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Concepts of experimentation and measurement are explored using statistics educational fun items and illustrated by sharing our process in conducting an experiment on cartoon captions.

Thinking probabilistically is an essential part of thinking statistically, and the probability learning objectives that this article focuses on are those that are important in the underpinning of statistics and statistical models. Like mathematical statistics, probability can be considered purely from a mathematical viewpoint, but the focus here is on understanding concepts.

Jokes, cartoons, songs, videos, and quotes can be useful ways to engage students in discussion and learning key concepts about polling.

Jokes, cartoons, songs, and games can help engage students in discussion and learning key concepts about hypothesis testing.

Jokes, cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about regression.

The possible benefits of using music to enhance learning of STEM content are numerous, diverse, and largely unproven. We sought to determine which (if any) of these possible benefits are commonly experienced by undergraduate students and are thus especially worthy of further investigation. Four hundred ninety-three students in nine physiology courses at two midsized American universities rated the usefulness of short instructor-penned mathematical physiology songs and explained in their own words why each song would or would not be a useful study aid. The students collectively perceived the usefulness of each song to depend on both academic factors (e.g., the lyrics' clarity or relevance to the course) and aesthetic values (e.g., the appeal of the rhythm or the quality of the singing). Most strikingly, although students' free responses were brief (median length: 18 words in study "phase 1", 16 words in study "phase 2"), nearly one-half of them (1,039 of 2,191) concerned memory, suggesting that many students see educational songs primarily as mnemonic devices. A second major theme of students' comments concerned the conciseness and information density of the songs. Though all 10 songs were brief, lasting 17-54 s, students seemed to prefer shorter songs (perhaps better called "jingles"). This first-of-its-kind data set on student perceptions of educational songs should inform the creation and usage of such songs, as well as further research on their possible value.

The study presented in this paper sought to offer a group of 21 preservice teachers with opportunities to learn about interdisciplinary mathematics pedagogy, plus the experience of implementing it with elementary students. It provided the participating preservice teachers' with an opportunity to reflect upon the potential advantages, as well as challenges, involved in developing music into an educational resource for teaching engaging elementary mathematics lessons. Analysis of the 391 pieces of qualitative reflections that were collected from the participating preservice teachers during focus group discussions, individual interviews, and self-refection essays revealed the participants' general perceptions about the benefits and challenges of teaching mathematics through music activities.

The use of cartoons, songs, and quotes can be a useful way to engage students in discussion and learning key concepts about quantifying the uncertainty in statistical estimates.

Cartoons, songs, poems, and games can be useful ways to engage students in discussion and learning key concepts about correlation.

Recently adopted state standards for middle grades and high school mathematics content have an increased emphasis on statistical topics. With this change, teacher education programs may need to adapt how they prepare preservice secondary mathematics teachers (PSMTs) to teach statistics and require measures related to statistics teaching to assess the impact of programmatic changes and track teacher growth. Using responses from a sample of 290 PSMTs from 20 institutions across the United States, this study presents validity and reliability evidence for the high school version of the Self-Efficacy to Teach Statistics (SETS-HS), which could be used to assess statistics teaching efficacy. Confirmatory factor analysis results via Rasch modeling support the use of three subscales, which exhibit adequate reliabilities and correspond to the three levels in the "Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education" endorsed by the American Statistical Association. Item and rating scale analyses indicate that the 46 items and the six-category scale employed in the SETS-HS perform as intended.

Two articles in the January 2013 issue address the need for teachers to focus on student learning rather than on what the teacher does (Scoufis, 2013) and make learning the object of inquiry (Cerbin, 2013). A big part of making this happen is reducing or eschewing lecture that is one-directional and one-dimensional. This often means that teachers must overcome many habits, biases, or misconceptions about lecture. Like many (if not most) professors, I began my teaching career as a strictly-by-the-book lecturer and have gradually over time worked through my own limitations and prejudices to incorporate more and more active learning strategies, such as classroom voting (Lesser, 2011) or liberating structures such as 1-2-4-whole (Lipmanowicz & McCandless, 2010).

Edutainment has recently been a major growing area of education, showing great promise to motivate students with relevant activities. The authors are among innovators who have developed cutting-edge fusions of popular culture and STEM concepts to engage and to motivate middle school students, using vehicles such as music/song and skateboarding. The importance of using relevant and practical methods of instruction and curriculum delivery that build on student interests and increase enjoyment in the learning process are critical at the middle school level, especially in the STEM fields. The use of edutainment in this manner is meant to inspire broader interest in mathematics and science for middle school students and to develop a culture of education that makes learning more accessible to all students. This paper surveys and illustrates the use of such immersive modalities to involve middle school students actively with concepts and suggests further directions for the use of demonstrations and videos in educational settings.

This article describes the process used to develop and assess an NSF-funded instructional innovation: an online collection (https://www.CAUSEweb.org/smiles/) of 28 interactive songs of high esthetic quality designed to span literature-based learning objectives of introductory statistics that develop statistical literacy and reasoning. The interactive songs are also designed to reduce statistics anxiety and require little time or instructor expertise. The songs are interactive in that the interface solicits (and provides hints and feedback on) student contributions (concepts or examples) and then plays back the song with student inputs integrated and highlighted. After providing a brief background, this article describes requirements, challenges, and opportunities in educational songwriting for the mathematical sciences, then describes the intervention and how its special nature affected the development process. Pilot studies at a research university and at a majority Black two-year college showed that students found the innovation to be a good tool to help their learning, reduce their anxiety about statistics, have an easy to follow interface, and use high quality songs. Analysis of log files from the use of the software shows some evidence of better performance on assessments after use and informs improvements of the automated feedback. Supplemental materials for this article are available online.

Educational fun items can be readily found and used to increase student motivation and learning. We illustrate resources and strategies for a specific piece of content: Simpson's paradox.

The interaction between language and the learning of statistical concepts has been receiving increased attention. The Communication, Language, And Statistics Survey (CLASS) was developed in response to the need to focus on dynamics of language in light of the culturally and linguistically diverse environments of introductory statistics classrooms. This manuscript presents a cross-cultural evaluation of the characteristics of the CLASS III (third generation of the instrument) and provides a user-friendly cross-culturally valid version of the CLASS. Mixed methods are employed to investigate further characteristics of the CLASS III and provide a scale (CLASS IV) that may be utilized in diverse settings. These research results have implications for instructors, professional developers, and researchers to improve instruction with culturally and linguistically diverse student populations.

This literature-based, classroom-tested novel innovation of educational song (with pedagogical scaffolding) may help engage students explore and address common resistant misconceptions in probability (e.g. all outcomes are equally likely) and in statistics (e.g. correlation must imply either causation or coincidence).

English language learners are a growing demographic in secondary, two-year, four-year and research institutions where many students encounter their first course in statistics. In the statistics education literature, recent calls have been made to improve statistical education for underserved student populations, including English Language Learners (ELLs). Some have investigated how ELLs interpret instructional material and classroom practices in the statistics classroom. This study uses a sequential mixed methods approach to investigate how Spanish-speaking ELLs may respond differently to assessment items about measures of center and variation. Comprehensive analyses of this type are essential in order to identify bias and ensure fair comparisons across participant populations. Findings indicate that ELLs do not comprehend context or understand some statistical terms in the same way as non-ELLs. Study limitations, implications, and recommendations are discussed.

Mnemonics (memory aids) are often viewed as useful in helping students recall information, and thereby possibly reducing stress and freeing up more cognitive resources for higher-order thinking. However, there has been little research on statistics mnemonics, especially for large classes. This article reports on the results of a study conducted during two consecutive fall semesters at a large U.S. university. In 2014, a large sample (n = 1,487) of college students were asked about the usefulness of a set of 19 published statistics mnemonics presented in class, and in 2015, the students (n = 1,468) were presented 12 mnemonics related to inference and then asked whether or not they used mnemonics on that exam. This article discusses how students assess the usefulness of mnemonics and evaluates the relationship between using mnemonics and reducing anxiety. Additionally, the relationship between mnemonic usage and learning outcomes achievement will be discussed, along with this study's limitations and implications for teaching.

English language learners (ELLs) are a rapidly growing part of the student population in many countries. Studies on resources for language learners--especially Spanish-speaking ELLs--have focused on areas such as reading, writing, and mathematics, but not introductory probability and statistics. Semi-structured qualitative interviews investigated how a purposeful sample of six (Spanish-speaking) ELLs experienced a bilingual coin-flipping simulation applet (NLVM, 2015) and how students might use such resource to confront content misconceptions and language misunderstandings related to probability concepts covered in college introductory statistics courses. We discuss findings, limitations, directions for future research, and implications for teaching, such as handling the phrases "in the long run" and "longest run".

There has been a recent emergence of scholarship on the use of fun in the college statistics classroom, with at least 20 modalities identified. While there have been randomized experiments that suggest that fun can enhance student achievement or attitudes in statistics, these studies have generally been limited to one particular fun modality or have not been limited to the discipline of statistics. To address the efficacy of fun items in teaching statistics, a student-randomized experiment was designed to assess how specific items of fun may cause changes in statistical anxiety and learning statistics content. This experiment was conducted at two institutions of higher education with different and diverse student populations. Findings include a significant increase in correct responses to questions among students who were assigned online content with a song insert compared with those assigned content alone.

An anonymous survey was given to n = 73 students in an asynchronous online statistical literacy course at a mid-sized Hispanic Serving Institution. Informed by teaching experience, literature on lexical ambiguity, and everyday usage of statistics words and phrases, the first author designed the survey to yield insight into how students view phrases such as "average person," "random person," and "outlier person," and to explore possible connections or patterns with such phrases. Findings suggest that students view phrases such as "random person" in a way much further from standard usage than they do phrases such as "anonymous person." Considerations such as diversity, agency, and variable identification are identified as possibly affecting usage and meriting further investigation. Recommendations for teaching and future research are provided. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

A corpus of current editions of statistics textbooks was assessed to compare aspects and levels of readability for the topics of "measures of center," "line of fit," "regression analysis," and "regression inference." Analysis with lexical software of these text selections revealed that the large corpus can be described well by three index variables that summarize the lexical and grammatical complexity of the textbook excerpts. Assessment of those three variables indicates that substantial differences exist in the readability of the topics within textbooks with respect to lexical and grammatical complexity. This analysis suggests that general readability of introductory statistics topics within textbooks varies substantially and it is a recommendation that instructors: (1) be prepared to provide additional support for topics that are more grammatically and lexically complex, and (2) be aware that they can input their instructional materials into LexTutor VP or Coh-metrix as a quick screen for possible readability issues.

The framework of linguistic register and case study research on Spanish-speaking English language learners (ELLs) learning statistics informed the construction of a quantitative instrument, the Communication, Language, And Statistics Survey (CLASS). CLASS aims to assess whether ELLs and non-ELLs approach the learning of statistics differently with respect to the distinctive linguistic features of the field of statistics and with respect to language resources they bring to the class. The CLASS was administered to all (n = 137) students in an introductory statistics literacy course at a university with a majority Mexican-American student body. Findings suggest ELLs often have distinctive patterns in how they experience aspects of statistics instruction (e.g., wait time) as well as movement between mathematics/statistics and everyday registers. (Contains 5 tables.)

This study examines statistics instructors' use of fun as well as their motivations, hesitations, and awareness of resources. In 2011, a survey was administered to attendees at a national statistics education conference, and follow-up qualitative interviews were conducted with 16 of those ("N" = 249) surveyed to provide further context for interpreting the quantitative results. Motivations were similar for men and women, but female instructors admitted more hesitations in many areas. While many instructors are using or are open to using fun in the statistics classroom, the findings suggest that not having available resources at hand and not being aware of resources such as the CAUSEweb collection are major hesitations. Methods of alleviating hesitations are discussed.

Every two years in the United States, districts in each state elect representatives to the U.S. House of Representatives. The district boundaries are not permanent; rather, they are redrawn every ten years in a process known as redistricting. Mathematics is useful in understanding this important and often contentious process. Redistricting is a rich context for teaching and learning mathematics, one that illuminates both American democracy and important mathematical ideas. This article offers suggestions for classroom implementation as well as resources for further exploration. (Contains 4 figures, 1 table and 8 online resources.)

Undergraduate students who are pre-service teachers need to make connections between the college mathematics they are learning and the pre-college mathematics they will be teaching. Spanning a broad range of undergraduate curricula, this article describes useful lesser-known connections, explorations, and original proofs involving fractions. In particular, we use standard tools of number theory to investigate when an integer results from "bc/(b + c)", an expression that arises from the not uncommon situation of adding fractions with a common numerator.

The first day of a course has great potential to set the tone for the entire course, planting the seeds for habits of mind and questioning and setting in motion expectations for classroom discourse. Rather than let the first meeting contain little besides going over the syllabus, the instructor (Lesser) decided to use two sustained open-ended scenarios to put in place from the start the problem-based inquiry learning approach he wanted to use throughout most of the course. After reviewing the literatures involved, this paper shares a description of the lesson's design and instructional cycle and a discourse analysis of that lesson's implementation. Strategies identified by the case study analysis include varying participation structures, well-crafted problems, and the instructor's role as facilitator and co-learner. (Contains 1 figure, 2 tables and 1 footnote.)

The least squares method of fitting a line is not one that naturally occurs to students. We present three tasks to understand student views on how lines may be fit.

Being able to select, use, and interpret measures of center is expected of all secondary students. Discussing average class size can be a motivational vehicle for exploring this topic because students (and teachers) at all grade levels notice when they have significantly bigger classes and high school juniors and seniors see average class size touted in the publicity brochures they receive from colleges. Also, educators, administrators, policy makers, and parents are concerned about the impact class size may have on student achievement and equity. Finally, using situations that readily yield results that students initially find counterintuitive can be motivating. This article considers a classic example of class size and illustrates how the use of small data sets and simple numbers can have pedagogical benefits. (Contains 1 figure and 2 tables.)

This paper presents an overview of modalities that can be used to make learning statistics fun. Representative examples or points of departure in the literature are provided for no less than 20 modalities. Empirical evidence of effectiveness specific to statistics education is starting to emerge for some of these modalities--namely, humor, song, and cartoons. To reinforce their effectiveness as an intentional teaching tool, the authors offer practical implementation tips. (Contains 1 table.)

Though traditionally viewed as value-free, mathematics is actually one of the most powerful, yet underutilized, venues for working towards the goals of critical pedagogy--social, political and economic justice for all. This emerging awareness is due to how critical mathematics educators such as Frankenstein, Skovsmose and Gutstein have applied the work of Freire. Freire's argument that critical education involves problem posing that challenges all to reconsider and recreate prior knowledge reads like a progressive definition of mathematical thinking. Frankenstein (1990) supports the idea that critical mathematics should involve the ability to ask basic statistical questions in order to deepen one's appreciation of particular issues and should not be taught as isolated formulas with little relevance to individual experiences. In this article, the authors discuss why mathematics rarely makes connections between applications and theory and even fewer connections to culturally relevant issues in students' lives. They then share specific examples of social justice topics to which instructors have applied mathematics in the classroom. Lastly, they provide suggestions for teaching meaningful mathematics.

This article describes an innovative curriculum module the first author created on the two-way exchange between statistics and applied ethics. The module, having no particular mathematical prerequisites beyond high school algebra, is part of an undergraduate interdisciplinary ethics course which begins with a 3-week introduction to basic applied ethics taught by a philosophy professor (the second author), and continues with 3-week modules from professors in various other disciplines. The first author's module's emphasis on conceptual and critical thinking makes it easily adaptable to service-level courses as well as readily expandable for more mathematically sophisticated audiences. Through in-class explorations and discussions, the module made connections to contemporary topics such as the death penalty, equal pay for equal work, and profiling. This article shares examples, resources, strategies and lessons learned for instructors wishing to develop their own modules of various lengths. (Contains 1 figure.)