Can math scaffolding hinder learning?

When I was fourteen, we spent a year in Moscow. I attended a Soviet school that “specialized” in French–that is, it taught French from the early grades. The other subjects (math, literature, history, technical drawing, geography, physics, chemistry, and biology) were in Russian. No one expected me to participate in class, but I insisted on being added to the class list and asked teachers to treat me like a regular student. I was eventually doing the work in all of my subjects except for chemistry and biology, where I lacked the necessary background knowledge and was usually a bit lost. (I barely got by in physics, but I did learn something.)

My favorite classes were math and French. Here is a picture of the math textbook. It took us through algebra, beginning calculus, and some trigonometry. Its 220 pages contained more substance than many a hefty textbook I’ve seen since. When I returned to the U.S., I was ready for calculus but had to take a year of precalculus first, along with my classmates. (It didn’t hurt, as I got to do more trigonometry.)

Recently I have been wondering how this textbook manages to convey so much in such short space, and how I learned so much without finding it particularly difficult. To answer this question well, I would have to work my way through the textbook again, this time with pedagogy in mind. That’s a project for another time. In the meantime, I’ll toss out a few hypotheses.

Well, one obvious reason we were able to learn so much is that there was a standard curriculum through the grades. All students came to this course with similar knowledge and practice. Some were better at math than others, but it wasn’t because they had better preparation. (Of course this isn’t entirely true, as some students had additional resources at home and elsewhere.)

It could also be that the curriculum included fewer topics than math courses in the U.S. do; thus there was more time to learn them thoroughly.

But what strikes me about this little textbook is that it plunges right in. The first chapter talks about inductive proofs. The second goes into combinatorics. There are no pictures except for graphs of functions (and a few circles and rectangles). There are word problems, but they are relatively few. There are no needless “scaffolds.”

Scaffolds in instruction are temporary supports intended to bring students to the point of self-sufficiency. All good instruction uses them to some degree.  But certain kinds of “scaffolds” can actually  become barriers, complicating the student’s entry into the subject matter. In mathematics, excessive reliance on “visuals,” “manipulatives,” and “real-life” applications can stand in the way of the math itself.

This textbook, by contrast, “scaffolds” the instruction in one way only: it builds from simpler problems to more complex ones. It  lacks the “scaffolding” that plagues many a math textbook that I have seen: those colored graphics, tips and strategies, needless word problems, and so on. It has a few word problems, but there are reasons for them to be word problems. The vast majority of the problems use mathematical notation. Thus, students become fluent in it and learn to think in it.

I was recently looking at AMSCO’s Geometry–better than many in terms of presentation. Very little clutter. But even AMSCO has word problems like this: “Amy said that if the radius of a circular cylinder were doubled and the height decreased by one-half, the volume of the cylinder would remain unchanged. Do you agree with Amy? Explain why or why not.” There is no reason to bring Amy into this; Amy’s presence does nothing for the problem. Also, turning this into a matter of opinion (“do you agree or disagree”) confuses the matter. Instead, the student should be asked whether the statement is correct or incorrect.

In bending over backwards to make math “accessible,” we may actually make it inaccessible. What do you think?

E-book nation

E-book Nation
Brought to you by: OnlineUniversities.com

E-textbooks for K-12 schools aren’t ready for prime time, reports Ed Week’s Digital Education.

It’s not just the teachers, stupid

Good instructional materials are as important for student learning as good teachers, yet there’s a “scandalous lack of information” about what schools are using and what’s most effective, concludes a new report from Brookings’ Brown Center,  Choosing Blindly: Instructional Materials, Teacher Effectiveness and the Common Core.

Students learn principally through interactions with people (teachers and peers) and instructional materials (textbooks, workbooks, instructional software, web-based content, homework, projects, quizzes, and tests). But education policymakers focus primarily on factors removed from those interactions, such as academic standards, teacher evaluation systems, and school accountability policies. It’s as if the medical profession worried about the administration of hospitals and patient insurance but paid no attention to the treatments that doctors give their patients.

Choosing better instructional materials “should be relatively easy, inexpensive, and quick,” compared to improving teacher quality, write Russ Whitehurst and Matthew Chingos. They urge states, the federal government, nonprofit groups and philanthropists to fund research on effectiveness. That would start by collecting data on what instructional materials schools are using.

 

Smart phones, smarter students

As smart phones become common, smart instructors are helping students use their phones as study aids while they’re on the go.

Standardizing textbooks won’t save money and will undercut instructors’ autonomy, complain community college instructors in Texas.

 

E-textbooks: What’s the rush?

Don’t rush to adopt e-textbooks, advises Daniel Willingham. It’s not clear they’re better, at least as currently produced, and students prefer traditional textbooks. “Some data indicate that reading electronic textbooks, although it leads to comparable comprehension, takes longer.”

Further, many publishers are not showing a lot of foresight in how they integrate video and other features in the electronic textbooks. . . . multimedia learning is more complex than one would think. Videos, illustrative simulations, hyperlinked definitions–all these can aid comprehension OR hurt comprehension, depending on sometimes subtle differences in how they are placed in the text, the specifics of the visuals, the individual abilities of readers, and so on.

What works for e-books — putting the same words in a new format — may not work for e-texts, Willingham writes. “Textbooks have different content, different structure, and they are read for different purposes.”

 

Report: Textbooks boost Islam

Islam is presented positively — and inaccurately — in U.S. textbooks, charges a report by ACT! for America Education. It’s more “indoctrination than education,” says Brigitte Gabriel, the group’s president.

The report provides happy-think quotes from textbooks:

“The Quran granted women spiritual and social equality with men.”

ACT! responds:  The Quran does not grant “social equality” to women. “Muslim women cannot divorce except in limited circumstance—men can divorce at any time for any reason—and the testimony of one man equals that of two women in legal proceedings.”

“In Medina, Muhammad…fashioned an agreement that joined his own people with the Arabs and Jews…These groups accepted Muhammad as a political leader.”

Response:  The Jews did not accept Muhammad as a leader. He “expelled two of the Jewish tribes and destroyed the third, beheading the men and selling the women and children into slavery.”

“Shari’a law requires Muslim leaders to extend religious tolerance to Christians and Jews.”

Response: “Shari’a law imposes a litany of burdens and restrictions on Christians and Jews, both in their daily lives and in the practice of their religions.”

“In the early eighth century, Islam became popular in the northwestern part of the Indian subcontinent.”

Response: Islam spread through conquest.

In addition, textbooks spend many pages on European slave traders, ignoring the role of Islamic slave traders, the report charges.

Textbook writers hate controversy. I’m sure they accentuate the positive when writing about any religion — but not to this extent.

An iPad for every student?

Don’t expect to see the all-iPad classroom any time soon — at least not in cash-strapped California, reports the San Jose Mercury News.

Apple has partnered with three big K-12 textbook publishers to provide digital textbooks that require the iPad.

 What puts educators off is not just the $499 sticker price — $475 if purchased in batches of 10 — for the basic iPad (add $35 for a case) It’s also the requirement that schools buy the textbook software as vouchers for individual students, who will download the electronic textbooks onto their own iTunes accounts.

Every year, the school district will have to buy more $14.99 textbooks that it will never own.

“Everybody’s going to go to open-source textbooks” — which are free predicts Ann Dunkin, technology director for the Palo Alto Unified School District. “We’ve already bought textbooks. We’ll use them until they fall apart.”

Of course, the iBook can do things a standard textbook can’t do, such as show things in three dimensions and link to videos — or to social media sites.  Most teachers at Palo Alto’s Gunn High don’t let students use their iPads, issued as a pilot project, reports the Mercury News. Too many students were checking out their Facebook page in class.

Despite the cachet of Apple, “districts shouldn’t get crazed by technology. They should figure out what they want, then work backward,” said Michael Horn of the Innosight Institute, a Mountain View think tank promoting “disruptive innovation” in education. “The iPad is getting a huge amount of attention, a lot of districts are spending money on it, but they haven’t thought out why.”

Archbishop Mitty High School, a Catholic school in San Jose, is renting iPads for all students and teachers next year after a two-year experiment.

Tim Wesmiller created an online textbook “as a dynamic mashup of content from the Library of Commerce, YouTube and Google maps” for his religious studies class.

Valerie Wuerz, 17, peers into her iPad, where an app called 7 Billion breaks down the global impact of overpopulation in text, slides, video and forums where students can share ideas and develop projects. She calls the iPad “a great resource, because textbooks are expensive and heavy to lug around.”

Down the hall, science teacher Kate Slevin’s class focuses on the subject of momentum.

“OK, guys,” she says. “Open your iPads.” They use a note-taking, audio-recording app called Notability that lets users write notes with their fingers over text on the screen. They can import a syllabus or a book chapter, create bullet outlines, and record the lecture in case they miss something.

Mitty is adding the cost of iPad rental to tuition bills, figuring that parents will save money in the long run by having to buy fewer expensive textbooks.

New standards, tests may kill teacher ratings

New common standards, which will require new tests, may put the kibosh on value-added ratings of teachers, speculates WashPost columnist Jay Mathews.

California will switch to Common Core Standards in 2014, get new tests in 2015, but no new textbooks aligned with the new standards and tests until 2017, teacher Jerry Heverly learned at a conference organized by his union. The state can’t afford new books.

(Heverly) has no strong feelings about the current tests, but the big change in 2015 is akin to watching a rising tide approach sand castles carefully constructed on the beach.

Integrated Math I, II and III will replace the traditional algebra, geometry, advanced algebra sequence, Heverly was told.  (This is a blast from the past: California adopted integrated math — algebra, geometry and statistics are taught at each level — in 1992. After protests, districts won the right to choose a traditional or integrated approach. New math standards were adopted  five years later, which required a new exam. Integrated math went out of fashion.)

The new standards will require changes in other subjects, as well. And developers say the new tests will be quite different, stressing students’ ability to explain their thinking, not just right answers.  Mathews writes:

These new tests in nearly every state will delay, if not stop altogether, the national move toward rating teachers by student score improvements. School districts can’t do that when the tests change so radically. They might have to wait years to work out the kinks in the tests before using them to assess teachers.

Once the new tests are accepted as valid, it will take years of data on students’ progress to create valid value-added measures of teacher effectiveness.

Be afraid of your child’s math textbook

Be afraid — be very afraid — of your child’s math book warns Annie Keeghan, who worked in educational publishing for 20 years, in Open Salon.

There may be a reason you can’t figure out some of those math problems in your son or daughter’s math text and it might have nothing at all to do with you. That math homework you’re trying to help your child muddle through might include problems with no possible solution. It could be that key information or steps are missing, that the problem involves a concept your child hasn’t yet been introduced to, or that the math problem is structurally unsound for a host of other reasons.

After a series of mergers and buyouts, few educational publishers are left, she writes. Many are skimping on quality control to rush new books (especially math books) to market to beat the competition.

Tuning up higher ed

What does a bachelor’s degree in civil engineering mean? What about an associate degree in nursing? Colleges and universities in seven states are “tuning” courses and degree programs, setting clear standards for what graduates in a specific discipline should know and be able to do.

E-textbooks aren’t much cheaper than traditional books. Apple’s iBook app will require students to use an iPad. To really slash rising textbook costs, college students need access to o-books — free or very cheap open-source learning materials — advocates argue.