By guest
writers April Strom Scottsdale Community College and
James Álvarez University of Texas at
Arlington

*This is the third and final installment of Teaching Tidbits highlighting the new Instructional Practices Guide (*

*IP Guide*

*) from the Mathematical Association of America (*

*MAA*

*). This evidence-based guide is a complement to the*

*Curriculum Guide*

*published in 2015. The guide provides significant resources for faculty focused on teaching mathematics using ideas grounded in research. Many thanks to April Strom and James Álvarez , lead writers for the Classroom Practices section, for providing this post.*

Have you
wondered how to increase student engagement in your courses or searched for
ideas to help curious colleagues enhance their classroom practices? Well, the
Mathematical Association of America’s Instructional Practices Guide (MAA IP
Guide) may be an answer for you! The MAA IP Guide is purposefully written for
all college and university mathematics faculty and graduate students who wish
to enhance their instructional practices. A valuable feature of the MAA IP
Guide is that it doesn't need to be read from cover to cover. Rather readers
can begin, depending on their interests, with any chapter. The MAA IP Guide
contains 4 main chapters: Classroom Practices, Assessment, Design Practices,
and Cross-cutting Themes (such as Technology and Equity). In this post, we take
a deeper dive into the Classroom Practices chapter of the MAA IP Guide, which
can be downloaded in full for free here.

The
Classroom Practices chapter is partitioned into two primary sections: (1)
fostering student engagement and (2) selecting appropriate mathematical tasks.
Moreover, the chapter is designed such that quick-to-implement instructional
practices are presented upfront in the chapter followed by ideas that require
more preparation to fully implement. The message is clear: we want to embrace,
encourage, and support active learning strategies in the teaching and learning
of collegiate mathematics!

**Classroom practices aimed to foster student engagement can build from the research-based idea that students learn best when they are engaged in their learning (e.g., Freeman, et al., 2014). Consistent use of active learning strategies in the classroom also provide a pathway for more equitable learning outcomes for students with demographic characteristics who have been historically underrepresented in science, technology, engineering, and mathematics (STEM) fields (e.g., Laursen, Hassi, Kogan, & Weston, 2014). In this section we illustrate what it means to be actively engaged in learning and offer suggestions to foster student engagement.**

*Fostering Student Engagement:*
To foster
student engagement, the MAA IP Guide promotes the notion of building a
classroom community from the first day of class. Community and sense of
belonging are more likely to flourish in classrooms where the instructor
incorporates student-centered learning approaches (c.f. Slavin, 1996; Rendon,
1994). Thus, establishing norms for active engagement or taking steps to
increase a student’s sense of belonging to the classroom community also impacts
the quality of student engagement in the classroom. We begin by providing
suggestions on how to build a classroom community and then describe
quick-to-implement strategies (e.g., wait time after questioning and one-minute
papers), followed by more elaborate strategies that may require more
preparation (e.g., collaborative learning strategies, flipped classroom,
just-in-time teaching).

Of
course, fostering student engagement through active learning strategies
requires thoughtful consideration of the mathematical tasks that will support
the work you want to accomplish with your students. In the next section, we
focus on part 2 of the MAA IP Guide:

**Stein, Grover, and Henningsen (1996) define a mathematical task as a set of problems or a single complex problem that focuses student attention on a particular mathematical idea. Selecting appropriate mathematical tasks is critical for fostering student engagement because the tasks chosen provide the conduit for meaningful discussion and mathematical reasoning. But, how does an instructor know when a mathematical task is appropriate? There does not appear to be one single idea of what constitutes appropriateness in the research literature or in practice. Rather, appropriateness appears to be determined from a linear combination of a number of factors. The successful selection of an appropriate mathematical task seems to involve two related ideas:**

*Selecting Appropriate Mathematical Tasks:*- The
**intrinsic appropriateness**of the task, by which we mean the aspects of the task itself that lend itself to effective learning; and - The
**extrinsic appropriateness**of the task, by which we mean external factors involving the learning environment that affect how well students will learn from the task.

In this
section we elaborate on

**group-worthy tasks**, which provide opportunities for students to develop deeper mathematical meaning for ideas, model and apply their knowledge to new situations, make connections across representations and ideas, and engage in higher-level reasoning where students discuss assumptions, general reasoning strategies, and conclusions. Group-worthy tasks can be characterized in terms of the cognitive demand required and they are often considered as high-level cognitive demand (see Stein et al. (1996) for a discussion on low-level and high-level cognitive demand).
When
implementing active learning strategies in the classroom, it is important to
keep in mind the notion of communication: reading, writing, presenting, and
visualizing of mathematics. The MAA IP Guide leverages the Common Core
Standards for Mathematical Practice, specifically the idea of SMP3: constructs
viable arguments and critiques the reasoning of others, where students are
expected to justify their thinking publicly through verbal and written
mathematics. Students construct viable arguments as they engage in mathematical
problem solving tasks by articulating their reasoning as they demonstrate their
solution to the problem. These arguments can be made for solutions to abstract
problems and proofs as well as for mathematical modeling and other problems
with real world connections. Students should come to interpret the word
“viable” as “possible” so that during presentations students recognize that
they are considering a possible solution which requires analysis in order to
determine its mathematical worthiness.

**Impact on Teaching Evaluations**

Whenever
new teaching strategies are implemented in the classroom, faculty take a risk
that student feedback surveys of their teaching may not accurately reflect the
positive changes made or the deep learning achieved. Although the use of
student feedback surveys as the only tool for evaluating teaching is highly
problematic, in such cases it is important that faculty communicate their
efforts. Documenting significant efforts to implement new strategies and
collecting evidence of positive change can support this communication. Some
possible ways to do this include:

- Keep
notes; use them to write a brief summary of the changes made and the
rationale for the changes to be shared with administrators or tenure and
promotion committees.
- Document
positive student feedback and comments, especially regarding their
learning experience.
- Put
negative comments into perspective. For example, if students make negative
comments about working on open-ended problems, provide a rationale and
explanation for the implementation of these types of tasks.
- Save
examples of student work that represent the quality of the mathematical
work and learning taking place and include or explain this in the summary
of changes to the course delivery.

Although
negative student feedback surveys of teaching may be discouraging, it is
important to put the survey feedback into context and to remember that
implementing new strategies and techniques takes practice (i.e., don’t give up
after the first time you try it). Students also need time and practice to
acclimate to new ways of learning, so having several courses that require
active engagement may also affect the way they react to active engagement in
your course. Bringing these issues to the attention of the person or committee
that evaluates your teaching and collecting evidence of your efforts to
supplement student feedback surveys may help mitigate possible apprehension in
trying new strategies to encourage active engagement in the classroom.

To learn
more about Classroom Practice, download the MAA
IP Guide and use it as a resource to increase student engagement. And don’t
forget to share broadly with others!

**References**

Freeman,
S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., &
Wenderoth, M. P. (2014). Active learning increases student performance in
science, engineering, and mathematics.

*Proceedings of the National Academy of Sciences, 111*(23), 8410-8415.
Laursen,
S. L., Hassi, M. L., Kogan, M., & Weston, T. J. (2014). Benefits for women
and men of inquiry-based learning in college mathematics: A multi-institution
study.

*Journal for Research in Mathematics Education*,*45*(4), 406-418.
Rendon,
L. I. (1994). Validating culturally diverse students toward a new model of
learning and student development.

*Innovative Higher Education*,*19*(1), 33.
Slavin,
R. W. (1996). Research on cooperative learning and achievement: What we know,
what we need to know.

*Contemporary Educational Psychology, 21*, 43-69.
Stein, M.
K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for
mathematical thinking and reasoning: An analysis of mathematical tasks used in
reform classrooms.

*American Educational Research Journal*,*33*(2), 455-488.