The MAA Instructional Practices Guide

By Benjamin Braun, University of Kentucky

In December 2017, the MAA released the Instructional Practices Guide (IP Guide), for which I served on the Steering Committee as a lead writer. The IP Guide is a substantial resource focused on the following five topics:

  • Classroom Practices (CP)
  • Assessment Practices (AP)
  • Course design practices (DP)
  • Technology (XT)
  • Equity (XE)

The IP Guide was designed with the intention of having independent sections be relatively accessible, so reading it from start to finish is not necessarily the best way to use it — I do recommend that everyone begin by reading the Manifesto and Introduction in the Front Matter of the IP Guide. My goal in this article is to provide three suggested starting points for faculty who are interested in using the IP Guide to inform their teaching, since it can be a bit daunting to identify where to start with this document. I want to emphasize that these suggestions are meant to be inspiration rather than prescription. My hope is that this article might be useful as a roadmap for department leaders incorporating the IP Guide for seminars, workshops, or other professional development activities with their faculty.

My belief is that faculty can be effective teachers using many different teaching techniques — there is no single “best way” to teach. Thus, our goal for faculty should be to gradually expand the teaching techniques they are familiar with, in order to create a “teaching toolbox” full of methods, ideas, and activities. With this in mind, I will frame my suggested starting points for the IP Guide based on the level of previous experience a reader has had with different teaching techniques, assessment structures, and course design frameworks.

For Faculty With Experience Using Mainly “Traditional” Teaching Techniques, e.g. Instructor Lectures, Problem Sets for Homework, In-Class Exams, etc.

Many readers of the IP Guide will have had their primary teaching experience be with what I refer to as “traditional” methods — by this I mean that the majority of class time is spent in a lecture format (even if it is somewhat interactive), the students are evaluated using problem sets for homework given once or twice per week and using 3-4 in-class exams, and the goals for student learning listed in the course syllabus are a list of content topics to be covered. For faculty who feel that this generally describes their previous teaching experience, I recommend starting with the following sections.

  • CP.1.1. Building a classroom community
  • CP.1.2. Wait time
  • CP.1.3. Responding to student contributions in the classroom
  • CP.1.5. Collaborative learning strategies
  • AP.1. Basics about assessment
  • AP.3. Summative assessment
  • AP.4. Assessments that promote student communication
  • DP.1.1. Questions for design
  • XE.4. Attending to equity

The selections from the Classroom Practices chapter all focus on short and simple teaching techniques that can be used in any class. For example, CP.1.1. discusses how to handle the first day of class in a student-centered manner, and then the following CP sections build on this by providing examples of techniques such as think-pair-share or paired board work that use 3-10 minutes of class time to engage students. These are natural first steps for instructors who are most familiar with teaching exclusively via lecture.

The selections from the assessment chapter focus on two goals. The first goal is for instructors to be able to increase the quality of exams that are given to students, which is the focus of AP.3. on Summative Assessment. Second, the example assignments in Section AP.4. provide an opportunity for faculty to have students reflect on their experiences in their courses, both from a mathematical and personal perspective.

The final two sections regarding course design and equity are intended to spark reflection on the part of faculty members. For example, section DP.1.1. contains a list of important questions for faculty to ask themselves prior to the start of a course, and section XE.4. provides three concrete examples of ways in which faculty can and should include equity considerations in their teaching.

For Faculty With Experience Using Some Non-Traditional Teaching Methods, e.g. Think-Pair-Share, In-Class Group Work, Reflective Essays, Lab Reports, Take-Home Exams, etc.

For those faculty who have some experience with non-traditional teaching methods, I recommend starting with the following sections.

  • CP.1.7. Developing persistence in problem solving
  • CP.1.8. Inquiry-based teaching and learning strategies
  • CP.1.9. Peer instruction and technology
  • CP.2.1. Intrinsic appropriateness: what makes a mathematical task appropriate?
  • CP.2.2. Extrinsic appropriateness
  • CP.2.6. Communication: Reading, writing, presenting, visualizing
  • AP.2. Formative assessment creates an assessment cycle
  • AP.3.3. Creating and selecting problems for summative assessment
  • AP.4. Assessments that promote student communication
  • DP.1. Introduction to design practices
  • DP.2.2. Designing mathematical activities and interactive discussions
  • XE.2. Definitions (in equity section)

For the selections from the Classroom Practices chapter, these sections focus on more “ambitious” teaching techniques that are more approachable once an instructor feels comfortable with smaller-scale methods such as think-pair-share. The three subsections from CP.2. are not discussions of techniques per se, but rather general frameworks through which to consider questions about task design for student activities.

The three sections from the assessment chapter indicated here provide three perspectives on student learning. The first is through the lens of formative assessment, and AP.2. provides both research-based frameworks for defining formative assessment and examples of how to implement formative techniques. Complementing this, AP.3.3. provides a taxonomy for instructors to use when writing exams (summative assessments) to evaluate student learning. Finally, as mentioned in the previous set of starting points, the example assignments in Section AP.4. provide an opportunity for faculty to have students reflect on their experiences in their courses, both from a mathematical and personal perspective.

For instructors with more experience using non-traditional teaching methods, the idea of framing their activities within a more coherent overall course design should be a natural progression. Because it is most natural to begin to engage with deeper consideration of course design from the perspective of activities and discussions, DP.1. an DP.2.2. are the recommended sections to begin with. Supporting an increased awareness of the role of course design, section XE.2. discusses important aspects of equity that should play a prominent role in every course.

For Faculty With Experience Using Multiple Pedagogical Techniques and Strategies, e.g. Inquiry-Based Learning, Online Courses, Service Learning, Explicitly Designed Formative and Summative Student Assessment, Course Projects, Universal Design for Learning, etc.

For faculty who have extensive experience with a range of teaching methods, the sections of the IP Guide that will likely be of the most interest are those that dive into some of the theoretical frameworks for teaching and learning, such as the following.

  • CP.2. Selecting appropriate mathematical tasks
  • AP.2. Formative assessment creates an assessment cycle
  • AP.5. Conceptual understanding: What do my students really know?
  • DP.2. Student learning outcomes and instructional design
  • DP.4. Theories of instructional design
  • XE.Equity in practic

The extended Classroom Practices section on selecting appropriate mathematical tasks provides a broad discussion of theoretical frameworks such as Vygotsky’s ZPD theory and cognitive load theory, along with illustrative examples. Further, the discussion of Error Analysis in subsection CP.2.7. provides a refined perspective on how to handle student slips, errors, and misconceptions. The Assessment Practices section on formative assessment provides research-based frameworks for defining formative assessment and examples of how to implement formative techniques. The Assessment section on conceptual understanding is a detailed explanation of concept inventories, including examples and a discussion of how to incorporate items from concept inventories into assessment schemes.

Finally, the discussion of theories of instructional design in DP.4. introduce the reader to the frameworks of backward design, realistic mathematics education, and universal design for learning. Since these three topics are far too extensive to cover within a single section, references are given for further reading. The entire section on equity should be read by every instructor, as the ideas and language from studies of equity in mathematics education are not always widely-known; however, they are especially critical for faculty who have significant experience using ambitious classroom practices but who have not had much experience with explicit equity considerations in their classes.

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