Education Commons^™

Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma

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Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.

A Lab Skills Diagnostic Test, John Zwart

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The American Association of Physics Teachers recommends that physics majors have proficiency in the following lab skills: constructing knowledge, modeling, designing experiments, analyzing and visualizing data, and communicating physics. I have developed a brief multiple-choice questionnaire to assess incoming students’ lab skill level in these areas. It was administered as both a pre-test and post-test for the first semester of introductory calculus-based physics. Preliminary results indicate that little improvement on the skills tested occurs without explicit instruction.

Mentoring Undergraduate Research In Statistics: Reaping The Benefits And Overcoming The Barriers, Joseph R. Nolan, Kelly S. Mcconville, Vittorio Addona, Nathan L. Tintle, Dennis K. Pearl

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Undergraduate research experiences (UREs), whether within the context of a mentor-mentee experience or a classroom framework, represent an excellent opportunity to expose students to the independent scholarship model. The high impact of undergraduate research has received recent attention in the context of STEM disciplines. Reflecting a 2017 survey of statistics faculty, this article examines the perceived benefits of UREs, as well as barriers to the incorporation of UREs, specifically within the field of statistics. Viewpoints of students, faculty mentors, and institutions are investigated. Further, the article offers several strategies for leveraging characteristics unique to the field of statistics to overcome …

Systematic Errors In Video Analysis, Tim Martin, Kayt Frisch, John Zwart

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Video analysis helps students to connect physical, mathematical, and graphical models with the phenomena that the models represent and improves student kinematic graph interpretation skills. The wide-spread availability of easy to use software packages like Logger Pro (Vernier), Capstone (PASCO), and Tracker have led to many introductory physics courses adopting video analysis techniques in the classroom. Such uses include high-speed cameras to study rocket launches and other innovative applications. In this paper, we will look at ways in which some common systematic errors can affect outcomes.

Student Gains In Conceptual Understanding In Introductory Statistics With And Without A Curriculum Focused On Simulation-Based Inference, Beth Chance, Stephanie Mendoza, Nathan L. Tintle

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Using “simulation-based inference” (SBI) such as randomization tests as the primary vehicle for introducing students to the logic and scope of statistical inference has been advocated with the potential of improving student understanding of statistical inference, as well as the statistical investigative process as a whole. Moving beyond the individual class activity, entirely revised introductory statistics curricula centering on these ideas have been developed and tested. In this presentation we will discuss three years of cross-institutional tertiary-level data in the United States comparing SBI-focused curricula and non-SBI curricula (roughly 15,000 students). We examine several pre/post measures of conceptual understanding in …

Development Of A Tool To Assess Students’ Conceptual Understanding In Introductory Statistics, Nathan L. Tintle, Jill Vander Stoep

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Few tools exist to assess students’ conceptual understanding in post-secondary, introductory statistics courses. The CAOS test is widely considered to be the gold standard, but was first published in 2007 and does not necessarily reflect some of the changes in student learning at the secondary level. Furthermore, it may not be sensitive enough to measure student conceptual understanding in modern post-secondary statistics courses (e.g., simulation-based inference). In this paper we will describe the process of developing a new instrument which uses some CAOS items, as well as additional new items to improve validity and reliability. We will share the validity …

Finding Meaning In A Multivariable World: A Conceptual Approach To An Algebra-Based Second Course In Statistics, Karen Mcgaughey, Beth Chance, Nathan L. Tintle, Soma Roy, Todd Swanson, Jill Vander Stoep

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Although the teaching of the first course in statistics has improved dramatically in recent years, there has been less focus on a similarly conceptual-based second course aimed at non-majors. We present a curriculum for the second course, designed to expand statistical literacy across disciplines, which focuses on conceptual understanding of multivariable relationships through data visualization, study design, the role of confounding variables, reduction of unexplained variation, and simulation-based inference, rather than the mathematically-based discourse often used in the second course. Our curriculum uses a student-centered pedagogical approach, utilizing guided discovery activities based on real-world case studies, facilitated by student-focused technology …

Start A Math Teacher Circle: Connect K-12 Teachers With Engaging, Approachable, And Meaningful Mathematical Problems, Tom Clark, Mike Janssen, Amanda Harsy, Dave Klanderman, Mandi Maxwell, Sharon Robbert

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Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented perspective because they have an algorithmic understanding of mathematics. One solution is to create a math teacher circle (MTC), which provides conceptual and inquiry-based learning activities and builds professionalism among the teachers. In this paper, we describe the origins of two such MTCs, highlighting the process of identifying leadership team members, submitting the grant proposal for seed money, and hosting launch events, intensive summer workshops, and monthly meetings during the academic year. We also share opportunities for professional development for college and university faculty, including research …

Mathematical Justice?, Valorie L. Zonnefeld

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"I’d like to suggest the possibility of guiding students toward more just ways of seeing and being in the world in mathematics class."

Posting about human flourishing through mathematical study­­­­­­­­ from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

http://inallthings.org/mathematical-justice/

Specifications Grading In A First Course In Abstract Algebra, Mike Janssen

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Specifications grading offers an alternative to more traditional, points-based grading and assessment structures. In place of partial credit, students are assessed pass/fail on whether or not they have achieved the learning outcomes being assessed on a given piece of work according to certain specifications, with limited opportunities for revision of non-passing work. This talk will describe the learning outcomes and specifications grading system I used in my Fall 2016 abstract algebra course, as well as student responses.

Faith Connections In The Math Classroom, Valorie L. Zonnefeld, Ryan G. Zonnefeld

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Looking for ways to make faith connections in your math classroom? The Zonnefelds present a framework, developed in collaboration with local teachers, that synthesizes faith connections, the TfT framework, and Common Core standards.

Standards-Based Assessment In A Developmental Math Course, Valorie L. Zonnefeld, Michal Huizenga, Aaron Van Beek, Kate Van Weelden

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Learn why we decided to try standards-based instruction in an undergraduate, developmental algebra course and what we learned in the process.

Assessing The Association Between Quantitative Maturity And Student Performance In Simulation-Based And Non-Simulation Based Introductory Statistics, Nathan L. Tintle

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The recent simulation-based inference movement in algebra-based introductory statistics courses has provided preliminary evidence of improved student conceptual understanding and retention of key statistical concepts. However, little is known about whether these positive effects in courses using simulation-based inference are preferentially distributed across different types of students. Recent studies investigating predictors of student performance in traditional, algebra-based introductory statistics courses (Stat 101) have focused primarily on mathematical achievement or competencies in high school and early college. Little consideration has been given to how prior experience and competency with statistical thinking may be associated with student performance in college-level courses. In …

Effects Of Growth Mindset Training On Undergraduate Statistics Students, Valorie L. Zonnefeld

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Undergraduate introductory statistics courses have experienced numerous changes in the past century, for instance, increased enrollment and diversification of students required to take the courses. Promising research has been conducted on mathematical mindsets, however, no research is available for introductory statistics courses. This presentation addresses the effect of growth mindset training on students in mathematics.

Broadening The Impact And Effectiveness Of Simulation-Based Curricula For Introductory Statistics, Nathan L. Tintle, Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson, Jill Vanderstoep

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The demands for a statistically literate society are increasing, and the introductory statistics course “Stat 101” remains the primary venue for learning statistics for the majority of high school and undergraduate students. After three decades of very fruitful activity in the areas of pedagogy and assessment, but with comparatively little pressure for rethinking the content of this course, the statistics education community has recently turned its attention to focusing on simulation-based methods, including bootstrapping and permutation tests, to illustrate core concepts of statistical inference within the context of the overall statistical investigative process. This new focus presents an opportunity to …

Mindset Training For Undergraduates In Developmental Mathematics, Valorie L. Zonnefeld, Kate Van Weelden

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This poster highlights the work of an individual study that student Kate Van Weelden did in Dr. Zonnefeld's Math 100 class. Kate was a teacher assistant who led a lab session for 6 of the students in the Math 100 course. Throughout the semester Kate implemented incremental mindset training for her 6 students. The results showed a promising avenue for improved achievement, especially among males.

Analyzing Unique-Matching Games Using Elementary Mathematics, Calvin Jongsma, Tom Clark

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We present here an analysis of the game of Spot It! that can be used as background information for the purpose of leading a math circle around the game. The presentation here follows the progression of solving the puzzle for simple cases first and culminating in the solution of the original game.

Student Performance In Curricula Centered On Simulation-Based Inference: A Preliminary Report, Beth Chance, Jimmy Wong, Nathan L. Tintle

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"Simulation-based inference"(e.g., bootstrapping and randomization tests) has been advocated recently with the goal of improving student understanding of statistical inference, as well as the statistical investigative process as a whole. Preliminary assessment data have been largely positive. This article describes the analysis of the first year of data from a multi-institution assessment effort by instructors using such an approach in a college-level introductory statistics course, some for the first time. We examine several pre-/post-measures of student attitudes and conceptual understanding of several topics in the introductory course. We highlight some patterns in the data, focusing on student level and instructor …

Combating Anti-Statistical Thinking Using Simulation-Based Methods Throughout The Undergraduate Curriculum, Nathan L. Tintle, Beth Chance, George Cobb, Soma Roy, Todd Swanson, Jill Vanderstoep

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The use of simulation-based methods for introducing inference is growing in popularity for the Stat 101 course, due in part to increasing evidence of the methods ability to improve students’ statistical thinking. This impact comes from simulation-based methods (a) clearly presenting the overarching logic of inference, (b) strengthening ties between statistics and probability/mathematical concepts, (c) encouraging a focus on the entire research process, (d) facilitating student thinking about advanced statistical concepts, (e) allowing more time to explore, do, and talk about real research and messy data, and (f) acting as a firmer foundation on which to build statistical intuition. Thus, …

Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld

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Learn about our experiences co-teaching a K–8 methods course using 1:1 tablets in a high-tech lab. This innovative course included a move away from a textbook to a dynamic research-based curriculum supported by NCTM resources and CCSSM as well as integral utilization of apps, web 2.0 tools, and professional learning networks.

Mathematician's Apology, Tom Clark

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"Better standards may help all math teachers to shape our classes to better reflect the creativity and play at the heart of mathematics."

Posting about ways to improve math's negative image­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/a-mathematicians-apology/

Practical Applications Of An Integrally Christian Approach To Teaching Mathematics, Valorie L. Zonnefeld

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Descriptions of various frameworks and approaches to integrating Christian faith in the mathematics classroom are explored, as well as examples and techniques. In particular, a subject-centered approach is advocated in contrast to the traditional teacher-centered approach or, more recently, the student-centered approach.

Subject-Centered Approach To Integrate Faith And Learning, Valorie L. Zonnefeld

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No abstract provided.

Mindsets, Attitudes, And Achievement In Undergraduate Statistics Courses, Valorie L. Zonnefeld

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The purpose of this study was to determine the effects of theories of intelligence and an intervention of incremental mindset training on students’ attitudes toward statistics and their mastery of content in an introductory statistics college course. The sample was 547 undergraduate students at a small, faith-based, liberal arts college in the Midwest.

A pretest-posttest design was used for the three instruments implemented. The Comprehensive Assessment of Outcomes in a first Statistics course (CAOS) assessed students’ statistical literacy. The Student Attitudes Towards Statistics – 36© (SATS©) assessed six components of students’ attitudes toward statistics including affect, cognitive competence, difficulty, effort, …

Students Learning From Atlanta Public Schools Cheating Scandal, Thomas M. Van Soelen

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Access full-text article on publisher's site:

http://exclusive.multibriefs.com/content/students-learning-from-atlanta-public-schools-cheating-scandal/education

Developing The Horizon Content Knowledge Of Teachers Through A Math Teachers’ Circle, Tom Clark

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Although much of the training pre-service mathematics teachers receive is either in mathematical content or educational theory and pedagogy, research indicates that mathematical knowledge for teaching (MKT), which lies in a sense at the intersection of the two, is a factor in teacher quality. Unfortunately, none of the recent improvements in teacher preparation necessarily affect in-service mathematics teachers. One successful program affecting in-service teachers nationwide is the Math Teachers’ Circle Network. One strand of MKT that I believe math teachers’ circles are in a position to affect is Horizon Content Knowledge (HCK). Although taking advanced mathematics courses may improve HCK, …

Love, Creation, Virtue As Models For Environmental Education, Jeff Ploegstra

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A look at how love, creation, and virtue should shape our conversations about the environment and environmental education.

Team Analysis And Review: Using Group Assessment For Learning, Kayt E. Frisch

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Team work is widely reported to be a highly desired skill by prospective employers and professional schools. To help my students develop teamwork skills I have been using group quizzes called “Team Analysis And Review” (TAARs) in my introductory algebra-based physics course. A TAAR takes the full 50-minute class period and the students will review the material on the quiz three times during the period: individually, in an assigned group, and finally as a whole class. The individual TAAR allows the student to identify personal gaps in their understanding of the material. The group TAAR encourages peer instruction and offers …

Weaving Experimental Skills Throughout The Introductory Laboratory, John Zwart

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The laboratory portion of an introductory course sequence can be used to meet a wide variety of goals ranging from illustrating phenomena studied in class, to building intuition about how the physical world works, to confronting the unexpected. Helping students develop experimental skills is a crucial goal that needs to be addressed in lab, especially in light of the fact that most introductory textbooks do not specifically address this topic. Important skills that students should learn in lab include how to analyze data, how to communicate results and the art of designing an experiment. This presentation will discuss how we …

Quantitative Evidence For The Use Of Simulation And Randomization In The Introductory Statistics Course, Nathan L. Tintle, Ally Rogers, Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson, Jill Vanderstoep

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The use of simulation and randomization in the introductory statistics course is gaining popularity, but what evidence is there that these approaches are improving students’ conceptual understanding and attitudes as we hope? In this talk I will discuss evidence from early full-length versions of such a curriculum, covering issues such as (a) items and scales showing improved conceptual performance compared to traditional curriculum, (b) transferability of findings to different institutions, (c) retention of conceptual understanding post-course and (d) student attitudes. Along the way I will discuss a few areas in which students in both simulation/randomization courses and the traditional course …