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STEM Education Poetry

Notes on Notation

Begin here with music: note how the notation
Relies so intently on rightly-read clef.  
If reader takes bass for the treble relation,
Then trouble’s pronounced and musician’s bereft.  
Mentation frustration without keen attention:   
I see in particular paradigm shift

That’s flung into vantage point, yielding dissension
When ref’rence frame crumbles with signposts adrift. 

In chemistry classrooms, such unwanted hazards
Persist even further with vocab galore.
(HIO4, periōdic the acid;
While chart periǒdic is Table explored.)

Recall I a moment in own chem endeavor:
Confusing two units’ shared (seeming) veneer,
In reading wavenumber as “cm” whenever
The energy unit on paper appeared.  
(A decade-plus passes before my chagrin 
Fades at reaction clear in my own teacher’s face.
I understand now, but as novice, I didn’t; 
Embarrassed I was, and my question, erased.)

Find “why” in a Feynman piece: read repercussions
Acknowledged if STEM’s talk is not standardized.
Hence we facilitate complex discussion,
With common notation that’s pinpoint-precise.  

Mentioned in Music, a key introduction:
“By learning notation, we’ll open bookshelf.”  

Learning Chem’s shibboleths: Why?
Lede is buried, I ruefully note to my Past Student Self.  

As alluded to over the last few weeks, these July essays will be a more random collection from some ideas that have been percolating through a few years of teaching; clearly, they’ll vary in length, as well.

This poem addresses the challenging nuances of learning symbolic notation, especially as they pertain to chemistry; its consistent meter helped me arrange some scattered thoughts somewhat more coherently.  Its themes are not novel.  Many have written far more eloquently than I about the differences between experts and novices in a discipline; Saundra McGuire’s Teach Students How to Learn has been particularly illuminating, during my past few years in a chemistry faculty career.   Rather, I am using this space to better organize my thoughts before the (ever-more-rapidly approaching) autumn term.  

Begin here with music: note how the notation /
Relies so intently on rightly-read clef.  /
If reader takes bass for the treble relation, /

Then trouble’s pronounced and musician’s bereft. /
Mentation frustration without keen attention: /  
I see in particular paradigm shift
/
That’s flung into vantage point, yielding dissension /
When ref’rence frame crumbles with signposts adrift.  

Before I shift to my chemistry-focused discussion, I will start with a more familiar disciplinary convention: reading music. 

Though I have never taken music theory coursework, I know from playing piano for several years that the bass and treble clefs of a piece of music are vital contextual information, as are the key and time signatures.  In band classes and piano lessons, I spent much time learning how to read these important signifiers.  If a musician is given a piece of music written in the bass clef, but accidentally interprets it as being in the treble clef, dissonance ensues!  They would be performing the wrong notes in the wrong octave: musically bereft.

I’ve had a few such experiences in my life when practicing piano; upon realizing it, my “reference frame crumbled” until the “signposts” of that notation re-resolved themselves in my mind.  (I borrowed Thomas Kuhn’s phrasing of “paradigm shift” to illustrate the idea of reframing the experienced world, admittedly on a tiny scale.) 

I’ve also seen this “mentation frustration” in chemistry.

In chemistry classrooms, such unwanted hazards /
Persist even further with vocab galore. /
(HIO4, periōdic the acid; /
While chart periǒdic is Table explored.)

With its complex vocabularies, chemistry has all sorts of inherent stumbling blocks, where similar wordings can mean very different things.  Interpretation requires an awareness of context, analogous to knowing the staffs in musical notation.  

The example I cite here is well-known.  The molecular formula HIO4 corresponds to a molecule called “periōdic acid,” where the word “periodic” is pronounced with a long O (as in “boat”).  The word “periǒdic” as it pertains to the “Periodic Table of the Elements,” by contrast, is pronounced with a short O (as in “fox”).   

In the first example, “periodic” is a name communicating information about the atoms in the molecule; in the second example, “periodic” describes how elements’ properties recur as organized in their famous table.  These two terms are spelled identically but pronounced differently; they differ completely in their meaning.  None of this is immediately obvious to a new student.                    

Recall I a moment in own chem endeavor: /
Confusing two units’ shared (seeming) veneer, /
In reading wavenumber as “cm” whenever /
The energy unit on paper appeared. /
(A decade-plus passes before my chagrin fades /
At reaction clear in my own teacher’s face. /
I understand now, but as novice, I didn’t; /
Embarrassed I was, and my question, erased.)

These lines recount my own experience with a similar challenge.  Centimeters and wavenumbers are both units used in chemistry.  Centimeters are abbreviated as “cm,” while wavenumbers are “inverse centimeters,” abbreviated as “cm-1.”  The units look similar [they have a “shared (seeming) veneer”], but they measure different quantities; centimeters are units of length, while wavenumbers are units of energy, most directly useful for chemists in expressing spectroscopic information.  The abbreviations have different meanings.  

I remember vividly a question I once had as an undergraduate student, in my own “chem endeavor.” This question concerned an infrared spectrum, in which the pertinent data are presented in wavenumbers.  In talking to the course professor, I started to ask my question, incorrectly expressing the unit as centimeters (the poem’s meter here requires the unit to be read as the separate letters: “c”;“m”).  My professor blanched and emphatically corrected me: “WAVENUMBERS.”  I was embarrassed and promptly forgot whatever question I’d actually had.    

Years later, I understand the vehemence of my professor’s reaction.  To a trained chemist, my question was the gauche equivalent of “referr[ing] to George Eliot as a ‘he’ in a room full of English professors,” to take this into yet another discipline and quote The Well of Lost Plots, from Jasper Fforde’s inventive Thursday Next series.  But as a student, I was surprised and chagrined; my takeaway was that I had insulted a professor I respected, by phrasing my question incorrectly.    

Find “why” in a Feynman piece: note repercussions /
Acknowledged if STEM’s talk is not standardized. /
Hence we facilitate complex discussion, /
With common notation that’s pinpoint-precise.  

Something that I never found directly acknowledged (as a student) was “why” I was spending so much time on a doubly difficult subject: the obvious concepts were challenging enough; why was there also an important symbolic layer that was comparatively de-emphasized in class?  Eventually, I saw the symbols enough that they became second-nature, and again, I forgot the question.   

Years later, I would find a Richard Feynman essay that directly addressed these concerns.  Feynman discusses creating his own set of symbols as a student, with which he describes his findings in his home lab.  He notes a classmate’s confusion at these non-standard representations, though, and recounts, “I thought my symbols were just as good, if not better, than the regular symbols– it doesn’t make any difference what symbols you use– but I discovered later that it does make a difference…. I realized that if I’m going to talk to anybody else, I’ll have to use the standard symbols.”  Even later, I would hear Hope Jahren speak eloquently of the tension between disciplinary and everyday language in an interview regarding her outstanding memoir Lab Girl and her deliberate choice to avoid jargon in writing it: “[Scientific terms] are part of a language that takes years to learn and that scientists speak amongst themselves. So by describing these things in terms that you use every day, I’ve made the choice to come to you using your words in order that you understand me.  And that’s breaking a rule.”  (In both quotes, the emphasis is mine.)   

As a student, I was keenly interested in both English and chemistry.  I was aware that language was functioning differently in my science classes than in my writing coursework; I was frustrated that I couldn’t fully understand or articulate that difference. Both Feynman’s and Jahren’s candid comments would have been immensely useful.      

Mentioned in Music, a key introduction: /
“By learning notation, we’ll open bookshelf.” /  

Learning Chem’s shibboleths: Why? /
Lede is buried, I ruefully note to my Past Student Self.  

Learning music begins with direct acknowledgements of the notation: why did I want to learn it, as a student?  So I could “open [the] bookshelf,” find a songbook, and play music on the piano.  Teachers consistently explained this; music was accessible and fun; the motivation was clear.  

The “Why?” behind learning chemistry’s symbolic language is comparatively hidden, even though it’s similar.  To collaborate with other scientists, one needs to be able to speak with them, using their “pinpoint-precise” notations for challenging concepts.  That unacknowledged language-learning is a big part of General Chemistry.  The textbooks are filled with unintentional shibboleths: generally defined in the margins and sidebars but rarely recognized as equivalent in importance to “getting the right answer” to algorithmic questions and calculations on exams.    

My last line acknowledges that this crucial information, the lede, is buried.  It also highlights my current “rueful” distance from my student experience: how nearly completely I’d forgotten that sense of frustration.  I will work to remember and empathize, as I approach the new academic year.

Categories
STEM Education Poetry

Summer Terms

As days pass, June’s suddenly waning.
From writing work, I’ve been refraining.
But… annual insight:
The summer is finite.
So, back to a routine, maintaining.  

In honor of June 30, this non-Twitter poem depicts my yearly realization of the moment when June disappears.  It is useful for me to set some concrete goals for this space, over the next few weeks.    

As days pass, June’s suddenly waning.
It was a major accomplishment to reach the end of this academic year, with all of its challenges.  The remainder of May then brought many meetings and much paperwork, with discussions of both 2019-20 and 2020-21.  

June has thus been, as ever, the month where I’ve scheduled everything “else”: all the errands and appointments that are overdue after the busyness of spring term.  It is a relief to know the blocks of time are available, but the days go quickly, and I often find the month is “suddenly waning.”  That’s certainly a pronounced feeling at the moment.           

From writing work, I’ve been refraining.
The summer term brings miscellaneous academic tasks: research in the lab; faculty book groups; conferences and workshops.  So far, time has been short enough that I haven’t been posting here.  I have several Twitter poems still to “translate,” from Fall 2020 and NaPoWriMo 2021, but those brief essays fit best in the academic year.  

But… annual insight: /
The summer is finite. /
So, back to a routine, maintaining.  
It should not be shocking, after so many years in academia, but the shift from “summer-as-the-break-from-the-spring” to “summer-as-the-time-to-prepare-for-the-autumn” still manages to surprise me, each year (“annual insight:/ [t]he summer is finite”).  

I’ve found it useful to write regularly here, so I’ll aim to return to “a routine, maintaining.”  Each Wednesday, through July, I plan to post an essay drafted during the past few years; I hope that this goal will provide motivation to finish and edit those pieces.  (As for August, we’ll see: the shift from July to August brings challenges of its own!)  

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STEM Education Poetry

Asynchronous Marches

“Since pomp and circumstance are,
In this Sunday’s scene, secluded,
To lines in verse instead,
Re: 2020, I’ve alluded…
We’ll tell this– not with sighs, but cheers–
In all the ages hence:
The story of our class for whom,
In March, grad march commenced.”

The 3 May 2020 poem was written in honor of the Spring 2020 graduates from my institution; they unfortunately were unable to have their scheduled graduation ceremony, due to the COVID-19 pandemic.  This upcoming weekend marks the commencement ceremony for the Class of 2021, and so this essay provides a logical place to pause these updates for a few weeks: to celebrate the conclusion of another challenging academic year.    

“Since pomp and circumstance are, /
In this Sunday’s scene, secluded, /
To lines in verse instead, /
Re: 2020, I’ve alluded…”
The pomp and circumstance of commencement ceremonies generally provide a welcome and fitting end to an academic year.  During Spring 2020, these attributes were necessarily “secluded”; it was not possible for students and faculty to gather for a celebratory event.  

In the days leading up to what would have been the 2020 graduation ceremony, I thought often of some of the phrases in Robert Frost’s “The Road Not Taken.”  I referenced these “lines in verse” in this poem, in writing about the circumstances of the spring (“Re: 2020”).  

“We’ll tell this– not with sighs, but cheers– / 
In all the ages hence: /
The story of our class for whom, / 
In March, grad march commenced.”     
Whenever I mention an existing poem in one of my own verses, I am torn; Twitter’s character limit prohibits exploring any nuance in a given post, and I lack the expertise to do so, even had I sufficient space.  All that said, though, I built on Frost’s description of “telling this with a sigh / [s]omewhere ages and ages hence,” in my last four lines.  

We will remember our 2020 graduates far into the future, but with a celebratory air, rather than a melancholy one.  These students achieved significant accomplishments in successfully finishing their coursework, despite their early departures from campus: despite the fact that their “grad march” technically began in March 2020.       

Happily, though, this weekend, we will celebrate the classes of both 2020 and 2021.  Thus, the graduation march described in this poem has turned out to be a path delayed, but still taken.  

Categories
STEM Education Poetry

Pacing Around

“The weekend’s lost its ‘free-time’ grace;
My kitchen’s now my classroom’s place.
I walk around apartment space:
My courses are all quite self-paced!”

The 18 April 2020 poem directly noted the unique circumstances of teaching in the Spring 2020 semester, as all classes abruptly shifted online in mid-March due to the COVID-19 pandemic.      

“The weekend’s lost its ‘free-time’ grace; / 
My kitchen’s now my classroom’s place..”
The 2020-21 academic year has been a challenging mixture of online and in-person teaching, but Summer 2020 at least provided time to learn about resources and optimize an approach.  In contrast, March and April 2020 were truly a blur, with everything suddenly and immediately online.  Each day blended into the next, and it was vital to use the weekends to prepare course materials for the coming week, since the weeks themselves involved a steady stream of email conversations and meetings.  The weekends no longer provided any break (they lost their “‘free-time’ grace”).  

As I’m guessing was the case for many faculty members, my kitchen table became “my classroom’s place,” replacing my home desk; a computer, textbooks, notes, and a document camera required more space than a personal desk could provide!  

“I walk around apartment space: /
My courses are all quite self-paced!”
Looking back at Spring 2020 from Spring 2021, I note that, although the current moment is still strange, it’s far less uncertain than those first weeks seemed.  I spent most of last spring walking in only the geographical space of my apartment complex (“around apartment space”), as so many businesses and public spaces were also suddenly closed.    

In terms of my teaching, the work alluded to in the first lines primarily involved creating asynchronous resources: providing documents and videos that could be linked online, so that students (whose schedules had likewise shifted enormously in only a few days) had as much flexibility as possible in learning the material.  These could also be construed as “self-paced” courses… a description which mimicked my daily routine. 

Categories
STEM Education Poetry

Remote Possibilities

“Working through past few weeks, most confounding;  
Wand’ring lonely in quiet, surrounding: 
To my classrooms– remote now–
Resolutely, I’ll note how
Spring’s hope, still, is eternally sounding.” 

On 26 March 2020, I posted the first Twitter poem reacting to what had been, since its second week, a thoroughly discombobulating month!  This limerick summed up some major changes in my teaching and non-teaching times, as my chemistry classes moved online during the COVID-19 pandemic.    

“Working through past few weeks, most confounding; /
Wand’ring lonely in quiet, surrounding…”
It is difficult to remember how strange that initial shift in Spring 2020 seemed.  New data and best practices were emerging every day, if not every hour.  Moving to fully online courses, when I’d previously used our classroom management system primarily to store files, was “most confounding.”  One useful routine was an early-morning walk; borrowing a turn of phrase from Wordsworth and “wan’dring lonely” along the path near my home, I had time to gather my thoughts before teaching and meetings. 

“To my classrooms– remote now– /
Resolutely, I’ll note how /
Spring’s hope, still, is eternally sounding.”  
By late March, my students and I were adjusting to our remote set-up, which would take us through late April and the end of the spring term.  I was glad to have the opportunity to speak synchronously (in real time) to some of my classes; this note of normalcy was welcome.  Another silver lining was the arrival of many typical signs of spring in the midst of these challenges and uncertainties.  Seeing flowers, birds, and blue skies provided much hope, “eternally sounding,” in an uncertain time.  

The first part of this poem echoed William Wordsworth; the second echoed Alexander Pope;  both were acknowledged in the hashtags.  While it seemed trivial to mark the occasion with a Twitter poem then, I’m glad to revisit the verse now.  Moreover, writing this particular poem helped convince me to repeat the previous April’s effort of NaPoWriMo, starting a few days later.  Much like my morning walks, the writing routine would provide some much-needed structure.

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STEM Education Poetry

Fall Finale

“The campus is in Finals Week,
And stress is thus at Finals Peak,
With projects, tests, reports at stake.
Five days to go; then, take a break!”  

The 9 December 2019 poem celebrates the end of a semester… as does this brief essay.  

“The campus is in Finals Week, /
And stress is thus at Finals Peak, /
With projects, tests, reports at stake.”  
Finals Week always provides a busy end to the semester, with exams, papers, and presentations due in a wide array of subjects.  Campus stress levels are collectively at a maximum, referred to here as “Finals Peak”!  

“Five days to go; then, take a break!”
In Fall 2019, this was posted on the Monday of Finals Week; only “five days to go” remained until the Friday of that week and thus the start of students’ winter break.  (Certainly, for faculty, grading is a remaining final hurdle before break, but it is generally simpler to accomplish that when meetings and classes are done.) 

Fall 2020 is remarkably different in many ways from Fall 2019, and so it is a particular relief to see Finals Week approach in the days ahead.  While the poem does not quantitatively represent the number of days remaining in this particular autumn, we are qualitatively near the curricular finish line, having reached the Thanksgiving break.   

I will take a cue from the 2019 poem and pause updates here for a few days, until I can reassess my writing plans during a welcome semester break.  Meanwhile, I will remember the immense patience, creativity, and fortitude that all of campus brought to the challenges of this historic year, and I know that pattern has been repeated in many other schools and colleges around the world.    

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STEM Education Poetry

Under Pressure

“We’re in the home stretches of classes:
For Gen Chem, the chapter on gases.
(Last subject to finish—
Its volume’s diminished 
In pressure-increased circumstances.)”

The 2 December 2019 limerick builds on two key variables used in the specific context of gas chemistry to acknowledge a curricular constraint often seen at the end of a busy semester.  

“We’re in the home stretches of classes: /
For Gen Chem, the chapter on gases.
I’ve used a variety of textbooks in General Chemistry during my teaching career, but the break between fall semester coverage and spring semester coverage has consistently fallen between the discussion of gases and the discussion of condensed phases (solids and liquids).  Thus the “home stretch” of General Chemistry 1– the final conceptual distance covered– is “the chapter on gases.”  

“(Last subject to finish… /
Its volume’s diminished /
In pressure-increased circumstances.)”
One of the laws historically developed to describe gas chemistry was Boyle’s Law, which relates the pressure of a gaseous system to its volume; the law is named for Robert Boyle, who was a chemist and physicist who worked in the 17th century on many questions of scientific interest.  Boyle’s Law states that as the pressure of a gas increases (assuming a constant amount at constant temperature), the volume decreases; as the pressure decreases (assuming a constant amount at constant temperature), the volume increases.  The most widely used equation that expresses this relationship is p1V1 = p2V2, where p and V represent pressure and volume, respectively.  

The last few lines of this limerick extend this relationship to the reality of a rapidly ending semester: when faced with the “pressure-increased circumstances” of the approaching final exam, instructors often must curtail coverage of a last chapter, causing its volume to diminish, in terms of the time devoted to it in class!

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STEM Education Poetry

Molecular Modeling

“Calculations’ iterations
Cycle towards convergence.
Geometric, spectrometric
Data find emergence.
Supplement experiment:
These calcs will henceforth service,
Illustrate.  Once-obfuscating
Concepts thus gain purchase.” 

The 18 November 19 Twitter poem had the hashtag of “#ComputationalChemLabIntro”; it attempted to summarize the main ideas of computational chemistry for a student audience. I’m most used to doing this in a pre-lab lecture: a brief explanation in a lab setting before students try out a technique on their own. (Such lectures are necessarily quite prosaic, so this was an interesting change.)     

“Calculations’ iterations /
Cycle towards convergence.”
One typical computational chemistry calculation involves optimizing a molecule’s geometry: finding the three-dimensional arrangement of the molecular structure that will lead to the lowest energy possible.  Such an undertaking tends to be complex and lengthy.  Chemistry calculations undergo an iterative (cyclical) process until convergence is reached: until the outputs of consecutive cycles agree to a reasonable extent.       

“Geometric, spectrometric /
Data find emergence.”
Once a calculation is complete, the results can be used to explore the molecule’s optimized geometry (what are the bond lengths and angles in this now-minimum-energy molecule?) and to model its spectroscopic behavior (how does this molecule behave in the presence of different energies of light?).  Thus, the “data find emergence,” and a chemist can use these data to better understand a molecule or reaction of interest.  

“Supplement experiment: /
These calcs will henceforth service, / Illustrate…”
Computational chemistry work completed in lab can supplement findings from previous experiments, illustrating and visualizing molecular-level behaviors responsible for macroscopic observations.   

“…Once-obfuscating /
Concepts thus gain purchase.”
Moreover, being able to observe molecular geometries or spectroscopic properties often can clarify a previously-confusing (“once-obfuscating”) concept from lecture.  

This was an attempt at a Gilbert and Sullivan-esque rhyme scheme for a Twitter poem.  The title here, “Molecular Modeling,” is both a common phrase for computational chemistry work and an allusion to their famous song “I Am the Very Model of a Modern Major-General.” This musical number has seen far more famous and skillful chemistry-related uses, but I enjoyed striving for the many internal rhymes in this particular poem. 

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STEM Education Poetry

Basic (and Acidic) Principles

“Reactions termed neutralizations
Involve acid-base situations.
In the intro chem locus,
Brønsted-Lowry’s the focus.
Water, salt gen’rally form at cessation.”  

The 11 November 2019 Twitter limerick focused on acid-base chemistry, a common topic in introductory chemistry coursework that can be viewed through multiple theoretical lenses.    

“Reactions termed neutralizations /
Involve acid-base situations.”
For a chemistry student, the discussion of acid-base chemistry first arrives in the chapter on aqueous reactions.  Via Arrhenius theory, an acid ionizes in water to produce hydrogen ions (H+); a base ionizes in water to produce hydroxide ions (OH).  When an Arrhenius acid and an Arrhenius base react, water (H2O) forms as one characteristic product of the reaction; water has a neutral pH.

“In the intro chem locus, /
Brønsted-Lowry’s the focus.”
Acid-base principles arise multiple times in chemistry coursework.  Different frameworks (Arrhenius acid-base theory, Brønsted-Lowry acid-base theory, and Lewis acid-base theory) are used to understand different types of reactions.  Brønsted-Lowry theory is a major focus of General Chemistry 2 (an “intro chem locus”).  While it is related to Arrhenius theory, it can account for non-aqueous reactions (those not in water) as well: acids are proton (H+) donors, and bases are proton acceptors.  Lewis theory is commonly used in Organic Chemistry.  It presents acid-base chemistry in terms of electron behavior: Lewis acids are electron-pair acceptors, and Lewis bases are electron-pair donors.        

“Water, salt gen’rally form at cessation.”
This last line revisits the first two, describing characteristic products of a neutralization reaction from the discussion of Arrhenius theory.  For example, hydrochloric acid (HCl) and sodium hydroxide (NaOH) react to form water and sodium chloride (table salt), as shown below.
HCl (aq) + NaOH (aq) → H2O (l) + NaCl (aq)

This limerick conflates two theories to serve the rhyme scheme, a point that is useful to acknowledge here with a less constrained character limit!   Lines 1, 2, and 5 allude to Arrhenius theory most directly, while Lines 3 and 4 reference Brønsted-Lowry theory. Students will encounter both views in General Chemistry.  

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STEM Education Poetry

Solution Focused

“This math quantifies a dilution;  
Molarity of new solution, 
M2, can be found.
Shift equation around: 
M1 times V1; over V2.  Done!” 

This Twitter poem, originally posted 4 November 2019, discusses a common equation taught in General Chemistry, taking significant advantage of chemical shorthand to fit into the limerick structure.  One focus of an introductory chemistry course involves solution stoichiometry: the arithmetic governing reactions that take place in aqueous solution (in water).   

“This math quantifies a dilution…”
Quantifying (calculating) what happens when an aqueous solution is watered-down, or diluted, involves a key equation, the terms of which will be defined subsequently: M1V1 = M2V2.

“Molarity of new solution, /
M2, can be found.”
Chemists use “molarity” as a convenient unit of concentration: how much of a solute of interest, represented in moles, will be present in one liter of a solution

Using the equation above, we compare the molarity and volume of a stock solution– properties of a reagent we could take off the stockroom shelf, denoted here as “solution 1”– to the molarity and volume of a new solution, denoted as “solution 2.”  Specifically, we can find the molarity of the new solution, represented correctly as M2 and in the poem as M2.  (As ever, I lament my inability to have used subscripts with the original post.)     

“Shift equation around: /
M1 times V1; over V2.  Done!”  
This is a strained set of lines: algebraic explanations are not poetic.  However, this is how I’d teach the concept in class, manipulating the variables of molarity (M) and volume (V).  

Starting with the equation of interest (M1V1 = M2V2) and rearranging to solve for M2, we end up with M2 = (M1V1)/V2.  To get there, we “shift the equation around.”  The product of the molarity and volume of the original solution is in the numerator (“M1 times V1”), while the volume of the new solution (“V2”) is now in the denominator.  That completes our calculation (“Done!”).  The double meaning of “solution” is interesting to consider here, as we find the solution to an algebraic calculation that itself involves the characteristics of an aqueous solution.