"Bugs"

In my recent post about foreign-language learning, I recommended that students and teachers embrace errors.  This recommendation, however, shouldn’t be restricted to the study of another language but should be applied to almost all learning.   Unfortunately, we all too often treat errors as failures rather than as necessary and important ingredients of learning. 

There are several important benefits to treating errors as an essential part of learning.  First of all, the goal of learning should be some kind of performance, such as doing a certain kind of mathematical calculation, writing an insightful, interesting paragraph, playing a piece of music on a particular instrument, or executing some maneuver in a sport. When a person who is attempting any of these endeavors commits an error, that means, of course, that she has not yet achieved the desired level of performance.  But it rarely means that the person should abandon the endeavor!  An environment in which errors are understood as a necessary part of attempting something interesting or important encourages a person to continue with his efforts until he has achieved the desired outcome.   In short, it helps to build perseverance and resiliency.

Another benefit of  to treating errors as an essential part of learning is that it helps a student develop analytical skills.  If after making an error, one repeats the effort without any reflection, it is very easy to make exactly the same error again.  To avoid that fate, it is necessary to analyze one’s own performance to figure out what went wrong.  Thus, it is important for teachers to help students learn how to monitor and reflect on their performance so that they can determine the cause of any errors and consider how to avoid the error in the future.  For this reason, in ABeCeDarian teachers usually respond to errors not by saying or writing a word correctly, but telling the student where in the performance the error lay.  It is then up to the student to use this information and try again.  For example, if a student says /map/ when he is trying to read the word “mop,” the teacher responds, “You said /map/, with an /a/ here <pointing to the “a.”>  But that isn’t /a/.  It’s /o/.  Try again please.”  As students progress, the teacher shifts more responsibility for analyzing the student’s performance to the student himself by responding to an error simply by asking him to explain why the word he wrote or said couldn’t be correct.

We often think of practice as a phase or step of learning that is separate from the kind of investigation and reflection involved in exploring something new.  Moreover, the practice phase is frequently presented as inherently tedious.  Critics of traditional phonics programs, for example, often speak of “drill and kill,” meaning, students in such programs receive so much drill in decontextualized subskills that their interest and motivation in reading suffer.  However, if errors are treated not just as something for teachers to tally, but as something for students to analyze, then practice becomes infused with the same problem-solving focus as other parts of instruction.  Both student engagement and performance improve, creating a powerful virtuous circle.  Practice becomes more engaging, and so students do more of it, and so their performance improves, which motivates even more practice, and so on.

One of the most illuminating discussions of how to treat errors productively is in the superb book, Mindstorms, by Seymour Papert.  In that book, written in the 1970’s, Papert talks about how the personal computer can transform education, not as many educators believe, as a tool for providing more individualized practice to students, but as a tool that the students can use to make things by means of computer programming.  As students engage with the computer in this way, almost immediately they encounter the concept of “debugging.”  Rarely is it the case that a person writes computer code that performs exactly as the programmer expected.  After writing code, the programmer has to evaluate it, and when some part of the program doesn’t perform as expected, the programmer has to analyze the problem.  The relevant questions for the programmer when analyzing these errors are:  Can the problem be fixed, and if so, how?  “Bugs” are failures, in a sense, but they are both ordinary and, in most cases, temporary.  They aren’t faults that should be punished, but obstacles to be overcome.

The concept of “debugging” in computer programming thus provides an accessible and evocative metaphor for how to treat errors in general that can help prevent both teachers and students from embracing the false and debilitating notion that challenging and worthwhile tasks can be accomplished without making mistakes.

Resources for foreign language learning

As promised in my last post, here are some excellentl resources for foreign language learning.

Assimil

Assimil, published in France, is one of the best language learning programs I have found.  The general lesson structure follows the principles that I advocated in my last blog post.  The core of each lesson is a dialogue spoken by native speakers.   A transcript is provided along with a translation.  Grammar points are introduced as necessary to understand expressions in the dialogue.  The dialogues are short and witty.  In addition to listening to, reading, and reciting the dialogue, there are only two other exercises during the first half of the program: translating 5 sentences each lesson from your target language into English, and filling in missing words in 5 sentences written in your target language.  A third exercise is added to each lesson after the student has completed the first half of the program, namely, returning to the earlier dialogues in turn and translating the English into the target language.

Foreign Service Institute Language Courses

The Foreign Service Institute is the office in the United States government responsible for training the country’s diplomatic corps and others who work for the U.S. State Department to advance American interests overseas.  In the 1950’s, 60’s, and 70’s, this office developed intensive courses to learn many languages.  These materials are now in the public domain and available for free. The lessons are generally rather dense, but there is a tremendous amount of material contained in them.  Like the programs in Assimil, they contain dialogues spoken by native speakers, accompanied by transcripts and translations.  Unlike Assimil, though, each lesson includes a large number exercises.  One frequent exercises is a replacement drill, in which a basic sentence is given and then the student has to say a new sentence that involves a slight modification of the preceding one, such as using a different pronoun or verb tense.

https://www.livelingua.com/fsi-language-courses.php

I have come across 2 polyglots who provide excellent recommendations and resources for people learning a foreign language.

Fluent Forever

In this book author Gabriel Wyner provides recommendations for an overall approach to foreign language learning as well as enormous number of invaluable resources, including a list of the 600 most common words in various languages and guidance about how to make outstanding flash cards using Anki, a spaced-repetition computer-based flash card program.  Wyner also provides recommendations about outstanding grammar books and dictionaries for several languages as well as information about various web-based services to find people to correct one’s writing and to provide opportunities for conversation.  

https://fluent-forever.com/

LingQ

This site has been developed by the polyglot, Steve Kaufman, who also blogs frequently about themes related to foreign language learning.  The LingQ website is a tremendous resource of text and audio from many different languages.  A special feature of the site is the ability to keep track of new words in passages as well as how many words one knows.  I have been especially persuaded by Kaufman’s strong advocacy of focusing on maximizing input, which in practice means lots and lots of reading and listening, followed by frequent writing and speaking.

https://www.lingq.com/

News in Slow Spanish, French, Italian, and German

These websites provide weekly news articles spoken slowly.  Each news story is followed by commentary spoken slowly.  Users also have the option to hear the text read at a normal speed.  New vocabulary is highlighted and a translation of that vocabulary is immediately provided when one places the mouse cursor over the highlighted text.  In addition to the podcasts on current events, every week a new dialogue is presented on a theme of general interest that contains many examples of a particular grammar point.  The programs also provide a dialogue each week repeatedly using a common idiomatic expression.  This is an absolutely amazing resource, a virtually inexhaustible supply of high-quality, interesting text and audio with numerous, clever aides for the foreign language student.

https://newsinslowspanish.com/

https://newsinslowfrench.com/

https://newsinslowgerman.com/

https://newsinslowitalian.com/

Linguee

There are many useful online dictionaries now, but Linguee I think stands out.  It not only provides definitions and audio with proper pronunciation, it also access an enormous data base to provide examples of words and phrases as they are used in text.

www.linguee.com

Phrase Books

Phrase books are generally designed for travelers who want to learn a number of useful phrases in a language, but who do not necessarily care to study it at length in order to be able to speak and read at a high level.  Nonetheless, they can be very useful tools to help a beginning student get started with his serious and more extensive language study.  Two excellent series are those by Rick Steves and those by Lonely Planet.

There are many other excellent resources that I haven't mentioned, including many that deal with learning one language in particular.  But one of the overwhelming aspects of beginning to learn another language is figuring out where to start, and these resources will quickly help you begin efficient and organized study.

Thoughts about good foreign language instruction

Although I studied Latin, German, and ancient Greek in high school and college, I never achieved anything beyond rudimentary abilities in these languages.  For many years after college I had no strong motivation to pursue any additional language study.  Over the last 10 years, however, I have had the opportunity to travel to a number of other countries, and to prepare for these travels I have done quite bit of foreign language study on my own.  

I would like to share some lessons I’ve learned from these recent experiences as a language student. I hope they may be useful both to adults who want to learn another language and to teachers who want to teach foreign languages to children as effectively as possible.

Focus on reading and listening at the beginning with just enough grammar to allow for understanding

As I discussed in previous posts, a good lesson structure involves providing students with some relevant experience and then analyzing it.  For foreign language instruction, the relevant experience, of course, is listening to speech or reading text. Grammar instruction is necessary, but it is best addressed in the second step, the analysis step.  For example, when introducing a new tense to a student, I wouldn’t begin by saying, “Here are the endings used in the future tense.”  Rather, I would have the student read some text with this construction and then point out the words in the future tense and analyze how they are formed. 

Focusing on listening and reading thus keep the focus on developing the student’s ability to comprehend the new language, which, of course, is the goal of language study. It is all too easy for grammar to assume a role not as a tool used to acquire understanding, but almost as an end in itself.  I know this was the case with much of the foreign language study I did in school.  When grammar becomes the focus of lessons, valuable time is taken from working to understand speech and text, and students often become overwhelmed and confused. Grammar points are much easier to learn when they are directly related to a student's experience with the language rather than in isolation and out of context.

A initial focus on listening and readiing also allows the student to postpone significant work in speaking and writing until he has acquired a vocabulary of several hundred words and the ability to understand simple expressions using basic sentence structures.  Postponing speaking and writing has several benefits. I have worked with a few programs that emphasized developing speaking skills from the outset, but they did so at the expense of developing oral language comprehension.  As a result, I could express some simple ideas quite early in my studies, but I was not able to understand what a person was saying to me.  Receptive tasks, such as oral comprehension, are generally easier than expressive tasks, such as speaking, so it makes sense to start with the easier tasks that are the foundation of the more difficult ones. 

Another benefit of postponing speaking and writing is that it can reduce the anxiety often associated with foreign language learning.  It is psychologically quite demanding to try to say something when one has very words in one's vocabulary and very little knowledge of how to string words together in the language. If extensive work on speaking is delayed until the student has a more extensive vocabulary and ability to understand more speech and text, that is, when he has more experience with the language, it is much less daunting to speak and much easier for the student to be able to express a reasonably complex idea.  Indeed, I suspect students who follow this sequence not only often find themselves ready to say quite a bit but can surprise themselves as well with how eager they are to do it.

Train with audio (and lots of it)

I have tried using some books that didn’t have any associated audio. This approach is effective if the only goal is to read the language.  However, if one wants to be able to understand when others speak and to be able to speak oneself, it is absolutely essential to listen to lots of the language spoken by native speakers. Fortunately, thanks to the wonders of digitized sound, the personal computer and the internet, there is a tremendous amount of audio readily available, much of it free.

The most efficient way to learn from audio is to study it in conjunction with a transcription.  An excellent routine is for the student to listen to the audio a couple of times without reading the text, trying to understand as much as possible.  After these initial trials, the student can then read the transcript in order to understand the passage thoroughly.  During the reading the student can figure out, moreover, why he wasn’t able to understand certain parts.  Was it because the speakers used vocabulary new to the student, or was it because he wasn’t able to recognize the pronunciation of a known word.  This analysis is tremendously useful.  Then the student can go back and listen to the audio again without looking at the text.  Students should continue this process until they can understand the spoken text easily.  When I follow this routine, I not only comprehend a new passage thoroughly by the end of the routine, but also I find that my ability to comprehend new speech improves quite dramatically.

Once a student is familiar with a particular text, he should then try to read the text out loud along with the native speaker.  At first it is advisable to play a phrase, pause the audio, and then repeat it.  Once the student is able to pronounce all of the words easily, then he should go back and try the exercise again, but this time he should try to read the text at the same time as the speaker. It is an extremely challenging but powerful exercise.

A final step is to for the student to memorize a few sentences or a paragraph and recite them without looking at the text, repeating this exercise until he can recite the text at a normal conversational rate.

Embrace errors

The more errors a student makes, the faster he will learn. This counterintuitive phenomenon occurs because the best way to commit something to memory is to try to recall it.  In other words, the best way to practice is to test oneself constantly.  However, it takes many repetitions to remember new information and how and when to apply it correctly, especially when the learner is embarking on a new area of study.  Therefore maximizing repeitions, which should be a primary goal of instruction, naturally leads to many errors.

There is, of course, another condition that needs to be met to make this practice as efficient as possible, and that is that the student needs to receive feedback about his errors, including help to analyze them so that he understands why his mistakes were mistakes.  Those of you familiar with the ABeCeDarian Reading Program know how much I discuss the nature of good error correction and how important it is to the program.  I’ll have more to say in future blog posts about specific techniques for dealing with errors, both in foreign language instruction in particular and in other areas as well.

In my next post I will present a number of resources I have found invaluable in my own foreign language studies.

Two key components of good lessons

If you asked people what makes a good lesson good, I suspect most of them would identify the clarity with which the teacher explained the subject.  A good lesson, they would maintain, has a clear theme, appropriate background information, illuminating examples, precisely connected points.  I’m sure we have all suffered through enough lessons that didn’t have these features to appreciate just how much they contribute to our understanding of a topic.

I would argue, however, that this emphasis on clear presentation assumes that the general structure of an academic lesson involes a person explaining or demonstrating something to some students.   I think it is more useful, however, to think of lesson in broader terms, as a set of experiences that help students learn something.  When we expand our conception of a lesson in this way, I think we will find that explaining or demonstrating, while certainly one kind of experience students can have, is a rather limited and generally overused technique.

The problem with direct explanation or demonstration is that helping students understand something new cannot be accomplished simply by adding information to their brains.  The development of understanding requires a further step, namely, integrating the new information with what is already known.  Now,  a good lecture attempts to do this, but it can do so only in a rather crude way, making assumptions about what the person already knows and thinks. Moreover, the connections a lecturer makes in his lecture enter the mind of a student in a weakened form because the student aquires them, in a sense, too easily.  They are predigested and second-hand, and not hard won through the student’s own active exploration.

In this light, I would argue that one key component of a good lesson is selecting the right task or tasks for the student to do at the very beginning.  These tasks must be familiar to the student, or at least have a structure that provides her with all she needs to perform the task.  In addition, they should require the student's active participation and engagement.  The final challenge in developing suitable tasks is to carefully embed something new within the familiar elements.  The something new, of course, is the focus of the lesson.

Certainly, giving students experiences is, by itself, an inefficient and indirect way to develop a student’s understanding.  To allow the experience to yield new connections and new understanding the teacher needs to include the second key component of a good lesson, and this is to ask the student questions to help her analyze some experience. 

The questions I am referring to here are not those that ask a student to recall specific facts per se, but rather the kind that focus on identifying patterns and relationships.  These questions include, “What’s the same between this and that,” “What’s different,” “What patterns do you see” and “How is this connected to something you already know?"

For those of you already using ABeCeDarian, I encourage you to review lessons you have done to see this general structure: giving the students a task in conjunction with analysis of the task.  To assist you, let me point out three examples of this structure in ABeCeDarian lessons.

As I’ve discussed in an earlier blog post, the very first thing that a beginning student does is to spell the word “mop” as part of an activity called a Word Puzzle.  After the teacher states very briefly that the student is going to help spell the word “mop,” the teacher then asks, “What is the first sound you hear in the word ‘mop?’”  The activity includes a number of supports that help the student answer this question.  The lesson thus begins with the experience of hearing a familiar word “mop,” and the teacher prompts the student to analyze this experience by asking “What is the first sound?”

Here is another example, this one from Level B-1.  When a student has learned the one-letter consonants and vowels, she then begins to learn to read 1st grade level words with vowel digraphs such  as “boat,” and “rain”  (Digraphs are two-letter spellings used to represent a single sound, such as the “oa” in “boat,” and the “ai” in rain.)  The student's initial task at this level is to examine a list of words that all have the so-called “long-o” sound and sort the words depending upon how that sound is spelled.  Students begin the task by reading the words.  If they don’t know the word immediately, they sound it out, a task that they have done hundreds of times in the earlier level.  What is new is a spelling for the long-o sound.  Most can figure this out without help from the teacher.  But if they don’t, the teacher simply tells the student the sound.  That is the whole activity, reading and then sorting.  Again, the student begins with a task, reading the word, and then analyzes it by sorting, prompted by the teacher’s question, “How is the /oa/ sound spelled in this word?"

My final example comes from Level C of ABeCeDarian, a level suitable for students at a 3rd to 4th grade reading level. This level address word parts, namely, prefixes, suffixes, and root words. Many programs covering this material begin with a statement such as, “Words are made up of parts that we call prefixes, suffixes, and roots.”  In ABeCeDarian, in contrast, students are are introduced to the topic by reading the following list of words:  helpful, unhappy, landed, rebirth, starting, refill, landing, started, careful, and untruthful.  Then the teacher asks them to identify all of the syllables that appear more than once in the words.  As in the other examples, the lesson has the same basic structure:  the student is given a task that requires them to analyze and identify a key feature of words. 

As I have mentioned before, I am currently preparing a series of math lessons to add to the ABeCeDarian lineup.  These math lessons are also organized in the same way:  Students are given tasks and then, with the aid of precise questioning from the teacher, they analyze what they have done in order to develop new skills and to see new patterns and relationships.  I will be writing more about these new math materials in the coming months.

In the meantime, I hope you will reflect a bit about how close or far apart other lessons you have your students do are from the structure I have just described.  And if you are not happy with how your students are doing in those lessons, one area to examine is the extent to which the student performs some relevant task and then analyzes it with your help.

More tips to improve practice routines

Last week I talked about the importance of providing short practice sessions spread out over time (distributed practice and spaced repetition) and making sure that practice sessions involve a variety of the skills (interleaving practice).  Today I want to touch on a couple of other points to keep in mind when setting up practice.

When the content allows, it is extremely useful to present practice activities that reveal the underlying structure of what they are investigating. For example, a difficult part of learning how to spell the word “president,” is to know that the vowel in the second syllable is written with an “i.”  This is difficult to remember because the sound we say in the word in the second syllable is a little “uh," a vowel sound called a schwa that is common in the pronunciation of unaccented syllables.  Unfortunately, this sound can be spelled with any of the one-letter vowels.  It so happens, however, that there is a form of the word in which the second syllable is accented, namely, “preside,” in which we say the so-called “long sound” of “i.”  If the student’s practice routine involves connecting the word “president” to the word “preside,” he will be able to recover the underlying sound of the vowel and thus find it much easier to remember the spelling. Moreover, the practice will have reinforced some of the structural ways that words are related in English.  This same relationships can be used to help remember the spelling of hundreds of words.

Practicing letter/sound relationships as students do in phonics programs likewise helps them connect the reading and spelling of  particular words with other words and reinforces a central part of the structure of our writing system.

The study of elementary math provides many opportunities for enhancing practice by highlighting critical structural relationships, although most curriculum materials do not take advantage of these opportunities.  When learning how to do calculations with decimals, for instance, it is extremely useful to investigate the same calculation when using common fractions.  Even something like memorizing the multiplication facts can be made much easier by practice that stresses relationships.  For instance, when I am reviewing multiplication facts with students and they have difficulty recalling a fact, I ask them to connect it to something that they know.  If a student forgets the product of 6 x 6 but knows the product of 5 x 6, he can talk himself through the problem by adding 6 to the product of 5 x 6.  Another option is to draw an array on a grid board that corresponds to the multiplication problem.  When trying to figure out 6 x 6, for example, this means drawing a 6 by 6 rectangle.  The student can then divide that shape into 2 or 3 parts and then calculate the product by adding the parts.  Of course, the ultimate goal of this practice is for the student to have rapid and accurate recall of the facts.  But by emphasizing the way every fact is part of a broad network of relationships, you will accelerate how quickly your students achieve fluency and, at the same time, help them develop a sense that the various things they are learning in math aren’t random and isolated but tightly interconnected.

Of course, not everything we want to learn has the kind of structure we find in our writing system or in mathematics.  Some things, such as learning the order of the colors of the rainbow, the order of the planets in the solar system, or the capitals of the states, are associated in arbitrary ways.  Many of us have learned such things with brute-force memorization, simply repeating the order of the items and their connections over and over.  This technique often works eventually, but in most cases, there is a faster and easier method.

Since antiquity there have been people interested in developing systems to help with memorization. What these memory system have in common is that they provide ways to impose a structure on abstract, random information by associating it with something you already know.  As Harry Lorayne and Jerry Lucas write in their classic, The Memory Book, “In order to remember any new piece of information, it must be associated to something you already know."

This is the idea behind mnemonics such as the sentence “Every good boy deserves fudge,” to learn the order of notes represented by the lines on a scale.  This mnemonic works because it is much easier to remember common, familiar words organized in a simple sentence than to remember the order egbdf.  Memory trainers such as Lorayne and Lucas have developed flexible systems that utilize the same underlying principle and that can be applied to memorizing any content. The key to most of these successful memory systems involves developing ridiculous and wild images that connect objects.  In the Lorayne and Lucas book, they offer the example of trying to learn a random lists of 10 objects.  If the first 2 objects were airplane and tree, the person should make a crazy image in which the two are together, such as a tree that has small airplanes for leaves, or an airplane that has a variety of trees as passengers.  There are a variety of elaborations or extensions of this basic technique, but all successful memory systems rest on this fundamental strategy.

A number of years ago I had the opportunity to travel to China and wanted to try to study the language a little bit before the trip.  As you may know, it is quite a challenge to learn to read Chinese characters, because it is necessary to memorize thousands of them in order to attain even the most basic level of literacy.  In the course of my studies I found a really interesting book to learn the 800 most basic characters.  The technique used in each book was to break each complex character into parts, and have each part represented by a visual image.  They then constructed a little story that connected these images with additional clues about the words meaning, its pronunciation, and its tone.  Thus, for each character, one had an easy to visualize story that connected all the essential elements needed to read the word.  I found this approach very useful and much easier than the brute-force approach I had tried previously.

The Chinese book gave me the idea to try to adopt this technique to prepare an English spelling book, and thus I developed the ABeCeDarian Spelling Book B-1.  This book addresses first grade words such as “boat” and “rain.”  The first skill a person needs to spell well is an ability to break a word into individual speech sounds.  To spell a word such as “mop,” requires a person to break the word into its three sounds and then remember how each of those sounds is spelled.  This a a relatively easy task because there is not much ambiguity about how to spell each of these sounds.  But a word like “rain” offers an additional challenge because there are several common ways to spell its vowel sound.  Is it “rain,” or “rane,” or perhaps “ran” or “rayn”?  To overcome this confusion, the ABeCeDarian spelling book presents all new words within sentences that have silly clues about the correct spelling of any ambiguous part.  Students learn, for instance, that the word “ape” is used to signal the letter “a,” and the the word “I” to signal the letter “i.”  When learning to spell “rain,” they then read, analyze and copy the sentence, “The ape and I sit in the rain.”  When they practice initially, they don’t write the word in isolation but the entire sentence with the clue words to associate the spelling "ai" (the ape and I) with the word "rain." 

I'll try to make some short videos demonstrating some of these techniques.  It's much easier (and more compelling) to demonstrate them than to write about them.  And in a future blog post, I'll show you a technique for memorizing the first 20 digits of pi.

So, here are the key points for today.  When the content you are investigating with your student has structure, make sure that the practice activities of your students help them organize new information within a web of central relationships and connections.  And when the content that your students are trying to master has a more arbitrary relationship, help your students use the techniques of memory experts and impose a structure on the material with silly, and thus vivid, associations.

Two tips to improve practice activities

We are all familiar with the expression, “Practice makes perfect.”  Almost all teachers take this aphorism to heart and rightly include practice activities as part of their lessons.  But just including practice isn’t enough.  How the practice is presented makes a big difference in how quickly students will master new material.  Here are a few tips that can help you make practice activities as effective as possible.

 Distribute practice

It is common for teachers to have students practice a new skill many times just after they have been introduced to it.  For instance, I remember from my school days having to write spelling words five times, one right after the other.  I’m sure you have seen students do 10 or 20 or even 30 addition calculations involving carrying just after they have had a lesson on this procedure. This kind of massed practice can feel very rewarding because at the end of the effort, most students perform the task successfully, often relatively rapidly.  This success, however, is deceptive. 

 Every waking moment our minds are bombarded with an enormous amount of sensory information.  If you walked into the room where I am working now, you would see, for example, that I am wearing a blue sweatshirt, and if I asked you, you could tell me what I was wearing.  That information would reside in your working memory, the memory we use to engage our immediate environment, where we have the thoughts we are thinking about at the moment. But if I asked you weeks, or months, or years from now, “What was I wearing on September 14, 2016?” (and you didn’t have access to this blog!) it would be extremely unlikely that you would remember.  The information would long have vanished from your working memory without being stored in long-term memory.  This same forgetting, in fact, happens to most of the thousands of experiences we have each day.

But of course, even though we forget much, we also are able to remember many things.  What mental operations do we perform on the things that we remember that are different from the things that we don’t remember?  At heart, it is that we try to remember them!  When something first enters the mind, it starts to fade from memory fairly quickly.  But when you try to retrieve this information from your memory, the effort strengthens the ability of your mind to remember it in the future.  This system works rather well, in that the fact of trying to remember something is a good indication that it is important and worth being remembered.

 The deceptive limitation of massed practice is that the new information or skill is practiced only in working memory and isn’t recalled from long-term memory, which is our ultimate goal.  While massed practice may have a valuable role at the very beginning of learning something new, forming an enduring memory requires another very important step:  trying to remember the new information once some time has elapsed.

And the best time to try to remember the new information is the moment when we are about to forget it.  When we are first learning something, that moment is quite close to the time we first processed the information, perhaps seconds, certainly no more than minutes in most cases. But as we successfully remember something, the interval necessary to keep the memory accessible increases quite dramatically, until we are able to retain the information for years.  So the most efficient way to commit something to memory is to try to recall it across many intervals of time, ideally, intervals that increase in length.  Because this ideal practice is spread out over time, psychologists generally refer to it as "distributed practice."

There is quite about of information about the ideal intervals needed to remember material well, much of it referred to as “spaced repetition.”  I encourage you to investigate this technique, and if you are not familiar with computer flash cards programs such as Anki that use spaced repetition, I recommend that you learn more about them.  They are an invaluable learning tool

Interleave practice

I’m sure that you have seen practice sessions in which students had to 10 or 20 or 30 problems of an identical type, such as adding 2-digit numbers with carrying, or writing plurals for words that end in “y.”  As I mentioned above, with any massed practice like this, the students usually perform the task at a high level at the end of the practice session, and so they and their teachers have a sense of accomplishment.

If the ultimate goal werre, for example, to have a person be able to solve problems when they are told in advance, “All the calculations are sums with carrying,” or “All the words you have to spell involve the pattern of pluralizing a word ending in ‘y,’" then the practice routines I just described might very well be satisfactory.  Such a limited goal, however, is almost never what we have in mind.  We want people to be able to do all sorts of arithmetic calculations depending upon the situation, and to be able to apply a variety of spelling patterns correctly whenever they write.  In other words, the ultimate application of the skill involves a great deal of judgment about what is happening in a particular situation.  When very narrow skills are practiced without having to make judgments about the environment,  however, students continue to struggle using their new skills appropriately.

There was a fascinating study on this topic done with baseball team at California Polytechnic State University.  It is typical for a players batting practice to consist of 45 pitches, 15 fastballs in a row, 15 curveballs in a row, and 15 changeups in a row.  At the end of each practice session for a particular pitch, the batter would have “timed up” the pitch and would usually be able to hit the ball impressively.   In the Cal Poly study, though an experimental group still received 45 pitches of batting practice, but the pitches were presented in random order.  In other words, the batter did not know which kind of pitch he was going to receive.   As you can imagine, the immediate performance of the batters in the experimental group suffered because they were not only having to hit a fastball, but having to discriminate whether a particular pitch was a fastball, a curveball, or a change-up.  However, their batting during the game improved significantly!   I think it is easy to see why.  What they really had to do in the game wasn’t just hit a fastball, but to recognize a pitch as a fastball and then hit it.  That is to say, there were two things involved in doing the task well, a judgment and a performance.  When the judgment was omitted from the practice routine, they weren't practicing the complete skill they needed during a game.

So, as you structure practice routines, you will dramatically improve your students' learning if you interleave different types of items in a practice session.  For example, it is much better for students to have practice involving, at the very least, addition and subtraction, and not just one of these operations.  This not only helps to distribute practice of material learned earlier, but it forces them to pay attention to the relevant details of the situation (such as what the operation sign is in the equation!).  If you want examples of excellent interleaving, take a look at the math textbooks by Harold Jacobs.  He wrote most of his books in the 1970’s, before cognitive scientists had done much work on “interleaving,” but he knew nonetheless what a powerful tool it was.

So the lessons for today:  to make your practice as effective as possible, make sure that you spread it out over time and that you interleave various kinds of tasks in each practice session.

I'll have some more to say about improving practice routines in my next blog post.  See you then!

What's in a name?

In the last blog I talked about a lesson in which the teacher rushed to teach students how to manipulate symbols without first making clear to them what the symbols represented.   The students became so confused that the teacher llamented, “Subtraction is killing us.”

This problem is quite common in math education.  One of the reasons it arises is because math calculations can be performed correctly by memorizing a number of correspondences (such as the arithmetic “facts") and a number of procedures (such as how to multiply a multi-digit number by a multi-digit number, or how to do long division) without understanding how the procedures work or what the symbols mean. In addition, those of us who know the meaning of basic math symbols understand these so thoroughly that it is often difficult to remember or acknowledge how meaningless the symbols are to the novice.  As a result, there is a great temptation to focus instruction on manipulating the symbols without taking time to help students grasp what the symbols represent.

Teachers can avoid this problem by beginning math lessons with a relatively familiar and "unmathematized” experience.  In the case of introductory lessons on subtraction to first graders, this experience would involve removing objects from a group.  When the lesson is begun in this way, students immediately have a context for the discussion, analysis, and new information that arise during the class. This context makes it easier to learn new math symbols and to apply them appropriately, and almost always will help them learn new calculation procedures more quickly than if the teacher had begin focusing just on the symbols and the calculation procedure. They are learned faster and retained more easily precisely because, instead of being isolated facts to memorize, they are embedded within an existing web of known relationships.

This problem of focusing too soon on symbols is prevalent in math education, but it exists as well in other parts of the school curriculum. Those of you who are familiar with the very beginning lessons in the ABeCeDarian Reading Program know that, in contrast to the beginning of most phonics programs, the very first task the students do is a spelling task, in the form of a Word Puzzle. The rationale for beginning with a spelling task is that letters, like numbers and math signs, are symbols for a certain kind of thing.  In the case of letters, they are symbols for the speech sounds with which words are formed. To understand the logic of our writing system, therefore, involves understanding, first of all, that words can be broken into smaller units of sound, and, secondly, that these smaller speech sounds can be represented by letters and combinations of letters.  Almost all reading programs, even relatively thorough, explicit phonics programs, begin their instruction backwards, that is with the symbols first.  A common introductory lesson might have the teacher present the letter “m” to her students and then have her say, “This is the letter “m”.  It makes the sound /m/, as in “mouse,” and “motorcylce,” and “monkey.”

But this introduction does not do a good job at all of showing where the “m” comes from and how it functions. In ABeCeDarian, in contrast, the teacher says in her introductory lesson, “Today you will help me spell the word “mop.”  By beginning with a spelling task, we are presenting initially something that is familiar to the student, a familiar word, “mop.”  The teacher then proceeds by saying, “What is the first sound you hear in the word ‘mop?’”  There are a variety of supports the teacher provides to help the child understand what this question refers to and how to answer it.  After the sound /m/ has been identified as the first sound, only then is the letter “m” referred to.  Specifically, the teacher will ask, “Do you know what letter we use to write /m/?”  If the student knows, she identifies it (the letters needed to spell the word “mop” are on the work space in mixed-up order). If she doesn’t know, the teacher shows her.

I’m not saying, of course, that children are unable to learn how to read using what I’m calling the “backwards” approach of a traditional phonics program.  Most children who receive reading instruction do learn to read pretty well.  But this instruction is relatively inefficient and tends to obscure rather than to clarify what the child needs to know to understand how the code works.  In the ABeCeDarian approach, every bit of the logic of the code is embedded within an introductory activity that takes just a couple of minutes to conduct.

A similar sort of “backwardness” prevails in much instruction in which a teacher introduces some new vocabulary.  In thousands or perhaps tens of thousands of classroom each day, a teacher will greet her students with the announcement, “Today we are going to learn about _______.”  But even if the teacher immediately provides a definition, the students do not yet really grasp what ________ means, and so they cannot readily place it within a network of known relationships.  If instead teachers would withhold the name for the new thing until AFTER students had a chance to experience it and to explore it, I am quite sure there would be a dramatic improvement in how well students retained and used their new vocabulary.

I remember as a child playing a variety of made-up games with my brothers, and one of the key activities was coming up with new names for the events, steps, or procedures that we developed or encountered.  Any group of people sharing similar experiences, whether athletes, or shopkeepers, or parents, have similar experiences.  We love giving names to things we observe and interact with and use.  Indeed, we cannot stop ourselves from doing so.  But the names originate because of an experience that needs naming, and they are vivid and useful because we know exactly what experience they refer to.

I think all of these examples suggest the tremendous power of beginning lessons with some kind of experiences that are readily accessible and available to be explored and analyzed.  As students come to understand the “thing” they are exploring, it is a relatively straightforward matter to attach to it some symbolic representation, whether in the form of a math symbol, a letter, or a word.  This sequence returns us to what is the natural order of abstraction, namely, things first, names second.  And this order allows us to give new expressions to our students just when they are ripe for them.

"Subtraction is killing us!"

When my son was ready to enter first grade many years ago, my wife and I visited a number of private schools to help us decide where to send him.  In one of the classes we visited the students were being introduced to subtraction.  The teacher had given each student some small objects they could use to help them count the totals, and she demonstrated how to use these counters to solve basic subtraction equations.  The children then worked independently and came up with their papers one by one to have them checked.  To the horror of the teacher, most of the calculations were incorrect.  At one point she looked at us and sheepishly acknowledged, “Subtraction is killing us."

Why were the students in this class having such difficulty? The problem, I’m quite sure, was NOT with the student’s ability to grasp the concept of subtraction.  The idea of removing objects from a group is something common and recognizable to six-year-olds.  Moreover, all of these children were good at counting.  If I had asked them to count out five gummy bears and to give me two of the gummy bears and then count how many they had left over, they all would have been able to do this task easily.

The difficulty they were experiencing in class that day lay not in the complexity of the concept of subtraction, but rather in how the teacher presented the mathematical symbolization for it. Specifically, she began by presenting an expression such as “5-2” and then demonstrated how to use the counters to find the result.  But by starting with the mathematical expression, she began with something that the students were not familiar with, and so it was extremely difficult for them to make sense of the what she was showing them, even though I'm sure the teacher thought that by using the counters she was making that procedure quite explicit and clear.

The lesson would have worked much better with a very simple change in sequence.  Instead of starting with the unfamiliar mathematical symbols, the lesson should should start with the familiar experience of counting various objects, such as books, or pencils, or the children themselves. After the students had counted an intitial set of objects, the teacher should remove some of the objects and then have the students tally the number of objects that remained.  At each step she should show the class how each action (counting an initial set of objects, removing some of the objects, counting the objects that remained) was represented with mathematical symbols.  Only after the students could easily go from performing these actions with objects to recording the action with the correct subtraction equation would the teacher then work on having the students do the work in the other direction, that is, present them with a subtraction equation and have them represent the equation with a set of counters. This last step, of course, is where the teacher we observed had started, and in doing so, she left her charges thoroughly confused.

It is important to point out that the problem with the lesson wasn’t simply that it was being executed by an inexperienced or a bad teacher per se.   I believe the teacher was faithfully following the routine recommended in the curriculum the school asked her to use.  Rather the problem in this lesson was a tendency all too common in math education to put the cart before the horse by rushing to present mathematical symbolization without adequately showing students what the symbols represent.   I’ll have more to say about this point in the next blog post, where I will discuss how this problem bedevils not only math lessons but other areas of the curriculum as well, and how we can derive an extremely important teaching principle from it.

Epilogue:  We ended up sending our son to public school, and he remained in public schools until he graduated from high school in 2011.   We made the decision for several reasons.  One important reason was that from what we saw, the teaching in the private schools was in general not noticeably superior to that in the public schools.  Our son graduated from college with honors in 2015 and just started his second year in law school.

Two Examples of Bad Teaching (and What We Can Learn from Them)

In my last post I discussed the importance of focusing on good teaching instead of just trying to identify good teachers.  One of the cardinal principles of good teaching is to provide not only positive examples of a new concept, but also negative examples as well.  Learners who are trying to categorize information according to a criterion or set of criteria new to them need to know not only what the new thing is, but what it isn’t as well.

It is with that thought in mind that I will devote the next couple of posts to the topic of bad teaching. I hope that is is clear from my earlier posts (and my general disposition, for those who know me) that my purpose is not to embarrass or make fun of the teachers responsible for the bad teaching.  As I have mentioned, I have done bad teaching myself, and I will include this in the current discussion.  Rather, the goal of this discussion is to use examples of bad teaching to flesh out a description of good teaching and suggest some important ways to evaluate the quality of teaching, whether one’s own or that of another. 

One of the worst examples of teaching that I’ve seen involved a homework assignment for spelling practice required in a 6th grade classroom.  The teacher instructed the students to rewrite each of their spelling words in a code, with a tall rectangle used to represent any “tall” letters like “l” and “d”, a short square to represent “short” letters like “c” and “v”, and a tall rectangle below the base line to represent “basement” letters like “g” and “p.”

Now, even in this very bad assignment there is a kernel of a good element, namely, an attempt to help students analyze the content they are learning.  As I shall argue over and over, helping students analyze what they are studying is a critical component of good teaching. 

The problem with this particular assignment, of course, is that besides being tedious and requiring a significant amount of time to complete, it really has nothing at all to do with spelling. The kind of analysis required of the students to perform this activity involves absolutely no attention to the underlying patterns and relationships of our writing system.  These fundamental patterns and relationships include how individual letters and groups of letters represent individual speech sounds, how certain functional units such as “un” and “ed” and “ion”, known as morphemes, are used over and over in the formation of words, spelling patterns such as when to double a consonant when adding a suffix to a base word, how both the pronunciation and spelling of words can change as various morphemes are added to base, and how knowledge of a word’s origin can often provide insight into why it is spelled the way it is.  In other words, there is plenty of appropriate analysis that students can do to help them learn to spell words correctly. Moreover, this productive analysis helps students recognize fundamental patterns that reveal the architecture (and, dare say it, the beauty)  of our writing system.

A similar sort of problem bedevils a technique used in several classrooms I know of to teach 6th graders how to divide fractions. This practice entails having students memorize the phrase “Keep-Change-Flip” to help them perform a calculation such as 1/2 ÷ 3/4.  What it means is that the students are to rewrite the the equation by modifying it in the following way.  They are to keep the first number (unchanged), change the operation from division to multiplication, and then flip, meaning, write the reciprocal of, the second number, thus yielding the expression: 1/2 x 4/3.  

There are several problems with this approach.  First of all, it shares a problem that is very common in American mathematics instruction, namely,  it focuses student attention initially on a procedure for calculation without adequately developing an understanding of the underlying patterns and numerical relationships that make the procedure work.  Now, this technique is effective if the goal is to get a student to do a set of problems exclusively involving division of fractions as quickly as possible.  Only a few minutes of instruction is required to accomplish this objective.  But that objective is very useful.  Students will rarely ever confront a series of similar division problems all in a row.  It is much more likely that they will have to perform an unpredictable mixture of various arithmetic calculations, in which case, they have to remember which calculation procedure goes with which operation.  And there is nothing in “Keep-Change-Flip” that designates it as the procedure for dividing fractions.

This approach makes the procedure more difficult to memorize for another reason as well.  It is presented as an isolated fact about arithmetic, rather than as something firmly embedded within a set of fundamental patterns and relationships.  To see this limitation clearly, consider an alternative approach, namely, having students learn that “dividing by a number is the same as multiplying by its reciprocal.”  This statement, like “Keep-Change-Flip” provides all of the information students need to perform the procedure for dividing fractions correctly.  But unlike “Keep-Change-Flip,” it clearly identifies this procedure as something involved in the division (and multiplication!) of numbers.  It also includes another key concept, the idea of reciprocal.  And it places the procedure within the context of a fundamental pattern of arithmetic which the student can (and should) explore.  Indeed, it is very easy to give the student a set of investigations in which the concept of reciprocal is examined and then this fundamental relationship between division and multiplication is made apparent.  When taught correctly, in fact, the students use the experiences and analysis they have done in these preliminary investigations to state the procedure themselves.  All the teacher does is to give them the precise wording for a relationship the students already understand, as well as to provide sufficient practice to perform the calculation correctly.   (I will have lots to say in the future about both of these points, namely, providing vocabulary AFTER students have the relevant experience and hence know what the vocabulary refers to, and the characteristics of efficient practice.)

Now some readers may be thinking, “But the presentation of ‘Keep-Change-Flip’ is something like a mnemonic, that is,  a device that helps us memorize things.  Are you saying that mnemonics are bad?”  No, not at all. Mnemonics have a very important place in good teachingand I will talk a lot about such tools when I devote some blog posts to the topic of memory and helping students memorize. 

But the purpose of mnemonics lies primarily in helping people learn things that are related in an arbitrary way, such as the digits of pi, or the order of the planets in the solar system, or the order of the colors in the rainbow.  In contrast, the procedure for dividing fractions (as well as the skills involved in learning how to spell words correctly, in the first example in today’s blog post) do not involve isolated and arbitrary information.  On the contrary, both involve concepts that are connected to other material according to a set of underlying relationships.  And when we want students to learn this type of material, our job is to direct their attention first to these patterns and principles.

In short, good teaching helps students make connections.  The corollary is also true.  If some teaching does not involve helping students make connections, then there is almost always a way to improve it!

Good Teachers and Good Teaching

Much recent discussion about education reform has focused on the topic of good teachers.  A common form of this discussion argues that If only we could fire the bad teachers easily and hire enough new good teachers, then we would be well along the way to helping all of our students succeed in school.  There is indeed a seductive plausibility to this argument.  Who could reasonably be against the goal of providing all students with good teachers?  

This focus on the importance of good teachers, however, is problematic because it tends to obscure an issue of more fundamental importance. 

I find that this problem becomes clear when I think about my own teaching.  I have helped many, many students over the course of 35 years of teaching, and I think many parents and professional colleagues would call me a good teacher.  Nonetheless, I frankly admit that in addition to lots of good teaching, I have also perpetrated some bad teaching.  I think it is safe to say, moreover, that my situation is hardly unique.  Indeed, I suspect it is true that all people reputed to be good teachers have on some occasions done a bad job of teaching.  How can we resolve this seeming paradox?

I think the answer lies in the fact that the most relevant measure here isn’t the person per se but the person’s performance. Another way to put the point to to say that a person is a good teacher when she is doing good teaching.  That statement is completely free from paradox, unambiguously true in all cases.  And what it suggest is that the fundamental thing that is relevant in this matter isn’t the teacher but the teaching.

This certainly rings true when I think about the significant differences between the times I have done good teaching and those when I did bad teaching.  The difference was that when I was doing good teaching, I was in command of two critical tools that allowed me to structure the experiences of my students in efficient, engaging, and productive ways, namely, a good curriculum and good classroom management.  

Good curriculum shapes the activities of students in several important ways.  It ensures that the concepts and information the students are exposed to are comprehensive and organized in a sensible sequence.  It ensures that students perform relevant and interesting activities.  It ensures that the teacher has critical guidance about how best to pace students through the materials and how to correct their errors productively.  And finally, it ensures that the teacher is provided with a rich understanding of how people best learn the content covered and the challenges and potential confusions that new learners often experience.

Good classroom management (or, I guess, student management, in the case of one-on-one tutoring) complements the activities and interactions specified in a good curriculum by making sure that the teacher keeps all of the students engaged in significant activities for as much time during the lesson as possible. 

In suggesting the central importance of good curriculum and classroom management skills, I am hardly denying that there are some personal characteristics shared by good teachers, including robust knowledge of the content they are teaching, enthusiasm for their subject, genuine concern for their students, and dedication to work hard to master their craft.  But it is important to recognize that these personal attributes, while necessary for good teaching, are not sufficient.  I am quite confident that when I have done bad teaching, I still retained these personal characteristics.  What I was missing was the right emphasis, the right sequence, the right kinds of activities.

The point, I think, is that if we want to improve education, the most important thing to focus on is what goes on in the classroom, specifically examining how students are spending their time and what exactly they are doing.  Focusing on “good teachers” directs our attention at the wrong level, making it easy to blame bad teaching on the laziness or inherent limitations of certain individuals without really providing insight into how to correct the problem.  The focus on “good teaching,” in contrast, helps us examine precisely on the level where we will find the difference between success and failure, and gives us a much better grasp of what we have to do to prevent our children from enduring wasteful and unproductive lessons.

For this reason I am not a big fan of Teach for America and other similar programs that seek to improve schools by focusing on recruiting teachers from a certain group of people, namely, successful students at elite colleges and university, to be teachers.  As many of the those who have been teachers in these programs can attest, the kinds of so-called “boot camps” that the recruits attend in order to prepare them to be teachers are much too short to provide them with sufficient classroom management skills and command of a good curriculum.  As a result, the benefits of injecting these teachers into the schools, in spite of their intelligence, energy, and enthusiasm, are modest at best and almost always quite transitory.  An additional problem with this model of education reform is that there are not enough magna cum laude students out their who want to go into teaching to fill all off the teaching positions we need.  

Fortunately, however, there is no need that there should be.  People with a wide range of academic backgrounds and abilities can be effective teachers provided that we help them acquire the experience and classroom management skills to implement a good curriculum well.  This fact is something that homeschooling families typically both understand on a gut level and also demonstrate quite forcefully.  Sure there are some moms and dads with Ph.D.’s in astrophysics who are homeschooling their children well, but there are also plenty of parents without college degrees who do an excellent job as well.  And what is it that these successful homeschooling families all do?  They spend a lot of time finding good curriculum materials and learning how to use them!

So, yes, let’s strive to put good teachers in every classroom.  Yes, these good teachers must be knowledgeable, enthusiastic, and dedicated professionals,  But let’s not forget that in addition to having teachers with these essential personal attributes, we must also strive to make sure we have schools set up to give all of their teachers the tools of classroom management skills and good curriculum.  Only then can we be sure that our children’s school days will be filled with good teaching.

Verification -- a powerful teaching concept

One day, many years ago now, when my wife was picking up my son from kindergarten, he was very excited to read to her a story posted in the front of the room.  His rendering was true to the meaning of the passage, he did decode a couple of words incorrectly.  My wife was not going to say anything, but several of the other kids chimed in to correct him.  Unfortunately, having been taught a curious mixture of whole language and phonics in kindergarten, at that time he did not possess the tools to verify whether he was correct or whether the other students were, and he had to take them at their word (or not).

I have had similar experiences with several of my math tutoring students when I first met them.  I would ask them how to do some calculation, and they would light up and say that they had done that in school and they would proceed to go on their merry way manipulating the numbers, confident that they were accurately replicating a procedure that they had practiced at some point earlier.  The problem was that what they were doing made no sense at all.  The manipulations were not based on genuine number sense, but were arbitrary and misremembered procedures.  And like my kindergarten son, they did not possess the tools to verify whether their answer was correct, and indeed, they didn’t even have a sense that after they offered an answer it was their responsibility to review it to make sure that it was sensible.

These examples, I think, demonstrate a critical component of lessons that is generally not discussed very thoroughly and explicitly, a concept I refer to as “verification.”  By verification I mean the ability of a person to prove that what he has done is correct without reference to authority.

Now, of course, there is a fair amount to learn that involves arbitrary and solely conventional associations and therefore cannot be verified without recourse to some expert.  The shape we use for the letter “m” for instance, is just a matter of convention, as is the fact that we use it to represent the /m/ sound.  The association between this letter and its sound can be confirmed only by someone who already has learned this association of letter and sound.  (I will have quite a bit to say about how to learn such conventional material in future blogs.)  But the pronunciation of a particular written word is another matter.  For example, the word “mop,” is spelled the way it is because it has three individual speech sounds or phonemes, /m/, /o/, and /p/, articulated in that order, and the letters “m”, “o”, and “p” represent those sounds.  If a person understands this spelling architecture, then she can confirm the association between the written and spoken word.  The same type of confirmation is available in the domain of mathematics.  For example, the fact that 8 x 7 is equal to 56 is something that can be proven in any number of ways, such as counting the value of eight 7’s.

Understanding when verification is possible allows the teacher to correct errors in a very sophisticated and powerful way.  If a child reads the word “mop” as /map/, for instance, it is not especially helpful to say simply, “No, the word is /mop/.”  It is much better to point out that the middle sound she said doesn’t match the middle letter of the word and have her try again now armed with this additional information.   (Detailed directions for this kind of error correction, and many others, can be found in the ABeCeDarian Error Correction Guide.) This approach treats the error as a “bug” in her reading procedure that needs to be corrected.  The teacher doesn’t give the student the correct answer, but rather points out explicitly what the problem was and has the student try again.

This approach yields several benefits.  First of all, it makes the material easier to learn.  Instead of having to use brute force memorization to remember hundreds or thousands of things, the student learns how to use a relatively small set of known material in a relatively straightforward procedure to produce a correct response, a procedure that can be applied to get a correct response in any similar situation.  

What’s more, the material is not only easier to learn in the first place, but it is much more likely to be retained.  As long as some learned response is isolated and disconnected from other knowledge,  it is easily forgotten.  But when something is embedded within a rich network of associations and relationships, it is anchored in a way that helps keep it from drifting into oblivion.

Another benefit of this approach is that it encourages self-monitoring.  The student does not always need to rely on a teacher to know if she has provided a correct response.  She can determine this for herself because she is capable of figuring the thing out for herself. And it keeps the responsibility for doing the task firmly with the student.  The teacher serves as a coach, providing guidance and support, and when a student makes an error, it is not an occasion for her to give up and have the teacher do it for her, but to evaluate what the problem was and try again.   It is difficult to overstate how dramatically this improves a student’s attitude, her ability to apply herself, and her active engagement in her lessons.

Let me leave you then with two important questions to ponder as you think about your own teaching:   Are you aware of the parts of your lesson that allow for verification, that allow students to determine on their own whether they are right without relying on your authority?  And, when your students are learning content that can be verified, are you correcting errors not simply by providing the correct answer, but by helping identifywhere the “bug” in a faulty procedure was and having them try again.

Storybooks Launched for Reading Program

Dr. Michael Bend of ABeCeDarian Company in Ithaca, NY and Author/Illustrator Dr. Andrea Hazard of Danby, NY, announced the launch today of an illustrated series of 10 companion storybooks for the ABeCeDarian Company Reading Program.

read more.

Michael Bend, spends quite a bit of time summarizing the required knowledge for students to be able to decode words and to do it well: knowledge, skills, strategies and practice.

He goes into a lot of detail explaining why this knowledge is important and how it will be taught using ABeCeDarian.  I really appreciated this level of detail, as I am working with a very intelligent, yet struggling, 2nd grade reader who has been working on his reading skills by choice, since he was 3 years old and his big brother sat down for his first kindergarten lessons and he followed suit, though this had not been my plan.  No tubs of educational toys for this child, he wanted to do his lessons like his 3 older siblings.  He has a high level of concentration and comprehension, but has struggled to learn how to read.

read more.

FROM:  oldfashionedgirls

The ABeCeDarian reading program is a comprehensive phonics-based program that also teaches spelling and handwriting.

It teaches phonics through practice and familiarity rather than by requiring students to memorize rules. Rather than learning numerous rules, children learn to “flex” by experimenting with the various possible sounds that might be represented by the letters. All of the steps for learning to read are taught explicitly, which can be especially helpful for children who struggle with learning to read.

read more.

Level A | Interactive and E-reader versions now available

Interactive Level A and           e-reader versions of the Storybooks are now available!

A digital, interactive Level A student workbook is now available.  Put all of the tools you need to conduct Level A lessons on your smartphone, tablet, laptop, or desktop.  The interactive workbook contains exactly the same lessons in the same sequence as in regular Student Workbooks A1 and A2, so you can use the interactive book along with the paper workbooks or in place of them. 

THE STORYBOOKS FOR LEVEL A ARE ALSO NOW AVAILABLE IN E-READER VERSIONS ON AMAZON.COM AND THE APPLE IBOOKS STORE.

LEARN MORE ABOUT OUR LEVEL A STUDENT WORKBOOK

All the materials for Level A are now available in digital formats

in the form of an Interactive Student Workbook that can run from any device with a web browser and e-reader versions of the Storybooks for Level A.

The Interactive Level A workbook presents all of the lessons and activities contained in ABeCeDarian Student Workbooks A1 and A2, including Word Puzzles, Spelling Chains, Reading Chains, as well as handwriting and spelling practice.  The digital version can work in concert with Student Workbooks A1 and A2 or can replace them entirely. 

E-Reader Versions of the Storybooks for Level A

The ten companion Storybooks for Level A are available in e-reader forms for use in iBooks, Kindle, and other e-readers.  You can get a look at these books by clicking on a title in the box below.  The e-reader versions of the Storybooks are sold individually.

Try a free sample of the app.

Purchase the app.

Download a simple set of directions for the app.