Innovative teaching

The Department of Mathematics & Statistics has redesigned MAT 100: Mathematics Pathway, MAT 108: Algebra for Precalculus, and MAT 125: Precalculus and introduced the Lumberjack Mathematics Center (LMC) in the Fall of 2012. Students in these redesigned coursed learn by doing mathematics – a lot of mathematics. Research has shown that the essence of learning is doing, rather than passively listening and our students are doing mathematics with immediate help available when they need it.

The Lumberjack Mathematics Center (LMC) is a student learning space designed to help students learn mathematics through the use of technology. Students have class time as well as lab time and required open lab time. They spend time on individualized online homework, quizzes and tests in the LMC. There is help available online, but more importantly in person from their instructors and tutors called Math Jacks.

For more information, Please visit the LMC.

Barbara Boschmans, Shanna Manny, Katie Louchart, and Amy Rushall have been responsible for the course redesign.

A fourth course supported in the Lumberjack Mathematics Center is the liberal arts course MATH 114: Quantitative Reasoning which is taught using a blended learning approach. THis is a project based course in which student come to a regular classroom once a week, come to the lab with their instructor once a week, and in which further lab time is required. For more information, please visit the LMC.

A blended approach for the course was first tried by Nichole DuBal and John Hagood in 2009-10 with class time given up for on-line work. This approach has some resource savings but appeared to have little affect on overall student learning. When the redesign took advantage of the Lumberjack Mathematics Center in Fall 2012, with Matt Fahy at the helm, lab time was then required and greater student success followed.

In a traditional classroom, content is delivered in class; students work problems as homework with no help at hand if they get stuck. When the pedagogy is inverted, students get the content at home and come to class to have concepts reinforced before working on problems for much of the class period. This approach guarantees student engagement, and with help available there is efficiency in the time spent on learning.

Semester long approaches of this kind have been used at NAU by Amy Rushall (Finite Mathematics and Precalculus), Shannon Guerrero (Principles of Mathematics II), and Ellie Kennedy (Calculus II, Calculus III and Differential Equations). How to best implement the flipped classroom is an active research area.

Inquiry-based learning (IBL) manifests itself in different contexts. In particular, an IBL practitioner often modifies his/her approach from one class to the next . In many mathematics classrooms, doing mathematics means following the rules dictated by the teacher and remembering and applying these rules. However, an IBL approach challenges students to think like mathematicians and to acquire their own knowledge by creating/discovering mathematics. In general, IBL is a student-centered method of teaching mathematics.

According to the Academy of Inquiry-Based Learning, IBL engages students in sense-making activities. Students are given tasks requiring them to:

• solve problems
• conjecture
• experiment
• explore
• create
• communicate

Rather than showing facts or a clear, smooth path to a solution, the instructor guides and mentors students via well-crafted problems through an adventure in mathematical discovery. Effective IBL courses encourage deep engagement in rich mathematical activities and provide opportunities to collaborate with peers (either through class presentations or group-oriented work). These are known as the “twin pillars” in Sandra Larsen’s work on IBL.

There are two essential elements to IBL. Students should as much as possible be responsible for:

1. guiding the acquisition of knowledge, and
2. validating the ideas presented

Dr. Dana Ernst is currently a Special Projects Coordinator for the Academy of Inquiry-Based Learning and regularly blogs about the nuts and bolts of IBL, as well as its benefits on both his personal blog and Math Ed Matter, which is a monthly column sponsored by the Mathematical Association of America. For more information on IBL, see Dana’s IBL Resources page and his blog post titled, What the Heck is IBL?

Ellie Blair, Dana Ernst, Angela Hodge, John Neuberger and Nandor Sieben are all users of IBL, sometimes known as the modified Moore method, in their classrooms.

In the most traditional mathematics classrooms an instructor writes notes-definitions, theorems, and points of advice and examples-on the board while students frantically try to copy everything down. Many do not even try to comprehend what has been said, others are unsuccessful in their attempts to do so. The end product is another version of the textbook, this time in the student’s own handwriting.

Interactive Note Taking (INT) begins with a skeleton of the class notes in the form of a workbook. The students then add to this skeleton during class adding missing details and their own notes to what is already there. This allows students greater engagement with the material during class, a greater chance of comprehending the material there and an alternative to the text in which they have a degree of ownership.

Jeff Rushall has been the main promoter of INT at Northern Arizona University, and has applied this method in classes from Precalculus through Number Theory. Other faculty members have also used this approach.