Our school has been offering both the IB and the French Bac since its inception, and we are the first school west of the Mississippi River to offer the IB Diploma program.
    [Show full text]
  • University of Nevada, Reno Relationships Among Nevada-FIT
    University of Nevada, Reno Relationships among Nevada-FIT Camps, High School Grade Point Average, and Gender A thesis submitted in partial fulfillment of the requirements of the degree of Masters of Arts in Educational Leadership by Priya Ahlawat Dr Janet Usinger, Thesis Advisor August 2016 Copyright by Priya Ahlawat 2016 All Rights Reserved THE GRADUATE SCHOOL We recommend that the thesis prepared under our supervision by PRIYA AHLAWAT Entitled Relationships Among Nevada-FIT Camps, High School Grade Point Average, And Gender be accepted in partial fulfillment of the requirements for the degree of MASTER OF ARTS Janet Usinger, Ph.D., Advisor Patricia Miltenberger, Ed.D., Committee Member Eleni Oikonomidoy, Ph.D., Graduate School Representative David W. Zeh, Ph.D., Dean, Graduate School August, 2016 i Abstract College readiness, the level of preparation students need to enroll and succeed without remediation in credit bearing entry level coursework at a two or four-year institution, increasingly is an expectation for all high school students, not just students who have been traditionally considered college-bound. Numerous studies have documented the importance of high school grade point average (HSGPA) in predicting college readiness. However, even with the best of high school preparation, the transition to postsecondary education can be difficult. To facilitate the transition from high school to university level study, the University of Nevada, Reno has developed a Nevada-Freshman Intensive Transition (Nevada-FIT) program. A robust evaluation of the program is being conducted; however, a question not addressed in the evaluation is the academic characteristics of the incoming students. Using existing institutional data of 404 students from the Fall of 2014 Nevada-FIT camp, a quantitative, descriptive analysis with a post-facto design using the one way ANOVA, Kruskal Wallis H test, and an independent t test was conducted.
    [Show full text]
  • Applying Grade Inflation Adjustment Mechanism in an Ethiopian University: Differences in Nominal and Real Grades
    Technium Vol. 2, Issue 7 pp.77-93 (2020) ISSN: 2668-778X www.techniumscience.com Applying grade inflation adjustment mechanism in an Ethiopian university: Differences in nominal and real grades Lemecha Geleto Wariyo College of Education, Addis Ababa University, Sidist Kilo, Ethiopia Email: [email protected] Roman Alemu Kelbago College of Social Sciences and Humanities, Wachemo University, Hossaina, Ethiopia Email: [email protected] Abstract-Grade inflation is a recognized problem in universities around the world. The factors underlying grade inflation are also discussed by studies. The objective of this study was: firstly, to observe the degree of grade inflation by analyzing the difference between nominal grades and real grades of students across departments. Secondly, the study analyzes the relationship between aptitude test scores and college GPA. In order to achieve these objectives, the first semester grades of all Wachemo university first batch third-year students (total 435 students: male 287 female 148) were collected from the registrar and the nominal and real grades were calculated. The Grieves method of real grade analysis formula was used to analyze the real grades. The findings of this study revealed that although there was no severity of grade inflation in the semester, 4 departments out of 12 departments registered inflated grades. The correlation between nominal and real grades of students is positive and strong indicating that real grades are grade-inflation adjusted nominal grades. There was a zero correlation between aptitude test scores and the college GPA in this study. The similarity of grading system, and the similarity and the harmonization of the courses make the Grieve’s method of grade inflation adjustment mechanism to be applied in Ethiopian universities.
    [Show full text]
  • On Resolving Unfair Grading Practices by Reforming Swedish Upper Secondary School
    Stockholm School of Economics Department of Economics 659 Degree project in Economics Spring 2016 A for E↵ort: On Resolving Unfair Grading Practices by Reforming Swedish Upper Secondary School David Berselius (23159) and Richard Sunneg˚ardh(22971) Abstract: In 2011, upper secondary school in Sweden was reformed with the aim of reducing established di↵erences in grading standards by imposing redesigned curric- ula and a new grading scale. This paper investigates the e↵ect of this reform on grade inflation and evaluates its e↵ectiveness in promoting fairness in grading between in- dependent and public schools. We define grade inflation as the net di↵erence between final course grades and national test scores. Using 2011–2014 panel data, we examine how the reform a↵ects absolute levels of grade inflation and di↵erences between school types. We perform the analyses both on subjects aggregately and separately, by re- gressing with school-specific fixed-e↵ects. Our results indicate a significant increase in net grade inflation in total and in two out of three subjects. Furthermore, we find that the tendency of independent schools inflating grades more than public has de- creased overall, but that di↵erences have shifted di↵erently across subjects. Definitive conclusions of the e↵ectiveness of the reform are therefore difficult to make, but this paper shows that the it has had an e↵ect on grade inflation and grading practices. Keywords: grade inflation, grading standards, upper secondary school, criterion- referenced grading, reform JEL Classification: I20, I24, I28 Supervisor: Federica Romei Date submitted: May 15, 2016 Date examined: May 31, 2016 Discussants: Elin Bostr¨om, Elis Orjes¨ Examiner: Orjan¨ Sj¨oberg Acknowledgements We would like to extend our sincerest gratitude to our supervisor Assistant professor Federica Romei for guidance and constructive feedback.
    [Show full text]
  • Grade Inflation in High Schools (2005–2016 
    Grade Inflation in High Schools (2005–2016) Grade Inflation in High Schools (2005–2016) By Seth Gershenson Foreword and Executive Summary by Amber M. Northern and Michael J. Petrilli September 2018 The Thomas B. Fordham Institute promotes educational excellence for every child in America via quality research, analysis, and commentary, as well as advocacy and exemplary charter school authorizing in Ohio. It is affiliated with the Thomas B. Fordham Foundation, and this publication is a joint project of the Foundation and the Institute. For further information, please visit our website at www.edexcellence.net. The Institute is neither connected with nor sponsored by Fordham University. 2 Contents Foreword & Executive Summary 4 Main Report I. Introduction 8 II. Background 10 III. Methods 12 IV. Results 15 V. Implications 23 Appendices A. How This Study Improves Upon Earlier Efforts 26 B. Descriptive Statistics and Model Fit 27 Endnotes 31 3 Grade Inflation in High Schools (2005–2016) Foreword & Executive Summary By Amber M. Northern and Michael J. Petrilli Many of us, if we’re lucky, can fondly recall a time in elementary school when our parents proudly posted one of our A papers on the refrigerator door. Maybe it was a spelling test or set of multiplication problems—no matter. What mattered, though, was the outstanding achievement that mom, dad, and kid believed was embodied in that A, and the pride and satisfaction that we felt in seeing it every time we opened the fridge for a sandwich. Back then, we didn’t question whether that A was actually earned. We assumed that we had mastered whatever was being graded and our hard work had paid off.
    [Show full text]
  • What Is Wrong with Grade Inflation (If Anything)?
    What is Wrong with Grade Inflation (If Anything)? The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Finefter-Rosenbluh, Ilana, and Meira Levinson. 2015. "What is Wrong with Grade Inflation (If Anything)?" Philosophical Inquiry in Education 23, no. 1 (2015): 3-21. Published Version http://journals.sfu.ca/pie/index.php/pie/article/view/894 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:32228641 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Philosophical Inquiry in Education, Volume 23 (2015), No. 1, pp. 3-21 What Is Wrong With Grade Inflation (if Anything)? ILANA FINEFTER-ROSENBLUH and MEIRA LEVINSON1 Harvard Graduate School of Education Abstract: Grade inflation is a global phenomenon that has garnered widespread condemnation among educators, researchers, and the public. Yet, few have deliberated over the ethics of grading, let alone the ethics of grade inflation. The purpose of this paper is to map out and examine the ethics of grade inflation. By way of beginning, we clarify why grade inflation is a problem of practical ethics embedded in contemporary social practice. Then, we illuminate three different aspects of grade inflation—longitudinal, compressed, and comparative—and explore the ethical dilemmas that each one raises. We demonstrate how these three aspects may be seen as corresponding to three different victims of grade inflation—individuals, institutions, and society—and hence also to three potential agents of harm—teachers, schools, and educational systems.
    [Show full text]
  • Grade Inflation and University Admissions in Ontario: Separating Fact from Perception
    The Canadian Journal of Higher Education, Vol. XXV-3, 1995 La revue canadienne d'enseignement supérieur, Vol. XXV-3, 1995 Grade Inflation and University Admissions in Ontario: Separating Fact from Perception FRANÇOIS R. CASAS* & DIANE E. MEAGHAN* Abstract It is widely believed that high schools across Ontario have inflated grades in an attempt to help students secure admission to one of the province's univer- sities. Universities, in turn, have raised their entrance requirements to allocate available spaces among an expanding pool of applicants. The intensified com- petition for higher marks has put considerable pressure on students and teach- ers, leading to the emergence of a number of grade-enhancing practices which potentially distort the admission process at postsecondary institutions. This paper analyzes university admission data for 1983-1993 and concludes that (a) there has been only a moderate increase in entering marks across the system, (b) it is necessary to distinguish inflationary mark changes from changes reflecting demographic and budgetary factors such as the increase in the pool of applicants and in the available spaces, and (c) different trends in entering marks for various programs are largely the result of demographic factors. It is also shown that while increases in entering marks across the university system have been modest, entering marks at individual institutions have risen more sharply, a paradox explained by the redistribution of the first-year registrants among universities. * University of Toronto t Seneca College The authors gratefully acknowledge the helpful comments received from the referees and the assistance provided by Dr. D.W. Lang, Vice-Provost and Assistant Vice- President at the University of Toronto.
    [Show full text]
  • Fauw Forum Page University of Waterloo
    FAUW FORUM PAGE UNIVERSITY OF WATERLOO NUMBER 111 FAUW Forum NOV/DEC 2001 GRADE INFLATION AT UNIVERSITIES Harvard under fire; U of Windsor study shows grade inflation in Ontario universities As reported in the National Post (22 November 2001), marks. In order to provide some history, two articles Harvard University has once again come under criticism from the Boston Globe are reprinted in this issue of the for inflating students' grades. This time the criticism Forum: (a) the 23 October 2001 article on the decision by comes from within – in a report issued by the Education Harvard's administration to investigate grading policies Policy Committee of Harvard's Faculty of Arts and Sci- (Page 10) and (b) the first (7 October 2001) of the origi- ence. The internal review of grading procedures was nal two-part series that investigated grade inflation at prompted by a Boston Globe study revealing that virtu- Harvard (Page 11). ally all Harvard students are awarded As and Bs, with 91% of students graduating with "honours." Only at Harvard, you ask? Paul Anglin and Ronald Meng of the Department of Eco- According to the Harvard report, some professors feel nomics, University of Windsor, have found that pressure to conform to their peers' grading practices and "significant grade inflation" has taken place in arts and are concerned that they will be singled out as "tough science programmes at seven Ontario universities. Their graders" if they give low marks. Others feel that most thought-provoking study, published last year in Canadian students are "above average" and likely deserve the high Public Policy, is reprinted in this issue (Page 18).
    [Show full text]