Calculus AB Research Articles

Investigating effective teaching practices in advanced placement calculus AB: A qualitative exploration of student recounts

Investigating effective teaching practices in advanced placement calculus AB: A qualitative exploration of student recounts

Stereotype threat, gender and mathematics attainment: A conceptual replication of Stricker & Ward.

Stereotype threat has been proposed as one cause of gender differences in post-compulsory mathematics participation. Danaher and Crandall argued, based on a study conducted by Stricker and Ward, that enquiring about a student’s gender after they had finished a test, rather than before, would reduce stereotype threat and therefore increase the attainment of women students. Making such a change, they argued, could lead to nearly 5000 more women receiving AP Calculus AB credit per year. We conducted a preregistered conceptual replication of Stricker and Ward’s study in the context of the UK Mathematics Trust’s Junior Mathematical Challenge, finding no evidence of this stereotype threat effect. We conclude that the ‘silver bullet’ intervention of relocating demographic questions on test answer sheets is unlikely to provide an effective solution to systemic gender inequalities in mathematics education.

Will We Ever Close the Gender Gap Among Top Mathematics Achievers? Analysis of Recent Trends by Race in Advanced Placement (AP) Exams

Analyzing the test scores of more than 10,000,000 students who participated in the Advanced Placement (AP) math exams from 1997 to 2019, this study examined the direction and magnitude of the trend in gender disparity by race in participation in and top achievement on AP Calculus AB, Calculus BC, and Statistics exams. The results of this study indicated that, in general, females’ representation in all three AP exams increased significantly. Although the findings indicated that the female-to-male ratios (FMRs) in participation in the AP math exams increased significantly from 1997 to 2019 and favored females for all races, the gender disparities among top achievers for all math exams are still substantial. The relationships between the FMRs in participation and top achievement for all AP math exams were also analyzed within races, and the possible impacts of these findings within the context of the underrepresentation of women in science, technology, engineering, and mathematics (STEM) fields were also discussed.

Advanced Placement Scores for Black Male Students from Connecticut, Florida, Maryland, Massachetts, and Texas

Differences in student performance were analyzed for Black males in Connecticut, Florida, Maryland, Massachusetts, and Texas on the Advanced Placement English Language and Composition, Calculus AB, Biology, and United States History examinations from the 2001 through the 2012 exam years. All analyses included in the comparisons of overall examination scores and U.S. History examination scores were statistically significant. Of the 48 individual examination comparisons, 26 yielded evidence of a statistically significant difference among the Black male students from the selected states. Massachusetts was the state with the highest percentages of Black male students who achieved an AP score of 4 or 5. Conversely, Texas was the state with the highest percentages of Black male students who failed to achieve an AP score of 4 or 5. Implications for policy regarding advanced placement testing as an avenue for preparing students for college and recommendations for future research are discussed.

ADVANCED PLACEMENT MATH SCORES FROM 2000 TO 2010: DOES GENDER STILL MATTER?

The relationship between gender and student performance on the Advanced Placement Calculus AB, Calculus BC, and Statistics exams for the spring 2000, 2005, and 2010 exam administrations were analyzed. Using College Board data for all students (ns > 100,000) in the United States for all three exams in each of the three years, statistically significant relationships were yielded between gender and performance on Advanced Placement math exams. In each of the three exams a higher percentage of boys earned a score of 3 or better than the percentage of girls earning scores of 3 or higher. The performance of boys and girls on these three Advanced Placement exams from 2000 to 2010 was relatively unchanged. Implications of the findings are discussed and suggestions for further research are made. Keywords: Advanced Placement, gender, student achievement

DIFFERENCES IN ADVANCED PLACEMENT EXAM RESULTS FOR BLACK STUDENTS ACROSS THREE STATES

Differences in Advanced Placement exam results for Black students in Texas, Georgia, and California were examined. Existing data from the College Board 2010 Report were used to compare overall Advanced Placement exam performance and individual Advanced Placement exam performance in English Language, U.S. History, and Calculus AB. Statistically significant differences were present in the performance on Black students on the overall Advanced Placement exam, as well as the three individual AP exams among the three states. Effect sizes for the statistically significant differences were small to trivial. With Advanced Placement exams being the same across the country, these findings depict differential performance for Black students as a function of the state in which they lived. Keywords: Advanced Placement exams, Black student performance, three state comparisons

Stereotype Threat in Applied Settings Re‐Examined

Stricker & Ward (2004) examined stereotype threat with a national sample of students taking an Advanced Placement (AP) Calculus exam, and a smaller sample taking Computerized Placement Tests (CPT). They inquired about gender either before (traditional) or after the test (which can reduce stereotype threat). They reported no significant effects of question timing. We reanalyze their findings, and argue that their conservative criterion for evidence led them to overlook significant stereotype threat effects with real practical implications. Women benefited substantially on the Calculus test, and on the CPT–Reading when demographics were asked after testing rather than before. This simple, small, and inexpensive change could increase U.S. women receiving AP Calculus AB credit by more than 4,700 every year.

Investigating the Population Sensitivity Assumption of Item Response Theory True-Score Equating Across Two Subgroups of Examinees and Two Test Formats

Dorans and Holland (2000) and von Davier, Holland, and Thayer (2003) introduced measures of the degree to which an observed-score equating function is sensitive to the population on which it is computed. This article extends the findings of Dorans and Holland and of von Davier et al. to item response theory (IRT) true-score equating methods that are commonly used in the nonequivalent-groups anchor test (NEAT) design. Using data from the Advanced Placement Program Calculus AB exam, which contain multiple-choice (MC) and free-response (FR) sections, the authors investigate the population sensitivity of the IRT equating functions computed for the MC section only and for the MC and FR sections together. The degree of population sensitivity is also compared across three equating methods: the IRT true-score equating method and two observed-score equating methods, chained equipercentile and Tucker linear equating.

IRT True-Score Test Equating

This article discusses the assumptions required by the item response theory (IRT) true-score equating method (with Stocking & Lord, 1983; scaling approach), which is commonly used in the nonequivalent groups with an anchor data-collection design. More precisely, this article investigates the assumptions made at each step by the IRT approach to calibrating items and equating tests and discusses the approaches that one might take for checking whether these assumptions are met for a particular data set. We investigated two types of tests: tests that consist of multiple-choice items only and tests that consist of both multiple-choice and free-response items. Real data from the AP® Calculus AB exam are used to illustrate the application of the IRT true-score equating method as well as for the comparisons.

A DIDACTIC APPROACH TO THE USE OF IRT TRUE-SCORE EQUATING

This paper discusses the assumptions required by the item response theory (IRT) true-score equating method (with Stocking & Lord, 1983; scaling approach), which is commonly used in the nonequivalent groups with an anchor data-collection design. More precisely, this paper investigates the assumptions made at each step by the IRT approach to calibrating items and equating tests, and discusses the approaches that one might take for checking whether these assumptions are met for a particular data set. We investigated two types of tests: tests that consist of multiple-choice items only, and tests that consist of both multiple-choice and free-response items. Real data from the AP® Calculus AB exam are used to illustrate the application of the IRT true-score equating method as well as for the comparisons.

Stereotype Threat, Inquiring About Test Takers' Ethnicity and Gender, and Standardized Test Performance1

Steele and Aronson (1995) found that the performance of Black research participants on ability test items portrayed as a problem‐solving task, in laboratory experiments, was affected adversely when they were asked about their ethnicity. This outcome was attributed to stereotype threat: Performance was disrupted by participants' concerns about fulfilling the negative stereotype concerning Black people's intellectual ability. The present field experiments extended that research to other ethnic groups and to males and females taking operational tests. The experiments evaluated the effects of inquiring about ethnicity and gender on the performance of students taking 2 standardized tests—the Advanced Placement Calculus AB Examination, and the Computerized Placement Tests—in actual test administrations. This inquiry did not have any effects on the test performance of Black, female, or other subgroups of students that were both statistically and practically significant.

Using Subpopulation Invariance to Assess Test Score Equity

Score equity assessment (SEA) is introduced, and placed within a fair assessment context that includes differential prediction or fair selection and differential item functioning. The notion of subpopulation invariance of linking functions is central to the assessment of score equity, just as it has been for differential item functioning and differential prediction. Advanced Placement (AP) data are used for illustrative purposes. The use of multiple‐choice and constructed response items in AP provides an opportunity to observe a case where subpopulation invariance of linking functions does not hold (U.S. History), and a case in which it does hold (Calculus AB). The lack of invariance for U.S. History might be attributed to several sources. The role of SEA in assessing the fairness of test assembly processes is discussed.

APPLYING THE ONLINE SCORING NETWORK (OSN) TO ADVANCED PLACEMENT PROGRAM® (AP®) TESTS

ABSTRACTThis project explored the feasibility of using the ETS Online Scoring Network (OSN) to score selected Advanced Placement Program® (AP®) tests. In particular, the quality of scores obtained from traditional large‐scale readings was compared with the quality of scores obtained from OSN scoring. (For the former, readers convene in a central location to evaluate student responses in a paper‐based format; for the latter, they work alone from remote locations to evaluate responses that are transmitted via the Internet.) The study also obtained readers' reactions to OSN training and to OSN capabilities for monitoring reader performance online.The results, based on more than 11,000 test takers who had taken either the AP English Language and Composition exam or the AP Calculus AB exam, revealed little if any difference between scores assigned at traditional central readings and those assigned when readers used OSN. The lack of differences applied to (a) score level and variability, (b) interreader agreement, and (c) passing rates on the two AP exams that were investigated. Study participants did, however, suggest several areas in which improvements could be made to OSN procedures.

MINORITY STUDENT SUCCESS: THE ROLE OF TEACHERS IN ADVANCED PLACEMENT PROGRAM® (AP®) COURSES

ABSTRACTThis project described the characteristics and teaching behaviors of those successfully teaching AP® Calculus AB and AP English Literature and Composition to underrepresented minority students. Its purpose was to assist educators in improving the participation and performance of underrepresented minority students in AP classes. Study results showed successful teachers of minority students are good teachers for all groups. They express a high opinion of students, both majority and minority, and hold them to high standards. They make sure that students understand and can apply the fundamental concepts in the discipline. They also help students and parents understand and feel comfortable about college.

INQUIRING ABOUT EXAMINEES' ETHNICITY AND SEX: EFFECTS ON AP® CALCULUS AB EXAMINATION PERFORMANCE

ABSTRACTSteele and Aronson (1995) found that the performance of African‐American subjects on test items portrayed as a problem‐solving task, in a laboratory experiment, was adversely affected when they were asked about their ethnicity. This outcome was attributed to “stereotype threat”: performance was disrupted by the subjects' concerns about fulfilling the negative stereotype concerning African Americans' intellectual ability. Extending that research, this field experiment evaluated the effects of inquiring about ethnicity and sex on the performance of examinees taking the Advanced Placement (AP) Calculus AB Examination in an actual test administration. With a minor exception, this inquiry had no statistically and practically significant effects on the test performance of African‐American, female, or other subgroups of examinees.

The Advanced Placement Course in Statistics: Increasing Students' Options

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) stresses the need to empower all students and to encourage students to study mathematics throughout their four years in high school. For the past forty years, the Advanced Placement program of the College Board has offered students the opportunity to pursue collegiate-level course while in high school. The offering in mathematics consists of a full-year course in either Calculus AB or Calculus BC. Each Advanced Placement course culminates with an examination, typically three hours in duration, for which students may receive college credit or advanced standing when entering college.

Computer-based advanced placement calculus for gifted students

A computer-based course in Advanced Placement Calculus AB, developed at the Institute for Mathematical Studies in the Social Sciences at Stanford University, was completed by 13 gifted students in grades 7–10 from seven different junior and senior high schools. This article covers the selection procedures for students, the day-to-day progress of the calculus students during the 1990–91 school year, details of the derivation system developed, operational aspects of the hardware and software systems that were used, and analysis of individual differences that appear in the self-placed environment. The 13 students took the Advanced Placement Calculus AB examination in May 1991. All students passed. Six scored 5 (the highest grade); Six scored 4, and one scored 3, for an average score of 4.4.

EXPERIMENTAL STUDY OF THE EFFECTS OF CALCULATOR USE ON THE ADVANCED PLACEMENT CALCULUS EXAMINATIONS1

ABSTRACTAdvanced Placement Calculus examinations were administered to nearly 7,000 students from more than 400 high schools in order to determine the impact of calculator use. Both the Calculus AB and Calculus BC experimental examinations had two sections. Section I items were designed so that a calculator was not needed to arrive at the correct solution. Approximately half of the students were permitted to use calculators on this section. Section II items were developed to require a calculator to arrive at the correct solution. All students were permitted calculator use for these items. Analyses indicated that calculator use resulted in a substantial improvement in performance for 3 of the 40 Section I items. Those with calculators capable of graphics or the taking of derivatives performed better on both sections of the exams than those with scientific calculators. The internal consistency reliability of the Section I items was higher for students not permitted calculator use. A pattern of negative D‐DIF values for the Section II items indicated that these items were differentially more difficult for females than the Section I items. The D‐DIF value of only one Section I item appeared to be substantially impacted by calculator use. Total test scores were found to be higher for those permitted to use calculators, for males in comparison to females, and for those reporting the use of advanced calculators in comparison to those reporting the use of scientific calculators.

The Advanced Placement Program in Mathematics—Update 1975

The recently released 1973 Calculus AB and BC examinations offer some challenging problems for your students.

The 1969 Advanced Placement Examinations In Mathematics-Complete And “Unexpurgated”

Under the direction of the College Entrance Examination Board the Ad-vanced Placement Program in Mathemat-ics has evolved in content as steadily as it has grown in size. (See table 1.) Course descriptions are under constant review and are revised biennially by the Com-mittee of Examiners to keep pace with trends in school and college mathematics instruction. This gradual evolution can be detected by comparing successive edi-tions of the course descriptions from 1955 to the present. The most significant change in content occurred in 1968-69 when a choice of two courses and two examinations (Calculus AB and Calculus BC) was instituted [1].*