Elegant Grapheme-Phoneme Correspondence: a Periodic Chart and Singularity Generalization Unify Decoding

Ann. of Dyslexia DOI 10.1007/s11881-017-0150-x

Elegant grapheme-phoneme correspondence: a periodic chart and singularity generalization unify decoding

Louis Gates 1

Received: 20 January 2017 /Accepted: 7 September 2017 # The International Dyslexia Association 2017

Abstract The accompanying article introduces highly transparent grapheme-phoneme relationships embodied within a Periodic table of decoding cells, which arguably presents the quintessential transparent decoding elements. The study then folds these cells into one highly transparent but simply stated singularity generalization—this generalization unifies the decoding cells (97% transparency). Deeper, the periodic table and singularity generalization together highlight the connectivity of the periodic cells. Moreover, these interrelated cells, coupled with the singularity generalization, clarify teaching targets and enable efficient learning of the letter-sound code. This singularity generalization, in turn, serves as a model for creating unified but easily stated subordinate generalizations for any one of the transparent cells or groups of cells shown within the tables. The article then expands the periodic cells into two tables of teacher-ready sample word lists—one table includes sample words for the basic and phonogram vowel cells, and the other table embraces word samples for the transparent consonant cells. The paper concludes with suggestions for teaching the cellular transparency embedded within reoccurring isolated words and running text to promote decoding automaticity of the periodic cells.

Keywords Automaticity. Decoding . Grapheme-phoneme correspondence . Letter-sound relationships . Phonics

Randall, a Harvard theoretical physicist, wrote, BData and theoretical consistency together are the uncompromising arbiters of what is right^ (2015, p. 371). According to this standard, both the letter-sound data and theoretical postulates as stated within grapheme-phoneme generalizations display countless inconsistencies. Summarizing a review of letter-sound studies, Johnston wrote, BIt is impossible to neatly categorize sounds and letter combinations in such a way that simple generalizations will work reliably^ (2001, p. 142). Echoing this idea, Duke declared, BWe can’t boil down English orthography into a few simple generalizations…^ (2014).

* Louis Gates [email protected]

1 Columbia School District #400, Burbank, WA, USA L. Gates

Common sense and general agreement with Johnston and Duke led the present author to deduce that a renewed study would merit little efficacy. Regardless, letter-sound irregularities became painfully personal when, as a rookie teacher, I failed to help Barry unmask letter-sound patterns—decoding befuddled him like deciphering fish from ghoti. Barry, a bright middle school student with special reading needs, faced the challenge akin to Clymer’s seminal study of letter-sound statements in which he mused that many letter-sound generalizations left him with Bno clear indication as to what was to be done^ (1963, 1996,p.183). Remembering Barry and with a nod to the model periodic chart from chemistry and the singularity theory from physics, the author conducted the following study that improbably led to a decoding table, an associated singularity generalization, and companion teacher-friendly tables that include model words for each transparent letter or letter combination. Against logical odds, the study revealed that shrouded beneath the confusing surface rests a surpris- ingly simple but amazingly cohesive decoding elegance.

Pivotal decoding research

The letter-sound confusion in the New World began as the mayflower moored with eager young children on board clutching the earliest decoding system embedded within hornbooks. These hornbooks typically included a wooden or metal paddle overlaid with a transparent cow horn jacket that protected artful calligraphy on parchment which intro- duced the upper and lower case alphabet, followed by nonsense two-letter phonograms and then a benediction. Predating the age of modern science, phonograms, like the decoding generalizations that would follow, understandably evolved without the aid of grapheme-phoneme research. Basal readers from the late nineteenth through the early twentieth centuries evolved to present up to 18 weeks of nonsense phonograms—ba, ca, da—that Betts described as the Bhiss and groan^ method of teaching reading (1955). Intrigued by their pervasive popularity within popular basal readers, Gates amassed 1200 phonograms from which he identified 167 that occurred with enough regularity to warrant additional study. Gates concluded that even these selected phonograms revealed Ba very complex situation^ (1928, p. 146). Although his powerful pen blunted their teaching, phonograms persist to this day (Kress & Fry, 2015). Primers, which included the Protestant Tutor from England and later Webster’s American primer, known endearingly as the Blue-backed Speller, added phonic generalizations to the single letters and phonograms from the hornbooks. In the 1930s, embrac- ing decoding generalizations eclipsed the declining popularity of phonograms. Brown (1930), for example, popularized the unbridled adoption but notably inefficient generalization that some schoolchildren sing today as, BWhen two vowels go a-walking, the first one does the talking.^ Curious about their efficacy, Clymer culled 150 generalizations from four popular basal readers. Musing that many of these generalizations left him with Bno clear indication as to what was to be done,^ heparedthemdownto45promising statements. Clymer discovered that 25 of the promising ones, including the two- vowel rule, lacked a minimum transparency of 75%. Furthermore, the remaining 20 transparent generalizations displayed a haphazard array of statements (1996/1963). While flourishing in many early reading classrooms, decoding generalizations and Elegant Grapheme-phoneme Correspondence: A Periodic Chart and... the single letters and phonograms that they reference continue to display wide-ranging confusion (Meese, 2016).

Parameters of the study

To address the letter-sound confusion, the present study began by creating in Excel a column for the 16,928 words that occurred at least once per million running words within the word study by Zeno, Ivens, Millard, and Duvvuri (1995), exclusive of contracted, abbreviated, dialectical, hyphenated, slang, or proper nouns. The second column matched each word with its pronunciation according to the American Heritage Dictionary (online version); as opposed to some dictionaries, this one negated the need to merge allophones into phonemes and the subsequent criticism that this could draw (review this concern in a pivotal study by Hanna, Hanna, Hodges, and Rudorf (1966), 13–14). The juxtaposition of the words with their dictionary respellings enabled sorting of either the word or the pronunciation column. The limitations of the computer analysis follow.

Word sorting

The replace and sorting options in Excel helped to classify each periodic cell within the 16,928 words. This included a straightforward classification for some of the cells, such as those within words containing the single consonant z (zip), words that included the ee vowel digraph (see), and words with the ight phonogram (night). Other periodic cells presented more complexity and required multilayered sorting. These included, for example, words containing the single vowel a. In this instance, the Excel color-coding option under the replace feature helped to build a file for all of the words containing the letter a within the Zeno word corpus. Next, to catalog single vowel a words, including words that share this pattern and the letter a tied to other periodic cells, the Excel replace option assisted in applying a simple and interchangeable alphanumeric code (A = 01, B = 02, C = 03;... X = 24, Y = 25, Z = 26). This numeric code included the letter a as a part of a vowel digraph (ail=01.09.L), the final -aCE pattern (bate =B.01.20.05), and the phonogram all (pall =P.01.12.12). The final resorting formed a list of words comprised of the single vowel a cell (at, cat, catch), including words containing this cell coupled with the newly formed code (avail=AV.01.09 L, abate = AB.01.20.05, appall = APP.01.12.12). Furthermore, each decoding cell, whether straightforward or more complex, included at least two blind sorts. Discrepancies between the word sorts of a given cell led to further analysis and sorting of the words to reconcile differences.

Transparency standard

The study parameters included at least the 75% transparency threshold proposed by Clymer (1996, 1963) but sought 90% transparency. The study limited the analysis to the initial occurrence of an identical letter or letter combination within a particular word—this analysis included just the first of the three a’sandthefirstn in banana. Nonetheless, the research addresses variant letters and letter patterns within individual words—the report includes data, for example, for both the basic single vowel i and the i in the phonogram ight (midnight). In addition, the study considered look-alike letter combinations as if they were the decoding cells L. Gates under study—the consonant letters t and h in juxtaposition within the compound word boathouse counted against the transparency of the th digraph.

Vowel and consonant category parameters

The parameters for the study included a set of broad parameters for the vowel and consonant categories, which follow in bulleted form for ease of reading:

& For decoding purposes, the study merged the schwa sound (travel) and the syllabic consonant (cattle)—the use of a syllabic consonant or the schwa sound makes little difference for decoding cattle—kat’l, ka'təl. & The single vowels included the short i (pretty) for the single vowel e; embraced the sounds heard in super, numerous, and popular as variant long u sounds; and excluded the prefixes un- and sub- from consideration for open syllable u-consonant-vowel (uCV) pattern (unable, subatomic vs. super, music). & The study excluded from the single vowel inquiry an a, e, i,oro as the V in the final single vowel-consonant-e (-VCe) when this distinctive letter combination remained intact in front of a suffix (aged, ekes, tides). On the other hand, the V usually lowered the single vowel transparency for these letters when a suffix masked the -VCe pattern (aging, eking, tidal) (The most pronounced impact revealed 97 and 94 masked -VCe words within the 377 and 396 exceptions to the single vowel a and i, respectively.). & The nontransparent letter combination, quaa (squad, quagmire, equal), regularly shared nontransparent phonemes similar to the nontransparent letter combination waa (water, wagon, was). With this exclusion, the study treated qu (quit, quiet, quite) as a consonant digraph throughout the study. & The tables include distinctively different sounds for y when it functions as a consonant in the beginning of words (yard) and when it functions as a single vowel at the end of words (happy,fly,satisfy). The medial y, on the other hand, loses this straightforward distinction—depending upon the word, the medial y may serve as a consonant or as a vowel within an array of root words, compound words, and inflected roots. This complexity led to the decision to exclude the medial y from the accompanying periodic cell tables. & The research included the ten transparent vowel digraphs that occurred at least 100 times within the Zeno list and the two less frequent but highly transparent and popularly taught digraphs found in jaw and toy. & For ease of description, the study grouped both vowel digraphs and diphthongs as vowel digraphs. & As shown in the table, the letter r controls 18 of the 22 basic vowel cell categories—single vowels, -VCe, vowel digraphs.

Phonogram parameters

The term phonogram lacks an agreed upon definition (Johnston, 2001;Pei,1966). Accordingly, for purposes of this research, phonograms embody consistent patterns of vowel and consonant combinations. The study identified two distinct types of phonograms—signal phonograms and word family phonograms. Signal phonograms include signaling letters that control the sounds of juxtaposed letters or letter combinations—cell, Elegant Grapheme-phoneme Correspondence: A Periodic Chart and... cent, sauce;ruby,duty,music. Word family phonograms, on the other hand, represent like phonogram groupings—all,ball,call;book,hook,look. The study also highlights inde- pendently functioning letter-sound decoding cells:thewordnight, for example, includes two decoding cells—the consonant n and the phonogram ight;furtherreductionofthese cells would eliminate the single consonant n and destroy the integrity of the ight phonogram.

Morphological and etymological parameters

Finally, as noted in various cells within the tables, the study isolated certain morphemes, such as the prefix un-andsub-fortheuCV pattern described above. Moreover, at times, root words and words with morphemes share common letter patterns—the phonogram ation in the root word nation and in the suffix in taxation share the same letter-sound combination. Similarly, the -ed suffix, found as a signal phonogram for the letter d,showa variety of sound combinations for the e and the d (called,asked,acted) (Notably, the decoding complexity of varied sounds represented by these combined letters, which function as a suffix and a signal phonogram, confuses many students when they first begin to read.) To the point, unless otherwise noted, the decoding transparency uniformly describes basic and phonogram cells notwithstanding the morphological or etymological foundation of the words.

Periodic table of decoding cells

As Table 1 shows, the study unveiled a symphony of elegant patterns of letter-sound basic cells coupled with their linked transparent phonograms and nontransparent decoding cells. These patterns rest within five letter-sound categories of basic cells: (1) single vowels (bat, cut), (2) -VCe (gate,cute), (3) vowel digraphs (bait, coat), (4) single consonants (bib, mom), and (5) consonant di/trigraphs (thatch, wrath).Thefivecategories of grapheme-phoneme correspondence and their linked phonograms and nontransparent cells robustly describe the letter-sound relationships. At first, these five categories seemed too simplistic. However, triple and quadruple vowel and consonant combinations usually appear in one of four discernible combinations: (1) triple consonants in consonant blends—each separate letter counts as single consonant (scrap, splat, strap); (2) consonant trigraphs that appear as basic cells (ought ,patch); (3) up to five-letter phonograms that blend vowels and consonants (spacious,cautious); and (4) triple and quadruple combinations of vowels or consonants that form two or more syllables (most-ly, hun-dred, view-er, earth-ling). In short, apart from infrequent letter combinations, the basic letters and letter patterns and their linked phonograms and/or nontransparent cells neatly package into one of the five basic decoding cell categories. Moreover, the five categories along with the linked cells led to unveiling the elegance of the letter-sound system. The computer sort began with identifying the relative transparency of single vowel and consonant letters (bib, fanm), andmo vowel and consonant di/trigraphs (t oy,sock,patch). The investigation next isolated transparent phonograms that raised the transparency of single letters and/or digraphs—night,book,nation; lastly, the examination excluded the ten nontransparent cells that failed to complement the single letters, digraphs, or phonograms. In short, the research began with the smallest grain size and moved to larger sizes L. Gates

Table 1 Periodic table of decoding cells

Decoding Cell Basic Decoding Signal Word Family Nontransparent Categories Cells Phonograms Phonograms Cells Vowel Cells catr edgee balla coldo +pedal, about; except qua 3,537/3,914 -CCe except –Cle 303/310 1 syllable roots 51/52 1 syllable roots 56/58 Singularity Generalization penr goo tablea colto waa + travel, pretty, -Cle; except –ed 4,346/4,508 ends words; except do, to 49/51 ends roots 17/17 1 syllable roots 13/13 105 words A basic cell or a linked phonogram r u a o Single pig ruby range over usually has the sound heard in one or + pupil 4,960/5,356 uCV + music, popular; except un-, sub- 465/511 ends words & suffixed 26/28 root word 48/48 Vowels popr ratinga satisfyy ia one of two key words, except + hog, pivot 2,147/2,692 53/53 ends 3 + syllable words 13/13 see phonograms with ia 179 words nontransparent cells. bugr flyy nationa houndou ienie + discus 1,369/1,442 ends 1 syllable words 14/14 312/321 127/139 74 words lily nighti famousou io ends words 1,293/1,304 100/100 root ending 55/56 see phonograms with io 175 words nailr faunr jawr dietie mouse/rouseou oodoo 299/332 108/120 65/68 except y to i 15/17 31/32 61 words r r r oo ou hay tea/head bee ie book out ou Vowel 112/114 + ea in real; no re + a 592/626 315/316 pie 42/43 69/75 see phonograms with ou 124 words Digraphs chiefr soapr oilr 1 syllable roots; except y to i + suffix 13/13 footoo advice/officei-e -ilei-e except y to i + suffix 85/92 112/127 roots 100/104 13/13 2+ syllable roots15/16 2 + syllable roots 19 words moonr cow/tow toy palacea-e massivei-e -inei-e 182/197 214/219 31/31 2 + syllable roots (palace/surface) 8/8 33/33 2 + syllable roots 40 words caker gener bike imagea-e captivei-e Final 158/167 22/24 accept –ire 249/268 2 + syllable roots 48/50 92/92 o-e r r < > a-e o-e -ove -VCe bone dune/use < > relate/senate handsome 14 words 112/125 80/86 2 + syllable roots 67/67 (some/handsome)9/10 Consonant Cells bib cat dad added/fixedd specialc 1,904/1,940 2,898/2,901 2,996/3,136 1,974/1,974 37/37 fan gag hat cellc partialt 1,629/1,632 939/945 704/746 687/690 22/23 Transparency: Word Study: jug kid lip cityc preciousc Basic cells & A corpus of 198/199 716/716 5,446/5,483 except ciV216/216 13/13 Single mom nut pop cyclec cautioust phonograms 16,928 words Consonants 2,933/2,933 5,966/5,977 3,215/3,234 61/61 7/7 average 97% (Zeno, et al., quiz/plaque rat sun/his gemg musicianc transparency, except 1995) formed 203/203 7,900/7,901 7,659/7,686 except gge, ger, g + suffix 284/305 12/12 tot vet web magicg mission/visions nontransparent the foundation 6,108/6,160 1,403/1,403 610/619 except root onsets, ggi, g + suffix 132/143 121/121 cells. for this study. tax/exit yak zoo gymg actiont 354/360 begins words 54/55 238/244 except ggy 29/31 except phonogram ation 311/322 chin/chemist sock judge catus/picturet 491/505 333/333 56/56 2 + syllable roots 201/201 caught sign knot < > whowh wholewh gh Consonant except phonogram ight 45/45 ends roots & suffixed 30/30 begins words 31/31 4/4 5/5 see basic cell ght 66 words fang/change phone ship Key: (1) Bold and Italics identify the decoding cells—nation.(2) Italics only highlight decoding Di/trigraphs 1,732/1,773 134/141 487/490 cell signal letters—e signals a soft c in cell. (3) A slash (/) divides key words with variant patch thin/this whip phonemes—mow/town. (4) Alpha exponents associated with phonograms and nontransparent cells 89/89 486/496 83/86 refer to corresponding basic cells—the exponent in balla refers to the basic cell in cat. (5) R- wrap (r) 52/52 controlled exponents accompany 18 of the 22 basic vowel cell categories. as necessary in an attempt to clarify greater decoding transparency across sizes (Ziegler & Goswami, 2005). In reflection, little separates the difference between the historical siloing of the digraphs from single letters and the siloing within the present study of the phonograms and nontransparent cells from single letters and digraphs. Conversely, highlighting the distinction between individual letters, digraphs, phonograms, and the nontransparent cells unshrouded the amazing transparency within the letter-sound system of periodically reoccurring decoding cells. The accompanying periodic table of decoding cells embraces the five quintessential letter-sound categories. Of the 103 individual transparent cells, the single vowel o displayed 80% transparency (hop, dog), the vowel cells iet and oa showed 88% transparency (diet,boat), while all of the remaining cells met or exceed 90% transparency; these transparency percentages clearly exceeded the minimum of 75% proposed by Clymer (1996/1963). This table also showcases that a proper understanding of the interlinked basic, phonogram, and nontransparent cells unravels much of the letter-sound befuddle- ment that Clymer and others subsequently faced. The far left column of the table divides the vowels and consonants into the five categories of basic cells. The columns immediately to the right of these cells show the 57 basic cells divided into the five letter-sound categories as noted above. Next, the table shows two general categories of phonograms—periodically recurring combinations of vowel and consonant letters—that include 13 signal phonograms and 33 word family phonograms. The last column of the table includes ten nontransparent cells. Furthermore, exponents link phonograms and nontransparent cells to basic cells—balla,bookoo, whowh. Each transparent cell includes a ratio of transparent words to the total number of words representing the cell; nontransparent cells include the total words analyzed. The cells also include notes as needed. The table reinforces the idea that some of the basic cells, such as the Elegant Grapheme-phoneme Correspondence: A Periodic Chart and... consonant digraphs in sock and knot, show stand-alone transparency. Conversely, disaggre- gating linked phonograms and/or nontransparent cells improves the transparency for the other basic cells—the transparency for the basic single vowel y in lily improves, for example, after considering the linked signal phonogram in fly (one syllable word endings) and word family phonogram in satisfy (three or more syllable words). The table also shows certain periodic cells with multiple key words. Of these, 17 contain words with similar phonemes—8 cells include stressed/unstressed phonemes (cat/about, pen/ travel/pretty, big/pupil, mop/pivot, bug/discuss, locate/senate,advice/office, some/handsome); 5 cells embrace unvoiced/voiced phonemes (sun/his,mouse/rouse, added/fixed, thin/this, mission/vision); and 4 cells reveal similar phonemes or, depending upon the dialectical region, related allophones (mop/dog, use/dune, ruby/music/popular, palace/surface). The remaining seven cells include distinctly dissimilar dual phonemes (tea/head, cow/tow, quiz/plaque, tax/ exit, chin/chemist, fang/change, status/nature). Arguably, aside from these seven representative words, the phoneme differences within the dual key words present minimal decoding complexity. The accompanying table also excludes r-controlled single vowel and vowel digraph situations identified with r exponents. Furthermore, the table shows that r-controlled transparency occurs for the signal -Vre phonograms—are, ere, ore,lure/pure.However,sincethey usually share the same phoneme, the sound for the letter i in -ire remains embedded within its corresponding basic cell (bike/tire). For the most part, the ten nontransparent cells, which represent 857 of the 88,124 discreet basic, phonogram, and nontransparent letters and letter combinations represented within Table 1, play a minor role in initial decoding. A closer examination also shows the four nontransparent cells appearing without an exponent function much like basic cells; these include one consonant digraph (gh) and three vowel digraphs (ia, io, ou). Furthermore, the 478 combined occurrences of these three nontransparent vowel digraphs link to 1138 reoccurring transparent phonograms; this illustrates and strengthens the argument for isolating and highlighting the linkages between the basic, phonogram, and nontransparent cells. Within the table, the 103 transparent decoding cell length or grain size ranges from single letters to five-letter combinations. Arguably, these transparent cells, consisting of 57 basic cells and 46 phonograms, embody the major letter-sound cells and their grain size alike. It follows that these periodic decoding cells represent a robust and straightforward decoding singularity.

Singularity generalization

Unexpectedly, organizing the decoding cells within the periodic table of decoding cells helped to create the following simple and reliable singularity generalization for decoding:

A basic cell or a linked phonogram usually has the sound heard in one or one of two key words, except nontransparent cells.

Deeper, this statement forms a coherent model for anchoring generalizations for all transparent cells within the table. With little doubt, this decoding generalization meets the L. Gates standard set by Lightman, a MIT theoretical physicist, who wrote, BThe fewer parameters and principles needed to specify a system, the greater the understanding^ (2013,p.74).The statement also forms a singularity—oneness—for creating broad decoding generalizations, such as creating individual statements for the following five basic cell categories:

& A single vowel cell usually has a short (or schwa) sound, except linked cells. & A final single vowel-consonant-e word usually has the long sound of the first vowel and a silent final e, except linked cells. & A vowel digraph usually has the sound or sounds heard in one or one of two key words, except linked cells. & A single consonant usually has the sound or sounds heard in one or one of two key words, except linked cells. & A consonant di/trigraph usually has the sound or sounds heard in one or one of two key words, except linked cells.

Similarly, the singularity generalization also serves as a model for creating straightforward but narrowly anchored statements for any one of the 103 transparent cells shown within the periodic table of decoding cells. For example, the following highlights the final single vowel y oneness with the singularity generalization:

& A final single vowel y usually has the sound in kitty, except linked cells. & Asinglevowely phonogram ending one-syllable words usually has the sound heard in fly. & A fy phonogram ending three- or more syllable words usually has the sound heard in satisfy.

One-syllable r-controlled patterns include a narrow transparency for the sound heard, respectively, in far ([87/88] except the word family in war/onward [73/75]), fern(19/ 21), fir (25/25), for (59/59), and fur (27/27). In addition, a limited transparency occurs for signal -Vre phonograms—care (27/28), there/mere (17/19), ore (26/26), and lure/ pure (24/28) (Sharing a common phoneme, the -ire pattern, remains embedded within the basic -iCe cell.) Significantly, while restricted in application, the r-controlled starter cells provide a decoding starting point for these otherwise nontransparent but frequently occurring cells. For the most part, these generalizations serve to describe decoding situations as opposed to serving as statements for memorization. Moreover, the foregoing decoding generalizations stemmed from identifying letter-sound patterns from the present study as opposed to revisiting the transparency of generalizations that evolved over time. Significantly, anchoring letter- sound statements to the singularity generalization circumvents the centuries-old trap of creating fragmented assertions that puzzled Clymer.

Applying the decoding cells

With little doubt, understanding and applying the periodic decoding chart coupled with the singularity generalization would have helped Barry unravel the grapheme- Elegant Grapheme-phoneme Correspondence: A Periodic Chart and... phoneme correspondence. Stahl and his coauthors’ formative review of decoding suggested that BThere are three types of practice that might be provided^ in a decoding program—Breading words in isolation, reading words in [running text]…, and writing words^ (1998, p. 342). Importantly, automatic recognition of transparent letter-sound word patterns increases activity in areas of the brain best posed for reading (Yoncheva, Wise, & McCandliss, 2015). The key word or dual words shown in each cell in Table 1 clearly highlight the periodic structure of the decoding cells. However, the model words embraced in Table 2 for the vowels and cradled in Table 3 for the consonants, while somewhat blurring the periodic structure of the tables, significantly enhance the application of the periodic cells for classroom use. Isolating words also allows students to Bexamine the patterns in words without the distractions of context^ (Stahl, Duffy-Hester, & Stahl, 1998, p. 342). With the idea of reducing, whenever possible, distractions of context and, arguably, content, the sample words displayed in Tables 2 and 3 and within the sample generalizations represent letter patterns with compact content—these sample word patterns replace more complex letter arrangements for the single vowel a in bland, flank, and planwiththesimplerpatternsinban, fan, and pan (Hintikka, Landerl, Aro, & Lyytinen, 2008). Finally, these patterns support Willis, a board-certified neurologist and licensed teacher, who noted that BWhenever new material is presented in such a way that students see relationships [or patterns], they generate greater brain cell activity (forming new neural connections) and achieve more successful long-term memory storage and retrieval^ (2006, p. 15). Accordingly, Tables 2 and 3 show compact word lists for most of the basic cells—ape,cape,tape; oat,boag t, oat; bath,math,path. As these words suggest, the model word lists include rhyming word patterns whenever possible. The following includes field-tested ideas and recommendations for teaching the decoding cells to students within general and specialized reading classes alike. First, much like the conspicuous display of periodic charts in chemistry and other science classrooms, recreate and prominently display Table 1, the periodic table of decoding, within classrooms that teach reading. Reference and use this chart to show at a glance the decoding elements much like a science teacher references and uses the periodic chemistry table to teach chemistry elements. Second, recreate Table 2—periodic vowel cells—and display this prominently in primary, special education, and developmental reading classrooms. As necessary, use the words within this chart to assess decoding skills. For example, ask each student to read these words at an automaticity standard rate of 1 second per one-syllable words and half a second per syllable for two- or more syllable words. Mark each word that shows student failure to meet this automaticity standard. Third, begin teaching the practice cells—those cells that include two or more missed words. As required, use the same automaticity standard as used for testing to teach a daily mini lesson focused upon the single vowel cells for a, e, i, o,andu until mastered. Once students master the single vowel cells, use the automaticity standards and teaching strategies to test and teach the vowel digraphs, -VCe, and their linked phonograms. To maximize the instructional efficiency, teach three cells at a time—when students master one list, introduce another. Fourth, use a variety of methods to teach the single vowel cells and the other cells alike, such as direct instruction, cross-age tutoring, and speech recognition apps. The L. Gates

Table 2 Periodic table of decoding cells: the vowel cells

Decoding Cell Basic Decoding Signal Word Family Nontransparent Categories Cells Phonograms Phonograms Cells canr dancee balla oldo fan lance hall cold man dense mall fold pan fence tall sold Singularity ran rinse wall told Generalization denr goo ablea bolto hen lo cable colt waa A basic cell or a men no fable colts pen so gable jolt linked phonogram ten yo table jolts usually has the sound binr rangea over o heard in one or one of fin ranger overdid pin mange overfill two key words, rubyu tin change overlap Single duty Vowels except nontransparent win changed overrun r unit a y cells. cop human bating satisfy hop music dating unify mop gating modify ia pop hating gasify top rating citify bumr nationa houndou Transparency gum nations mound The vowel cells, excluding the single hum station pound ienie vowel o, average 94% transparency byy sum stations round except nontransparent cells. my yum vacation sound fly i ou lily ply fight famous Word Study billy light bulbous A corpus of 16,928 words (Zeno, et. sly al, 1995) formed the foundation for filly might callous io this study. hilly night joyous silly sight fabulous failr faunr jawr dietie douseou jail daub law diets house (noun) mail laud paw dieting louse oodoo

nail maul raw quiet mouse (noun) tail taut saw quiets souse bayr eat headr beer bookoo outou day tea heads fee cook bout

hay pea dead gee ie hook pout ou pay sea deaf see pie nook rout ray leaf death tee die took tout lie Vowel fieldr oatr oilr footoo advice officei-e tie Digraphs yield boat boil football device pumice vie i-e lien coat coil footpath devices novice -ile niece goat foil afoot sacrifice malice piece moat soil barefoot sacrifices lattice moonr cow own boy palacea-e massivei-e loon how sown coy necklace passive noon now tow joy furnace expensive -inei-e soon vow low soy surface excessive boon wow bowl toy menace impressive baker ever bike imagea-e activei-e cake eke dike baggage captive fake ekes hike cabbage festive lake gene like message motive Final rake genes pike package votive < > -oveo-e -VCe boner cute r locate senatea-e someo-e cone dune locates climate awesome hone jute < > donate chocolate handsome lone lute donates private lonesome tone mute locate pirate tiresome Key: (1) The ratios show transparent/total cells. (2) Bold in red identifies the decoding cells—nation.(3) Italics in red highlight decoding cell signal letters—a u-consonant-vowel pattern signals a long u sound as in ruby. (4) A slash (/) divides key words with variant phonemes—mow/town. (5) Alpha exponents associated with phonograms and nontransparent cells refer to corresponding basic cells—the exponent in balla refers to the basic cell in cat. (6) R- controlled exponents(r) accompany 18 of the 22 basic vowel cell categories. latter, by the way, shows individualized instructional promise for teaching words and promoting reading automaticity in running text (Baker, 2017). Occasionally, students memorize and repeat the list of words in each cell, paying little attention to the Elegant Grapheme-phoneme Correspondence: A Periodic Chart and...

Table 3 Periodic table of decoding cells: the consonant cells Decoding Cell Basic Decoding Signal Word Family Nontransparent Categories Cells Phonograms Phonograms Cell bib cat did added buckedd specialc bid cab dig ragged ducked facial big cam dill dogged lucked racial bin can dip wicked sucked social Singularity bit cap din ended tucked crucial 1,904/1,940 2,898/2,901 2,996/3,136 1,974/1,974 37/37 Generalization fib gag hug cellc initialt fig gab hub cellar nuptial A basic cell or a fit gal huff cent spatial fix gap hum center martial linked phonogram fizz gas hut cement partial 1,629/1,632 939/945 704/746 687/690 22/23 usually has the job kid lab cityc viciousc sound heard in one jobs kill lack cinch gracious jock kin lad civic spacious or one of two key jog kiss lap civil precious words, except Single jot kit lax acid luscious 198/199 716/716 5,446/5,483 except ciV 216/216 13/13 nontransparent Consonants mom nun pig cyclec cautioust mob nut pick cyber ambitious cells. mock nuts pill cyclic fictitious mop nub pin cyst nutritious moss null pit cymbal infectious 2,933/2,933 5,966/5,977 3,215/3,234 61/61 7/7 quiz plaque rack sad is gemg musicianc quick plaques ram sag his gel magician Transparency quill bisque ran sap as gest logician quip cheque rap sat has gee optician The consonant cells quit masque rat sax hers gene technician 203/203 7,900/7,901 7,659/7,686 except gge, ger, g + suffix 284/305 12/12 average 99% tot van wick magicg mansions transparency, except the tog vans wig logic passion nontransparent gh cell. tom vac will digit mission top vat win rigid session toss vats wit vigil tension 6,108/6,160 1,403/1,403 610/619 except root onsets, ggi, g + suffix 132/143 (variant: vision) 121/121 ax exit yell zig gyveg actiont fax exist yen zigs gyro diction Word Study sax exam yep zip gym fiction tax exact yes zit gyp section A corpus of 16,928 words wax exert yet zits edgy suction 354/360 54/55 238/244 except ggy 29/31 except phonogram ation 311/322 (Zeno, et. al, 1995) chin chemist ick edge cactus texturet formed the foundation for chins chemical kick hedge status fixture this study. chill chemistry lick ledge stratus mixture chip ache sick wedge datum culture chips echo tick ridge septum vulture 491/505 333/333 56/56 2 + syllable roots 201/201 ought sign knot whowh wholewh bought design knob whom wholes fought resign knock < > whose wholesome gh sought align knit whoso wholesale

thought assign knee whoever wholesales see basic cell ght except phonogram ight 45/45 ends roots & suffixed 30/30 begins words 31/31 4/4 5/5 66 words bang change phone ship fang range phones ships Table Key Consonant hang strange phase shim Di/trigraphs rang hinge graph shin Key: (1) The ratios show transparent/total cells. sang plunge graphs shiv (2) Bold and red identifies the decoding cells— 1,732/1,773 133/141 487/490 batch thin the whim patch. 3) Italics only highlight decoding cell hatch thins then whip signal letters—e signals a soft c in cell. (4) A slash latch thick than whips match thud this whit (/) divides key words with variant phonemes— patch thug thus whiz sat/his. (5) Alpha exponents associated with 89/89 486/496 83/86 wrap phonograms and nontransparent cells refer to wrack corresponding basic cells—the exponent in whowh wring refers to the basic cell in whip. wrist writ 52/52 periodic letters and letter combinations themselves. Break this memory chain by reversing the order or presenting the words randomly. L. Gates

Next, utilize web browser word finders, such as wordfind.com, worddetector.com,or wordhippo.com, to create lists of additional pattern words for added practice as desired. For example, a web browser search of Bwords that begin with ch^ (chap, chip, chop) or Bwords that end in ight^ (right,sight,tight) produces instant decoding cell lists from the simplest one- syllable words to complex polysyllabic words. Furthermore, personalize the periodic vowel and consonant decoding cells by adding model words, such as names of classmates (Dan, Jan, Van), objects within the classroom (book,hook,nook), and classroom movement activities (bat, pat, sat). Most students learn the single consonants in conjunction with the basic vowel cells. Nonetheless, after demonstrating appropriate mastery in decoding the three vowel categories and their linked phonograms a few students require further practice to master specific single consonant phonograms, consonant di/trigraphs, and/or their linked phonograms. If so, present these as necessary using testing and teaching strategies described above. Finally, for successful decoding to occur, students assigned to classes above the primary grades must exhibit running text automaticity for the periodic cells. Deeper, according to our observations, students at the upper elementary level and beyond will struggle with reading automaticity when they fail to automatically decode all but a mere handful of the most infrequently occurring phonogram pattern words. Accordingly, test and teach, as necessary, the decoding cells as described above. Turning to syllabication, of the 45 phonic statements that Clymer studied, 14 related to syllabication, a hint at its importance. In fact, students who easily decode transparent consonant-vowel-consonant (CVC) words may fail to decode disyllabic words with automaticity (van Gorp, Segers, & Verhoeven, 2017a). Nonetheless, to decode increasingly complex text, students must automatically decode transparent disyllabic as well as polysyllabic words. Deeper, beginning-level books typically use an abundance of one- and two-syllable words spread within simple sentences; on the other hand, an increase in readability typically corresponds with an increase in the number of polysyllabic words embedded within longer, more complex sentences. Accordingly, develop transparent syllabication word lists such as the following:

& Two-syllable words with like medial consonants: jelly, baggy, puppet, bullet, tummy, muffin, bunny, rabbit, muddy, wedding; & Two-syllable words with unlike medial consonants: jacket, bucket, cupful, dismiss, basket, sandy, helmet, napkin, canvas, picnic; & Three-syllable words: magnetic, telescope, principal, family, festival, gravity, magical, elastic, pajamas, invention; and & Three- to five-syllable words: penalty, invisible, medication, satisfy, incubation, magnify, mathematics, disability, multiplication, musician.

As needed, using these and other transparent words with similar syllable counts, guide students as they practice increasingly difficult syllabication patterns of words in isolation and in connected text; this promotes syllabication automaticity and decoding beyond the primary level. Instruct students to read daily in connected text, which reinforces the inescapable decoding cell patterns—reading fluently at an independent reading level coupled, as necessary, with oral reading promotes decoding (Allington & McGill-Franzen, 2013). Elegant Grapheme-phoneme Correspondence: A Periodic Chart and...

Notably, reading fluency includes (1) prosody that relates to expressive reading and typically connotes comprehension and (2) automaticity, which aligns most closely with fluid decoding. In addition to reading model words in isolation and within running text, when students continue to struggle with reading automaticity, apply oral repeated reading, which embodies one of the most powerful tools for promoting reading automaticity (Paige, Rasinski, & Magpuri-Lavell, 2012; Rasinski, 2017; Sayeski, Earle, Eslinger, & Whitenton, 2016, van Gorp, Segers, & Verhoeven 2017b). Thus, select reading passages of proper readabilities. As necessary, listen to students orally read and reread the same passage over the course of one or more days until they achieve acceptable automaticity. Once achieved, begin the process again with another passage; increase the passage readability as students show readiness. Guide students through these short repeated reading sessions until they automatically decode at or just above their current grade level or at the sixth-grade level (approximate Lexile score of 830), whichever comes first. Finally, reinforce the decoding cells using the third support strategy, writing practice. Assist students as they write stories and poetry sprinkled with decoding pattern words; as appropriate, teachers may also reinforce these decoding patterns with spelling lessons. Then, ask students to read their stories and poetry aloud stressing automaticity. Poetry writing lessons, in particular, reinforce the decoding cell patterns (Connect to poetry starter sites, for example, by searching Bfind lyrics and poems^ under the Rhyme Zone website.). Use a wide variety of poetry styles, including name poems, haiku, couplets, and limericks. For a bit of fun, show students how to create humorous or whimisical poems by adding an unexpected twist to the last word or phrase of couplets and limericks. Additionally, as Stahl’s team rightly reminds us, view letter-sound instruction Bnot as an end but as a means to help children read words automatically^ (p. 343). In short, research suggests that from 76% to 82% of students from the fourth through the ninth grades show Bthat difficulties in foundational competencies (word recognition and fluency [automaticity]) are a major contributor to reading difficulties early on and that if students do not develop early mastery of these foundational reading competencies, it is likely that these concerns will continue into the later grades and will have a profound, adverse effect on students’ comprehension and overall reading achievement^ (Rasinski, 2017, p. 521). Related, Seidenberg wrote, BTheorists on the education side also had the instructional demands of acquiring basic [foundational] skills and comprehension backward. Generations of teachers were then taught that skills come naturally and that comprehension requires extended instruction. That inversion made learning to read more difficult for children^ (2017, p. 274). Deeper, the periodic decoding cells shown in Table 1 unveil an unexpectedly high transparent decoding orthography—the results show an average consistency of 97% for the 103 transparent basic and phonogram cells. Arguably, this coherent array of periodic cells significantly moves the grapheme-phoneme correspondence of English toward other orthographically transparent languages and foreshadows improved outcomes for teaching beginning reading through easing the learning of word recognition, improving the acquisition of automaticity, and, ultimately, reducing reading difficulties (Arnesen et al., 2016; Seidenberg, 2017 p. 274; Willingham, 2017,p.194).

Discussion

Accentuating the linkage between the decoding cells unmasked a coherent medley of the grapheme-phoneme relationships as shown within the periodic table of decoding cells. L. Gates

Moreover, this table highlights the interconnected system of letter-sounds for the basic, phonogram,andnontransparent cells. Highlighting the differentiated decoding cell linkages led to the creation of the singularity generalization that models and anchors the wording for creating other decoding statements, such as generalizations for the five decoding categories or for any one of the 103 transparent cells. Most importantly, these transparent cells unveil a systematic grapheme-phoneme English orthography that simplifies decoding. Arguably, the data as presented within with the periodic table of decoding cells, conjoined with the theoretical consistency of the singularity generalization, arbitrates the elegance of much of what is right with the unveiled grapheme-phoneme system. Most importantly, understanding the decoding cell linkages sharpens the teaching and learning targets and enables general education and students with special decoding needs alike to more efficiently break the code, an essential step toward the enriching engagement within the delicious garden of print.

References

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