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

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

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

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

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.

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