By Fan (Luisa) Li
Fan (Luisa) Li, Educational Technology Specialist at the Center for Teaching and Learning, talked with Dr. Donna Molinek, Duke Kunshan University visiting math professor from Davidson College, about her use of reading guides in math classes to scaffold preparation process and improve student engagement.
Before I went to observe Prof. Donna Molinek’s class, Math202 Linear Algebra, I had the presumption that I would have learned so much about active learning for math, problem-based learning, low-stakes assessment, collaborative class activity, and effective use of digital resources. Yes, I did observe all of those. However, to me, the most unexpected instructional tool used in this math class is the reading guides. It took me quite some time to fully understand how important it is for students to use reading guides in a math class and why they love them.
Prof. Donna Molinek first heard of reading guides as a way to help students prepare ahead of time for math class at the 2017 Mathematical Association of America (MAA) MathFest. She was fascinated by the idea and has since used it in high-level math classes such as “Real Analysis and Topology,” and now in an introductory level course “Math202 Linear Algebra.” It is a common practice for math professors to instruct students to prepare in advance, for example, “Read Chapter 2, Section 1 and 2 before class.” But this instruction may not be helpful to a student just starting in college math. Prof. Molinek explained, “To a mathematician, to read something really means to understand.” Students need guidance to identify mathematical notations, understand the definition of a theorem, and work on the sample problems in the text.
Many math instructors from K-12 to college classrooms share the same concerns. Learning math is like learning a language (Adams, 2003).1 However rarely a math student is given proper instructions to comprehend and analyze a math text before going to the classroom. Some math professors have used similar advance organizer tools in different formats, such as Note Launchers (Helms & Helms, 2010)2 and Anticipation Guides (Adams, Pegg, & Case, 2015),3 to scaffold the preparation process.
Guided preparation before class
Prof. Molinek distributes reading guides (digital copy) to students before the class via the Sakai course site. They are usually 3-4 questions long. Students print them out and work through them when studying the text by themselves or with a couple of classmates. It helps students learn to read and understand math texts. A typical reading guide includes a brief instruction of the reading task and a set of relevant problems. Students might be engaged in:
- true/false questions about definitions or the hypotheses and conclusions of a theorem;
- creating examples which illustrate definitions or concepts;
- filling in details of computations that are left out of the text examples;
- explaining a line in a proof or a comment in the text;
- working an example following the method given in the text.
Reading guides are graded for completeness and corrections. Students are encouraged not to erase wrong answers, but cross out and correct their responses so they can reflect on what they’ve learned. Besides, they are encouraged to work in groups and discuss the text before finishing the reading guides individually. Talking with others is especially useful for this course because linear algebra is as much about explanation and reasoning as the computation of problems (Lay, Lay, & McDonald, 2015).4
“It is important to let students know that it’s okay not to master concepts from a first exposure, and developing an understanding is a back-and-forth process.” – Donna Molinek
Increased student engagement
So when students come to the class, they not only have read the text but have formed a basic understanding of the content. The first activity of each class session is to compare reading guide answers in small groups. Tables are arranged so that students sit and form small groups of 4 or 5 when they come in. Prof. Molinek goes through the reading guide quickly while walking between tables. Students take notes, look, and talk with each other, instead of just seeing the front of the class. Often a question that arises from their discussions launches a more in-depth conversation about the material being covered. The professor is able to start from where they are instead of introducing concepts and terms they haven’t seen or repeat things they already understand.
Naturally, there’s more time for discussion in the class and the discussion goes deeper and faster. At DKU, the fast pace means that getting behind or not following class discussions can have cumulative effects. Having reading guides almost every day helps students focus on what will be covered in class and let them be familiar with terms and examples ahead of time. Consequently, they may participate in class discussions more and even have more opportunities to help their peers by doing explanations and collaborative problem-solving. Students realize that learning mathematics is not a passive activity with someone telling them how they solve problems; but instead that they experiment, revise, and communicate.
Student feedback
Within a couple of weeks, students have gotten used to a beautiful (because math is beautiful!) weekly learning cycle composed of readings, reading guides, class discussions, level-up assignments, writs (between quizzes and exams), and extra office hours. “There’s still a lot of work,” one student commented. “But now I go to the class with a clear understanding of the content that’ll be covered.” Some other students concurred. They prefer this type of interactive class to the traditional lecture class. A student laughed, “Now I cannot fall in sleep in the class.” More importantly, students feel they are supported while learning independently outside the classroom. Reading guides are perfect to help them navigate through difficult math text before the class and lead them to take a deep dive during group discussions and level-up assignments.
References
- Adams, A. E., Pegg, J., & Case, M. (2015). Anticipation guides: Reading for mathematics understanding. The Mathematics Teacher, 108(7), 498-504.
- Adams, L. T. (2003). Reading mathematics: More than words can say. The Reading Teacher, 56(8), 786-795.
- Helms, J. W., & Helms, K. T. (2010). Note launchers: Promoting active reading of mathematics textbooks. Journal of College Reading and Learning, 41(1), 109-119.
- Lay, D. C., Lay, S. R., & McDonald, J. J. (2015). Linear Algebra and Its Applications (5th ed.). Boston: Pearson.
Faculty Introduction
Donna Molinek
Professor of Mathematics, Davidson College 1992-present; Duke Kunshan University Fall 2019
Dr. Molinek’s research interest is in dynamical systems. More recently her interests have focused on using cellular automata to model the spread of disease (specifically HIV) in the body. She also enjoys working with students on research projects they are interested in.
Dr. Molinek loves teaching any course in the curriculum. She especially enjoys seeing how math is applied and relates to topics within the classroom. Dr. Molinek is also invested in making sure that all students feel included and can thrive while studying mathematics.
She received her degrees in the following universities:
Bachelor of Science in Mathematics. University of Alaska, Anchorage. 1984.
Master of Science in Mathematics. Northern Arizona University. 1986.
Ph.D. in Mathematics. University of North Carolina at Chapel Hill. 1992.
