This week's Memo draws mainly on strong issues of American Educator and the Harvard Education Letter.

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Quotes of the Week

“They sandbag by moonlight. The school superintendent and the judge, the police sergeant and the mechanic, the Amish man in a straw hat and the young man in a Budweiser T-shirt, they lay down sandbags as if making peace offerings to a vexed god called the Mississippi.”
Dan Barry leading off his front-page New York Times article, “A Hand-to-Hand
Struggle with a Raging River” (June 19, 2008)

“Confusion and frustration in the lower grades sets students up for failure in later years.”
Matt Frisch, a New York City teacher, in a letter to American Educator agreeing with
an earlier critique of poorly written state standards (Summer 2008, p. 2-3)

“[T]his is why we do scientific research. Common sense does not always turn out to be the truth. If we only relied on common sense, we would still think the sun revolves around a flat earth.”
Claude Goldenberg on bilingual education (see item #1)

“If a child, or even a whole class, does not understand something, you should not assume that the task you posed was not developmentally appropriate. Maybe the students are missing the necessary background knowledge. Or maybe a different presentation of the same material would make it easier to understand.”
Daniel Willingham (see item #2)

“If you wait until you are certain that the children will understand every nuance of a lesson, you will likely wait too long to present it.”
Daniel Willingham (ibid.)
 

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1. Key Research Findings on Teaching English Language Learners

In this comprehensive article in American Educator, Stanford education professor Claude Goldenberg sums up the findings of two major reports on ELL education completed in 2006: the National Literacy Panel (NLP) and the Center for Research on Education, Diversity, and Excellence (CREDE). Goldenberg shares a few quick facts for starters:
- American ELL students come from more than 400 different language backgrounds.
- 76 percent of elementary ELLs and 56 percent of secondary-school ELLS were born in the U.S., but 80 percent of their parents were born abroad.
- Since 1990, the number of ELLs who are not able to participate fully in mainstream classes has gone up from one in twenty to one in nine; by 2018, it will be one in four.
- By far the biggest language group – 80 percent – are Spanish speakers. The next largest group are those who speak various Asian languages – 8 percent. There is great diversity in both populations.
- About 12 percent of ELLs are in all-English instruction with no special supports.
- About 50 percent receive all-English instruction with some help from ESL teachers, special content-area instruction, aides, or other resources related to their language status.
- About 40 percent of ELLs are in programs that make some use of the home language, either bilingual education (some academic content in the native language), two-way bilingual programs, or scaffolding of English instruction with native language explanations.
- All three of these models vary widely in the number of years these extra supports remain in place and in the quality of instruction.
- While there are exceptions, it generally takes 3-5 years for ELLs to achieve conversational fluency in English, and 6-7 years for them to become proficient in academic English.
- The student achievement bottom line: At the fourth-grade level, ELLs are scoring 36 points below non-ELLs in reading and 25 points below in math. By eighth grade, the gap has widened to 42 points in reading and 37 in math. These gaps are significantly larger than the gaps between students who are eligible and not eligible for free and reduced-price meals.
- Since most state tests are in English, ELLs’ language barriers clearly play a part in these achievement gaps. It’s difficult for researchers to tell which is more important, language barriers or lack of content knowledge and skills.

Goldenberg then highlights three findings from the NLP and CREDE reports, and their implications for classroom instruction:
• First, teaching students to read in their first language promotes higher levels of reading achievement in English. Goldenberg says the latest research is solid and consistent on this point. When English language learners are taught to read in their native language first, or taught English and their native language simultaneously (at different times of day) in two-way bilingual programs, they end up more proficient in English. While the effect is not enormous – between .35 or .40 in various studies – it is significant. “Primary language reading instruction is clearly no panacea,” he says, “but relatively speaking, it makes a meaningful contribution to reading achievement in English.”
Goldenberg admits that this finding is counterintuitive to most people. “Doesn’t it just make sense that the earlier and more intensively children are placed in all-English instruction at school the better their English achievement will eventually be?” asked a colleague. When the goal is proficiency in English, delivering instruction in the native language seems to be heading in the wrong direction. “But this is why we do scientific research,” says Goldenberg. “Common sense does not always turn out to be the truth. If we only relied on common sense, we would still think the sun revolves around a flat earth.”
Why would native-language instruction produce higher achievement in English? Several explanations are possible, says Goldenberg, but it’s most likely because of transfer: understanding of knowledge and skills travels across languages, so that if a student learns something in one language, it can carry over to the second, even if the two languages use different alphabetic systems (although transfer of Spanish to English is easier than Chinese to English).
• Second, classroom practices that work for native English speakers work for English language learners. “Good instruction for students in general tends to be good instruction for ELLs in particular,” says Goldenberg, and lists some of the key success factors:
- Clear goals and learning objectives;
- Meaningful, challenging, and motivating contexts;
- A curriculum rich with content;
- Well-designed, clearly structured, and appropriately paced instruction;
- Explicit teaching of the components of literacy (phonemic awareness, phonics, vocabulary, comprehension, and writing);
- Encouraging students to higher levels of thinking, speaking, and reading at their instructional levels;
- Active engagement and participation;
- Opportunities to practice, apply, and transfer new learning;
- Feedback on correct and incorrect responses;
- Periodic review and practice;
- Frequent assessments to gauge progress, with reteaching as needed to attain mastery before moving on;
- Opportunities to interact with other students in motivating and appropriately structured contexts, including cooperative learning groups.
“There are, of course, individual and group differences,” says Goldenberg. “Some students might benefit from more or less structure, practice, review, autonomy, challenge, or any other dimension of teaching and learning. This is as likely to be true for English learners as it is for English speakers.”
• Third, when working with ELLs, teachers must modify instruction to take into account the double challenge these students face – learning academic content and skills while learning English. Goldenberg says that most teachers are better at accommodating the learning differences of native English speakers than they are with ELLs. Things are easier in the lower grades, where the main challenge is decoding, but get more difficult in the upper grades as content knowledge and higher-order thinking kick in. Goldenberg suggests the following instructional modifications:
- Make reading English more comprehensible by using materials with content that is familiar to students – for example, stories with themes and content from students’ cultures.
- Build vocabulary in English – which includes clear explanations in context, using visuals, acting out words (charades), analyzing word meanings, and making connections.
- Use the primary language for support – This might include introducing ideas and words in the native language and then translating them to English, and also comparing and contrasting words and ideas in the native language to English.
- Assess knowledge and language separately – “Because language limitations are likely to obscure what children actually know and can do,” says Goldenberg, “it is essential that ELLs be assessed in a way that uncouples language proficiency from content knowledge.” For example, a teacher asked kindergarten students to name a word that rhymed with lake to test their knowledge of rhyming. Students were unable to answer because their vocabularies weren’t robust enough, even though they may have understood the concept. A better assessment would have been to give students pairs of words and ask them which rhymed.
- Promote productive interaction among ELLs and English speakers – Unfortunately, a lot of contact between native English speakers and ELLs is awkward and unproductive; it takes skill and planning for teachers to maximize the potential of peer instruction.
- Add time – “Given that ELLs have more to learn – the regular curriculum that everyone must learn, plus English – it makes sense to consider ways to provide them with extra time for learning,” says Goldenberg. This includes extending the school day, after-school programs, summer school, and extra years to earn a diploma.
In addition to these, Goldenberg suggests a number of generic classroom supports that work for all struggling students and might be especially helpful for ELLs who are in English-only settings. He says the research shows that solid instructional practices are more helpful to ELLs’ learning than culturally accommodated practices. Among the basics:
- Predictable and consistent classroom management routines, aided by diagrams, lists, and easy-to-read schedules to which the teacher refers frequently;
- Graphic organizers that make content and the relationships among concepts and different lesson elements visually explicit;
- Additional time and opportunities for practice, either during the school day, after school, or for homework;
- Redundant key information, e.g., visual cues, pictures, and physical gestures about lesson content and classroom procedures;
- Identifying, highlighting, and clarifying difficult words and passages within texts to facilitate comprehension, and generally emphasizing vocabulary development;
- Helping students consolidate text knowledge by having the teacher, other students, and ELLs themselves summarize and paraphrase;
- Giving students extra practice in reading words, sentences, and stories in order to build automaticity and fluency;
- Providing opportunities for extended interactions with teacher and peers;
- Adjusting instruction (teacher vocabulary, rate of speech, sentence complexity, and expectations for student language production) according to students’ oral English proficiency;
- Targeting both content and English language objectives in every lesson.

Goldenberg concludes with a list of questions highlighting areas in which the research has yet to come up with definitive conclusions:
- For which ELLs is native-language instruction most helpful – those with stronger or weaker language skills?
- What level of skill in the native language should ELL teachers have?
- In English-immersion classes, what is the most effective way to use the native language?
- For how many years should students receive instruction in their native language?
- What are the best ways to accelerate oral English development?
- What is the optimal balance between direct instruction in syntax, grammar, vocabulary, pronunciation, and norms of social usage and application of the second language in meaningful and motivating situations?
- Is English language development best taught in separate or heterogeneous classes?

“Teaching English Language Learners: What the Research Does – and Does Not – Say” by Claude Goldenberg in American Educator, Summer 2008 (Vol. 32, #2, p. 8-23, 42-44)
http://www.aft.org/pubs-reports/american_educator/issues/summer08/goldenberg.pdf
 

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2. A Thoughtful Refutation of Piaget’s Developmental Stages

In this column in American Educator, cognitive psychologist Daniel Willingham argues that Piaget’s four stages of development (sensorimotor, pre-operational, concrete operational, and formal operations) are not a helpful guide for teachers as they plan and execute instruction. Research over the last 20 years, says Willingham, has refuted the two assumptions behind Piaget’s stages – that children’s cognitive development occurs in discrete stages, and that the effects of a child’s current stage are pervasive, affecting all tasks consistently.
The problem with Piaget’s research, says Willingham, stems from the questions he asked children and the tasks he had them perform – for example, his three-mountain scenario to demonstrate egocentrism or his pouring-water-from-a-wide-glass-into-a-thin-glass experiment to demonstrate conservation. When asked different questions by modern researchers, children showed much more variability depending on the way questions were asked and the nature of the tasks – and they didn’t fall into Piaget’s neat categories. “Development looks more continuous than stage-like,” says Willingham, “and the way children perform cognitive tasks is quite variable. A child will not only perform different tasks in different ways; he may do the same task in two different ways on successive days!... The problem is that cognitive development does not seem amenable to a simple descriptive set of principles that teachers can use to guide their instruction. Far from proceeding in discrete stages with pervasive effects, cognitive development appears to be quite variable – depending on the child, the task, even the day…”
What are the implications of these findings for teachers’ everyday decisions? Willingham draws the following conclusions:
• Be aware of key principles, but don’t over-apply them. Some general developmental insights are correct – for example, centration, preschoolers’ tendency to focus on a single dimension of a situation when more than one dimension is important. But teachers should guard against the tendency to over-use a principle and realize that with instruction and appropriate tasks, children can be taken beyond their default tendencies.
• Use what works. Some instructional strategies work for children and some don’t – without regard to developmental stages. Willingham urges teachers to keep track of effective approaches and constantly exchange notes with their colleagues. “If the teachers in your grade don’t already meet regularly,” he suggests, “consider setting up such a meeting for the express purpose of exchanging information about projects, activities, books, and other specific tasks that have (or have not) worked well in the past.”
• Think about why students don’t understand. “An important message from the research cited here,” writes Willingham, “is that any one task that the child attempts at any one time is not a perfect window into the child’s abilities. Children’s cognition is variable… If a child, or even a whole class, does not understand something, you should not assume that the task you posed was not developmentally appropriate. Maybe the students are missing the necessary background knowledge. Or maybe a different presentation of the same material would make it easier to understand.”
• Recognize that no content is inherently developmentally inappropriate. Willingham comes close to endorsing Jerome Bruner’s contention that any subject can be presented in some intellectually honest form to any child at any stage of development. There are limits to this, of course, but Willingham’s point is that we should not be blinkered by arbitrary stages. Preschool children can understand (if not completely) that Martin Luther King, Jr. was a person who is no longer here. “Their mistaken belief that they might encounter him at a local store, or that he lives at a school that bears his name, will be corrected in time,” says Willingham. “Indeed, how do children learn that some people are fictional and some are not? Not by a magical process of brain maturation. Children learn this principle as they learn any other – in fits and starts, sometimes showing that they understand and other times not. If you wait until you are certain that the children will understand every nuance of a lesson, you will likely wait too long to present it. If they understand every nuance, you’re probably presenting content that they’re already learned elsewhere.”

“Ask the Cognitive Scientist: What Is Developmentally Appropriate Practice?” by Daniel Willingham in American Educator, Summer 2008 (Vol. 32, #2, p. 34-39)
http://www.aft.org/pubs-reports/american_educator/issues/summer08/willingham.pdf
 

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3. Insights About Elementary Math Teaching

In this Harvard Education Letter interview by Mitch Bogen, Harvard professor Katherine Merseth talks about the critical importance of elementary students mastering fractions – and explains why this area of mathematics is so instructionally challenging. Some excerpts:
• For a third grader who has learned to add and subtract whole numbers, it’s entirely logical that 1/2 plus 1/3 should equal 2/5. Similarly, it makes perfect sense that 1/4 should be bigger than 1/3, since four is greater than three. “It’s absolutely rational. Kids rarely do things randomly,” says Merseth.
• The problem, she continues, is that many teachers, feeling under the gun from high-stakes tests and pacing guides, put a big red X by these incorrect answers and don’t take the time to understand their students’ thinking. “Why can’t we slow down and listen to the kids?” asks Merseth. “Because they are making sense. It just doesn’t happen always to be the sense that we’d like them to make.”
• “If you ask me, ‘What is the one thing you’d do to help teachers teach math more effectively?’ I would train them to listen and to be able to ask questions that would pursue the thinking of the child. Until we work to understand what a child is thinking, it may remain undetected by the teacher in the child’s head. And there is cognitive research to show this as well, that we hold on to our misperceptions and don’t readily give them up.”
• When a teacher asks a student what seven times seven is, and the student answers 14, the most common response is to say, “No!” A more highly skilled approach, says Merseth, is to say, “Oh? Really? Well, then, what is seven plus seven?” or “What if I asked seven plus seven instead?” (Many students quickly correct themselves after being asked these questions.) Instead of telling students they are wrong, says Merseth, teachers should bite their tongues and try to understand the faulty reasoning and correct it.
• There isn’t enough dialogue in math classes, says Merseth – student-to-student, student-to-teacher, and student-to-class. “Asking students to draw, to count, to verbalize in math class is critical, because math language is very important and needs to be very precise,” she says. “We need to help children become comfortable in talking about math. It’s so important to take the time to stop and say: ‘What does the problem mean? Can you tell me in your words what it means?’”
• Merseth believes manipulatives can help students understand math concepts at a deeper level, but acknowledges that many teachers think they can’t afford the extra time that hands-on materials take. “Well, my response is that if you don’t take time now, you’ll have to take time later,” says Merseth. “Pay now or pay later. Which would you prefer? And which do you think will be less painful for the student?”
• Fractions are “an area of mathematics that can be a real minefield for both students and teachers,” says Merseth. For example, the fraction 3/4 can be expressed in a number of different ways:
- Drawing a circle, dividing it into quarters, and shading in three parts of the whole;
- Drawing four disks and shading in three of them;
- Drawing a number line from zero to one and shading in up to the three-quarters mark;
- Talking about the relationship between the numerator and denominator;
- A division problem
To students, these look very different, and the teacher’s challenge is to explain that even though they appear to be different, they all represent the same fraction. “Imagine being the student who just learned to take three parts out of four,” says Merseth. “‘Now you’re telling me it’s a division problem? Come on!’”
• Students can get through mathematics without mastering fractions, says Merseth, but things will get increasingly difficult, especially when they hit algebra. “There are no shortcuts, and students need to learn all the core concepts,” she says. For older students who missed the boat in elementary school, it’s important to help them catch up with age-appropriate examples, not problems about three tricycles.
• Parents and communities must be encouraged to infuse numbers into their children’s lives from a young age, says Merseth, including the statistical aspects of baseball, soccer, and other sports they love, as well as the application of math to jobs and careers. “There are almost unlimited examples of ways to help young people become comfortable and friendly with math,” she says. “Most of them involve taking math out of the books and into the everyday world of children.” Merseth describes a public park in Melbourne, Australia that features a mathematical walking tour. One station has a sign saying, “Look at the leaves in this tree. Do you notice that they are in the relationship of 3 to 5 to 8, depending on where they branch out?” Another sign says, “Look at the spirals in this sunflower. Do you see how they unfold in a mathematical relationship?”
• Math proficiency is a vital 21st-century skill, says Merseth. “The whole world must be literate in mathematics because it grounds the rationality of so much of what we do: decisions about voting, decisions about spending millions or billions of tax dollars, concepts about risk. And it comes down to personal quality of life. Can I afford to take out that subprime loan?” All students can master this level of mathematics, says Merseth. “It’s very teachable. Mathematics is accessible to everyone.”

“When 1/2 + 1/3 = 2/5: Investigating Student Thinking to Teach Fractions Well”, an interview with Katherine Merseth by Mitch Bogen in Harvard Education Letter, July/August 2008 (Vol. 24. #4, p. 4-5); this article can be purchased at
http://www.edletter.org/current/index.shtml#fractions
 

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4. The Importance of Well-Chosen Wrong Answers

In this Harvard Education Letter article, testing expert Rebecca Kopriva makes an impassioned plea for carefully thought-out wrong answers in multiple-choice tests. The wrong answers on most commercial tests, she says, are usually random distractors – for example, reversing the digits in a number answer or listing greatest common divisor instead of greatest common denominator to confuse students. “Thoughtfully conceived wrong answer choices,” she says, “can generate valuable clues about misconceptions students may have or reveal that they are using inappropriate strategies to solve a problem. Furthermore, answer patterns that require students to navigate these kinds of errors and misunderstandings can provide a stronger basis for making inferences about students’ abilities even when they have identified the correct responses.” In other words, well-written tests can help teachers get insights into their students wrong answers – insights that can improve teaching and learning.
Here’s a sample middle-school math problem that requires students to find the greatest common divisor (the best method is to multiply together the prime numbers common to both numbers): Joseph is trying to distribute daffodils and tulips among vases so that each vase has the same number of daffodils and each vase has the same number of tulips. If there are 126 daffodils and 210 tulips and all were used, what is the greatest number of vases that Joseph can assemble? Here is an unsophisticated set of answer choices:
- 24 (this distractor reverses the digits of the correct answer)
- 6 (it can be divided into both 126 and 210, but it’s not the greatest common divisor)
- 42 (the correct answer)
- 44 (close to the correct answer)
A more thoughtful and revealing set of choices, accompanied by the requirement that students show their work, would help teachers find out: (a) Do students understand what the question is asking? (b) Do they have misconceptions about how to solve this kind of problem? and (c) Do they use “backsolving”, trying out each of the answer choices to see if it works, but using sloppy calculating?
- 7 (this is the largest prime number that can be divided into both 126 and 210, but that’s not the same as the greatest common divisor);
- 14 (a possible error using backsolving with errors);
- 42 (the correct answer – looking at students’ work can tell if the student understood the concept or made a lucky guess);
- 84 (this is the answer when 126 is subtracted from 210; students often subtract when they have no idea what to do).
“With the help of these kinds of wrong answers,” says Kopriva, “teachers can focus instruction on identifying and addressing weak conceptual and/or procedural mistakes. Conversely, if students’ answers demonstrate a mature approach to items such as this, teachers can feel confident of their mastery and understanding.”

“What’s Wrong with Wrong Answers?” by Rebecca Kopriva in Harvard Education Letter, July/August 2008 (Vol. 24. #4, p. 8, 6-7); this article can be purchased at
http://www.edletter.org/current/index.shtml#fractions.
 

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5. Does Keeping Back First and Second Graders Work?

In this New York Times article, reporter Winnie Hu describes the controversy around the East Ramapo (NY) school district’s decision to retain 12 percent of its first and second graders in five pilot schools and place them in a separate “Gift of Time” classes for a year. The transition classes are limited to 15 students, focus mostly on reading and math, and have a reading specialist, extra tutoring, field trips, teacher training, and additional materials, at an additional cost of $2,000 per student.
But some experts worry that holding back and segregating low-performing students is a double whammy that will damage self-esteem and increase the likelihood of their dropping out later on. University of Colorado/Boulder professor Lorrie Shepard is quoted saying that transition classes for failing kindergarten students were tried in the 1980s, didn’t work academically, and produced more negative attitudes toward school. One East Ramapo parent fought to keep her son out of the program, saying, “We believe that for you to have to repeat first grade, it means that you are not capable, you are a dunce child. It was bad enough to repeat, and then to repeat in a Gift of Time class. I thought it was a polite way of saying he’s a special-needs child.” Betty Fitzgerald, a Delaware principal whose school experimented with separating repeating third graders, explained why she turned against the idea: “It’s like saying, ‘You all are low kids, and you all didn’t pass.’”
Supporters of the program push back, arguing that the smaller class size and homogeneous grouping lets students learn at their own pace. Iraida Hada, the principal of one of the participating East Ramapo schools, asked, “How are we going to make it work the second time around, if it didn’t work the first time? … I believe this program has afforded them another opportunity.” Several parents said they were pleased with their children’s academic and social progress and gains in self-confidence. And district administrators say the program is working: by the end of the last school year, close to 80 percent of the first and second graders in Gift of Time classes were reading at grade level (although they were a year behind the peers they left behind), and about 30 percent of the first graders and 11 percent of the second graders were performing above grade level. Because fewer rising second graders are failing, the district feels it needs to hold back only first graders next year, at a savings of $100,000.

“Holding Back Young Students: Is Program a Gift or a Stigma?” by Winnie Hu, New York Times (June 25, 2008, p. C13)
http://www.nytimes.com/2008/06/25/education/25gift.html?_r=1&scp=2&sq=Winnie+Hu&st=nyt&oref=slogin
 

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6. Is Reading Recovery an Effective Intervention for ELLs?

In this article in TESOL Quarterly, four researchers report on their study of the effectiveness of Reading Recovery on the text reading skills and phonemic awareness of first-grade English language learners compared with that of native English-speaking peers. The study found that Reading Recovery is “effective in accelerating the progress of ELLs to reach average levels of performance.” Working with the lowest readers in each classroom, Reading Recovery teachers got 76 percent of native speakers and 69 percent of ELLs to grade-level reading performance.
Analyzing their data, the researchers found that the same factors that make Reading Recovery effective for low-achieving native-speakers operate with second language learners:
- Strong relationships between teachers and students, which support risk-taking and learning;
- Precise one-on-one differentiated instruction based on students’ strengths;
- Incorporating each child’s fund of knowledge into lessons to enhance motivation;
- Expert teaching and scaffolding to accelerate learning;
- The teachers’ sound theoretical understanding of literacy learning;
- Each lesson chockerblock full of reading, writing, and conversation.
In addition, Reading Recovery classes give ELLs intensive practice using English in a protected, supportive, and mastery-oriented climate.
The researchers conclude that Reading Recovery should be available to all ELL first graders who are struggling to learn to read. “The evidence suggests,” they write, “that regardless of their proficiency in English, it is likely that many ELLs will benefit greatly from the expert instruction provided by RR teachers. We find no reason for school administrators to withhold RR services from ELLs, an often-marginalized group.”

“Learner Outcomes for English Language Learner Low Readers in an Early Intervention” by Patricia Kelly, Francisco-Xavier Gomez-Bellengé, Jing Chen, and Melissa Schulz in TESOL Quarterly, June 2008 (Vol. 42, #2, p. 235-260), no e-link available
 

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7. Short Items: a. Arts website; b. A website for ELLs’ teachers and parents;

a. Arts website – In this sidebar in American Educator, the editors bemoan the fact that state standards for the arts are generally unimpressive. However, they highly recommend the Core Knowledge Foundation’s “clear, specific, knowledge-building art and music standards,” at: www.aft.org/pubs-reports/american_educator/issue/spring08/arts.

“Standards for the Arts Also Need Clear, Specific Content” in American Educator, Summer 2008 (Vol. 32, #2, p. 3)

b. A website for ELLs’ teachers and parents – This site delivers research-based information for the teachers and parents of English language learners, including reading, assessment, and research summaries. The primary emphasis is on Spanish, but other languages are being added: http://www.ColorinColorado.org.

“Colorin Colorado: A Research-Based Web Site for ELLs’ Teachers and Parents” in American Educator, Summer 2008 (Vol. 32, #2, p. 16-17)
 

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