Dr. Paul Nolting's Academic Success Press Blog: A Publication Dedicated to Math Success
Dr. Paul Nolting's Academic Success Press Blog: A Publication Dedicated to Math Success
Thoughts on "Instructional Delivery in Developmental Mathematics" by C.A. Zavarella and J.M Ignash
Hello! Happy Wednesday! As our regular readers know, we typically use this day's post to bring attention to various research and field studies published in major developmental learning journals roughly during the past five years. Today, we have chosen to focus on "Instructional Delivery in Developmental Mathematics" by C.A. Zavarella and J.M. Ignash (published in The Journal of Developmental Education in 2009).
In this extremely fascinating article, Zavarella and Ignash present a quantitative study, which aims to measure the probability of student withdrawal from computer-based developmental math courses in comparison to that of traditional lecture-based courses. According to the study’s authors, students tested were more likely to withdraw from computer-based courses than traditional courses, usually after citing “personal reasons” on exit exams.
The authors are out to answer a number of questions with this study. First, they want to know whether a relationship exists between students’ learning styles and their completion or withdrawal from developmental math courses. Second, they want to determine whether the motivations for taking a particular course in a particular format play a significant role in the eventual withdrawal process. Third, they want to explore the relationship between College Placement Test scores and withdrawal rates.
The study followed three groups of students: a, 69 students enrolled in three sections of traditional lecture courses; b, 67 students enrolled in hybrid courses; and c, 56 students enrolled in three sections of distance learning courses. The authors collected data from a learning styles inventory each of these students took, as well as from an institutionally developed survey, which asked students for the reasons they decided to take certain courses. Finally, they tapped into their test institution’s CPT database for information on placement scores.
Ultimately, the study showed dropout rates were much higher for hybrid and distance learning students. Approximately 42% of the test subjects dropped hybrid courses, while 39% dropped an online course. Only 20% dropped their lecture course. This happened, the authors argue, because many of these courses “presented challenges [students] did not expect.” More than 50% of the students who dropped a computer-based course implied that they did not fully understand “what it takes to learn mathematics in a computer-based format.”
Our own thoughts on this: This particular study is intriguing, as it largely corroborates our own research on the topic. More often than not, when students drop online courses, they say something along the lines of “I thought it would be easier and less time consuming.” With this in mind, we recommend that institutions create a two-way channel of communication between themselves and their students. Students must understand the unique challenges of online courses.
For more, please see: Zavarella, C.A., Ignash, J.M. “Instructional Delivery in Developmental Mathematics: Impact on Retention.” Journal of Developmental Education, Volume 32, Issue 3, Spring 2009. Pages 2-13.
Looking Back to The Beginning of the Redesign Movement: A Discussion of B.S. Bonham and H.R. Boylan's 2012 Article "Developmental Mathematics: Challenges, Practices, and Recent Initiatives."
For the foreseeable future, the ASP Blog plans to use Wednesdays to bring attention to various research and field studies published in major developmental learning journals roughly during the past five years. Given that we are running the first of these articles between Part One and Part Two of our interview with Hunter R. Boylan, we thought we'd start by revisiting an important article Boylan published with B.S. Bonham in the Winter 2012 edition of the Journal of Developmental Education.
This article is particularly important, as it shows just how little things have changed in the post-redesign world. Written in 2012, it describes what was then “the current state" of developmental education. It also "discusses major initiatives designed to reform and improve success rates, and identifies research-based teaching practices associated with improved student performance in developmental mathematics courses.” Bonham and Boylan describe in detail how developmental education came to enter the very center of the national debate over higher education, especially with regards to efficacy and budget concerns.
Throughout the study, the authors explore the debate over developmental mathematics, chiefly the mainstream contention that developmental math courses often serve as “frightening obstacles” for underprepared students, many of whom have to take and retake these courses, which ultimately lengthens their time in college. According to this argument, many of these students ultimately withdraw from school. While the authors concede that this phenomenon does exist for certain students, they also point out that those students who pass their developmental mathematics course requirements “[are] just as successful in subsequent mathematic courses as those who were not required to take a developmental math course.”
The authors go on to contend that successful developmental programs utilize “multiple teaching and learning strategies.” This includes a greater focus on technology, math labs, project-based instruction, academic counseling, and proper placement policies. They also discuss at length the “math redesign model,” which first came into use during this period: chiefly, emporium, online, buffet, replacement, and linked workshops. The most effective of these “redesigns” employ research-based practices built upon “multiple teaching approaches rather than a single method.” As an example, the authors point to programs at Virginia Tech and the University of Alabama, which use technology when appropriate (i.e. for tests, quizzes, homework), but also provide supplemented instruction by small groups of teachers and tutors. “This approach,” they argue, “fosters greater student engagement with the material.”
Finally, the authors champion an industry-wide focus on affective characteristics. Research indicates, they say, that affective factors such as low self-efficacy and anxiety “can have a ‘negative and inhibitory impact on learning and performance in mathematics’” (De Corte, Verschaffel, Depaepe, 2008, p.25). This means that developmental educators must employ strategies to “help alleviate mathematics anxiety, build self-confidence, and maximize student learning.” One of these strategies, according to the authors, is to focus on study skills. Citing our own Dr. Paul Nolting’s Winning at Math text, the group explains that helping students develop these skills increases the odds that they will persist through (and not avoid) their math courses.
For more, please search for the full article at one of many article aggregators or library websites.
Bonham, B.S., Boylan, H.R. “Developmental Mathematics: Challenges, Practices, and Recent Initiatives.” Journal of Developmental Education, Volume 36, Issue 6, Winter 2012.
Developmental Education Expert Dr. Hunter Boylan Interviews Paul Nolting for the Journal of Developmental Education (Archives 2011)
In a few weeks time, we at the Academic Success Press Blog plan to a publish an extremely exciting interview we conducted last month with renowned learning expert Dr. Hunter R. Boylan. One of our main directives for the upcoming year is to cast a wider net in our coverage of the national math redesign movement. This means putting more of an emphasis on developmental learning and its current standing in the greater world of academia. Dr. Boylan, of course, is one of the leading experts on this front, and he had plenty of interesting things to say on the matter.
In the meantime, to prepare you for the conversation, we thought we'd share an article published in 2011 in which Boylan himself interviewed Dr. Nolting for the Journal of Developmental Education. The majority of the conversation revolves around the relative ineffectiveness of certain types of developmental mathematics programs, as well as the many ways institutions might fix their problems through a pedagogy dedicated to study skills, anxiety-reduction techniques, and affective characteristics. Nolting also discusses the importance of effective placement strategies, before laying out 10 “common themes” that have helped countless colleges and universities improve their developmental math programs.
As a company that has cut its teeth on promoting the importance of study skills and behavioral characteristics, it should not come as a surprise that we at Academic Success believe that students—particularly those with certain challenges—need to understand how to study before they ever set foot in a college classroom. Most high schools, however, do not prepare students with learning behaviors/study skills, especially in the area of mathematics. This is particularly true for students in developmental math courses.
With this in mind, a couple of years ago, we came across a fascinating article in the Journal of Developmental Education, which used an enlightening study to prove that study behavior is the second most important factor in student retention and success, just behind course placement. Conducted by Kevin Li, Richard Zelenka, Larry Buonaguidi, Robert Beckman, Alex Casillas, Jill Crouse, Jeff Allen, Mary Ann Hanson, Tara Acton, and Steve Robbins, the study followed just over 1,000 students who took developmental math courses between Fall 2008 and Spring 2009 at a school in the Midwest. The group recorded these students’ initial math readiness, course behavior, math knowledge, and course success.
In the end, the study found that students only succeeded in courses for which they were prepared, both in terms of math readiness and behavioral readiness. The group recommended using a model in which “each new student is assessed from both academic and behavioral risk perspectives and subsequently referred to resources for academic and behavioral skill development.” Just as important, the group recommended that institutions avoid using “one-size-fits-all” approaches to developmental courses. Instead, institutions should “take a multifaceted approach to assessing and identifying student academic and behavioral skill gaps, and, in turn, provide resources designed to address these gaps.”
We at Academic Success agree wholeheartedly. For years, Dr. Nolting has travelled the country preaching the importance of motivation, study skills and the ability to understand exactly how and when certain learning challenges affect a student’s capacity to learn and succeed. Additional research has shown teaching developmental and non-developmental students math study skills/learning behaviors during the first half of a math course has improved math success. Recently, Dr. Nolting and others at the AMATYC, NADE and MAA National Math Summits have focused on the need to improve student math learning skills as part of the national redesign movement. Wholesale approaches rarely work for developmental students—or for that matter, students without learning challenges. Each student learns in his or her own unique way. This means that it is incredibly important to work with each and every one of our students either before they reach the classroom or during the first few weeks of the semester in order to assess and compensate for any perceivable hurdles a student may have to jump on his or her way to graduation.
Readiness, Behavior, and Foundational Mathematics Course Success. Li, K., Zelenka, R., Buonaguidi, L., Beckman, R., Casillas, A., Crouse, L., Allen, J., Hanson, M.A., Acton, T., and Robbins, S. Journal of Developmental Education. 14-22.
Revisiting Bloom and the Importance of Affective Characteristics in Developmental Math Courses
As many in the field of developmental education likely already know, psychologist Benjamin Bloom first published his famous “Taxonomy of Educational Objectives” in 1956. Within this incredibly important document (and its subsequent revisions), Bloom, among many other achievements, deconstructed the importance of learning variables and assigned them value-based percentages, which created a hierarchy of sorts for the factors involved in the learning process. According to Bloom, the major variables that contribute to academic success are: IQ and cognitive entry skills (50%), quality of instruction (25%) and student affective characteristics (25%).
For years, we at Academic Success have used these percentages in our books and multimedia. For now, they remain the standard in educational psychology. According to a new study, however, Bloom may have greatly underestimated the role of one of these variables, at least as it pertains to developmental math courses. In a study conducted in 2013, Zientek, Ozel, Fong and Griffin (2013) indicated that affective variables contribute to 41% of developmental math grade variance.
According to the aforementioned authors, the following variables, among others, add up to account for over 41% of grade variance for students in developmental math courses: attendance, beliefs in resource management strategies, beliefs in motivational strategies, repeating a mathematics course, beliefs in self-regulated learning, students’ interpretations of how often teachers explained to student what will happen if they do not complete their homework, and beliefs in meeting others’ expectations.
This study provides hard data for what many of us already know through our first hand experiences with students: study skills, self-efficacy and persistence are what ultimately tip the scales for students teetering on the edge of failure. This is especially true for students in non-traditional and online courses, which require students to become better independent learners.
For more information on this subject—particularly the other nine variables the authors used to determine their percentages, please see:
Zientek, L. R. , Ozel, Z. E. Y, Fong, C. J. & Griffin, M. (2013). Student Success in developmental mathematics courses. Community College Journal of Research and Practice, 17, 990-1010.
Dr. Nolting is a national expert in assessing math learning problems, developing effective student learning strategies, assessing institutional variables that affect math success and math study skills. He is also an expert in helping students with disabilities and Wounded Warriors become successful in math. He now assists colleges and universities in redesigning their math courses to meet new curriculum requirements. He is the author of two math study skills texts: Winning at Math and My Math Success Plan.
American Mathematical Association of Two-Year Colleges presenter, Senior Lecturer-Modular