2024-08-26

Phonics Makes a Comeback

Lee Anna Vasquez, a reading interventionist, uses a sound wall to teach students the articulatory features of phonemes

As a long-time instructor of remedial math at a community college (among other things), I've always felt strongly that our discipline is closely tied to basic natural-language literacy, and to the teaching of reading and writing. 

Teaching basic symbolic math is fundamentally the ground-floor of a particular writing language for the sciences. If a student entering an algebra class can't read a sentence (either to follow a direction, answer a word problem, or see the parallel with algebraic equations), attend to fine structure, or understand assertions about symbolic parts-of-speech, then they will flounder. I've written about this here multiple times (see: The War on Structure and Phonics and Bases). Note the subtitle of the blog with its essential spotlight on clear expression.

Two articles in American Educator in the last year so give some hope that the science of structurally-focused reading instruction, with phonics instruction as a key part, may (with great struggle) finally be making a comeback. Both are by reading researchers who have been at the wheel for many decades.

The first is by Louisa C. Moats in Spring 2023, Creating Confident Readers. Moats has developed and taught a program for graduate-program service teachers called LETRS (Language Essentials for Teachers of Reading and Spelling) in some form since the early 1990's. It leans into service teachers becoming knowledgeable about how sounds are articulated in the mouth, how they vary across languages, how they map to written graphemes in English, and how students can decode new texts on their own when necessary. 

I think that Moats put the most interesting part at the end of her article (perhaps out of a sense of gently downplaying the section that might be considered the most inflammatory), which I'll highlight here:

Teachers often experience complex emotional reactions as they learn more about the science of reading and the structure of language. Some teachers express grief and regret over their past use of ineffective (but widespread) practices and anger that their prior opportunities to learn about teaching reading were inadequate or even misinformed. A common reaction of participating teachers to their experience in LETRS is, “Why didn’t anybody teach me these things before?” The value of the information is readily apparent when students begin to make progress. Student growth quickly validates teachers’ efforts to teach language, reading, and writing explicitly.

I immediately recognized  this comment about “Why didn’t anybody teach me these things before?” — I've gotten this exact response from students in remedial algebra courses, at key moments where I was identifying and trying fix broken understandings that their K-12 teachers had hopelessly mangled. Moats continues:

In translating concepts and guidance from research, we encourage teachers to confront and abandon ideas, practices, and programs that many have used or been taught—often under district or state standards and requirements—that do not align with current understandings grounded in evidence. For example, many districts are still wedded to programs and approaches based on “cueing systems,” a tenet of guided reading that does not recognize the central role of phonology or phonic decoding in learning to read and spell. An underlying assumption that reading is primarily a visual imprinting activity drives other misconceived but all-too-common practices, such as posting “sight” words on an alphabetic word wall regardless of the beginning sounds in the words (e.g., posting out, once, only, and often under o). Many district and state standards require kindergarten and first-grade readers to memorize dozens of words on flash cards or spell lists of words by rote visual memory, even though in reading science, all words are eventually learned “by sight” through a process of speech-to-print mapping, beginning with phoneme-level processing. Turning away from common but unsupported practices poses dilemmas for teachers and schools because the misconceived ideas have been established in reading education for so long. Many published programs have yet to catch up to the science...

We can see here implications of the primary mistake that proponents of the catastrophic "whole word" approach made — they thought about how proficient readers function (mostly identifying familiar, known words on sight), and assumed students could jump directly to that level without passing through the scaffolding phases that naturally occur beforehand (connecting spoken sounds to written symbols). Moats says this more directly elsewhere:

The ability to recognize printed words out of context, quickly and accurately, is gained not by a visual imprinting process, but by building a mental map connecting speech with print. By learning incrementally how graphemes (letters and letter combinations) represent speech, novice readers and spellers gradually build a mental storehouse of known words that can be instantly recognized and recalled. Every phase of this process depends on the ability to recognize and mentally manipulate the phonemes or speech sounds that make up words (phoneme awareness). From pre-alphabetic, to partial alphabetic, to full alphabetic, and then to consolidated word recognition and recall, children must gradually differentiate the sounds in spoken words and map them to letters and letter sequences.

And another interesting observation:

When teachers have not had ample opportunities to learn how to explain words’ spellings, they are much more inclined to believe—and teach—that the English writing system is chaotic and nonsensical. Believing that is the case too often leads educators to rely on “sight” word methods such as “using your eyes like a camera,” drilling with flash cards, telling students to look at pictures and use context to guess an unknown word, or reciting letter sequences to memorize words.

One central goal of LETRS is to put meaning over rote memorization. That’s why part of the phonics lesson plan is working with the meanings of words that students are learning to decode or spell. Our theoretical frameworks emphasize the importance of connecting sound, meaning, and spelling while the mental code-mapping process is under construction...

On the same theme, another article appeared by Linna C. Ehri in Fall 2023, Phases of Development in Learning to Read and Spell Words. In large part, she reiterates the same natural structure noted by Moats above: (1) pre-alphabetic, (2) partial alphabetic, (3) full alphabetic, and (4) consolidated alphabetic phases. The thing I want highlight here is the rather unsettling introduction of the word "phonics" in a tone that suggests trained K-12 reading instructors have likely never heard of it (!):

To move into the full alphabetic phase, children need to acquire the major letter-sound (grapheme-phoneme) relations of the writing system. They need to acquire decoding skill to sound out letters and blend the sounds to form words. The type of reading instruction that helps children master these skills is called phonics. In systematic phonics instruction, teachers follow a “scope and sequence” chart to teach the major letter-sound relations; they also teach segmenting sounds, decoding words, and spelling skills. Phonics instruction can reduce the time that students spend in the partial alphabetic phase and move them quickly into the full phase, typically by the end of kindergarten or in first grade. The skills children acquire help them store words in their memory for reading by sight and spelling words correctly.

Given that, phonics is the cornerstone to the conclusion of the piece:

In school, children benefit most from systematic phonics instruction to acquire these skills. One great way to support your child’s growth at home is to create lots of opportunities for them to practice reading—and to talk about what you’ve read together to boost their comprehension. And if your child is not progressing through the four phases, be sure to go to their school to ask for additional supports.

I thought that both of these articles were well worth the time spent reading them. If only solid, structural reading skills were taught, we could see widespread benefits not just in language arts, but in other important subjects like math, science, logic, computing, and other technical fields.

2024-08-05

Duality of Floor and Modulus

Floor and modulus symbols

Have you ever considered the duality of the floor and modulus operators, in that either one can be expressed in terms of the other (along with multiply, divide, and a subtraction)?

This became practically important for me when my institution switched from the Blackboard learning management system to Brightspace. Both of these have testing systems with a type of question that presents test-takers with questions incorporating randomly-determined base values, and then automatically check their answers via a mathematical formula set up by the instructor. On Blackboard this type of question is called a "Calculated Formula", and among the supported functions, it includes floor but not modulus. On Brightspace it's called an "Arithmetic" question, and its list of functions has the inverse coverage: modulus but not floor.

Now I use this facility to make tests for the introductory C++ programming courses that I teach. Modulus is one of the likely new basic arithmetic operators that we want to test for. Floor is arguably even more essential, in that it's what I need to represent integer division truncation, something really fundamental to how integer math works on a computing system.

So, on Blackboard, if I want to test students' knowledge of the behavior of the expression \(a \% b\) (remember that in the students' view, the \(a\) and \(b\) will be filled in with literal numbers), then in the answer formula I have to use the expression: \(a - b * \lfloor a/b \rfloor\).

In other words: Use the floor function to find the largest whole-number of times that \(b\) goes into \(a\), and subtract that maximal product from \(a\), leaving the modulus as a remainder.

Meanwhile, on Brightspace, if I want to assess awareness of the truncation that happens automatically with an integer division \(a / b\), then every time that occurs in the answer, I need to make use of the expression: \(a/b - a/b\%1\).

That is: Use modulus by 1 to find the decimal remainder in the ratio \(a/b\), and subtract that from the full \(a/b\), leaving behind only the integer part.

Having translated all of my test questions from one to the other in the last week, I'd say that for CS purposes the floor function is more essential, as it's baked in naturally to any integer math expressions, and so it was overall more natural for the work to be done in Blackboard. Use of modulus is more of a special-case check in my assessments, so that arcane formula only showed up a few times. On the other hand, switching to Brightspace, there were about twice as many instances where I had to conjure a floor truncation via the modulus operator that exists there.

Obviously, it would be best if either system supported both of these basic operators, but as we've discovered, you are operationally complete with either one of the pair.