Study: Blended math boosts learning

Students learned significantly more when they used Carnegie Learning’s hybrid algebra program — a blend of online and classroom instruction — reports a two-year Education Department study, which used a randomized control group.

There were no significant results in the first year, reports Ed Week‘s Inside School Research.In the second year, students who used Cognitive Tutor Algebra I improved by 8 percentile points.  That’s double the amount of math learning most high school students achieve in a year, said Steve Ritter, a founder and the chief scientist of Carnegie Learning, in Pittsburgh.

The improvements were similar across students of different ethnic and socioeconomic background, and high, regular, and low initial math ability, Ritter said. The researchers found similar improvements among participating middle school students—higher-performing math students typically take algebra in 8th grade rather than in high school—though the middle school sample was not large enough to show significant effects in the same way as the high school students.

Usually students worked with the individualized tutorial program for two days a week and spent three days learning in the classroom.

Beyond blended learning

After trying blended learning for a year, two San Jose charter high schools redesigned the math program, writes Diane Tavenner, CEO of Summit Public Schools, on Getting Smart.

In our pilot this year, we have five math instructors and two learning coaches who work as a team to support 200 students at one time. . . . Our math team serves as coaches and mentors, curriculum curators, developers and intervention specialists.

. . .  students are not in ninth or 10th grade and are not taking a defined math course such as Algebra or Geometry. Instead, they are progressing through a competency-based curriculum dependent on their own path and pace.

Each student has a personalized Math Guide that details what they already know (highlighted in green), what they should be focused on today (highlighted in yellow), and what they are not quite ready yet to tackle (highlighted in red). Students use their guides to set daily and weekly goals.

Our students begin math each day at their individual workstation.  They first log into their email to read a daily message from the math team, including a schedule of learning opportunities offered that day, along with available projects and seminars. Depending on their learning goal, our students can choose whether to remain at their workstation for individual, or with their peers, learning and practice using a host of online resources available to them as ‘Playlists,’ or participate in a seminar and other small-group projects taking place in the four learning spaces off of the main room. For those students who struggle with this autonomy, our math team provides mentorship and coaching to ensure students are on the right path.

Summit is collecting data to see how well the new system works.

Data myths

Defusing myths about classroom data will help teachers reach all students, argues the Dell Foundation.

Common education data myths stifle progress

Special education for all?

The New York City Department of Education is currently implementing special education reform. One of its principles is that “all schools should have the curricular, instructional, and scheduling flexibility needed to meet the diverse needs of students with disabilities with accountability outcomes.” At the same time, “students with disabilities must have access to the Common Core Learning Standards (CCLS).” 

How do you meet the students’ diverse needs and make the standards accessible for them? Welcome to Universal Design for Learning (UDL), a “framework” that enables teachers to design curricula for diverse learners in advance, instead of on the fly. On the one hand, it’s difficult to object to something like this. Shouldn’t teachers consider students’ needs when planning curricula? Shouldn’t the curricula reflect the students, at least in part? On the other, it could distract from subject matter. It could send students the message that they need pictures, sounds, activities, strategy instruction, and so forth whenever they don’t understand something.

According to the UDL guidelines, the current curricula are not simply flawed; they are disabled (in terms of who they can teach, what they can teach, and how they can teach. (Why do people find it necessary to disparage the old when presenting the (supposedly) new? Aren’t some curricula better than others?) UDL addresses these “disabilities” by making the curricula more accessible to learners: that is, by providing multiple means of representation, expression, and engagement.

For instance, according to the guidelines, ”an equals sign (=) might help some learners understand that the two sides of the equation need to be balanced, but might cause confusion to a student who does not understand what it means.” Therefore a teacher should provide “alternative representations” (instead of, say, telling the student what the equals sign means).

Or consider this: “While a learner with dyslexia may excel at story-telling in conversation, he may falter when telling that same story in writing.  It is important to provide alternative modalities for expression, both to the level the playing field among learners and to allow the learner to appropriately (or easily) express knowledge, ideas and concepts in the learning environment.” But shouldn’t any student, including a student with dyslexia, learn how to write? Granted, the student should have the opportunity to speak as well. That is nothing new or fancy. It is possible that a student might have difficulty with both speaking and writing. What to do but practice?

Multiple representations and modes of expression are far from the whole of UDL. Teachers are supposed to ”scaffold” the development of the “executive functions” of students’ brains: “The UDL framework typically involves efforts to expand executive capacity in two ways: 1) by scaffolding lower level skills so that they require less executive processing; and 2) by scaffolding higher level executive skills and strategies so that they are more effective and developed.” For instance, when it comes to “higher level executive skills,” teachers should guide students in the formation of their own personal learning goals and help them develop strategies for learning. All of this is fine in moderation, but (a) it can take up a great deal of class time and (b) it can send students the wrong message about their own responsibility and role.

In my experience, students who study at home (that is, who don’t just zip through the homework, but think about it until they understand it) are rarely in need of strategy instruction, multiple representations, and so forth. The strategies come to them as they wrestle with the material. A few tips can help, but they need not be elaborate. In class, these students benefit from challenging instruction. This includes a variety of representations (such as when the geometry teacher says, “Or think of it this way”).  It includes some clarifications, review of basics, hints about how to learn this material, questions pointing to the next step, and exposition of new material. Students then seize this material and work on it. 

By no means am I arguing that a teacher should leave students in the lurches, ignoring them when they stare blankly at the wall or doodle in their textbooks. Of course she should think about what students need and how to draw them in. But take this too far, and you won’t have a lesson that compares the formulas for the hyperbola and ellipse. You won’t have a discussion of Donne’s “A Valediction: Forbidding Mourning.” You’d end up teaching material that required less intensive study–because you’d have to bring in all your multiple this and that.

If UDL is meant as a collection of suggestions and principles, then much of it makes sense (though I still take issue with the equals sign example). But the word “universal” makes me wary, as does the blanket dismissal of current curricula. Teachers have incorporated UDL-like practices for centuries. It is important to question and refine what we are doing; it is damaging to bring in some sweeping change, some revolutionary lawnmower that tears up the field.

Addressing disabilities in the classroom is a tricky matter; it requires knowledge, skill, and good judgment. But we do students a disservice, overall, when bending too far to accommodate them. One learns by wrestling with things. If students understood this, if at home they pondered and practiced what they were learning in class, we’d see a profound difference in our schools. Teachers, then, would have more room to wrestle with the material at higher levels and plan challenging, well-crafted lessons.

Teach to students’ commonalities

Instead of always trying to individualize instruction or teach to different “learning styles,” teachers should spend more time teaching to what students have in common, advise Daniel Willingham and David Daniel in Educational Leadership. For example, all children need factual knowledge, practice and feedback from a knowledgeable source to learn.

The pitfalls of personalization

Mass personalization is a big concept with a subtle sting. It involves gathering data on individuals and groups in order to tailor products and services to them. It surrounds them with stuff that supposedly reflects their likes and needs; it can be quite hard to get through this customized swarm.

For instance, Google Instant predicts your search strings as you type, stores your responses to its suggestions, and uses the data to improve its predictions. Facebook gathers information on what you and your friends “like” and then displays advertisements based on your “likes.” Amazon recommends books on the basis of your purchase patterns and the patterns of those who have purchased similar books. The general idea is to figure out what you’re likely to buy and then get you to buy it–that is, to make the probable actual.

In education, mass personalization is supposed to deliver individualized instruction for all. The hope is that all students will make progress if the instruction is matched to them. In its National Education Technology Plan, the U.S. Department of Education describes the ASSISTment system, used by more than 4,000 public schools in Worcester, Massachusetts. This system collects data on students’ performance and problem-solving behavior (such as their help-seeking patterns), and offers students personalized hints and tutoring.

Along similar lines, Wireless Generation sells software that, according to GothamSchools, allows teachers to record their observations of students with a mobile device. The software then sorts and analyzes the data. The New York City Department of Education plans to renew its contract with Wireless Generation; this will allow the company to sell its mobile devices and software to New York City schools.

Several existing Wireless Generation products may be involved. The mClass® assessment and analysis tools consist of mobile device and data-analyzing software. The mobile device gives the teacher a question to ask the student (in reading or mathematics). The device then records the student’s answer and enters it into a database. Having gathered data, the software generates reports and individualized learning plans. It makes suggestions for groupings of students, homework activities, and more.

There is something unsettling about this contract, beyond the possible conflict of interest (former NYC schools chancellor Joel Klein is now executive vice president at News Corporation, which purchased Wireless Generation shortly after he accepted the position). [Read more...]

Beyond tracking

To eliminate bad tracking — dumping some kids in dead-end classes — reformers have eliminated honors classes and dumped “all agemates in the same class” regardless of their preparedness, writes Mike Petrilli on Education Gadfly. He hopes to get beyond tracking by customizing instruction.

It doesn’t take a rocket scientist—or even a cognitive scientist—to know that kids (and adults) learn best when presented with material that is challenging—neither too easy so as to be boring nor too hard as to be overwhelming. Like Goldilocks, we want it just right. Grouping kids so that instruction can be more closely targeted to their current ability levels helps make teaching and learning more efficient.

Online-learning technologies and more targeted assessments should enable schools to “pinpoint exactly what students know and serve up instruction that meets them there,” Petrilli writes.

At School of One, a middle school math program in New York City, students are placed in specific learning modules based on their performance the previous day, and on a sophisticated algorithm. Some kids are sent to small-group instruction with similarly-abled peers; others head to one-on-one online tutoring; others work independently on a computer; others get more traditional classroom instruction. It’s all customized to match the students’ needs and abilities. (Read more about School of One and other models of individualized instruction in this excellent Education Next article.)

Teachers are struggling to “differentiate instruction” to meet the needs of students with a wide range of abilities and disabilities, performance levels and English fluency. Half the teachers in high-need schools say they’re not able to do it well, according to the MetLife survey. I think this is a major cause of teacher burn-out.

School of One

Once a school troublemaker, Ta-Nehisi Coates became a successful journalist.  He wonders if a personalized education would have worked for him. In The Littlest Schoolhouse in The Atlantic, he looks at the School of One, a personalized after-school math program for seventh graders at a three New York City middle schools.

Joel Rose, a Teach for America veteran, uses computers to teach each child at his “optimal level.” He worked with Wireless Generation to create an algorithm weighing a student’s academic needs, learning preferences and classroom resources.

. . . first, the student and his parents and teachers are surveyed about his classroom habits. Then the student takes a diagnostic test to see how well he understands basic math. Those data are then sent to the New York Department of Education’s headquarters in Lower Manhattan, where School of One’s algorithm produces a tentative lesson plan. That lesson plan is then e-mailed to the student’s teachers, who revise it as they see fit. At the end of every day, the student takes another short diagnostic, which is used to create another tentative lesson plan that appears in the teachers’ inboxes by eight o’clock that evening.

The result is that one student might learn to add fractions at a dry-erase board with a small group, while another student uses the Internet to practice calculating the area of a circle with a tutor in Kentucky, while still another student learns about factoring through a game on his laptop.

Piloted in 2009 as a summer program at a Chinatown middle school, School of One raised scores by 28 percent. Coates visited tech-savvy I.S. 339, a Latino-and-black school in the South Bronx that’s trying the program.

Principal Jason Levy, who started as a Teach for America teacher, had tried to personalize education by “grouping his teachers into teams assigned to the same students, enabling them to compare notes and design specific strategies for kids who were faltering.”  Test scores rose dramatically with 62 percent of students now on track in math, up from 9 percent six years ago.  Levy welcomed School of One.

. . .  30 or so kids in small groups were hashing out the nuances of seventh-grade math. Some worked by themselves on laptops, with headsets linking them to a virtual tutor. Others were at a dry-erase board with a teacher or high-school tutor. At the front of the room, a large electronic monitor, like an airport arrivals board, identified every student in the room and the station where he or she should be working.

Next year, School of One will replace the math curricula in the three pilot schools. Most of the funding will come from private foundations.