# Formula-Work-Answer-Explanation (FWAE): A Teaching and Learning Strategy

In his seminal text, Scholarship Reconsidered: Priorities of the Professoriate, Ernest Boyer (1990) directed attention to the scholarship of teaching and learning (SoTL). Those faculty who successfully engage in SoTL focus on crafting a meaningful learning experience for the student.  They use deliberate practices, which are centered on effective teaching, in course instruction.

SoTL requires that faculty take a constructivist view of their daily work, thereby becoming reflective practitioners whose efforts have a demonstrable practical bent in their classroom settings (Levinson, 2003). Simply put, faculty who engage in SoTL research are interested in examining their teaching practices and how they impact student learning.  These scholar practitioners continually seek new and innovative ways to present the curriculum and then take a retrospective look at how that innovation improves student learning.  Those who conduct SoTL research emphasize teaching for learning (Lyons, McIntosh, and Kysilka, 2002).

## The procedure

Given my propensity for learning-centered instruction, I continually seek ways to incorporate SoTL research into my classes. Formula-Work-Answer-Explanation (FWAE) is a learning-centered strategy that can be easily deployed in mathematics and statistics instruction.  It has proven to be an effective four-step strategy through which I model solving word problems in coursework.

I encourage my students to use this step-by-step strategy to arrive at a structured solution to application problems (word problems). The FWAE method is helpful and suggested for both traditional mathematical problem-solving, as well as application problems, common in advanced mathematics and statistics curricula. Accordingly, I have used this learning-centered strategy in both introductory and senior-level mathematics and statistics courses to enhance student learning success.

How does the FWAE strategy work?  It provides a four-step structured methodology to support students in critically analyzing and solving application problems.

• Step 1: Often, a formula is associated with the solution of a mathematics and/or statistics problem. If no specific formula and/or equation is associated with a given word problem, the original expression can be substituted for step 1 in the FWAE solution strategy.
• Step 2: Work – I refer to it as “plug and chug.”  Here, students extract needed information from the word problem and substitute those values into the appropriate mathematical or statistical formula.
• Step 3: Answer – Students are required to state the “answer” to the mathematical or statistical problem.
• Step 4: Explanation – Ideally, once a word problem is solved, the student should return to words to clarify meaning.

## Goal

The goal of FWAE enables students to develop a strategic method for solving mathematical and statistical problems.  This structured technique allows students to develop a consistent strategy for solving problems: formula, work, answer, explanation.  FWAE provides a tried-and-true strategy for modeling problem-solving. It is useful in helping students to connect with course content in an active learning community. It can be thought of as a way of incorporating social and emotional learning (SEL) practice into online delivery, thereby subliminally introducing compassion and consistency in the instructional process.

## Originality

Especially for those students who say, “I hate word problems. I’ve never been good at solving them.” FWAE counters that claim and offers a structured method that aids students in the development of problem-solving skills.  Proven to be a useful activity to elicit student engagement and academic performance, FWAE also helps to effect small-group interaction during implementation of live chat sessions and/or office hours.

## Transferability

While I have used the FWAE strategy almost exclusively in mathematics and statistics instruction, it is not limited to these disciplines.  Any course where students are required to create a product deliverable may benefit from a structured approach.  As important, the FWAE method taps students’ use of critical analysis skills, reading comprehension, and writing across the curriculum.

Below are two examples of how to use the FWAE methodThey are for illustrative purposes only and use basic problems in an introductory mathematics and a basic statistics course, respectively.

Example 1: Find the area of a room that is 10 feet wide and 12 feet long.
Step 1 Formula: Area = Length x Width. (Use the formula for finding the area of a rectangle.)
Step 2 Work: 10 ft. x 12 ft.
Step 3 Answer: 120 square ft.
Step 4 Explanation: The area of the room is 120 square feet or 120 ft2. Area is measured in square units. Feet x feet is square feet or feet raised to the second power. Remember that this is an application of exponents.

Example 2: Given a mean of 100, standard deviation of 5.2, what is the z-score for 120?
Step 1 Formula: Z = (Raw score – Mean)/Standard deviation. (Use the formula for finding a standardized score.)
Step 2 Work: Z =  (120-100)/5.2
Step 4 Explanation: This tells us the score 120 is 3.85 standard deviations above the mean.  It would likely be an outlier for symmetrical data where most data are usually found within 3 standard deviations of the mean.

## Scope and impact

Typically, I solve examples, step-by-step, using my strategy: Formula, Work, Answer, Explanation (FWAE).  As a proactive teaching strategy, I provide supplemental problems as uploaded curriculum files to support the learning success.  If students request a solved “sample problem” for a topic or lesson in which extra guidance is needed, I model the FWAE strategy for students in my response.

## Effectiveness

Online faculty are constantly faced with challenges in facilitating successful learner-content interaction.  I have used the FWAE strategy to promote student engagement and learning success in mathematics and statistics.

FWAE provides students with a repetitive learning strategy for critical analysis and problem-solving in mathematics and statistics. I have consistently incorporated this basic strategy into general education instruction as well.

As a teaching and learning strategy, I use FWAE to involve students in active learning; to encourage them to collaborate with other learners; and to support student interaction with content.  Using FWAE has enabled me to support student engagement in course content with success.  By modeling a consistent strategy for problem-solving, I have noted empirical data indicative of student success in terms of course completion and retention.

## Final thoughts

First, let me share: I love teaching online. The adult learners whom I serve are real people with authentic life responsibilities and challenges.  Throughout my nearly 40 years of teaching experience in secondary and postsecondary education, I have been fortunate to serve learners who are striving to better themselves and the lives of their families.

I also love the fact that I have adopted a student-centered and learning-centered philosophy of teaching and learning.  Invariably, at the end of each course, I find myself missing the students whose lives I touched but will likely never interact with again.  FWAE is one way that I focus my SoTL research on crafting a meaningful learning experience for students that has maximum impact on their acquisition of knowledge. Ultimately, I hope they will adopt and adapt this strategy to other courses and their overall academic and career success.

Dr. Ruby Evans is the executive director & senior research consultant for Academic Consulting Exchange and adjunct faculty and associate professor at Colorado Technical University in Colorado Springs, CO. She has teaching and administrative experiences that span nearly four decades and institutional settings, both public and private, across the K-20 educational spectrum.

References:

Boyer, E. L. (1990).  Scholarship reconsidered: Priorities of the professoriate.  New York: The Carnegie Foundation for the Advancement of Teaching and Jossey-Bass.

Levinson, D. L. (2003).  Introduction to faculty scholarship in community colleges.  Community College Journal of Research and Practice, 27, 575-578.

Lyons, R., McIntosh, M., & Kysilka, M. (2002).  Teaching college in an age of accountability. Upper Saddle River, NJ: Pearson Education.

Author’s note

The author wishes to acknowledge the editorial assistance and internal peer review provided by Iris Rose Hart. Retired professor of English, Santa Fe College, whose knowledge and skill improved the manuscript immensely.