Some introductory thoughts on verification and practice

Verification, which I discussed briefly in my last post, is essentially the student’s own proof of his understanding.  Insisting that student’s verify their own statements is psychologically of great importance because it keeps the focus of classroom work on sense-making, which is a great challenge.  The best way to make students think that schooling is ridiculous is to require them to parrot information that makes no sense to them.  This is hardly a new insight.  The original intention of progressive education was to counter just such mindless recitation so prominent in traditional schooling of the late 19th and early 20th centuries.  It is also at the heart of the reforms urged by the National Council of Teachers of Mathematics over the past 20 years, as well as the Whole-Language Movement of the 1980’s and 90’s.

While the underlying motivations of these reform movements were quite sensible, the way they their ideas have been developed and implemented has often failed to help improve student performance and understanding.  Many progressive educators often lost sight of the original goal to connect experience to words and came to treat raw experience as superior to words.  This attitude, of course, destroys the possibility of education because It is only words that allow experience to be organized in such a way as to be learned from in the first place.  The whole-language movement failed because it fundamentally misunderstood the relevant experiences necessary for good reading.  Whole-Language provided students with no systematic means of verification, as I indicated in my last post with my comment about my son’s reading experience in kindergarten.  And while there are many good things in the NCTM reforms of the last decades and there is quite a bit of potential in them, it is unclear if they have as yet given the typical classroom teacher a better set of tools to help develop student understanding.

While verification is a very important element of instruction, it is not wholly synonymous in and of itself with learning.  The other key element is practice, practice not only to mastery but to fluency. There is a large and growing body of evidence that exceptional accomplishment from sports, to chess, to music, to academic excellence is the result of putting in the hours, much more the product of nurture than nature.  The importance of fluency can hardly be overstated, and it is, unfortunately, another area that many progressive educators and their constructivist progeny have not understood properly.   For once a person can perform a task automatically, that skill becomes a tool that can be combined in new ways with other performances to solve problems and assimilate new information.  This is the fascinating and incredibly powerful idea of generativity discussed by the people Morningside Academy and derived in part from the animal laboratory work of Robert Epstein and his colleagues.

In my next post, I’ll take these very general, theoretical observations and discuss how they apply specifically to developing understanding in reading and math.

Verification

I said in my last post that I would talk about role of mental representation in comprehension.  Before I get into that topic, however, I need to discuss a somewhat related idea I have been thinking about quite bit as I have worked with some of my students, namely, the importance of structuring lessons to allow students to verify their answers and their thinking.

The following story about my son provides a nice example of the importance of what I am calling verification.  One day when my wife went to pick my son up from kindergarten (nine years ago)  he wanted to read to her a story that the class had read together that day.  The reading of the story was done not by showing the students how to “sound out” the words, but through repetition and predictability of the text.  My son apparently read the whole story correctly, except that he read some small function word incorrectly, perhaps “in” for “on”  Some of the other students who heard him read the story corrected him immediately.  However, because he had simply memorized the text pattern rather than learned how to translate the letters into sounds, he became upset.  Moreover, there was no really good way to repair the error so that he understood the mistake:  I suspect in his mind, it was not an error of translation, but an error of memory.

This sort of thing happens countless times with our students, and those of us who work especially with struggling students see that such instructions ends up teaching students to guess constantly and to approach their work un-strategically, confident that it will never entirely be fully understandable to them.  The problem of such mis-understanding in education is quite large:  Howard Gardner has an interesting book called The Unschooled Mind that discusses a significant body of research that demonstrates that even students with high achievement in typical measures of academic performance have persistent and fundamental misunderstandings about what they seem to have learned.

As I’ve worked with students, the curricula that I find the most effective as well as enjoyable to use are those that are founded upon sense-making and require students to prove their answers in terms and with explanations that make sense to them.  This can be as simple as having a student verify a number fact by counting on his fingers, and demonstrating that his subtraction calculation was correct by using base-ten blocks or some similar physical representation.

Much of this can be built into a curriculum systematically.  But one of the great arts of teaching, it seems to me, is to figure out how to help a student assimilate new information and new experiences within the terms of his own understanding.  

 

Math and Reading Workshop

Last week I had the opportunity to help lead a professional development workshop on the topic of Math and Reading for middle school and secondary level teachers in the Ithaca City School District. I was invited by my friend and neighbor Dani Novak, a math professor at Ithaca College who is dedicated to bringing the joy of math to everyone, as well as working to eliminate the fear and anxiety that riddle so many math classrooms (www.ithaca.edu/dani/).

There were eight teachers who participated in the workshop. All were extremely interesting. Five were from DeWitt Middle School, and most of these did not know that the others had registered. Propitiously, I suppose, the final report of the National Mathematics Advisory Panel was released the day before the workshop (www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf). I haven’t had time to read the document carefully, but at first glance it seems very sensible, pointing to the critical importance of algebra instruction, and looking at how to focus elementary and middle school instruction to better prepare students for algebra. (A key lack now seems to be instruction in fractions.)

In preparing for the workshop I read a book called The Number Sense by Stanislas Dehaene. The book was written in 1999, but there was just a New Yorker profile about Dehaene this month, and the parent of one of my students alerted me to it. Dehaene argues that humans have a hard-wired number sense, observable in the behavior of human babies as well as in other mammals, and that a great deal of the problems children have with math instruction is because the instruction usually fails to build sensibly upon these sets of inborn mathematical intuitions.

There is much to ponder here. One of the questions I raised with the group was the difference between understanding a nonsensical and a “sensical” sentence: “The morphius is under the zinderfloss,” v. “The cat is under the table.” At first the teachers wanted to say that they didn’t understand the first sentence at all, and yet, they could all correctly answer the question “Where is the morphius?” As we discussed the matter further, the key difference appeared to be that they could make a mental image of the second, but not the first, even though they understood some purely formal, grammatical relationships expressed in both sentences. The interesting question that thus emerges with regard to comprehension of mathematics (and, indeed, of comprehension generally) is the role of mental representation. I’ll share some more of this discussion in my next post.

The teacher’s themselves came with some excellent questions, including:

• what are good ways to teach mathematical vocabulary
• how can we best help students who don’t read thoroughly and completely
• what are the underlying brain activities that are related to math
• how can we get students motivated about math
• is it wrong to give middle school students a printed multiplication table when doing their work
• what are cultural differences that influence student performance

I’ll try to discuss all of these topics as well in future posts.

Thoughts on “sight words”

Although the term “sight words” is used frequently in discussing beginning reading instruction, it is the source of considerable confusion.  The reason for the confusion is that people use the term to refer to three related but nonetheless distinct concepts.

Sometimes the term “sight words” is used to refer to words that students have learned to recognize extremely rapidly, or “on sight.”  A more precise term would be a “rapidly recognized” words.  Hence, the word “mop” is a sight word for student if he can read the word quickly and it is not a sight word for that student if he cannot yet read it quickly. Recognizing a large number of words rapidly is necessary to become a good reader and it should therefore be one of the fundamental goals of all beginning instruction to help students read the several thousand most frequent words in English in this rapid, automatic way.    Researchers have operationalized the concept of “rapidly recognized” by constructing fluency tables based on the normal distribution of oral reading rates for students at different ages and grades.  (One of the most comprehensive of these tables can be found at brt.uoregon.edu/tech_reports.htm).  This sort of information can be used to identify whether students are recognizing words rapidly enough for likely reading success, and it is the basis of such prominent early reading assessments as the Test of Word Reading Efficiency (TOWRE) and the Dynamic Indicators of Basic Early Literacy Skills (DIBELS).

The term “sight words” is also often used as a synonym for high-frequency words, such as those found on lists compiled by Fry and Dolch.  It is worth noting that the use of the term in this sense refers to a characteristic of the word itself independent of the student’s skill.  Lists of high-frequency words are very useful because, as I mentioned before, one of the fundamental goals of beginning reading instruction is to help students recognize the most common words rapidly.  Using these lists of high-frequency words, educators can create lessons intelligently and assess student performance effectively.

Finally, “sight words” is also used to refer to irregularly spelled words that don’t fit common phonics generalizations, words such as “was,” “could,” and “laugh.”  Like the concept of “high-frequency” word, and unlike the concept of “rapidly-recognized” word,  the concept of “irregularly-spelled” word refers to a characteristic of the word itself and not the learner’s skill.  Most reading programs explicitly identify the irregularly-spelled words as a special category of word, labeled with terms such as “outlaw words,” “rule-breakers,” and “words that don’t play fair.”  Students are typically asked to learn these words not by repeatedly sounding them out, but as visual wholes, that is, without analyzing how the letters represent the sounds in the word.  

Although this technique for teaching irregularly-spelled words is quite common, its necessity is hardly obvious.  The reason is that irregularly-spelled words typically have only a single letter/sound correspondence that is irregular.  For instance, in the word “was,” the letters “w” and “s” represent typical sounds—it is only the “a” that is irregular.  If the words “was” is taught only as a visual whole, then the underlying relationship between its letters and sounds is hidden from the student.  This relationship is a powerful tool for helping the student learn the word accurately and quickly.  Moreover, it is rarely the case that an irregular letter/sound correspondence is unique to a particular word, but is usually shared in at least one or two other common examples.  For instance, the unusual vowel sound in “was” also appears in the word “what.”  Similarly related words include “any-many,” and “would-should-could.”  Since the human memory is associative, it would seem to be quite natural as well as helpful to make these relationships obvious to students.  Furthermore, the more extensively the letter/sound relationships in the word are analyzed explicitly, the easier it is for teachers to help students learn the difference between words with similar spellings such as “want” and “went.” 

 These comments do not mean that I think it is particularly harmful to teach irregularly-spelled words as visual wholes.  Indeed, I do believe that there is some benefit from teaching a small number of words in this way.  The benefit lies in helping a beginning student read a number of common function words without going over the sounds in those words.  One does not need to teach words with the /ew/ sound, for example, to teach a very beginning student the word “to.”  Once the beginning student knows a few of these function words, he is able to read some simple sentences, and therefore extend his reading skill.   In addition, there are a handful of very common words such as “of” in which all the letters are irregular and there are no other words with a similar spelling pattern.  However, the list of extremely useful function words like “to” and high-frequency words with unique spellings like “of” is quite small, perhaps no more than a dozen.

What is the moral of this story?  It is probably a good idea to retire the ambiguous term “sight words” and replace it as appropriate with the more precise phrases:  rapidly-recognized words, high-frequency words, and irregularly-spelled words.  Once equipped with these precise distinctions, what should the good reading teaching do with them?   She should teach all high-frequency words and words with common spelling patterns so that students can recognize them rapidly.  This work should involve prominently making the letter/sound relationships in the word explicit and only very rarely should involve presenting irregularly-spelled words as unanalyzed visual wholes.  

Thoughts on Teaching Letter Names to Beginning Readers

Teaching letter names is a common feature of beginning reading programs.  In spite of its ubiquity, however, its connection to beginning reading success is not as straightforward as many teachers, administrators, and curriculum authors assume.

One of the main reasons that kindergarten and first grade teachers teach their students the names of the letters is that there is a very strong correlation between letter-name knowledge at the beginning of kindergarten and reading performance at the end of second and third grade.  In other words, students who enter kindergarten knowing all or most of the letter names tend to be better readers at the end of third grade than their fellow students who know few or none of the letter names.  This correlation is extremely well-established and beyond dispute.  However, the correlation itself doesn’t tell us whether learning the names of the letters is a direct cause of learning to read well.  There is also, for instance,  a very strong correlation between foot size and reading ability for people ages 5-10:  In this population, the children with bigger feet are on average better readers than the children with smaller feet.  But no one will ever come out and advocate that the stretch kids feet in order to improve their reading skill because in spite of the correlation between foot size and reading skill, foot is very clearly NOT the direct cause of reading ability.  Rather, foot size is a kind of marker for those things which are truly the cause of improved reading, such as more schooling, more reading experience, and more reading practice.

Although not quite so obvious as the foot-size example, the effect of letter names is likewise not a direct cause itself, but rather a marker for the underlying cause.  In this case, the underlying cause most likely has to do with the child’s experiences with books and language and the variety of knowledge and skills that such experiences provide.  

The functional components of learning how to recognize printed words are knowledge of letter sounds, the skill of phoneme blending, and perhaps a certain kind of visual memory as well.   Teaching and developing these things is directly related to improving the reading performance of beginning readers.  So teaching letter names is probably a very inefficient thing to do with beginning readers, whereas teaching letter-sounds is extremely productive.

Not only that, but teaching letter names to a non-reader in kindergarten or first grade, might actually delay his acquisition of beginning reading skill.  If the student has memory difficulties, adding the letter names to the list of things he is to learn ties up a valuable mental resource and slows his learning of the letter sounds.  Also, the teaching of letter names to the non-reader may very well obscure the nature and logic of our writing system, namely, that letters represent sounds.  This is because the relationship between letter names and letter sounds is haphazard and confusing.  Some letter names have the letter sound at the beginning of the name (“bee,” “dee,” “kay”); some letter names have the letter sound at the end of the name (“ess,” “ef,” “em”) and some letter names have no connection to the letter sound (“double-u,” “aitch).  Moreover, just knowing the letter names of a word doesn’t directly help a person know what the word is.  The relationship between “dee-oh-gee” and the pronunciation of the word “dog” is hardly obvious.  

Does this mean that we shouldn’t teach pre-school children to sing the alphabet song?  No, not at all.  This is a perfectly fine activity for pre-schoolers, since the job for pre-school education isn’t to teach reading directly, but to provide a variety of language experiences that are important for success in school.  (It wouldn’t hurt, of course, to help pre-schoolers learn the letter sounds as well as the letter names.)  My argument also doesn’t mean that letter names are not important at all.  Knowing them is certainly a part of language arts knowledge that any educated person needs.  They are important for communication about the spellings of words, for using the dictionary, and for other related activities.  The question isn’t WHETHER to teach letter names, but rather WHEN to teach them.  For students who come to school not knowing the letter names, I would strongly recommend waiting until after they had learned the letter sounds and also had learned how to read.  Once they have these skills, the knowledge of letter names is generally quite easy to acquire.  As I tell any audience that I speak to, I have met people young and old who knew the letter names but who couldn’t read, but I have never met anyone who could read who didn’t know the letter names.

Next post:  related thoughts about teaching so-called “sight” words. 

Thoughts on teaching phoneme blending

As I discussed in my last post, phoneme awareness (PA) is a critical skill to develop in beginning readers, and one of the most important PA skills is the ability to blend the isolated phonemes that comprise a word (e.g., /m/ /o/ /p/) and translate them into the whole word (“mop”).  This skill is generally referred to as phoneme blending.   

Anyone who has worked with beginning readers knows that this skill can be difficult for some students to develop.  Before I developed ABeCeDarian, I worked with many kindergarten and 1st students who didn’t learn this skill in spite of the instruction and practice I provided using techniques from the generally excellent Lindamood Phoneme Sequence Program (LiPS), Reading Mastery, and Phono-Graphix.  Almost invariably, these student with severe difficulties learning how to blend phonemes were significantly behind their fellow students in reading skill, often able to read just one or two words even after many hours of intensive individual instruction.

At some point in my studies and experiments to improve my teaching I was struck by a very interesting fact about PA, namely that PA and decoding have a reciprocal relationship.  What that means is that while improving PA generally improves decoding ability, improving decoding ability also generally improves PA.  Being able to identify and manipulate speech sounds helps a student learn to read more words accurately and quickly, and reading more words accurately and quickly helps a student identify speech sounds.  This relationship should not come as much of a surprise.  My first grade teacher in 1965 never even heard the term “phonemic awareness”, let alone tried to actively stimulate it in her students.  And yet, nonetheless, I developed PA, and I did so, most probably, because of what I learned about the structure of our language as I learned to read and spell.

Another way to think about this reciprocal relationship is that the development of PA occurs in both a bottom-up and a top-down way.  It occurs in a bottom-up way as students learn letter/sounds and are encouraged to use these letter/sounds to sound out words.  PA develops in a top-down way as students learn through repeated exposure to read whole words and have to spell or analyze the words they have learned back into individual speech sounds.  

So the key is to have students hear the isolated phonemes connected to the whole word (This is the word “mop,” /m/ /o/ /p/ /mop/), but also to learn how to read a number of words as wholes.  When I say this, I do not mean that the students are asked to memorize the word just by looking at it as an unanalyzed whole.  On the contrary, students are constantly doing some activity that requires them to say all of the individual phonemes of the words they are learning and then immediately hear the whole word.    Yet many students do memorize these words by dint of repetition before they can sound them out because only 6 words are presented in each unit, and students practice reading these until they can do so easily. 

Thus, what I’m doing now in these routines that I didn’t do before when I failed with a number of students is to have them focus their attention on a small number of words until they have learned to recognize them easily without necessarily yet being able specifically to sound them out.  At the same time, the students are hearing the isolated phonemes of the word connected to the whole word dozens if not hundreds of times.  Added to this regimen is a key support offered by the teacher.  If a student looks at a word he has been studying and he says all the isolated speech sounds but can’t figure out the word, the teacher offers to say the word in Turtle Talk, that is, with all of the continuant sounds elongated (/mmmooop/).  (I really should offer these as podcasts!  Coming soon, I hope.)  This combination seems to give students just what they need to develop phoneme blending skill, and to do so relatively quickly.  As we have shown in our extensive kindergarten study, a group of students who were one standard deviation below average on PA skills at the beginning of the year advanced as a group to the average range by the end of the school year (www.abcdrp.com/support.asp).  Moreover, it can be done with essentially no frustration on the part of the student because of the adroit teacher support, such as the use of Turtle Talk, built into the activities.

In my next post I will share thoughts about teaching letter names and sight words.  Happy Teaching!

An Iconoclast’s View of Phonemic Awareness

The importance of phoneme awareness in beginning reading instruction is by now quite well-established.  “Phoneme Awareness,” often abbreviated PA, refers to the ability of an individual to perceive the phonemes embedded in words.  Phonemes are the smallest unit of speech sound that make a difference in the meaning of words, such as the sounds /b/, /t/, and /a/.  English has over 40 phonemes (there is debate about the exact number).  Our writing system is to a very large extent a symbolic representation of phonemes.  Thus, the word “cat” has three letters because the spoken word has three phonemes, /k/ /a/ /t/.  The /k/ sound is represented by the letter “c,” the /a/ sound by the letter “a,” and the /t/ sound by the letter “t.”

The “awareness” in “phoneme awareness,” refers to an individual’s ability to identify and manipulate these speech sounds.   This ability can be manifested in any task that requires an individual to take apart or put together the sounds of a word.  These tasks include:

recognizing rhyme (“Do ‘cat’ and ‘hat’ rhyme?”)

producing rhyme (“Tell me a word that rhymes with ‘cat.’”)

onset-rime blending (“Say /k/ /at/.  What word do those sounds make?”)

identifying the first or last sound of a word (“What’s the first sound of ‘cat?’”)

blending isolated phonemes (“Say /k/ /a/ /t/.  What word do those sounds make?”)

segmenting a word into isolated phonemes (“Tell me the sounds of ‘cat.’”) 

There is a very strong correlation between a student’s PA skill at the start of kindergarten and his reading ability at the end of second grade.  That is, students with high PA typically have high reading achievement and those with low PA have low reading achievement.  We know also that teaching PA improves student reading performance.  Logically, it is not at all surprising that PA might be helpful when learning how to read, since it gives the student access to much (though certainly not all) of the logic behind why a particular group of letters is used to represent a particular word.

While there are many kinds of performance that indicate the existence of PA, only two PA skills are directly related to reading and spelling: phoneme segmenting and phoneme blending.

Phoneme blending helps not only with sounding-out unfamiliar words, but it probably also helps makes it easier to learn to recognize words automatically without overtly sounding them out.

Phoneme segmenting helps students understand the logic of our spelling system (i.e., that letters represent sounds) as well as helps students with spelling.  In addition, like phoneme blending, it might also help make it easier to develop the robust memory trace involved in recognizing known words automatically.

While these two skills are generally considered the most germane to beginning reading, they are also generally considered the hardest of the typical PA tasks.

This leads to an interesting and extremely important question.  Given this hierarchy of PA skills, what is the most efficient way to develop skills at phoneme blending and segmenting.  Is it most efficient in the long run to postpone addressing blending and segmenting until a student can perform some of these easier PA skills well, or can one start developing blending and segmenting skills from the very outset of instruction, even with young students who have very weak PA?

For preschool students, who are too young for formal reading instruction, PA activities clearly should focus on the simpler forms of phoneme awareness that can be stimulated by such activities as reciting poems and singing songs that have lots of rhyme and other language play.  This approach is suitable for these very young children because the goal of pre-school should not be to teach children how to read, but to provide them with a variety of language experiences that will help them succeed in school.

The question about the right kind of PA activities for for kindergarten and first grade students, however, is not so obvious.  If one surveys kindergarten and first grade reading curricula, it is clear that the conventional wisdom is that students need to develop the easier PA skills before tackling blending and segmenting.  For instance, the Florida Center for Reading Research suggests that some students “may require segmenting and blending at the syllable level followed by onset and rime blending” (www.fcrr.org/assessment).  The National Reading Panel Report of 2000 makes a very similar statement: 

Among readers in 1st and 2nd grades, there may be variation in how well children can perform more advanced forms of PA, that is, manipulations involving segmenting and blending with letters. The best approach is for teachers to assess students’ PA before beginning PA instruction. This will indicate which children need the instruction and 

which do not, which children need to be taught rudimentary levels of PA (e.g., segmenting initial sounds in words), and which children need more advanced levels involving segmenting or blending with letters. (NRP Report, p. 2-6).

My own experience, however, tells me that this conventional wisdom is wrong.

Carmen McGuinness has shown in Phono-Graphix, first of all, that it is quite possible to embed phoneme blending and phoneme segmenting within beginning reading and spelling activities rather than as a separate component.  ABeCeDarian utilizes this very same embedding of phoneme segmenting and blending within every activity at the start of the program and, also like Phono-Graphix, eschews other types of PA activities.  How is it possible for students with very poor PA to succeed in these lessons?  The key is a lively and focused set of routines that have students saying the isolated sounds of all the words they are learning over and over and over, always in connection with the whole word.  This dynamic repetition helps students recognize quickly how whole words are comprised of isolated speech sounds.

How do students do with such accelerated PA instruction?  Amazingly well!   ABeCeDarian’s multi-year project with low-performing kindergarten students in Delaware (www.abcdrp.com/support.asp) showed repeatedly that using this approach to teaching PA,  groups of students who started the year a standard deviation below average in PA skills developed average PA skills by the end of the year.

The success of young students who use Phono-Graphix or ABeCeDarian suggests that phoneme blending and segmenting can be stimulated and developed in kindergarten and first greade students with very poor PA by providing the right kind of focus, explicitness, and practice, without spending times on easier PA activities, and that this sort of instruction is best able to improve the students’ reading skill.  The implications for developing the most efficient reading instruction are quite profound.

The more general point beyond the relatively narrow matter of PA is that there are powerful efficiencies in instruction that careful curriculum design can achieve, and that seemingly small and nuanced differences in how material is presented can produce big differences in how quickly and easily students will learn.

In my next post, I will describe in some detail the way that ABCD teaches students how to blend isolated phonemes into words.  Although none of the individual steps is original by any means, the way the steps are organized and sequenced is unique, and provides teachers with what I believe is the easiest and fastest way to teach phoneme blending they will ever find.

Welcome

Welcome to an adventure and an experiment.  In this blog I will be writing about various topics in education.  I am primarily a reading teacher and an author of reading curriculum materials, so much of what I will write about will be about reading education.  But my thoughts and interests certainly roam more broadly, and include in general how children learn and how schools function (or don’t function so well). 

Although I suppose that technically what I am presenting is a blog, it will be, at least at the start, something of an anti-blog, more a set of very short essays.  Most blogs are for insiders of one sort or another, and so references throughout the blog assume quite a bit of background knowledge.  I’ll try to assume no special knowledge on the part of my readers, but only an interest in the topics.  I will write most of the posts relatively quickly, but perhaps not quite as quickly as most blogs are written.  What I lack in alacrity I hope I will make up for in insight.

Happy Teaching and Good Reading!