Sunday, June 19, 2011

Art and technology

My school is losing half of its art position next year. As a "technology school", one may wonder why this might be big deal, but I beg to differ. A technology school without a strong arts program is a perversion of education. It reveals an absolute lack of understanding of cognitive development; and a lack of vision of human beings, education, even the spirit. The decision-makers bow before the dumbest, unhuman aspects of the machine. It is the devil's work.

At my school, CPS pays for 1/2 of an art position, and the principal has made up the other half of the position out of discretionary budget money. School budgets have been cut, and my principal is saying that the discretionary money isn't there any more for the school's half of the art position. So next year we will have a part-time art position. By a rough calculation of 2.5 days a week times 6 class periods, she could serve 15 periods a week; we have 20 classes. The math is ugly.

This, of course, is especially disruptive for the art teacher. I mean it really sucks. It also tears at the social cloth of the school, more so because the art teacher is woven deeply into that fabric. We are all diminished. How much this was weighed in the decision of where to cut and what to cut, I don't know. Very little I suspect. I don't mean to minimize the personal or social aspects of the cut. There is, though, I think, a less obvious part of this -- the revealed lack of understanding, the lack of vision of how art provides the foundation, the skills, the experiences for work with technology.

Say, for example, that we take the National Educational Technology Standards for Students (NETS-S) as a starting point. The first two standards say nothing about technology operations -- they deal with creativity and innovation, collaboration and communication. The best education theory pushes students to be directors of their learning, and up Bloom's hierarchy of thinking. We want students to express themselves in many media, with posters and sound and video and photographs. Students cannot do this well without a solid art background. Art is where they learn the phonetics and grammar of media literacy. Art is where they learn how colors combine and clash, about foreground and background, about dimensions and perspective, about highlighting and shading, about seeing critically, about enlivening the imagination and creating. Implementing NETS-S without art instruction is impossible.

There are other starting points than NETS-S. Hand work is critical for brain development. Learning how to draw, how to color, how to use one's hands to create things and so on -- the kinds of things students do in art class -- is not "just art" but fundamental to developing thinkers. Art also exposes students to the joy of creating. It exposes the possibilities of discovering and expressing feelings. It exposes students to different possibilities for being in the world. And based on the success of art-intensive programs in working with at-risk youth, I can argue that art also helps with students' social and emotional development. Basically, we develop better human beings when we teach them art. When we don't teach them art, we handicap them. Devil's work.

The more we inject computers into instruction, the more we need to balance it with traditional art instruction -- working with hands, working with different materials, looking at and really seeing the real world. Computers suck the user into virtual space, imagined by someone else, shallow and incomplete. Students are taken out of the world, which can only be okay if their virtual experiences are tempered by real reality. The more students go into virtual worlds, the more armor of critical thinking and visual literacy they need to protect themselves. The most interesting and exciting computer use I think involves constructionist tools where the students create and express. But again, the basic units of understanding what to do effectively with these tools are cultivated, in large part, in art class.

The slide into the confusion of computerized spaces with real spaces, and computerized instruction with human instruction is the slide into idolatry. In the confusion, the role of the human being, the teacher, is lost. The teacher is reduced to a machine, albeit a resistant machine. And one machine can always be replaced with another. My school will have more computer-based instruction next year (e.g., Achieve3000 is mandated by our area for next year, but not paid for, approx. $6000), and fewer people to work with students.

Given the CPS budget issues, was there a choice? There are always choices. Recognizing choices though requires transparency, understanding, vision. (And, I might add, creativity and innovation, and communication and collaboration).

jd

Sunday, June 12, 2011

An analysis of Scantron testing

Below is a link to a paper (PDF file) I did on Scantron testing at my school. It was done for a course requirement:


It's written in an academic mode, as opposed to a critical or agit-prop mode, with lots of tables and basic statistics. Of some interest: mode effects overall appear small; a large number of students spoil tests; there is a large discrepancy between Scantron national percentile rankings and ISAT NPRs; there is a relatively high general correlation between school-level Scantron results and ISAT results, which breaks down when you look at individual classrooms. The final "recommendation" in the paper is that the tests should not be used for either teacher evaluation or student promotion.

jd

Sunday, May 29, 2011

Drunk driving

We had a staff meeting at my school on Friday. Classroom teachers received forms for sorting their students into Tier 1, 2 and 3 groups for implementing Response to Intervention, or RTI. K-2 grades will use DIBELS data to sort students, and grades 3 - 8 will use Scantron data. Since I work on organizing the Scantron testing at my school, and end up sifting through the data, I was especially interested in the choice of Scantron data to slot students into RTI tiers.

The form passed out came from our Area office, and uses Scantron National Percentile Rankings (NPR) for sorting. Students in the 24th percentile and up fall into Tier 1 (the lowest priority for special interventions). Students between the 11th and 24th percentiles fall into Tier 2, and students under the 11th percentile fall into Tier 3. (I may be off by a percentile or two -- I'm doing this from memory.)

I have written about the problems of standardized testing and "data-based decision making" before, likening it to the drunk looking for his car keys under a streetlight, not because that is where he dropped them, but because that is where the light is. The light in this case is the pale beam of standardized test data -- it doesn't tell us nearly enough about the student, and for many of the neediest students, it is hopelessly distorting. We won't find the keys to student success with the data, but it's easy for administrators to collect, and to pretend that it means much more than it does. Drunk on data, and wandering off course from the outset.

For example: After we completed the math testing this Spring, about 8 percent of students at my school dropped more that 100 points from their Fall scores. The numbers were worse for reading -- almost 11 percent of students had dropped more that 100 points. These are big numbers, well outside of the statistical error range. Excepting epidemic of brain injury, such a drop can only be attributed to subjective student factors: boredom, disinterest, a desire to be done with test, difficulty with the computer medium, etc.

The belief that these initial numbers were faulty was confirmed when we made students retake the test. Most of the re-takers did much better, erasing most of the drop, and in many cases swinging into solid gains for the year.

The point, again, is that testing students is not the same as taking their temperature, and so much depends on the subjective factor. But the RTI strategy doesn't appreciate the subjective factor -- it's all about the data, as goofy as it may be. One student at my school went from dropping over 200 points, landing in the 7th percentile, to increasing over 50 points for the year (not a great gain, but keeping him at grade level) after he retook the test -- moving from Tier 3 (deserving special interventions), to Tier 1 (no special interventions). [Value-added alert!] It should be said that the possibility of testing into a higher percentile is not very likely, so the general danger is that students will be assigned to tiers they should not be in, consuming time and resources that perhaps should go to needier students.

One of the ironies in all of this is that all of teachers I have talked to already have a sense of their students abilities, and could quickly categorize their students without the Scantron numbers in front of them. After all, they assess their students every day. And the teachers can tell which numbers are off. And all would probably say that the time and the resources to provide interventions to all the students that really them is just not nearly enough; and the process to get the help needed is too long and places too much burden on the already over-stretched teacher.

jd

Saturday, May 28, 2011

Clarification

I want to clarify my previous post. As a reminder of one of the many pitfalls awaiting the tech-heavy lesson.

I am teaching a course at Dominican U., Integrating Technology Into the Curriculum. On the first night of class, I have the "candidates" (how DU refers to folks in the teacher education program, to distinguish from "students", whom the future teachers will be teaching) get set up with the basic Web 2.0 tools. They create a blog if they don't have one already, set up a wikispaces account to work on a course wiki we create, and they set up a Diigo account to begin a professional library of web resources and also to experience social bookmarking.

For blogging, I suggest Google's blogger, mainly because it is what I am familiar with. I haven't created a new blogger account in a while, but "it worked fine when I tried it".

In class, however, things went differently. After the candidates created their blogs, Google prompted them to enter a phone number as a final confirmation step. I assume this is to prevent mass creation of bogus blogs for whatever spammish purpose. The confirmation process was a surprise to me, beyond the inscrutable, illegible "type these letters" images Google usually uses. The privacy warning flags went up immediately in most everyone's mind I think, compounded by having watched, a few minutes earlier, the Onion's Google Opt-Out Village hilarity, which only compounded the distrust). "Okay, I'll sacrifice myself for the class. You can use my cell number if you don't want to provide your number." Except we were in the "Lower Level" of Parmer Hall (trans. "basement"), with no cell signal. So big embarrassment. As soon as I did get a cell signal, I received a dozen or so texts from Google for the new blogs, but the texts did not identify which blogs they went to, so they were useless.


Google Opt Out Feature Lets Users Protect Privacy By Moving To Remote Village

I understand why Google has the additional confirmation steps. But the cell phone number request seems too much, especially if you are trying to create the accounts someplace where there is no cellphone coverage. Perhaps an email address confirmation is too easy to automate and circumvent Google's defenses. I don't know what a better mechanism might be, but it certainly interfered with what I hoped to do.

And hence the previous post, done during class to illustrate how to make a blog posting, and how to comment on a blog posting.

Now, I think a fundamental rule of using tech in the classroom is to go through all of the steps first, before class -- a dress rehearsal. Which of course I didn't do. On the other hand, perhaps it was the multiple attempts to create new blogs from the same IP address or pool of IP addresses perhaps triggered some additional confirmation process. A classic quality assurance engineering problem -- not testing under the actual conditions of use -- and how do you easily simulate, ahead of time, a class of students doing the same thing at the same time? Yes I know there are special apps to simulate multiple users doing something at the same time, but I don't see using such for the case described above. Experience is perhaps the better guide -- I have seen similar problems when creating GMail accounts in a class, so I should have known there might be issues.

Memo to self: In the future, ask adult students to create their accounts before class. For younger students, stick with sites where I can create their accounts.

jd

Monday, May 9, 2011

Starting a new class

Having problems with Google's new account verification scheme.

Sunday, May 8, 2011

Common Core and math

The new Common Core State Standards (CCSS) are coming, ready or not. Illinois and 43 other states have adopted them. As if everything else going on in education wasn't enough, CCSS will be a Big Deal for teachers in all grades when they go into effect in the 2014-15 school year (which right now sounds like it is sometime in the 23rd century).

For a good write-up about CCSS in relation to math education, see the latest column by the J. Michael Shaughnessy, president of the National Council of Teachers of Mathematics, titled "CCSSM and Curriculum and Assessment: NOT Business as Usual". From his write-up, expect new curricula, lots of PD and powerpoints, and much general wailing and gnashing of teeth as the oil tanker of math education is turned.

Two things stand out for me re: the math standards (especially the way Shaughnessy explains it).

One is the emphasis on both math content and math practice. According to CCSS, there are eight math practices that students should master:
  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.
With the exception "model with mathematics" (#4), the math practices outlined in the new core standards are more generally life-persistent skills in thinking and solving problems. If teachers are allowed to organically infuse the classroom with these practices, education may well look very different.

The other thing about Shaughnessy's write-up that stands out for me is how standardized testing will change to reflect the new standards. He includes links to some initial draft assessments, including the Math Assessment Project (MAP) and the Inside Mathematics initiative. The sample assessments are much more about solving problems -- "performance tasks" -- than simple skill assessment (as is the case of most of the current standardized tests).

This emphasis on performance tasks is supposed to be reflected in the two initiatives to revamp standardized testing. (Illinois is supporting the Partnership for the Assessment of Readiness for College and Career (PARCC) initiative; the other one is SMARTER Balanced Assessment Consortium (SBAC); both are supported by the Department of Education.) Both initiatives will be administered online. PARCC calls their tests, to be administered four times a year, "next-gen assessments".



I am not sure how "performance tasks" (think of ISAT's extended response as a possible example) will be done online, if at all. Both consortia are talking about computer-adaptive tests for portions of the tests, which makes me wonder how they will be different from, say, the Scantron Performance Series tests we are taking right now. From PARCC's powerpoint, it appears that the assessment process will drive the instructional frameworks that will end up driving the implementation of CCSS. This doesn't have to be a bad thing (that is, tail wagging dog), it all depends on whether really good assessments can be developed from CCSS that actually can assess a student's math practice.

The general drift in math standards, to me, reflects similar changes made to the National Educational Technology Standards (NETS), revised in 2007. NETS focuses not on technical skills, but on how the tools are used. Only one of the six NETS for Students standards refers to technique ("Technology Operations and Concepts"), the other five emphasize creativity, communication and collaboration, information fluency, critical thinking, and citizenship. That is, both CCSS math practices and NETS emphasize a meta-approach to learning -- how to think, how to create.

The mere existence of NETS does not mean of course that they are implemented in a deep way. Nor will the mere existence of thoughtful standards for math practice mean that they will improve math education. So much depends on if teachers will be allowed to implement them.

jd

Sunday, March 20, 2011

Tedious tech

I accidentally clicked on an old Parallels Edubuntu virtual machine instead of Windows, and thought, okay, might as well update it -- it was several hundred days (over 800? is that possible? not launched since I played around with setting up an Edubuntu server at the school in late 2008? Which never went anywhere.)

Several hours later, after downloading and installing all of the packages, cleaning up, rebooting -- oops, the X server wouldn't load, so no GUI. It was probably to be expected -- I have held off on upgrading the Parallels Desktop client -- I felt Nova was just randomly changing the product to keep a cash stream flowing. But this update might actually be necessary to get the latest Edubuntu to work.

So the new Parallels finally finished downloading, but before I upgrade it, I'm thinking I should back up the Windows disk images, just in case. So I do that backup, and twenty minutes later, I'm ready to install Parallels 6, but the installer informs me that an update is available, and I should download that.

And at the same time, I have been trying to get my tweets -- which I don't do very often -- to automatically show up on my Facebook page. The Twitter app for Facebook (which has a useless and ambiguous interface) is supposed to do that, but for some reason it stopped working. Sorting out problems with Twitter and Facebook seems like a hopeless cause. I found another Facebook app called Selective Tweet which only posts tweets that end with #fb. That seems to work, and the help page is, well, helpful.

While trying to write this, the Google search widget on this blog has stopped showing search results. Not a Firefox 4.0 issue, as it happens with Safari too. Finding help on Google products is a tedious process, sifting through Google Search results, with no date filter (the blogger search widget seems to have a history of problems).

I tried to make this post as boring as the process that it documents. But it is also a test to see if the change I made to Twitterfeed, to post these blog updates to both Twitter and Facebook, works. Because every word is precious.

jd

For want of a nail, etc.

Some interesting articles in the NYT today on the economics of the earthquake/tsunami in Japan:

Stress test for the global supply chain, by Steve Lohr (3/19/2011)
  • "Chain" is misleading, because it really is a network, or a system ("Modern global supply chains, experts say, mirror complex biological systems like the human body in many ways"). Where there is redundancy and resilience, the disruptions are manageable.
  • "The good news for the world’s manufacturing economy is that the sectors where Japan plays a vital role are fairly mature, global industries." Mature networks have developed redundancy and resilience, and moved away from single source.
  • "Still, Japan produces a far higher share of certain important chips like the lightweight flash memory used in smartphones and tablet computers." Even if Japan makes "only" 35% of the flash memory chips, that is still a big chunk of source.
  • "The field of buying and shipping supplies has been transformed in the last decade or two. Globalization and technology have been the driving forces. Manufacturing is outsourced around the world, with each component made in locations chosen for expertise and low costs. So today’s computer or smartphone is, figuratively, a United Nations assembly of parts." Attempting to separate "globalization" (as it is meant today) and "technology" as two distinct things is silly -- globalization is a function of new technologies; capitalism in the age of electronics.
  • "That means supply lines are longer and far more complex than in the past." Which makes them more tenuous and vulnerable. The term for comlex procurement networks and long supply lines is "thin strands."
  • "The ability to manage these complex networks, experts say, has become possible because of technology — Internet communications, RFID tags and sensors attached to valued parts, and sophisticated software for tracking and orchestrating the flow of goods worldwide." Exactly -- this is why one can say globalization is a function of technology.
  • "'In the past, when you had a disruption, the response was regional,' says Timothy Carroll, vice president for global operations at I.B.M. 'Now, it’s globalized.'” So global supply networks should make it easier for producers to accommodate the Japan disaster.
  • Here is the really interesting insight for me: as the supply networks expand and complicate, "the difficulty and expense of seeing deeper into the supply chain increases." (emph. added) The problem becomes determining the impact on the parts used to make the parts, and the parts used to make the parts that make the parts, etc. etc., and even the raw materials to make the parts etc. etc. "For example, reports that a Mitsubishi Gas Chemical factory in Fukushima was damaged by the tsunami have fanned fears of a coming shortage of a resin — bismaleimide triazine, BT — used in the packaging for small computer chips in cellphones and other products."
  • "The Japan quake, some experts say, will prompt companies to re-evaluate risk in their supply chains." Rich, deep, redundant, resilient networks as risk minimizers (for more see a thing I did called "Networks and Globalization"). In this case, it might prompt "a shift from focusing on reducing inventories and costs, the just-in-time model, pioneered in Japan, to one that places greater emphasis on buffering risk — a just-in-case mentality."
  • Redundancy is one strategy -- multiple sources; resiliency is another -- the ability to quickly develop alternatives in case of emergency.
A Crisis That Markets Can't Grasp by Jeff Sommer (3/19/2011)
  • How do you price risks that are relatively remote, where there isn't much experience, if any? 9/11, Hurricane Katrina, the BP oil spill, and now the Japan earthquake/tsunami? "So perhaps a bigger question is whether the markets — in which we have come to place so much trust — can put a true price on outsize risks like this."
  • “Past performance is no guarantee of future success."
  • Nassim Taleb, who popularized the term "black swan" (referring to rare or difficult to predict high impact events) "argues that we have psychological biases that blind us to the enormous role played by rare events — like a 9.0-magnitude earthquake. And yet we rely on history for guidance."
  • "Whatever else they may be, markets are immensely complex counting machines. They assign values to products, whether computer chips or potato chips, based on the canny appraisals and gut beliefs of people around the planet. From day to day, it is often hard, if not impossible, to know exactly why a certain price moved the way it did. Those daily movements are often just the white noise of global capitalism."
  • And then "there are stretches of extreme volatility, periods when no one quite seems to agree about where anything is going."
  • And nuclear power... "The financial markets have always had a difficult relationship with nuclear power, largely because the costs — and potential risks — associated with nuclear plants are so huge. Day to day, nuclear power is cheap. But it is unclear how to accurately assess the cost of disposing of nuclear waste over the long run — or, perhaps, the cost of disasters like the one in Japan." Economists, politicians, capitalists may just ignore the externals, the environmental costs, either because someone else (namely you and me, the general public) will pick up the tab, or because it is too complex to calculate, or there isn't enough information to figure it out. "Professor Stavins said, 'You can argue that the markets have never really had a chance to price nuclear power.'”
  • "In the face of black swans — also known as fat-tail events, for the way their occurrences are distributed along a probability curve [those outlier events, low probability, but possible, like winning the lottery) — market pricing may be impossible."
The last comments relate to this final article:

Lessons from Chernobyl for Japan by Ellen Barry (3/19/2011)
  • The contaminated area around Chernobyl will remain contaminated for more than 300 years.
  • "One had to look at Ukraine to understand the sheer tedium and exhaustion of dealing with the aftermath of a meltdown. It is a problem that does not exist on a human time frame."
  • An eerie instance of an abandoned civilization: "The wild world is gradually pressing its way in... 'This is a city that has been captured by wilderness,' he [ said. 'I think in 20 years it will be one big forest.'"
  • According to one worker involved in maintaining the shell around the defunct reactor: “'Nobody knows what to do with what is inside,' he [Anton Yukhimenko, who leads tours of the dead zone] said. 'There will be enough work for my children and my grandchildren.'"

jd

Sunday, March 13, 2011

Diane Ravitch in Chicago


Diane Ravitch, author of The Death and Life of the Great American School System: How Testing and Choice Are Undermining Education and frequent critic of what she refers to as "corporate education reform" spoke to over 400 people on Saturday (March 12, 2011) at the UIC Forum. The event was sponsored by the Chicago Teachers Union.

An iPhone is not the easiest thing to take notes on, but here is an assortment of what I was able to take down. The bits below end up sounding like tweets, and it so happens Ravitch is a prolific tweeter ("I am not on Facebook").

"Is this an age of insanity or an age of stupidity?"

"[Corporate education reformers are ] standing on children to push agenda. School reform as a front to destroy public sector unions."

Referring to events unfolding in Wisconsin and there potential impact on education there, "Where is Arne Duncan? Will Arne Duncan meet me in Madison? Where is President Obama?" And "Money was not the point. -- killing collective bargaining was the real goal.

"We can't let the corporate reformers destroy public education."

"The NCLB mandate [that all students be proficient in reading and math by 2014] is utopian. It can't be met. No country has done it. NCLB is a timetable for the destruction of public education. Private entrepreneurs are waiting in the wings." By analogy, if NCLB was extended to police departments: "If the United States is not crime-free by 2014, close all of the police departments, and give a badge to anyone who wants one."

"The future of public education is in the balance. It is the cornerstone of democracy. It should not be privatized."

Synonyms for Race to the Top:
  • NCLB 2.0
  • Race to the Trough
  • Dash to the Cash

On testing:
  • "Testing is not the same thing as instruction."
  • "Take test scores with a box of salt."
  • "Testing is not a science." Testing is a social construction.
  • "Data is just a representation of reality, it is not reality."
  • "How can you evaluate teachers on data that is meaningless."
  • "We need a broader vision of education. We need tests for diagnostic purposes. But high stakes testing is a corruption of the test."
Poverty is the the problem, not teachers. Where the Harlem Children's Zone (Geoffrey Canada, hero of Waiting for Superman) succeeds, it is because it is an antipoverty program. Poor children arrive at school with an achievement gap already in place. Teachers had nothing to do with that. Education in the United States as a whole is not failing, only poor peoples' schooling.

"Merit pay makes no difference." See work by Daniel Pink and Edwards Deming.

See http://www.saveourschoolsmarch.org/

jd

Sunday, March 6, 2011

Computers and chess

I continue to be fascinated by the ways in which computers (and new technologies in general) change the terrain in so many (all?) fields. Dylan Loeb McClain's chess column in the March 5, 2011 New York Times, titled "Still No. 1 in the World, by the Thinnest of Margins", comments on the fact that the world's three top-ranked players are only separated by a range of 9 points (out of 2,800 points). Garry Kasparov, the top-ranked player for 20 years until he retired in 2005, was, McClain notes, was often 30 or 40 ratings points ahead of his closest rival.

What I find of interest is that McClain attributes this to the fact that players today have access to the same databases of games (want to review the Immortal Game? you can find it in any number of places, and step through each amazing move. What about a match between Salo Flohr and Max Euwe, 1932? Yep. Or all of Bobby Fischer's games, or ... see chessgames.com, or chess.com). Plus they have access to powerful computer chess engines to experiment with. And for the average punter, online play can dramatically expand one's board experience. So the tools of preparation are more evenly available: "Today, players have access to the same databases and computers when they train, and native ability is more important than ever" (which is another interesting insight).

Also see this post re: an article by Kasparov on computers and chess.

jd

Sunday, February 27, 2011

Wired article on global manufacturing

The latest Wired (19.03) has an interesting article on small to midsize U.S. manufacturers returning production to the U.S.

These days, labor, while an important cost, is often not the critical one to determining where to produce, due to continuing advances in automation and robotics. With China's rising labor costs, currency revaluation and quality control problems, the overall cost of making things in China is getting more expensive. Add in the distance to market and the related travel and shipping costs (still a big factor when moving matter) , producing closer to market is making more sense for many manufacturers.

The article puts this in network terms: the longer and more tenuous the links between the nodes of the global economy, the more fragile the network and prone to problems.

The article isn't on the website yet, but should be in the not too distant future.

jd

3/6/11 update: The article is available online now: Made in America: Small Businesses Buck the Offshoring Trend, by Brendan Koerner.

Monday, February 21, 2011

Solving math word problems

A teacher asked me a question re: strategies for solving word problems. This is what came to mind:

1. Consider the popular 4-step problem-solving strategy (adapted from Michael Polayi, appears in the MathThematics text; there is a good description on the this Scholastic.com page) as an overall approach. The basic steps are:
  1. Understand the problem
  2. Make a plan (there are lists of basic strategies like "guess and check", "use a formula", "draw a picture"; see the Scholastic link above for a longer list).
  3. Carry out the plan
  4. Look back (review, reflect, evaluate)
2. As part of step 1, understanding the problem, Ms. Schumacher at our school has students mark the problem text in different ways to isolate the key parts of the problem. She has her students underline the portion of the problem that says what to do, or what the question is asking for. They circle numbers or number words that are important to the problem. And they draw boxes around the actions they need to perform on the numbers (see next point). Reading math problems is a kind of literacy, and this deconstruction of the text can help comprehend the problem.

3. Again related to step 1: Since reading math problems is a kind of literacy, students need to understand the vocabulary of math. There are addition words, subtraction words, and so on for each basic math operation. For example, addition words are words like "sum", "plus", "add", "increased by". Subtraction words are words like "less", "difference", "decreased by". Being able to recognize key math words, and what operations they are calling for (as well as what order to put the operands in) is important. Purplemath has a table of "key words". Here is a link to a table students and I put together last year. (It is also important to be able to determine what is important information for solving the problem, and what is extraneous or irrelevant information).

4. Students have different skill levels when it comes to what strategies they might use, but it might be useful to reinforce that a strategy that works is a good strategy, the main trade-off being effort to arrive at a solution. Guess-and-check (or using "brute force") is okay if you have the time and patience; algebraic methods are very flexible and powerful but may be prone to error if the student isn't comfortable with them. It is also important I think that students recognize that a combination of strategies is frequently used (e.g., I find it useful to first draw a picture or diagram, or make a table, to understand the problem before thinking of an algebraic solution).

5. The last step is very important. Is the answer reasonable? Does it actually solve the problem? Was there an easier way to tackle it? Will it work for other problems?

6. Regarding teaching strategies:
  • Whatever can be done to help students de-code the problem can help. I am thinking of comprehension strategies used with other kinds of texts.
  • A think-aloud of how the teacher might approach the problem could model the problem-solving strategy for the students.
  • After students have highlighted the key parts of the problem (what the problem is asking for, the key numbers, the operations), modeling how to put the pieces together can help.
  • A KWL chart might structure the process, especially if students are familiar with the format. The Know part, "what do we know already?" = the numbers and operations that the students have highlighted. The Want to know part = what the problem is asking for. The Learned part is the problem solution.
  • Having students make up their own word problems for other students might help them understand the structure or genre of math word problems.
  • Writing in a math journal about what they did to solve a problem might help gel the process for them.
  • Re: thinking about general problem-solving strategies, posing practical problems for the students might build their confidence in their problem-solving abilities and connect with strategies they already use, but don't think of them as such ("activating prior knowledge"). For example, a million dollars is waiting for you at the Lincoln Park Zoo -- how are you going to get it?
  • Having a context for understanding a word problem is important. If the problem deals with things the students don't know anything about, it is hard to understand what the problem is asking. This starts to slide into the area of math and social justice -- presenting math in terms that connect in deep ways with the lives of the students. Students need to be engaged enough with the material to want to solve the problem.
  • There are lots of other words that have math meanings, separate from different ways of referring to the basic operations and relations. See the ISBE Math Frameworks Glossary for words and definitions that are important to know when approaching word problems.
  • Being able to talk to students about how they solved or didn't solve a problem can be very useful for understanding their thinking and the source of possible misunderstandings.
This just touches on some strategies. Any comments are welcome. Literacy Strategies for Improving Mathematics Instruction, by Joan M. Kenney et al. (an ASCD book) has insights into different aspects of math and literacy.

Since most real-world problems that require math present themselves as word problems, I think it is important that students are fluent in translating them into math terms, and using math tools for finding solutions. It is one of the important ways that math becomes meaningful.

jd