Shane Goodwin
Mathematics Faculty Member
Shane Goodwin was born in Evanston, Wyoming and served a full-time mission in Guayaquil, Ecuador. He received a bachelor’s degree in mathematics education from BYU, a master’s in computer science education from the University of Oregon, and many years later, a Ph.D. from the University of Idaho in adult education.
Brother Goodwin taught mathematics, Spanish, and coached for seven years in the public schools before coming to Ricks College over 25 years ago. He helped organize the original Math 108 course, “Mathematical Tools for the Real World.”
Over the years, he has served in a few campus ward bishoprics and high councils, and was recently called as a ward clerk in his home ward. Brother Goodwin and his wife, Gail, have one son, two daughters, and two wonderful grandchildren.
Spiritual Preparation
Please respond to the question below on the devotional discussion board:
In my devotional message I will be discussing the role of external and internal motivators for learning, including the importance of finding connections that ultimately bring us small measures of joy. Please briefly share an experience you have had with either or both of these connections:
- The connections we find between two completely different disciplines. Have you ever learned about a principle or skill in one class and then discovered it playing a key role in an entirely different class?
- The connections we find in applications outside the classroom. Have you applied a principle or skill learned in a class to a job, family-life setting, or other area beyond the classroom?
Throughout all three levels of my high school, junior college, and university teaching, I have tried to gain a better understanding and appreciation of both the pressure and joy we experience in our learning. My intent is to share some simple examples of joy that may come through finding connections and making deep dives. Spoiler alert: there will be some mathematics, but it should be relatively pain-free and may even bring you a small measure of joy. I noticed, President Eyring, it appears no one is running for the exit doors.
From the outset of the Restoration, the Prophet Joseph Smith modeled what it means to be a lifetime learner. Recall that in 1832 in Kirtland, Ohio, Joseph received a revelation from the Lord instructing him to organize a “school of the prophets.” This term “school of the prophets” was at times used by Harvard and Yale in the 17 th and 18 th centuries to refer to their seminaries which helped clergy prepare for the ministry. [1] In the revelation Joseph called “the olive leaf,” we hear the Lord’s voice: “Seek ye diligently and teach one another words of wisdom; yea, seek ye out of the best books words of wisdom; seek learning, even by study and also by faith.” [2]
Joseph encouraged elders in the Kirtland area to gather intermittingly during the winter months of 1833 to 1836, to learn of both spiritual doctrine and secular topics such as history, grammar, languages, and yes, even arithmetic. As we noticed from Munyinda’s scripture [3] he shared with us today, the Lord was very much aware of the higher education His newly organized Saints would need.
It should not surprise us that Joseph, not having much formal education during his earlier years, would have developed a very focused thirst for more knowledge and wisdom. He didn’t take his learning for granted; he taught that “a man is saved no faster than he gets knowledge,” [4] and in the spring of 1843, the Prophet instructed the Saints in Illinois that
whatever principle of intelligence we attain unto in this life, it will rise with us in the resurrection. And if a person gains more knowledge and intelligence in this life through his diligence and obedience than another, he will have so much the advantage in the world to come. [5]
I find it interesting that the footnote to the word “advantage” in this verse references two scriptural examples—one being more of an external or extrinsic advantage while the other more internal or intrinsic. I will leave it to you to explore that footnote if you have an interest.
Here is a brief list of some possible extrinsic motivators for learning you surely have experienced in some fashion. Academic realities and pressures like deadlines, grades, graduation requirements, and upcoming employment opportunities help keep us moving down our individual paths of education. I believe we can find joy in our learning, both in spite of and because of these accompanying pressures, as we make steady progress one semester, one class, even one assignment at a time.
Speaking of semesters, you and I know that they can be fast-paced 14-week experiences feeling very much like academic marathons in which both professors and students pretty much have to be sprinting the full distance. Perhaps this reality of educational compression was what British zoologist and medical statistician Lancelot Hogben was referring to when he wrote,
The best therapy for emotional blocks to math is the realization that the human race took centuries or millennia to see through the midst of difficulties and paradoxes which instructors now invite us to solve in a few minutes. [6]
Regardless of whatever difficult subject area you and I are trying to learn, it is crucial that we keep our struggles in proper perspective. Simply put, mastering difficult concepts is challenging and, at times, even frustrating. When my students begin to express feelings of doubt in terms of their learning and their overall grade for the course, I try to remind them of a classic verse from Proverbs:
Wisdom is the principal thing; therefore get wisdom: and with all thy getting get understanding. [7]
Or to put it somewhat metaphorically, perhaps the understanding is like the cake, while the academic grade is like the frosting. I caution my students to not just focus on the frosting of a grade at the peril of missing out on the actual flavor and texture of the cake of understanding. In other words, as we focus our efforts and energy primarily on the cake of understanding first, rather than expending a lot of worry and stress on just the frosting of the grade, more often than not, we can lower the anxiety level of learning. Perhaps at times, when things go well, we might even be able to say that a particular concept, assignment, or exam was “a piece of cake.” Undoubtedly, grades tend to motivate us from the outside, but if we can look to motivation from inside and aim for real understanding, we will actually accelerate our learning and find more joy.
So, here is a simple flow chart that may help remind us it does take time and consistent diligence to reach “understanding.”
But if that understanding leads to small measures of joy, I believe the good news is this can re-motivate us to deeper study and faith as we repeat the cycle of learning.
I would also suggest that being motivated by extrinsic rewards only is sort of like putting in hard work while biking, hiking, or snowshoeing to get to the top of a mountain, yet never actually spending any time enjoying the amazing views during the trip.
Some of you (like our three children Matt, Katie, and Claire in this photo from several years ago) probably have hiked to the top of Table Mountain, which is located just west of the Grand Teton and rises to 11,106 feet of elevation.
What an amazing view we can get both from the top and during the long hike up. These periodic pauses we take to admire the vistas are akin to enjoying the small moments of joy in our learning and understanding, motivating us along our personal educational trails.
A very natural thing we often do in life is to look for connections. For example, how often when you meet someone for the very first time do you try to see if you both know a specific individual from your hometown, stake, or mission. Also, you probably have noticed, we try to connect in some way back to the previous week’s devotional message. With that in mind, I really appreciated Brother Ben Fryar’s message last week on the importance of connecting by sincere listening and his simple example of the connection the Savior made with the woman in the crowd touching His robe.
Now, let me introduce intrinsic motivations for learning by way of two basic connections in terms of associations within our field of study and also with regards to beauty and pattern.
Consider the following basic summation question known as a geometric series [8]—in this case, infinite sums of one-half being raised to a higher and higher power. As you are aware, the ellipsis (that is, the dot-dot-dot) signifies that the pattern continues indefinitely. Now, mathematicians like to say—tongue in cheek—that it isn’t always about finding x, but sometimes it’s about discovering why. [9]
At first, we could reason that since we can always take half of something, no matter how infinitesimally small it is, our sum would surely just keep getting bigger and bigger although at a slower and slower pace. While that is definitely true, there is a little more insight and joy to be discovered.
One way to answer the question would be to calculate partial sums looking for indications of either a convergence to an actual number or perhaps a divergence away from any particular number at all. Using a scientific calculator or spreadsheet, we get this result:
It appears our partial sums just might be converging to 1.0. But perhaps we are not 100% certain since we may have this nagging worry that sooner or later, the next iteration might total up over the 1.0. This is where the joy of finding a connection within our discipline comes to bear fruit.
Suppose we re-examine the question—not by way of a numeric approach—but rather by imagining a simpler geometric approach. Consider a square that is one unit by one unit; therefore, its complete area is one—that is, one unit-squared.
Now imagine cutting that square into two rectangles of exactly the same area (one-half of a unit-squared).
Next, we cut the upper rectangle into two squares to represent one-half of one-half, or in other words, one-fourth. Notice the numeric calculation below the figures. Each alternating iteration creates either a new smaller rectangle or a new smaller square.
Ultimately, we can see with this sketch that as we continue to take one-half of the previous square or rectangle, the sum of the individual area quantities must approach what we call a limit in mathematics.
And so on and so on.
In other words, as the squares and rectangles become infinitesimally smaller and smaller, the overall area surely has to approach one unit-squared. There is no way for these combined areas to go beyond the limit of the area of the original square, and therefore the series summates to exactly 1.0. This notion of a “limit” is one of the key underpinnings in the study of calculus and the numeric and geometric relationship is an example of how interconnections within a discipline can bring a small measure of joy.
In terms of beauty and pattern, let me share a simple example from my past. [10] Because my mother married and raised a family at a very young age, she was unable to complete her high school education. However, many years later, she qualified for further education at the junior college level and completed an associate’s degree in art. After our first child and her first grandchild, Matthew was born, my mom gave us a baby gift, a colored pencil sketch of a tessellation of birds and elephants that she had created in an art class.
As she was explaining a little about what she had sketched, it was somewhat of a surprise to her when she realized I already knew about tessellations (that is, geometric tilings of figures in a plane that neither overlap nor create any gaps).
We experienced a little bit of joy when we found something in common to discuss and saw how beauty and pattern can blend the disciplines of mathematics and art together.
Two more connections I have found very useful are practical applications beyond the classroom and connections to other disciplines. Many of you shared your experiences with these on the discussion board.
Sue Moscynski opened her comments with “It has been interesting to see how interconnected my classes have been in my journey with Pathway and BYU-Idaho. I have experienced great joy in finding the connections from one class to another, but even better is when I can apply them in my day to day life at home and work.”
Of all the different connections I can think of, language and the gospel of Jesus Christ, are among my favorite. I love the interconnections that language can bring to our educational journeys as we try to absorb new vocabulary and definitions. For example, consider the simple term “integer” in mathematics. You might remember that integers are the whole numbers in our real number line—symmetrically situated on both sides of the zero.
Whether positive, negative, or zero, the integers in my mind represent the fence posts of the real numbers. They form the basis of a branch of study referred to as discrete mathematics (and no, there isn’t another branch called “indiscrete mathematics”). With a modest amount of exploration, you start to see the connection of “integer” back to words like “integral” and “integrity.”
It is all about wholeness, and when I think of “integrity,” I think of wholeness of character—that is, someone whose actual self is moving closer and closer to his or her ideal self. This bringing together of the actual and ideal self ultimately leads me to ponder the significance of the Atonement of Jesus Christ.
Years ago, the pondering of integers from negative infinity to positive infinity, enabled me to gain a greater appreciation of the Savior’s infinite Atonement. I asked myself the question “How was it possible that the Lord could have suffered for an infinite number of sins, pains, and afflictions (as Book of Mormon prophets beautifully taught) and yet accomplish this over a finite period of time (from Gethsemane to the Resurrection)?” I reflected on the fact that, unlike the integers which are discrete, the real numbers are continuous and have density. For example, notice that the integers 2 and 3 are not going to contain any more integers between them.
But contrast that with the question of how many real numbers in decimal form exist between 2 and 3. That is, because of decimal expansion, there are going to be an infinite number of real numbers, say between 2.4 and 2.5, or perhaps 2.49 and 2.50, or even 2.499 and 2.500 and so on, regardless of how close together we pick two real numbers from the real number line.
This kind of density and potential one-to-one correspondence between the real number line and the time continuum, helped me understand—at least to a certain degree—the miracle of how the Savior could suffer infinitely over a finite period of time. To put it more boldly, I have come to the conclusion that every sin, suffering, pain, and affliction of the human race for which the Lord suffered—no matter how small nor how great—on behalf of perhaps an infinite number of worlds in the past, present, or future could in fact logically be compressed and catalogued over a finite amount of time. When one merely considers the breathtaking beauty and immensity of the real numbers and how infinity works, not only forwards and backward but in-between, we can gain an even deeper appreciation for the Savior’s infinite Atonement for all mankind. In the outstanding book “The Infinite Atonement” by Tad R. Callister, he writes beautifully,
When we more fully understand the depths to which the Savior descended, the breadth to which he reached, and the heights to which he ascended, we can more readily accept that our own sins are within the vast sphere of his conquered domain. We then become believers, not only in the Atonement’s infinite expanse, but in its intimate reach. [11]
Finally, allow me to suggest that there is joy to be found in our learning when we occasionally make our own personal deep dives into an area of interest. I experienced just last year a deep dive while working on an article I titled “The History of the Name of the Savior’s Church: A Collaborative and Revelatory Process.”
Immediately following the October 2018 talk by President Russell M. Nelson titled “The Correct Name of the Church,” I started to research the details of how the name of our faith came to be. The more I read and studied the various back stories of its development and refinement, the more fascinated I became with our 11-syllable title “The Church of Jesus Christ of Latter-day Saints.” My deep dive of learning included 10 months of researching documents from The Joseph Smith Papers and many other sources, stimulating conversations with amazing colleagues in the math, history, and religion departments, an intimidating double-blinded peer review of my original draft, and then major re-writing with outstanding editors at BYU Studies. [12] The article was finally published last fall, just prior to the year anniversary of President Nelson’s talk.
One simple lesson that struck me almost immediately was when I contrasted the story of the Liahona and the ship from the Book of Mormon. I realized that the sacred compass, referred to as “Liahona” in the scriptures, [13] came pre-built that morning when Lehi opened the door of his tent. They didn’t have to design or build it; rather, they had to learn how it functioned by the principles of faith and diligence. [14]
The ship of curious workmanship, on the other hand, was not pre-built and simply waiting offshore, ready for the precarious voyage to the promised land. Instead, Nephi and his brothers had to build it from the bottom up using inspired spiritual blueprints, making their own tools, and obviously, exerting strenuous labor along the way.
In a similar vein, the name of our church could have come pre-built—that is, handed over to the Saints in complete form—on day one. But instead, the Lord respected the agency of these early restorationists and gave them the opportunity to build the name, one inspired iteration at a time.
In 1830 in upstate New York, Joseph and Oliver started with the name “Church of Christ,” inspired by the Savior’s command found in the Nephite record. [15] Later in Kirtland, Ohio in 1834, by way of a motion proposed by Sidney Rigdon at a conference of elders and passed unanimously, the name was changed to the “Church of the Latter Day Saints.” But not long thereafter, with a little bit of pushback from members who were probably missing the Savior’s name in the title of their fledgling faith, there came an unofficial and organic melding of the two names: the “Church of Christ of the Latter Day Saints.” Finally, the slight refinement of adding “Jesus” to this name in the early months of 1838 was then followed up by a revelation to the Prophet Joseph in Far West, Missouri on April 26, 1838 and now canonized as Doctrine and Covenants section 115.
We hear the Lord’s divine confirmation and approval of the name “For thus shall my church be called in the last days, even the Church of Jesus Christ of Latter Day Saints.” [16]
Just like the construction of the ship of curious workmanship or the refinement process of the name of our church, our personal experience with higher education has to be a collaboration of our hard work and heaven’s guidance. When President Nelson described his challenge of choosing counselors for the First Presidency, he said he first interviewed all of the apostles one-by-one and pointed out that “good inspiration is based upon good information.” [17] In essence, personal revelation requires us to do our homework as we seek for heaven’s guidance. This focused and deep dive brought me joy realizing just how much the Restoration really is an ongoing process, [18] and how inspired human input shouldn’t be a source of concern as much as it should be a cause for celebration.
You and I are blessed here at BYU-Idaho to be able to blend the best of both spiritual and secular study in our own version of a “school of the prophets,” collaborating with heaven as we seek good information and good inspiration. I bear my humble testimony that the glory of God is intelligence, that we can indeed find joy in our learning through both external and internal motivations, and that our Heavenly Father and His Son Jesus Christ love each of us with an infinite and intimate reach, I so testify in the name of Jesus Christ, amen.
[1] See “A School and an Endowment,” Revelations in Context, 2016, 175; see also footnote 8.
[2] Doctrine and Covenants 88:118.
[3] Doctrine & Covenants 88:77-80.
[4] Andrew F. Ehat and Lyndon W. Cook, “The Words of Joseph Smith,” 1980, 113–114.
[5] Doctrine and Covenants 130:18–19.
[6] Lancelot Hogben, quoted in Sheila Tobias, Overcoming Math Anxiety, 1993, 225.
[7] Proverbs 4:7.
[8] I appreciate my colleague Kent Bessey in the mathematics department for reminding me of this simple example that would be appropriate for this devotional talk.
[9] See Arthur Benjamin, “The Magic of Fibonacci Numbers,” TED; ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers?language=en#t-361752 .
[10] For a short but amazing view of pattern in nature see Cristóbal Vila, “Nature by Numbers”; vimeo.com/9953368.
[11] Tad R. Callister, The Infinite Atonement, 2000, 197.
[12] A special thanks to John Thomas and Bruce Satterfield of the religion department and Michael Lenhart of the history department who inspired me to keep researching and writing on this very narrow topic in Church history.
[13] 1 Nephi 16:10; see also Alma 37:38.
[14] See 1 Nephi 16:26–28.
[15] See 3 Nephi 27:5.
[16] Doctrine and Covenants 115:4 (1844 edition).
[17] Russell M. Nelson, “Revelation for the Church, Revelation for Our Lives,” Ensign, May 2018.
[18] Dieter F. Uchtdorf, “Are You Sleeping through the Restoration?,” Ensign, May 2014.