Difference between rote knowledge and inflexible knowledge

From Daniel Willingham's Inflexible Knowledge: The First Step to Expertise

Much of what is commonly taken to be rote knowledge is in fact not rote knowledge. Rather, what we often think of as rote is, instead, inflexible knowledge, which is a normal product of learning and a common part of the journey toward expertise.

• Rote knowledge is memorizing without meaning.
• Inflexible knowledge is memorizing with meaning. It can be described as concrete and superficial.
• Knowledge is flexible when it can be accessed out of the context in which it was learned and applied in new contexts.  It can be described as deeper and abstract.
• Inflexible knowledge is the unavoidable foundation for expertise.

When encountering new material, the human mind appears to be biased towards learning the surface features of problems, not toward grasping the deep structure that is necessary to achieve flexible knowledge.

An important goal of education is expertise, which can be defined as "understanding the deep structure of a large domain".  However, before expertise is achieved, there is a large middle ground where students must acquire inflexible knowledge.  Acquiring and working (including practice) with inflexible knowledge are vital steps in the educational process.

To many of us it appears that the educational establishment has a bias against inflexible knowledge, leading schools to skip over a vital step in the learning process.   They often push to teach critical thinking skills before students have sufficient knowledge of the topics about which they are supposed to be thinking critically.  My own enduring example of this is the assignment of a research project on global warming or overpopulation in the fifth grade.  It can be a fun, engaging assignment, but the results I've seen make me question its educational value.  Among other things, it usually consumes huge amounts of precious time, requires excessive parent involvement, treats topics in a superficial manner because some critical science fundamentals (inflexible knowledge) have not been taught beforehand and leaves the student with a better understanding about creating dioramas than about the underlying concept.  Rote learning, anyone?

Daniel Willingham's advice to educators:

Appreciate the importance of students' growing knowledge, even if it's inflexible: Don't be reluctant to build students' factual knowledge base. Some facts end up in memory without any meaning, and other facts have meanings that are quite inflexible, but that doesn't mean that teachers should minimize the teaching of facts in the curriculum. "Fact" is not synonymous with rote knowledge or with inflexible knowledge. Knowing more facts makes many cognitive functions (e.g., comprehension, problem solving) operate more efficiently. If we minimize the learning of facts out of fear that they will be absorbed as rote knowledge, we are truly throwing the baby out with the bath water.

Remember that inflexible knowledge is a natural step on the way to the deeper knowledge that we want our students to have: Frustration that students' knowledge is inflexible is a bit like frustration that a child can add but can't do long division. It's not that this child knows nothing; rather, he doesn't know everything we want him to know yet. But the knowledge he does have is the natural step on the road to deeper knowledge. What turns the inflexible knowledge of a beginning student into the flexible knowledge of an expert seems to be a lot more knowledge, more examples, and more practice.

Related:  A working definition of mastery
              Wikipedia co-founder argues for the importance of 'memorizing facts'

If my children were seriously considering business as a college major . . .

Some questions have been raised here recently about the value of a business degree.  However, if my children were seriously considering business majors for their undergraduate studies, I would look at the Bloomberg Businessweek rankings for help in selecting a college.  It looks as if it offers helpful information.

As part of Bloomberg Businessweek's annual ranking of the top undergraduate business programs, senior business students from the 139 participating schools were asked to assign letter grades—from A to F—indicating how well their business programs teach 14 specialty areas: quantitative methods, operations management, ethics, sustainability, calculus, microeconomics, macroeconomics, accounting, financial management, marketing management, business law, and corporate strategy, as well as entrepreneurship and international business, which were added this year. Based on those grades, scores were calculated for each of the ranked schools in each specialty area. 

Productivity resources from the U.S. Department of Education

From the Department of Education, this looks as if it could be useful.  (Maybe we shouldn't abolish this department just yet.)

Resources on Framing Educational Productivity

From the Education Gadfly

New Rochelle school district budget analysis shows skyrocketing costs and deficit projection

Adam D. Egelberg, CFA, a resident of the New Rochelle School District, has taken a close look at district finances and is writing a series of blog posts with important information that voters should review before going to the polls next week.  He has done an amazing job uncovering details and trends, something that I'd like to see done in my own school district.

(As a side note, it's noteworthy that  the school charged Egelberg $489.79 for budgets going back to 2000-01 that he requested through the FOIL (Freedom of Information Law) process.  He was charged for photocopying even though nine of the ten budgets he received were "left-over bounded copies from prior years" that had already been paid for by his property taxes.)

Spending in New Rochelle has skyrocketed in comparison to inflation and enrollment.  (Adding a student achievement measure to this chart would show if more money has resulted in better-educated students.)

In a nutshell, expenses are out of control. Over the past 10 years our health care and general welfare benefit costs have gone up by 138%. It is a shocking increase when compared with an 8% rise in student enrollment.

This chart confirms for me that the real choice area school districts have is either to cut student programs or cut compensation costs.  The reason I believe this is that since Westchester property taxes are already the highest in the country, I doubt taxes can be raised much more.

School districts should share historical and projected budget data with residents, preparing charts similar to those created by Mr. Egelberg.  How hard can it be?

More to come from Talk of the Sound.

Local school budget estimated to increase taxes by 7%

Our local school is one of only two among 11 area districts that are not giving voters an estimate of the tax rate increase associated with the proposed budget.

As voters head to the polls in less than two weeks to decide whether to approve their school districts’ 2011-2012 budget proposals, some voters will have more information than others. For voters in Tuckahoe and Eastchester, they’ll be making a decision without an estimate from the districts on how much their taxes will go up if they vote “yes.”

According to the school, it does not give an estimate because "that information is out of its control".  Declining property values and the related tax certiori filings mean estimating can be especially tricky these days.  The school doesn't even request the information needed to make an estimate.

Assistant Superintendent of Business Mary Ellen Melnyk said in an email that the district had not requested any information on the assessment level from the town assessor during the recent budget process.

But the town assessor gives helpful information.

According to Town Assessor Todd Huttunen, both the Eastchester and Tuckahoe school districts are looking at an estimated drop in assessment of around 2.3 percent. Though the actual formula used to calculate the final tax rate is more complicated, Huttunen said that a solid estimate of where the tax rate currently sits can be obtained by adding the percentage of tax levy increase to the percentage of the drop in assessment.
In Tuckahoe, that would put a tax rate estimate at around 4.77 percent, within the range estimated by Watkins. Eastchester’s tax rate estimate, based on those numbers, would come in at about 7 percent.

Some residents would like the schools to give voters more information.

To some in the community, though, not making any projection of the tax rate is even more misleading.
“You’re going to be voting on practically 5 percent [of a tax rate increase],” said Tuckahoe School District resident Joe Pregiato. “If people knew they’d be voting to jack up their taxes 5 percent again, a lot of people might vote no.”
Loretta Dalton, a resident of the Eastchester School District, noted that the 3.22 percent tax levy increase advertised by the Eastchester School District last year ended up translating into a roughly 7 percent tax rate increase for herself and several of her neighbors.
She said she felt the tax rate projection, even preliminary, is key to understanding the actual budget impact.
“I believe in transparency all across the board,” she said. “There is no reason for them not to be releasing it … We should be understanding what we’re voting for.”

Local school districts won’t publicly release tax rate estimates

No surprise on how NYSUT views their pension benefits

"Seeking to abolish basic labor protections or destroy the public pension system should not even enter the debate when we are discussing true mandate relief," Andrew Pallotta, executive vice president of New York State United Teachers, said at a state Senate hearing in February.

Pallotta called for reduced spending on charter schools and the spreading out of pension payments for schools.

I'm getting the message that New York teachers really want to keep their taxpayer-guaranteed pensions.  That might be hard to do, considering our state's economic crisis and that tax-funded annual contributions to the New York State Teachers’ Retirement System (NYSTRS) will more than quadruple over the next five years.

Read the entire story after the jump.

'career tragectory '

career tragectory as defined in the urban dictionary:

a career path marked by increasing amounts of tragedy, lameness, futility, ineptitude, respect, and/or pay.

"Vic's career tragectory included starting at Lehman Brothers, then Bernie Madoff's firm, then jail, and now he's working at the Wendy's drive-thru."

The experience of career "tragectory" is probably more common among those workers with jobs that are considered "professional" but are really just a mirage .

NYSUT candlelight vigil for school and jobs

The NYSUT Vigil for school and jobs is today in Albany.

Teachers, parents, community members and activists will gather at the West Capitol Park (between Swan Street and the Capitol) at 8 p.m. Monday, May 9 for a special "candlelight" vigil for schools and jobs....

Come to this vigil to shine a light on the union's fight to convince lawmakers to supplement the budget approved earlier this month. The best way to do that is to continue the income tax surcharge on the wealthiest New Yorkers and share the sacrifice.

If groceries were supplied like K-12 education

A post by Don Bodreux at Cafe Hayek begins with this.

Suppose that we were supplied with groceries in same way that we are supplied with K-12 education.

He goes on to describe an imaginary scenario where our groceries would be managed and distributed by the government in way similar to our system of public education.  He concludes:

Does anyone believe that such a system for supplying groceries would work well, or even one-tenth as well as the current private, competitive system that we currently rely upon for supplying grocery-retailing services?  To those of you who might think so, pardon me but you’re nuts.
To those of you who understand that such a system for supplying grocery-retailing services would be a catastrophe, why might you continue to count yourself in the ranks of those who believe that government schooling (especially the way it is currently funded and supplied) is the system that we should continue to use?

The 233 comments offer rebuttals and further debate on this issue.  I haven't read all comments, but I did see where one reader made the point that many poor urban residents do not currently have much choice in grocery stores, so how would a free market school system be any better than what we have now.  A response was that "ghetto" grocery stores still serve the public better than their public schools do.  Additionally, for urban residents who care about these things, the obstacles to shopping at a higher quality market are much less formidable than those blocking residents who desire that their children attend a school other than their local dropout factory.

An interesting discussion on this over at Kitchen Table Math.