Trends in Teaching Advanced Placement Statistics: Results from a National Survey

Abstract

This study provides a glimpse into the professional learning, beliefs, and practices of high school teachers of Advanced Placement (AP) Statistics. Data are from a survey of 445 AP Statistics teachers in late 2018. Results indicate many AP Statistics teachers have taken several statistics courses and engage in professional development related to statistics sponsored by the College Board (summer institutes, exam readings, and online community). They generally do not engage with resources developed by the American Statistical Association and the statistics education community. While AP statistics teachers structure class time with student–student interaction and use student-centered activities, they generally do not use statistics-specific technology tools and rarely engage students with datasets larger than 100 cases or with multiple variables. Teachers’ beliefs about teaching statistics do not always reflect their teaching practices. Personal time to improve, time with students (especially those on a blocked semester schedule), structure of curriculum and exam schedule, and lack of access to technology often prevent teachers from making changes to their practices. Findings call for targeted efforts to reach high school statistics teachers, engage them more in the statistics education community, and encourage curriculum and instructional approaches that more closely align with recommendations and trends in college-level introductory statistics.

KEYWORDS:

• AP Statistics
• High school
• Mathematics teacher
• Teaching practices
• Teacher Beliefs
• Technology

1 Introduction

Advanced Placement (AP) Statistics has been one of the fastest growing courses offered by the College Board over the past 20 years. The AP Statistics course offers high school students an opportunity to learn introductory statistics and potentially earn college credit for the course by earning a certain score on the final course exam. First offered in 1996–97, the course has grown to 219,323 taking the exam in 2019, with a drop to 187,741 in 2020 during the pandemic (College Board 2021). Teachers of AP Statistics are typically educated and licensed as high school mathematics teachers and the AP Statistics course is only one of the many courses that they teach. While lots of research effort has focused on college-level introductory statistics courses with regard to understanding students’ engagement and learning (e.g., Lunsford, Poplin, and Pederson 2018; Lawton and Taylor 2020) and teachers’ practices (e.g., Zieffler, Park, Garfield, delMas, and Bjornsdottir 2012; Justice, Zieffler, and Garfield 2017), we know very little about teaching and learning in the context of AP Statistics. Our purpose was to do a large-scale survey of AP Statistics teachers that could provide insight into the current state of teachers’ beliefs and practices related to content in AP Statistics (e.g., teaching strategies, tools used), and ways that AP Statistics teachers engage in professional development to develop their expertise in teaching statistics. These results can inform future research as well as needed areas for professional development efforts.

1.1 Confidence and Knowledge for Teaching AP Statistics

We know that many preservice secondary mathematics teachers do not feel very confident in their abilities to teach many statistics concepts (Lovett and Lee 2017) and point to their experiences as learners in teacher preparation programs as lacking in developing their statistics knowledge and understanding of how to teach it. A recent National Survey of Science and Mathematics Education (Banilower et al. 2018) indicates that practicing high school mathematics teachers do not feel prepared to teach topics in statistics and probability. In fact, only 31% of secondary math teachers report feeling very well prepared, compared to 74–89% of them feeling very well prepared for teaching topics such as measurement, functions, algebraic thinking, and number systems and operations (Malzahn 2020).

Lovett and Lee (2018) also reported that preservice secondary mathematics teachers struggle with having a conceptual understanding of many statistics concepts in the high school curriculum, especially inference topics included in AP Statistics. With an assessment specifically designed to assess AP Statistics teachers’ knowledge for teaching statistics, Haines (2014) established that AP Statistics teachers struggle with concepts related to statistical inference, as well as topics related to exploring data from the AP Statistics curriculum. Related to pedagogy, Haines found that AP Statistics teachers have difficulty in recognizing students’ errors and misconceptions, adjusting curriculum, instruction and assessment strategies, as well as understanding student learning, especially in exploring data and statistical inference.

In a recent study of classroom instruction, Harrison (2020) found that secondary statistics teachers’ beliefs about teaching, about learning, about statistics, and about technology all impacted their instructional decisions. Contextual factors often made it difficult, however, for many teachers to put beliefs into practice. In particular, beliefs about how students best learn and about how technology can support students’ learning were often difficult to put into practice due to factors including large class sizes, a lack of physical space, limited planning and instructional time, limited access to instructional materials and to technology, and the presence of external assessments such as the AP Statistics Exam.

1.2 AP Statistics Teachers’ Professional Learning

A decade ago, Franklin et al. (2011) noted that although “the number of students taking AP Statistics and the number of schools offering the course has continued to increase, the number of capable teachers has not kept pace” (p. 180). The College Board offers summer institutes for new AP Statistics teachers and hosts a very active discussion community. The ASA has led efforts to reach many AP Statistics teachers through webinars, Meeting-within-a-Meeting workshops held at the Joint Statistics Meetings, and the Beyond AP Statistics workshop series for experienced AP Statistics teachers (see https://www.amstat.org/ASA/Education/K-12-Educators). Other efforts emerged in the past decade that served local groups of AP Statistics teachers, such as supports provided in the Philadelphia Area Statistics Teacher Association.

Many high school and college statistics teachers have also engaged in professional learning online through efforts such as Massive Open Online Courses (e.g., Lee and Stangl 2017). Another major source of professional learning for AP Statistics teachers (and college statistics faculty) is participating in the “reading” (and scoring) of the open response items on the AP Statistics exam. The structure of this experience and the professional learning benefits of engaging in scoring assessment responses has been chronicled in other sources (e.g., Franklin et al. 2011; Jacobbe, Hartlaub, and Whitaker 2013; Rossman, St. Laurent, and Tabor 2015). Jacobbe et al. (2013) tell us that being part of a community is a large part of the professional development of AP Statistics teachers. Teachers especially feel part of a community when they engage as readers for the AP Statistics exam and use the College Board online discussion community for AP Statistics teachers (Jacobbe et al. 2013; Hedrick 2015; Whitaker 2016).

1.3 Our Research Questions

Given the lack of research specifically about AP Statistics teachers’ beliefs and practices, we aimed at answering the following research questions for a large sample of teachers:

1. What is the preparation of AP Statistics teachers, their involvement in the statistics education community, and their professional development for teaching statistics?

2. What are the beliefs and curricular and instructional practices of AP Statistics teachers?

3. Are there similarities or differences in beliefs, practices, and teachers’ preparation to teach statistics based on teachers’ level of experience as AP Statistics teachers?

2 Methods

In order to describe the current trends in AP Statistics teaching, we used a mixed methods sequential explanatory design (Ivankova, Creswell, and Stick 2006) with a quantitative approach through a survey, followed by a qualitative approach of interviews with volunteer teachers. This paper focuses on sharing major results from the quantitative part of our study.

2.1 Survey Development

The survey was developed and administered in fall 2018. Questions appearing on the survey were inspired by and modified from various sources. Several questions pertaining to teachers’ beliefs and practices were adapted from the Statistics Teaching Inventory for Introductory Statistics (Zieffler et al. 2012) to apply to AP Statistics teaching. Since AP Statistics students can potentially earn college credit, some questions were created based on recommendations for statistics teaching and assessment from the Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report (GAISE College 2016). Resources published by the College Board, including the AP Statistics Course Description (College Board 2010) and the AP Statistics Teacher’s Guide (College Board 2008), were used as a stimulus for other questions, particularly regarding course content and emphasis. Questions were also developed based on the authors’ own experiences with teaching statistics and with working with teachers of statistics in professional development.

To establish face validity and content validity of the survey, an initial version was sent to a group of reviewers for feedback. Reviewers included: three experts in statistics education who are familiar with AP Statistics and have worked with AP Statistics teachers in professional development settings, four current and past AP Statistics teachers, and one undergraduate preservice teacher who had completed AP Statistics as a student. Reviewers were asked to give feedback regarding the structure and format of the survey, the inclusion and ordering of questions, length of the survey, clarity of questions and answer choices, and any additional factors or issues that the survey failed to address. Based on this feedback, questions and answer choices were modified, and three questions were added. The survey was formatted in Qualtrics and administered to five pilot responders, all whom had recent or current experience teaching AP Statistics. Their responses and feedback assisted us in adjusting online formatting and functionality, making minor edits for readability, and establishing time estimates.

2.2 Format and Administration of Survey

Survey questions were designed to align with recommendations from survey methodologists. First, to promote valid and honest responses, the survey was designed so that all responses would remain anonymous (Ong and Weiss 2000). Questions regarding beliefs were closed-ended, with the scale developed to be bipolar (agree/disagree), included levels of intensity (e.g., strongly, somewhat), and included a six-option rating scale with corresponding meaning (e.g., 1 $=$ strongly disagree) (Groves et al. 2009). Questions asking teachers to estimate relative frequencies used qualitative terms (e.g., “about half,” “most”). For ease of use and to promote participants seeing a holistic view of the range of responses available, radio selection boxes were used instead of drop-down menus (Heerwegh and Loosveldt 2002). The online survey was divided into several sections rather than a single long page, and computer logic was used to filter questions that did not apply to certain participants through using built-in logic (Gunn 2002).

The final survey consisted of seven parts and is included in the Appendix. To ensure better validity of the teachers’ responses, we were only interested in having respondents who had taught AP Statistics very recently so that their reporting of beliefs and practices were likely to be reflective of current AP Statistics teachers. Thus, potential participants had to indicate whether they were currently teaching AP Statistics in the 2018–19 school year, or had taught it during 2017–2018. If yes, then they advanced to a page where the study was described and they were asked to provide informed consent to participate. If they agreed to participate, they advanced to the first set of questions in Part 1. If they indicated “no,” they were taken to a page that thanked them for their interest but stated they were not eligible to take the survey.

2.3 Survey Administration and Participant Recruitment

The survey was administered online via Qualtrics for a period of four weeks in November-December 2018. Participants were not required to complete the survey in a single setting; progress could be saved and a participant could return at a later time within the four week period. At the end of the survey, participants had the option of entering their contact information to be included in a raffle for a $30 gift card (20 names drawn), and a separate question about whether they wished to be considered for a follow-up interview. To protect anonymity, the information collection about the raffle and interview was done through links to separate survey forms and was not linked to survey responses. This paper only focuses on results from the survey.

Participants were recruited from a variety of sources and are a convenient and volunteer sample. The College Board reported that in 2018, there were 9372 schools that had at least one student register to take the AP Statistics exam. While the number of teachers is not reported, there is likely about one teacher per school, though some large schools will have several teachers, and very small schools may have so few participants that a single teacher serves several schools through remote participation). Without a complete list of all current AP Statistics teachers in the United States, a variety of recruitment methods were used. A survey invitation was posted in online communities and discussion forums specifically for AP Statistics teachers and AP Statistics Exam Readers. An invitation was sent via listservs of organizations involved in statistics education, asking to be shared with AP Statistics teachers in their local community. Personal statistics education contacts of the research team were asked to distribute an invitation to networks of AP Statistics teachers in their areas. In addition, approximately 1900 emails with invitations were sent directly to high school teachers based on previous contacts via statistics-focused professional developments, lists obtained from state-level education departments, and from internet searches to find public websites of AP Statistics teachers. The research team ensured that invitations were sent to contacts or directly to AP Statistics teachers in all 50 states and the District of Columbia.

2.4 Survey Respondents

A total of 571 respondents accessed the survey and answered the initial eligibility question. Of these, 537 reported they were eligible to participate (i.e., either currently teaching AP Statistics or taught during the previous year). Of those that were eligible, 493 consented to participate in the study. Out of those 493 participants, 384 reached the end of the survey. Another 61 participants responded to some items, but did not reach the end. The remaining 48 participants did not respond to any survey items after consenting. Thus, the number of respondents varied on items from 445 to 371 due to attrition and skipping items.

2.5 Data Analysis

All open-ended survey questions were examined for nonsensical responses (e.g., 2624 years of teaching experience). These responses were either deleted or recoded when an appropriate intended response could be inferred. If a large number of a participant’s responses were nonsensical, then the survey response in its entirety was deleted (four participants removed). Some responses to closed-ended questions with open-ended options (e.g., “Other: [Please describe]:”) were recoded to closed-ended responses when applicable (e.g., “I will have my masters this next spring in math. Otherwise, it is bachelor’s” was recoded to bachelor’s degree).

For quantitative items, we examined distributions and computed descriptive statistics, including means and standard deviations. For multiple-choice items, including ordinal and rating scale items, the percentage of participants giving each response was computed. Because we were interested in how a teacher’s level of experience in teaching AP Statistics may be related to their professional learning, beliefs, and practices, we disaggregated the data based on teachers’ experience in teaching AP Statistics. To subset these responses into groups, we used groupings often used in reporting trends in education based on years of experience (fewer than 3, 3–9 years, 10–20 years, and more than 20 years) in reports of the National Center of Educational Statistics (e.g., McFarland et al. 2019). Rather than separate the data solely on years of experience as a mathematics teacher in general, we specifically used their response to question 7.2 (see Appendix) where they estimated the number of times they have taught a section of AP Statistics. Thus, for our analysis of many items, we disaggregated results by experience teaching AP Statistics: 0–2 times, 3–9 times, 10–20 times, and more than 20 times. Our assumption is that experience teaching a statistics course serves as a major source of professional learning and opportunities to better develop one’s understanding of the statistical content, implement a variety of instructional strategies, and improve one’s teaching based on reflections on students’ questions and difficulties with particular topics (Cai and Gorowara 2002).

For quantitative items where we disaggregated by experience teaching AP Statistics, t-tests were computed to investigate whether mean responses differed for participants with more experience teaching AP Statistics than for participants with less experience teaching AP Statistics. For ordinal and rating scale items where we disaggregated by experience teaching AP Statistics, Goodman and Kruskal’s gammas (Goodman and Kruskal 1954) were computed to determine whether participants with more experience teaching AP statistics reported practices or beliefs that were significantly different than their peers with less experience teaching AP Statistics. Goodman and Kruskal’s gamma is computed by first examining every possible pair of participants and determining whether each pair of participants indicates a negative or positive association between variables. The number of positively associated pairs and negatively associated pairs is then used to compute gamma, which can be used to determine whether the differences between responses are statistically significantly different for participants with more experience teaching AP statistics than for those with less experience teaching AP Statistics. These differences, when applicable, are discussed in the findings below. No adjustments were made for multiple testing.

3 Results and Discussion

3.1 Teacher Demographics

Only 386 survey respondents completed at least part of the demographic section of the survey (see Appendix, Part 7). Survey respondents teach in 47 states, with two teaching outside the U.S. Due to many contacts within North Carolina, 26% of respondents taught in NC. Most participants (83%) teach in public schools, with 14% in private schools, and 3% in charter schools.

Overall the survey participants are highly educated, with 72% having a master’s degree, 4% with a doctoral degree, and 3% having some other degree (typically an education specialist degree). Some participants have degrees from multiple disciplines. At any educational level, 62% of participants hold an education degree (including mathematics education), while 58% have a degree in mathematics or a similar field (not including statistics or mathematics education), and 7% reported holding a degree in statistics or a similar field. Another 7% of participants did not hold a degree in education, statistics, or mathematics, and instead listed degrees from an engineering discipline, business, finance, or economics.

Participants are relatively experienced in teaching mathematics and/or statistics, with 1% having less than three years of general teaching experience, 19% having 3–9 years, 40% having 10–20 years, and 40% having more than 20 years of experience. Participants also reported how many times they had taught AP Statistics, counting multiple sections per year, if applicable, and including classes in their current semester (fall 2018). Eleven percent of surveyed teachers have taught 0–2 sections of AP Statistics, 41% taught 3–9 sections, 33% taught 10–20 sections, and 15% taught more than 20 sections. Twenty-one percent of respondents also have experience teaching statistics at the post-secondary level.

3.2 Course Characteristics

The mean of the typical class size of an AP Statistics course was 22.5, with a median of 24 students. Twelve percent of teachers had typical class sizes under 15 students, while 6% reported class sizes of 35 or more students. Related to the AP Statistics exam, 65% stated there was an expectation or requirement that students in their course take the AP exam, with teachers reporting a mean of 86% (SD $=$ 22%) of their students who actually take the exam.

The vast majority (75%) of AP Statistics teachers have similar amounts of instructional time in the school year, reporting either ∼90 min for half the days in a school year (35% with semester or year-long A/B blocks of time), or a traditional schedule of ∼45–60 min per day for an entire year (40%). However, some teachers described an “other” schedule with as little as ∼60 hr of instructional time per course (200 min a week for half a school year), and some as high as ∼270 hr (450 min a week for the entire year). Clearly, students’ opportunity to learn statistics as measured in class time with their teacher and how that is distributed throughout a school year varies greatly, with the most common arrangement being a traditional schedule of daily class periods of 45-60 min all year.

3.3 Teacher Preparation and Professional Engagement

Participants answered several questions regarding their preparation for teaching statistics. About half of respondents (49%) had taken three or more undergraduate or graduate statistics classes (with 19% having 6 or more classes in statistics in their background), while about a quarter of respondents (24%) had taken zero or one statistics course, and about a quarter (27%) had taken 2 classes. Thus, formal preparation in statistics for about half of AP Statistics teachers is less than the recommended three-course sequence for all high school mathematics teachers in the Statistical Education of Teachers report (Franklin et al. 2015). This is not surprising given that most high school mathematics teachers now teaching AP Statistics were prepared in teacher education programs prior to this three-course recommendation in 2015. However, it is exciting to see that many AP Statistics teachers have taken several courses in statistics beyond this three-course recommendation. Participants were also asked whether they had any experience analyzing and conducting statistical investigations outside of coursework. Not surprisingly, over half of respondents (57%) reported they had no or very little of this experience, with 32% having some experience, and 11% reporting a lot of experience. Thus, engaging in statistical practices or applying their statistical toolkit of knowledge is not a typical experience for these teachers.

Most respondents (69%) had never been an AP Statistics exam reader, while 4% had participated once, about 6% participated twice, and 21% had participated three or more times. The high number of exam readers (31%) was likely influenced by the partial recruitment efforts through known statistics education experts, many of whom had served as AP Exam readers and likely recruited high school teachers who had served as exam readers to participate in the survey.

When teachers estimated time in the previous two years spent participating in various types of professional development focused on teaching statistics, they generally reported 50+ total hr (Table 1). Overall, teachers that have taught AP Statistics more than 10 times are participating in more hours of professional development (approximately 70 hr over a two-year period) than teachers that have taught AP Statistics fewer than 10 times (approximately 50 hr over the same period) (t = 3.33, $p<0.001$). The most noticeable differences are that newer AP Statistics teachers are spending much more time at the AP Statistics summer institutes (t = 4.35, p < 0.001), while more experienced AP Statistics teachers are spending more time as exam readers (t = 7.09, p < 0.001). This is not a surprising finding given that most schools require new AP Statistics teachers to attend the summer institute and a minimum of two years teaching AP Statistics is expected for a high school teacher to be eligible to be a reader of the AP Statistics exam. The most experienced teachers (>20 times) spend less time than their less experienced peers with online professional development courses and webinars focused on teaching statistics (t = 1.69, p = 0.09), though the amount of time spent in online professional development for teachers with experience in 0–20 sections is very similar with 4 to 5 hr in the past two years.

Table 1 Hours in prior two years on type of professional development in teaching statistics.

	Mean and standard deviation for hours of professional development by sections taught of ap statistics
	0–2 (n = 44)	3–9 (n = 156)	10–20 (n = 125)	>20 (n = 59)
Live or prerecorded webinars	4.5 (12.3)	3.8 (10.2)	4.1 (7.1)	2.5 (4.4)
Workshops	10.3 (21.4)	10.9 (19.7)	10.7 (16.0)	7.8 (9.2)
In-person short courses/mini-courses	4.0 (11.6)	2.4 (7.5)	2.0 (5.9)	2.4 (5.5)
Online professional development course	4.7 (12.8)	4.2 (10.0)	5.4 (18.3)	1.6 (4.8)
AP Statistics summer institute	25.3 (27.9)	14.9 (21.7)	7.7 (15.9)	8.1 (21.5)
AP Statistics exam reader	0.2 (1.2)	12.4 (32.0)	35.6 (47.8)	44.5 (50.0)
Other	2.7 (17.9)	1.2 (7.7)	3.7 (16.4)	4.9 (20.5)
Total number of hours reported	51.7 (59.3)	49.8 (55.6)	69.2 (60.7)	71.8 (63.3)

Teacher professional learning also occurs through self-initiated use of journals, websites, and conferences. Not surprisingly, the AP Statistics online teacher community (hosted by the College Board) was the most frequently used resource, followed by the Mathematics Teacher journal (published by the National Council of Teachers of Mathematics, NCTM) (Table 2). A large majority of AP Statistics teachers had never heard of or never used the Journal of Statistics Education (now the Journal of Statistics and Data Science Education), Statistics Teacher, and STEW, all of which have been major efforts by the ASA to provide activities and lessons applicable to AP Statistics. Also of concern, over half of the teachers had never heard of CAUSEweb or STATS4STEM websites. If a participant had more experience teaching AP Statistics, then they were more likely to report higher awareness and frequency of use for several resources—the Journal of Statistics Education (G = 0.22, p = 0.03), Statistics Teacher (G = 0.31, $p<0.01$), and CAUSEweb (G = 0.31, p < 0.01), all of which are freely accessible online.

Table 2 Use of professional learning resources for teaching statistics.

		Percent of Teachers
	Sections Taught of AP Statistics	Never heard of it (%)	Aware but never used (%)	Used once once (%)	Occasional use (%)	Frequent use (%)
Mathematics Teacher (NCTM Journal)	0-2	12	21	21	44	2
	3-9	4	26	35	29	6
	10–20	2	26	26	37	10
	>20	3	25	32	34	5
	All teachers	4	26	30	34	7
Journal of Statistics Education (JSE)	0–2	37	51	12
	3–9	37	43	15	5	1
	10–20	22	48	12	18	1
	>20	24	47	14	14	2
	All teachers	30	46	13	10	1
Statistics Teacher Journal at ASA	0–2	43	48	7		2
	3–9	48	28	8	13	3
	10–20	19	44	14	18	4
	>20	22	34	20	22	2
	All teachers	34	36	12	15	3
Statistics Education Web (STEW)online lesson plans	0–2	55	29	10	7
	3–9	45	27	11	13	4
	10–20	30	38	14	16	2
	>20	34	34	15	17
	All teachers	39	32	13	14	2
CAUSEweb	0–2	71	21	5	2
	3–9	74	14	6	6	1
	10–20	50	22	11	14	2
	>20	49	24	10	17
	All teachers	62	19	8	10	1
STATS4STEM	0–2	73	13	15
	3–9	58	21	8	11	1
	10–20	45	20	14	16	6
	>20	49	31	8	10	2
	All teachers	54	21	11	12	3
AP Statistics online teacher community	0–2	14	12	14	26	33
	3–9	5	13	8	38	37
	10–20	1	6	9	37	48
	>20	3	3	14	37	42
	All teachers	4	9	10	36	41

Participants were also asked about their attendance at various conferences that include sessions on statistics education, and the impact that attendance had on their teaching of statistics. In 2008, the AP Statistics Teacher’s Guide included suggestions for professional conferences, all of which were included on the survey. Highest attendance was seen at the State-level (45%) and Regional/National (41%) Council of Teachers of Mathematics conferences. However, only 19% and 17% of attendees, respectively, reported that their attendance had a large impact on their teaching of statistics (though it may have had a large impact on their teaching of other mathematical subjects). The College Board Annual AP Conference had been attended by 30% of respondents, and of these attendees, 57% reported that attendance had a large impact on their teaching of statistics. Almost all teachers reported never participating in several statistics-specific conferences: US Conference on Teaching Statistics (USCOTS, 95%), Electronic Conference on Teaching Statistics (e-COTS, 96%), and the Joint Statistical Meetings (JSM, 95%). If a participant had more experience teaching AP Statistics, they were much more likely to have attended some of the following conferences and that the conference had a stronger impact on their teaching of statistics—the Joint Statistical Meetings (G = 0.64, $p<0.01$), a state-level Council of Teachers of Mathematics conference (G = 0.34, p < 0.001), and the National Council of Teachers of Mathematics conference (G = 0.30, p < 0.01). This finding seems to indicate that highly experienced AP Statistics teachers attend both statistics specific and mathematics teacher specific conferences and are able to get meaningful information that can impact their teaching of statistics.

When asked how well prepared they felt to teach an introductory course in statistics at the high school or college level, overall, 93% of respondents felt sufficiently (35%) or completely prepared (57%). However, particularly for newer teachers of AP Statistics, many teachers do not feel completely prepared, with 21% of teachers who have taught AP Statistics two or fewer times feeling at best somewhat prepared. Not surprisingly, the more experience teaching AP Statistics a respondent had, the more likely they were to report a higher level of feeling completely prepared to teach a statistics course ($G=0.48$, p < 0.001).

3.4 Teaching Beliefs

Participants were shown a series of statements and asked to rate the extent to which the statements reflected their beliefs (but not necessarily their actual teaching) regarding teaching and learning, assessment, and course/instructor development (Table 3). With regards to beliefs about teaching and learning statistics, some of the most agreed-with statements included: students should learn the importance of using appropriate methods for collecting data; students should learn connections between the quality/nature of the data and inferences that are made; technology should be used for most abstract statistics concepts; and that basic probability and theoretical probability distributions should be part of the curriculum. Teachers tended to disagree that lectures should be the primary mode of instruction. Their opinions were more varied related to beliefs about whether students should learn to use statistical tables and if they should learn fewer topics in depth. Related to assessment, teachers tended to agree that students should be assessed on their statistical literacy and ability to complete an open-ended statistical problem, that formative feedback should be given on all assignments, and that all assessments should be regularly reviewed to ensure that they are aligned with student learning goals. Teachers had more varied opinions about whether quizzes and exams should be used as the primary way to evaluate student learning. The AP Statistics teachers tend to agree that the course should be updated with advances in technology and that they should be involved in the statistics education community. They were less sure about whether statistics courses should be updated continually in response to recommendations such as Common Core.

Table 3 AP Statistics teachers’ beliefs about teaching, learning and assessment of statistics.

	Percent of Teachers
	Strongly disagree					Strongly agree
	(1)	(2)	(3)	(4)	(5)	(6)
Teaching and learning statistics beliefs
Students should learn fewer topics in greater depth instead of learning more topics in less depth in an introductory statistics course.	2%	8%	19%	30%	27%	15%
Basic rules of probability should be included in an introductory statistics course.	1%	2%	6%	20%	48%	25%
The topic of theoretical probability distributions (e.g., the binomial distribution) should be included in an introductory statistics course.	1%	5%	6%	21%	43%	24%
Students should learn how to read statistical tables of probability distributions (e.g., t-table, z-table).	4%	10%	10%	23%	27%	26%
Students should learn the importance of using appropriate methods for collecting data.	<1%	0%	<1%	6%	33%	61%
Students should learn connections between the quality/nature of the data and inferences that are made.	0%	<1%	1%	7%	37%	55%
Technology tools should be used to illustrate most abstract statistical concepts.	0%	1%	2%	26%	44%	27%
Students should analyze data primarily using technology.	1%	3%	10%	32%	37%	18%
Lectures should be the primary way for students to learn statistical content.	10%	19%	37%	26%	6%	1%
Assessment beliefs
Quizzes and exams should be used as the primary way to evaluate student learning.	1%	9%	22%	44%	21%	3%
Alternative assessments (e.g., projects, presentations) should be used to provide important information about student learning.	<1%	1%	3%	42%	42%	12%
All assessments should be regularly reviewed to see that they are aligned with student learning goals.	0%	1%	2%	13%	49%	36%
Formative feedback should be given on all assessments in order for students to improve their learning.	0%	<1%	1%	10%	44%	44%
Students should be assessed on their ability to complete an open- ended statistical problem.	0%	2%	<1%	10%	43%	45%
Students should be assessed on their statistical literacy (e.g., ability to read a graph, understand common statistical words, etc.).	0%	0%	<1%	4%	41%	55%
Course and instructor development beliefs
Statistics courses should be updated continually to keep up with advances in technology.	0%	1%	3%	17%	46%	33%
Statistics courses should be updated continually in response to recommendations such as Common Core.	5%	12%	20%	31%	22%	10%
Statistics instructors should be actively engaged in the statistics education community.	1%	0%	4%	21%	42%	32%

3.5 Teaching Practices

Teachers reported the amount of face-to-face class time devoted to various activities (n = 445 responses). A typical student in these classrooms spends over twice as much time working in groups ($\text{mean}=27\%,SD=14\%$) as they do working individually ($\text{mean}=12\%,SD=8\%$), not including time taking assessments ($\text{mean}=12\%$, $SD=5\%$), which is likely done individually. Teachers report that students typically spend approximately the same amount of time together as a whole class ($\text{mean}=38\%,SD=16\%$) as they do working in groups and individually combined.

Participants were given statements about their course, and asked to what extent a student that was fully engaged would agree or disagree with those statements (Table 4). Statements that teachers felt their students would most often agree with include that graphing calculators were regularly used, that the instructor asked challenging questions that made students think, and that the course frequently required students to work together. There is also relatively more agreement that the course content is presented through lectures. Statements that teachers felt would receive more varied agreement from students include that the course content was presented mostly through activities, that the course often used technology other than graphing calculators, and that the course encouraged students to discover ideas on their own. For the statement “The instructor asked challenging questions that made students think,” there was a strong relationship between the number of times a teacher had taught AP Statistics and their response, indicating that the more experience a teacher had, the more likely they were to respond that their students would more strongly agree with that statement (G = 0.27, p = 0.01).

Table 4 Teachers’ extent of agreement to aspects of an AP statistics course.

	Percent of teachers (n = 444)
	Strongly disagree					Strongly agree
	(1)	(2)	(3)	(4)	(5)	(6)
The content was presented mostly through lectures.	3%	9%	11%	34%	32%	10%
The instructor asked challenging questions that made students think.	0%	0%	2%	20%	57%	20%
The course frequently required students to work together.	1%	2%	7%	26%	42%	22%
The content was presented mostly through activities.	3%	12%	28%	39%	12%	5%
This course encouraged students to discover ideas on their own.	1%	9%	23%	47%	18%	2%
Students use graphing calculators regularly in this course.	1%	0%	1%	6%	23%	68%
This course often used technology other than calculators to help students understand concepts.	7%	17%	21%	31%	18%	5%

We asked teachers to indicate how much time they spent on preparing students to achieve various learning objectives (Table 5). Almost all participants report spending a moderate or a lot of time preparing students to answer questions using an investigative process, produce and interpret graphs and summaries, explain variability and the central role of randomness, and understand and use statistical inference. However, the more experience a participant had, the more likely they were to report spending a lot of time on statistical inference (G = 0.39, p < 0.01). Participants spend less time on preparing students to become critical consumers of media reports, gain experience with how statistical models are used, interpret output from statistical software, and be aware of ethical issues associated with statistical practice.

Table 5 Time spent preparing students for different aspects of statistical practice.

	Percent of teachers (n = 426)
How much time in your course is spent on preparing students to …	None (%)	A little (%)	Moderate amount (%)	A lot (%)
…become critical consumers of statistically-based results reported in popular media?	3	43	42	13
…recognize questions for which the investigative process in statistics would be useful?	1	28	53	17
…answer questions using the investigative process?	2	20	51	27
…produce and interpret graphical displays and numerical summaries?	1	14	50	36
…explain the central role of variability in the field of statistics?	1	17	53	29
…explain the central role of randomness in designing studies and drawing conclusions?	0	11	56	32
…gain experience with how statistical models, including multivariable models, are used?	7	40	40	13
…understand and use basic ideas of statistical inference?	0	1	32	67
…interpret and draw conclusions from output from statistical software packages?	5	42	41	12
…be aware of ethical issues associated with sound statistical practice?	4	57	31	8

We were interested in how much emphasis teachers put on assessing students about particular aspects of statistics (Table 6). Almost all teachers reported spending a moderate or a lot of time on building students’ ability to interpret results of a statistical analysis, to reason correctly about important statistical concepts, and to answer questions similar to those on the AP exam. They don’t spend much time critically examining statistics in the media on assessments but most teachers spend either a little or moderate amount of time on assessments focused on students using formulas or step-by-step calculations, with 16% and 17% spending a lot of time assessing students on these skills. Students’ ability to do statistical investigations are assessed a moderate to a lot of the time for 63% of teachers.

Table 6 Time spent assessing students’ abilities in various aspects of statistics.

	Percent of teachers (n = 426)
	None (%)	A little (%)	Moderate amount (%)	A lot (%)
Students’ ability to use formulas to produce numerical summaries of a dataset	3	41	40	17
Students’ ability to perform step-by-step calculations to compute answers to problems	4	46	35	16
Students’ ability to critically examine statistics in the media	10	51	30	9
Students’ ability to interpret results of a statistical analysis	0	3	36	61
Students’ ability to reason correctly about important statistical concepts	0	2	32	66
Students’ ability to successfully complete an entire statistical investigation (all four phases: posing a question, collecting data, analyzing data, and interpreting results)	5	32	34	29
Students’ ability to answer questions similar to those found on the AP Exam (e.g., using released exam questions for assessment)	1	2	24	74

When asked what prevents them from making changes to their teaching practices, teachers often cited a lack of personal time to engage in making changes (24%), particularly when they may teach several other mathematics courses at the same time. They also note the structure of their course schedule (especially those who teach in a semester block), pressure to finish content before the AP Statistics exam, lack of access to technology, and characteristics of their students (lack of motivation and knowledge) as all presenting barriers for making instructional changes. A few also commented on use of outdated textbooks, and computers not being allowed on the AP exam.

3.6 Use of Technology

When asked if their students used technology tools other than graphing calculators during the course, 296 of 424 respondents (69.8%) indicated positively. When examining whether or not being in a higher experience group resulted in a higher probability of answering this question positively, no statistically significant result was found ($G=-0.18$, p = 0.18). Thus, the use of tools other than graphing calculators is not related to a teachers’ experience teaching AP Statistics. The 30.2% of participants (n = 128) that responded No to this question were then asked to choose applicable reasons for not using tools other than graphing calculators. The most common reasons were that graphing calculators are the only technology allowed on the AP Statistics exam (61%), students are provided with statistical output (59%), and that there is a lack of time to incorporate other technology (50%). It is important to note that 25% of teachers indicated their lack of comfort in using technology as a barrier for its use, as well as 32% reporting that computing technology is not available for use.

There are many types of technology tools that could be used to support students’ learning in an AP Statistics course. Tools we asked teachers about included those that are useful for collecting and analyzing data (graphing calculators, spreadsheets, statistical software), multimedia statistics materials, online statistics homework tools, or general technology tools such as collaboration tools (e.g., Google Docs) and formative assessment tools (e.g., Kahoot). We provided participants with a list of tools and asked whether their students use them during activities, whether their students use them during assessments, and whether the teacher uses them to deliver course content (Table 7). By far, the most common technology tool used by both teachers and students is the graphing calculator.

Table 7 How technology tools are used by AP statistics teachers.

	Of those that use a tool, percent and number of teachers indicating use
	Students use during assignments activities and assignments	Students use during assessment	Teacher uses to deliver course content	Percent and number teachers not using tool
Graphing calculator with built- in statistical functions	96% (n = 396)	94% (n = 389)	88% (n = 364)	0% (n = 0)
Statistical software packages (e.g., Minitab, R, SPSS, JMP, StatCrunch…)	23% (n = 91)	7% (n = 27)	45% (n = 179)	50% (n = 201)
Spreadsheet tools (e.g., Excel, Google Sheets)	50% (n = 205)	6% (n = 25)	49% (n = 197)	34% (n = 137)
Web Applets (e.g., StatKey, Rossman/Chance)	52% (n = 213)	3% (n = 13)	67% (n = 275)	24% (n = 100)
Educational software (e.g., TinkerPlots, Fathom, CODAP)	11% (n = 43)	1% (n = 3)	32% (n = 128)	65% (n = 263)
Multimedia materials (e.g., ActivStats, Against All Odds, CyberStats, videos of mini-lectures or real world uses of statistics)	30% (n = 121)	1% (n = 5)	58% (n = 235)	35% (n = 143)
Collaboration tools (e.g., Google Docs)	65% (n = 266)	7% (n = 28)	39% (n = 159)	30% (n = 123)
Online statistics homework, tutorial, or assessment tools (e.g., WebAssign, MyStatLab)	30% (n = 120)	6% (n = 23)	13% (n = 52)	67% (n = 267)
Other assessment tools (e.g., Kahoot, Quizlet)	45% (n = 183)	9% (n = 36)	36% (n = 144)	41% (n = 164)

Over half of teachers do not use statistical packages (53%), educational statistical software such as Fathom or CODAP (66%), or online tutorial or homework tools specific to statistics (67%). When used, teachers are much more likely to use statistical software packages or educational software to deliver course content, likely by displaying their computer screen, than to have their students use these tools themselves. Students are more commonly using spreadsheet tools, web applets, collaboration tools, and assessment tools such as Kahoot for quizzes and formative feedback. Students are rarely using any technology tool other than graphing calculators on assessments, likely due to its use on the AP Statistics exam.

Teachers (n = 412) reported the purposes for students using technology more often are automation of calculations, data exploration, investigation of real-life problems, and promotion of collaboration and student involvement. Technology is less commonly used to support collecting, accessing, and importing real data, with a third of the teachers never using technology in this way. Technology is also used sparingly to visualize abstract concepts and conduct simulations, with 58% and 52% of teachers, respectively, at the best using technology a little of the time to support statistics learning in these ways.

3.7 Characteristics of DataSets Used

To dig into the ways teachers may engage students with real and large data, we asked a series of questions about characteristics of data used in their courses and then disaggregated responses by teachers’ experience in teaching AP Statistics. Interestingly, it seems like novice AP Statistics teachers are slightly less likely to use real-world data most or all of the time, but are more likely to use data collected by students most or all of the time. Neither of these trends were significant at the $\alpha =0.05$ level when examined across all groups simultaneously. Overall, 92% of teachers report that about half or more of datasets seen are real-world data, and 27% of teachers report that about half or more of datasets that are used are collected by students. Though the trend aligns with the GAISE College Report ASA Revision Committee (2016) recommendations to use real data, we do not know the sources for the real-world data used, but suspect that many are provided with course textbooks and this may explain why most teachers only occasionally use data collected by students.

Participants were also asked about the size of datasets students see, both in terms of number of cases and number of variables per case. The more experienced a teacher was, the less likely they were to use datasets with 100 to 1000 cases ($G=-0.26,p=0.01$); the less likely they were to use datasets with over 1000 cases ($G=-0.26$, p = 0.02); and the less likely they were to use datasets with more than 10 variables per case ($G=-0.27,p=0.01$). Overall, however, relatively few teachers are using datasets with over 1000 cases (11%) or more than 10 variables (12%) in about half or more of total datasets, with many teachers reporting that they never use datasets of this size (35% and 46%, respectively). Even more troublesome is that 60% of AP Statistics teachers never or rarely expose their students to a dataset with greater than 100 cases, even if it was of a single variable. Thus, students do not appear to get many opportunities in AP Statistics to explore and analyze larger datasets as suggested by the GAISE College Report ASA Revision Committee (2016) and increasingly present in college-level introductory statistics (Hardin et al. 2015; Hudiburgh and Garbinsky 2020).

4 Conclusions and Implications

Recall that our survey represents a convenient and volunteer sample of 445 AP Statistics teachers from 2018, recruited through a variety of methods including listservs, statistics education experts, state department lists of teachers, public teacher websites, etc. The results should be interpreted with this mind. In particular, it is highly probable that AP Statistics teachers that are at least somewhat involved in the AP Statistics community were the ones most likely to be contacted and may have been the most likely to respond to the survey request.

4.1 Teacher Preparation and Professional Learning

For the most part, AP Statistics teachers in our sample report feeling prepared to teach the course and regularly seek out professional learning opportunities. AP Statistics teachers have generally taken two or more statistics courses in either undergraduate or graduate programs (76%). Recall that in our sample, many of the teachers have a master’s degree or higher. It is important that initial mathematics teacher preparation programs and graduate programs for practicing mathematics teachers attend to the opportunities for all mathematics teachers to develop their understanding of statistics and of teaching statistics.

Overall, many (57%) AP Statistics teachers feel completely prepared to teach the subject. This is a much greater feeling of preparedness than all high school mathematics teachers, with only 31% of all high school mathematics teachers feeling very well prepared to teach statistics and probability topics (Banilower et al. 2018). AP Statistics teachers seemed to typically spend 50 or more hours in professional development over a two-year period directly related to being a statistics teacher, with most of that occurring in AP summer institutes for newer AP Statistics teachers, and as an AP exam reader for more seasoned teachers. This is much higher than what high school mathematics teachers in general reported in Banilower et al. (2018), with almost 60% reporting 35 or fewer hours spent in mathematics teaching professional development over the past three years. However, lack of personal time is also the most cited reason for not changing teaching practices in AP Statistics.

4.2 Misalignment of Teachers’ Beliefs and Practices

Participants expressed several beliefs that were not always reflected in their classroom practice. About two-thirds (66%) of teachers disagreed with the statement that lectures should be the primary way for students to learn statistical content. However, over three-quarters (76%) felt that their students would agree that the course content was primarily presented through lecture. Professional development opportunities should continue to assist teachers in creating student-focused activities that can be done collaboratively and in structuring whole group discussions that are not teacher-focused. As another example, 55% of teachers strongly agreed that “students should learn connections between the quality/nature of the data and inferences that are made” but reported placing far less emphasis on preparing students to be critical consumers of statistics in the media or in considering ethical issues in the use of data. With current efforts toward improving ethical use of data and preparing data literate citizens who can make sense of graphs and statistics reported in media, there should be more effort toward ensuring these aspects are incorporated into AP Statistics, both in the curriculum and instructional practices. It will be important to make sure AP Statistics teachers know about and utilize resources such as New York Times What’s Going On In This Graph and Skew the Script lessons that embed learning statistics for making sense of social, political, and ethical issues often presented in media.

Nearly all (96%) of teachers agreed that statistics courses should be updated continually to keep up with advances in technology. However, about 30% of AP Statistics teachers reported their students never use technology other than graphing calculators, and 45% felt that students would disagree with the statement that the course often used technology other than graphing calculators. Indeed, even when a small proportion of the teachers do use spreadsheets, statistical packages, or educational statistical software, it is mainly used by the teacher, with little direct use by students. This is likely related to the findings about the use of larger data sets–without appropriate technology, students will not be able to effectively process and analyze large data.

The findings that AP Statistics teachers’ beliefs do not always match their practices align with those of Harrison (2020), who observed that secondary statistics teachers often struggled with putting their beliefs about how students best learn and beliefs about technology into practice. Teachers could benefit from more assistance manifesting their beliefs into their practice, and specifically experiences with more statistics-specific tools with a focus on the use of larger multivariate data. Indeed, teachers in this survey identified factors that inhibited their ability to change instructional practices. These included the structure and requirements of the AP Statistics exam, that students only need to interpret output from statistical packages on the exam (and not perform the analysis themselves), limited class and personal time, and to a lesser extent a lack of access to computer technology and feeling less skilled in using these tools.

4.3 Engaging Teachers with Statistics Resources and Conferences

Most participants (95%) agreed that statistics instructors should be actively engaged in the statistics education community. While many (77%) report using the AP Statistics online teacher community at least occasionally, few are staying engaged through other online resources designed for statistics teachers, nor are they reading journals or attending conferences designed specifically for the statistics teacher community. Due to the recruiting methods for this survey, particularly with some recruitment efforts happening specifically within these communities and a large number of respondents having attended an AP Statistics exam reading, the engagement with these resources among all AP Statistics teachers is likely even lower than reported from our survey results.

The teachers in this study are often engaging with the larger mathematics education community, by reading and using journals such as NCTM’s Mathematics Teacher (now published as Mathematics Teacher: Learning and Teaching PK-12) or attending state, regional, or national NCTM affiliated conferences, though they report that these conferences have had relatively little impact specifically on their teaching of statistics. This finding, of AP Statistics teachers engaged in resources aimed at mathematics teachers, aligns with the findings from Whitaker (2016) of how the 12 AP Statistics teachers in his study had dual identities as statistics teachers and mathematics teachers. Those participants reported feeling isolated in regards to their statistics teaching and often struggled with finding ways to regularly engage with the statistics education community. The connections they did establish, however, were critical to developing their identities as statistics teachers. Thus, if we want to reach these teachers, we need to better advertise and incentivize them to engage with statistics-specific resources (e.g., Statistics Teacher, STATS4STEM, CAUSEweb), as well as distribute statistics-specific resources within the more general mathematics teacher community in journals and conferences attended by high school mathematics teachers. Since many AP Statistics teachers reported little involvement with conferences such as USCOTS, e-COTS, or JSM, concerted efforts may be called for to ensure that there are sessions at these conference specifically geared toward AP Statistics audience and that recruitments efforts and incentives are put in place (e.g., reduced fees) to attract high school AP Statistics teachers.

4.4 Toward the Future

We hope these survey results can assist many in the statistics education community who continue to invest their time in further developing the AP Statistics curriculum, instruction, and community. As college-level introductory statistics courses become more modern in their use of technology, real large datasets, and more active student-centered learning, it is imperative that students in AP Statistics get similar experiences, especially if they don’t get those experiences in college and are expected to apply them to their disciplinary majors. Teachers point to constraints related to the AP Statistics curriculum and exam as inhibiting their ability to make changes in their teaching practice or feel comfortable taking the time to engage students with computer-based technology tools and larger datasets. Perhaps it is time for the curriculum and exam to make some changes to reflect more modern content and approaches to statistics that are often, though not always, used in college-level statistics courses.

Our results represent a snapshot from fall 2018. A lot has happened since that time, including the release of a much more detailed AP Statistics College and Exam Description (College Board 2019) with a focus on overarching statistical skills such as selecting statistical methods, data analysis, using probability and simulation, and statistical argumentation. The updated PreK-12 GAISE II report has been released (Bargagliotti et al. 2020) and actively supported and advertised by the NCTM through presidential messages sent to members and posted online (e.g., Wilkerson 2020). Data science education has also emerged as a critical part of college-level statistics education, and is being advocated for in K-12 standards and curriculum (e.g., datascience4everyone.org).

Teachers’ beliefs and practices may have also changed since fall 2018. In 2020–21, the most AP Statistics teachers were using hybrid, online, and remote teaching during a pandemic. We wonder if the context of remote teaching and learning in 2020-21 has encouraged more teachers to use online technology tools (e.g., spreadsheets, web applets, CODAP, online tutorial and homework systems, multimedia videos) and situating statistics in real world issues and contexts (e.g., COVID-19, racial equity, immigration). Alternatively, with pressure of covering a packed AP Statistics curriculum, remote instruction may have primarily consisted of ZOOM lectures, direct instruction with videos and slide decks, even less use of activities for students to engage in collecting and analyzing data themselves, and merely completing more problems that emphasize skills and concepts similar to the AP exam. What will AP Statistics look like post-pandemic?

Our study helps to illustrate trends in AP Statistics teachers’ beliefs, teaching practices, and professional learning, and several implications should call the statistics education community to action. Future research with our survey data and the interviews with 18 volunteer teachers will add to the story of what teachers do in their AP Statistics classrooms and why. It may be worthwhile to repeat this survey, explicitly asking teachers if any of their beliefs and practices changed because of recent events (e.g., remote teaching during a pandemic, GAISE II, attention on data science) and how those changes seem to be impacting students’ learning experiences.

Students deserve access to a high-quality modern statistics course in high school. The quality is not just in the curriculum, but in the preparation of the teachers and what happens on a daily basis as AP Statistics teachers plan and implement lessons that shape students’ opportunities to experience aspects of statistics that will be meaningful to their lives and useful in future careers. AP Statistics teachers often take on this course when no one else in their department will, and some eventually develop an identity as a statistics teacher and a member of the larger statistics education community. We need to make a concerted effort to bring many more of them into the larger statistics education community and support them as they teach what many of us consider to be the most useful subject for a high school graduate.