Constructivizing STEM

by Robert Pondiscio
February 22nd, 2012

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Posted in Core Knowledge, Curriculum, Education News, Education Practice, Research and Reports, Students, Teaching | 2 Comments »

The following guest post is by Katharine Beals, who blogs about education at Out in Left Field, where this post also appears.  — rp.

It’s hard not to detect a certain worry among those who write STEM articles for Education Week that the drive to educate students for careers in Science, Technology, Engineering, and Mathematics might include a drive to increase core scientific and mathematical content at the expense of things that Constructivists hold dear. Things, for example, like “model building,” “data analysis,” and “communicating findings.”

These are what Jean Moon and Susan Rundell Singer, in their backpage Edweek Commentary on Bringing STEM into Focus, want to be sure schools are focusing on:

Re-visioning school science around science and engineering practices, such as model-building, data analysis, and evidence-based reasoning, is a transformative step, a step found in the NRC report, which is critical to STEM learners and teachers, both K-12 and postsecondary. It puts forward the message that knowledge-building practices found under the STEM umbrella are practices frequently held in common by STEM professionals across the disciplines as they investigate, model, communicate, and explain the natural and designed world.

Not that this is all that Moon and Singer care about. They also care about big ideas, which they divide into two categories: “crosscutting concepts (major ideas that cut across disciplines)”, and “disciplinary core ideas (ideas with major explanatory power across science and engineering disciplines.” The former include “scale, proportion, and “quantity or the use of patterns;” the authors don’t cite any examples of the latter.

Besides “practices” and ”ideas,” the authors mention “strategies” and “tools” (again, without specific examples). What they don’t mention is underlying content, except to say:

Lest some believe this is setting up another false dichotomy in science or mathematics education between content and process, let us quickly add a strong evidentiary note: Epistemic practices and the learning and knowledge produced through such practices as building models, arguing from evidence, and communicating findings increase the likelihood that students will learn the ideas of science or engineering and mathematics at a deeper, more enduring level than otherwise would be the case. Research evidence consistently supports this assertion.

I’m curious what “research evidence” means, but I gather that it doesn’t include the research evidence that cognitive scientist Dan Willingham cites in support of the idea that students aren’t little scientists and need a foundation of years of core knowledge before being ready to function as actual scientists.

In promoting their ideas as “transformative,” the authors are overlooking the fact that the kinds of constructivist practices they desire are already standard in many schools (particularly those held up as models for others). If they want to promote something truly transformative for STEM, they should instead be advocating a reinstatement of the years of solid, content-based instruction in math and science that many of our K12 schools used to offer (and that one still finds in schools in most developed countries around the world).

Katharine Beals, PhD is the author of Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School. She teaches at the University of Pennsylvania Graduate School of Education and at the Drexel University School of Education, specializing in the education of children on the autistic spectrum. She blogs about education at Kitchen Table Math and on her own blog, Out in Left Field.

An Inconvenient Truth About Teacher Quality

by Robert Pondiscio
December 5th, 2011

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Posted in accountability, Assessment and Testing, Curriculum, Education Practice, Literacy, Teaching | 11 Comments »

If teacher quality is the most important school-based factor in student outcomes, then why are math scores rising, while reading scores stay flat?  Do we just happen to have really good math teachers and really lousy reading teachers?  That can’t be: in the case of 4th grade teachers, the exact same teachers are responsible for both subjects.

Or maybe it’s not the teachers. Could it be the curriculum?

That’s the question posed by Dan Willingham and David Grismer in an op-ed in the New York Daily News this morning.  They point out intriguing data from the National Assessment of Educational Progress that has been hiding in plain sight:

“Reading scores over the last 20 years have been flat. But in math, scores have increased markedly. A fourth-grader at the 50th percentile in 1990 would score at about the 25th percentile compared to the kids taking the test in 2009. That’s an enormous improvement.

“This raises an uncomfortable question for teacher quality advocates: If teachers are so vitally important, why have fourth-grade math scores dramatically improved, but reading scores have flatlined, given that — at least at the elementary level — the same teachers are responsible for each?

Perhaps the secret sauce is not who’s teaching but what’s being taught.  It’s a lot easier to align standards, curriculum and assessment in math. “There is little controversy as to the subject matter to be covered, and the order in which one ought to tackle subjects is more obvious,” Willingham and Grissmer write.  “Indeed, substantial effort has been made over the last 25 years to develop coherent math standards and curricula from K-8.”

In reading? Not so much.

As we’ve discussed many times on this blog, there’s no direct correlation between the subject matter that gets taught and tested in reading.  We teach random, incoherent content that bears no relation to the passages children ultimately encounter on their reading tests.  We insist on teaching and testing the “skill” of reading comprehension when it’s clearly not a skill at all.  Willingham and Grissmer conclude:

“Yes, overall teaching quality would improve with a more sensible method to usher hapless teachers out of the profession. Better teacher training would help too. But in addition to these longer-term goals, policymakers ought to focus on ensuring that the unglamorous but vital work of curriculum design is done properly. The popular perception is that America’s teachers are largely ineffective compared to international peers. But the data show that when given a clear, cogent curriculum to work with, they’re a lot stronger than we think.”

Guest Post: Politics Driving Math Classes

by Robert Pondiscio
September 5th, 2011

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Posted in Education Practice, Parents, Teaching | 29 Comments »

Today’s post is by Laurie H. Rogers, a member of the executive committee for Where’s the Math? and author of “Betrayed: How the Education Establishment Has Betrayed America and What You Can Do About It.”  She blogs at Betrayed (http://betrayed-whyeducationisfailing.blogspot.com/) where this post also appears.

Several days ago, someone sent me an article on “teaching math for social justice.” I actually hit my desk while reading it, narrowly missing the cat. I shouldn’t read things like that first thing in the morning. It raises my blood pressure and gets the next 12 hours off to a bad start.

In the article, teaching math for social justice isn’t about math or justice; it’s about pursuing a narrow political agenda in the classroom, through the children. Math is relegated to the wings, used as a vehicle through which the agenda is delivered.

The article was in a 2010 special edition of the National Council for Teachers of Mathematics’ Journal for Research in Mathematics Education (JRME). This issue is dedicated to “equity” in math instruction, “with a focus on power and identity.” After years of advocacy, I shouldn’t be surprised by what comes out of the NCTM, but this special edition still was a cold shock.

The NCTM, you’ll recall, is responsible for the current incarnation of “fuzzy” math, born in the depths of hell in the 1980s. Many NCTM presidents and officers have their name on, and fingers in, today’s “reform” math curricula (including the curricula still sucking the lifeblood out of children in Spokane). Unhappily for this author, some now are involved in federal initiatives related to the Common Core State Standards and assessment consortia.

After decades of abject failure of the fuzzy approach, you’d think the NCTM would reject anything that further detracts from learning math. Instead, this trend to teach math through “equity and social justice” is gathering steam, fostered by social activists, self-interested groups like the NCTM – and well-meaning people who don’t realize the intent. For social activists, the agenda isn’t about “equity of opportunity” or justice under the law. It’s political, sociological activism, designed to move students in a specific political direction based on a particular world view. This activism, masquerading as math, is inappropriate and unhelpful. Read the rest of this entry »

Common Core Standards: A Cautionary Tale

by Robert Pondiscio
May 12th, 2011

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Posted in Curriculum, Education Practice, Teaching | 16 Comments »

Guest blogger Katharine Beals, PhD is the author of “Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School.”  She teaches at the University of Pennsylvania Graduate School of Education and at the Drexel University School of Education, specializing in the education of children on the autistic spectrum.  She blogs about education at Kitchen Table Math and on her own blog, Out in Left Field.

When the New York Times presents case studies in education reform, one can often spot between the enthusiastic lines at least a few reasons for skepticism. The latest front-page education article, a piece on the new Common Core standards, is no exception:

“The new standards give specific goals that, by the end of the 12th grade, should prepare students for college work. Book reports will ask students to analyze, not summarize. Presentations will be graded partly on how persuasively students express their ideas. History papers will require reading from multiple sources; the goal is to get students to see how beliefs and biases can influence the way different people describe the same events.”

At first glance this sounds pretty good–although it’s disturbing that it’s necessary to spell out that book reports should include analysis and that history papers should sometimes require multiple sources.

On second thought, however, one might worry about how teachers and their advisors will interpret “persuasively”: does it pertain to an argument’s rhetorical content, or is it a matter of charisma, body language and showy prompts? One might worry, as well,  about the implication that history is only about “higher level” thinking skills like sorting out biases and multiple perspectives rather than about learning a fact-rich core of basic, historical knowledge.  In other words, how much will the Common Core standards play out like a caricature of the New Math of the 1960′s, a.k.a. Some Math, Some Garbage?

Here, accordingly to the article, is what’s happening in Hillcrest, one of 100 New York City schools that are piloting the new standards:

“Until this year, Ena Baxter, an English teacher at Hillcrest High School in Queens, would often have her 10th graders compose papers by summarizing a single piece of reading material.

“Last month, for a paper on the influence of media on teenagers, she had them read a survey on the effects of cellphones and computers on young people’s lives, a newspaper column on the role of social media in the Tunisian uprising and a 4,200-word magazine article titled ‘Is Google Making Us Stupid?’”

So far, so good, though, again, it’s disconcerting to hear what the 10th grade papers used to be like. But then there’s this:

“Eleni Giannousis made a change in her 10th-grade English class that might make some purists blanch. She had students watch the filmed stage performance of “Death of a Salesman,” starring Dustin Hoffman as Willy Loman, before they read the play. The idea was to have students absorb information through a medium they use for entertainment, one way she was experimenting with her lesson plans to try to meet the new goals.

“It wasn’t about making things easier for the students, but about challenging them to experience a classic in a different way,” Ms. Giannousis said.

Yes, I’m blanching. And yes, I’m skeptical.

As for nonfiction:

“While English classes will still include healthy amounts of fiction, the standards say that students should be reading more nonfiction texts as they get older, to prepare them for the kinds of material they will read in college and careers. In the fourth grade, students should be reading about the same amount from “literary” and “informational” texts, according to the standards; in the eighth grade, 45 percent should be literary and 55 percent informational, and by 12th grade, the split should be 30/70.”

I’m all for elevating nonfiction, but the Times suggests that, at Hillcrest at least, the only medium for it is English class. History and social studies, assuming these are focused on content and not on so-called “higher-level” thinking, should also be a major venues for reading. Indeed, by giving the English Language Arts standards the specific title “Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects,” the Common Core underscores the importance of reading in all subjects. Nowhere, incidentally, does it mention film and video viewing as alternatives to reading.

As for math, the Common Core names Statistics & Probability as one of six core areas for high school. How is this playing out at Hillcrest in particular?

“A math teacher, José Rios, used to take a day or two on probabilities, drawing bell-shaped curves on the blackboard to illustrate the pattern known as normal distribution. This year, he stretched the lesson by a day and had students work in groups to try to draw the same type of graphic using the heights of the 15 boys in the class.

“Eventually, they figured out they couldn’t because the sample was too small,” Mr. Rios said. “They learned that the size of the sample matters, and I didn’t have to tell them.”

A whole day in groups for what could be a 5-minute survey and plotting of data points in front of the entire class?

While the Times article shows just a few snapshots of a single school’s attempts to implement the Common Core standards, these snapshots collectively suggest a basic problem with the standards in their current, schematic incarnation. As the Times explains:

“There are guidelines for what students are expected to do in each grade, but it is still up to districts, schools and teachers to fill in the finer points of the curriculum, like what books to read.”

Sticking to general guidelines reflects widespread concern about the federal government micromanaging education, but leaves way too much room for interpretation. Given the dominant Constructivist paradigm, there’s way too much room, in particular for a Constructivist interpretation and implementation of the Common Core standards, and, thereby, for even further Constructivist penetration of  America’s K12 classrooms. In the enthusiastic words of the Times, “In three years, instruction in most of the country could look a lot like what is going on at Hillcrest.”

To ensure that this does not happen, we must constantly remind the education establishment that what the Common Core calls for is a curriculum “intentionally and coherently structured to develop rich content knowledge” and therefore in opposition to much of the dominant paradigm.

Paper Tigers

by Robert Pondiscio
January 24th, 2011

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Posted in Education News | 5 Comments »

“How is it that the richest country in the world can’t teach kids to read or to multiply fractions? Taken as a parable, Chua’s cartoonish narrative about browbeating her daughters acquires a certain disquieting force. Americans have been told always to encourage their kids. This, the theory goes, will improve their self-esteem, and this, in turn, will help them learn.

“After a generation or so of applying this theory, we have the results. Just about the only category in which American students outperform the competition is self-regard. Researchers at the Brookings Institution, in one of their frequent studies of education policy, compared students’ assessments of their abilities in math with their scores on a standardized test. Nearly forty per cent of American eighth graders agreed “a lot” with the statement “I usually do well in mathematics,” even though only seven per cent of American students actually got enough correct answers on the test to qualify as advanced. Among Singaporean students, eighteen per cent said they usually did well in math; forty-four per cent qualified as advanced. As the Brookings researchers pointed out, even the least self-confident Singaporean students, on average, outscored the most self-confident Americans. You can say it’s sad that kids in Singapore are so beaten down that they can’t appreciate their own accomplishments. But you’ve got to give them this: at least they get the math right.”

From “America’s Top Parent,” Elizabeth Kolbert’s review of Amy Chua’s new book, “Battle Hymn of the Tiger Mother” in the current issue of The New Yorke

(h/t Bill Evers)

Confirmation Bias: When Educators Underestimate Children

by Robert Pondiscio
November 10th, 2010

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Posted in Curriculum, Education Practice, Parents, Teaching | 42 Comments »

Guest blogger Katharine Beals, PhD is the author of “Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School.”  She teaches at the University of Pennsylvania Graduate School of Education and at the Drexel University School of Education, specializing in the education of children on the autistic spectrum.  She blogs about education at Kitchen Table Math and on her own blog, Out in Left Field.

By Katharine Beals

Why underestimate what children understand?

Recent anecdotes from parents and recommendations from educators suggest that the underestimation of American children is alive and well in the world of K-12 education. In particular, more and more teachers and education experts  seem convinced that kids don’t really understand the words they read or the numbers they manipulate nearly as well as their parents claim they do. Thus, one mother learns from her daughter’s 2nd grade teacher that her child doesn’t understand the chapter books she’s been reading for pleasure since kindergarten. She should be reading picture books instead. Another mother learns that the multi-digit arithmetic that her 3rd grade son has been doing since preschool is mere calculation, devoid of conceptual understanding. He should be doing simpler calculations using manipulatives and repeated addition.

How, and why, have so many educators become so skeptical about children’s understanding?

How to become skeptical is child’s play. Simply ask the child a question that ostensibly probes comprehension, but is either vague enough, open-ended enough, or verbally challenging enough that the child is unlikely to give the “correct” answer: What is that? What is it about? Why did you do that? If further probing seems necessary, ask equally difficult follow-up questions.

Ground-breaking math education theorist Constance Kamii  has shown how this works with place value in particular:

1. Show the child a number like this: 27

2. Place your finger on the left-most digit and ask the child what number it is.

3. When the child answers “two” rather than “twenty,” immediately conclude that he or she doesn’t understand place value.

4. Banish from your mind any suspicion that a child who can read “27″as “twenty seven” might simultaneously (a) know that the “2″ in “27″ is what contributes to twenty seven the value of twenty and (b) be assuming that you were asking about “2″ as a number rather than about “2″ as a digit. 

How might you convince yourself that a 3rd grader doesn’t understand multi-digit arithmetic? Why not tap into her immature verbal skills? Ask her to elaborate how she subtracted 562 from 831. When she stumbles, ignore any suspicion that articulating why one borrowed from the 8 in the hundreds place and reduced the 8 to a 7 is beyond the verbal skills of your typical 8 or 9-year-old.

How might you convince yourself that a 2nd grader doesn’t understand his above-grade level chapter book? Here, a sufficiently open-ended question may do the trick. Ask him what the book is about, or what will happen next, or how the text relates to himself. Then interpret any hesitation, stumbling, vagueness, or reluctance to respond as an unequivocal sign of deficient comprehension. Dismiss any suspicion that this line of reasoning implies that a teenager who answers “What did you do today?” with “I don’t know” doesn’t comprehend his day.

Perhaps less obvious is why some educators seem determined to underestimate understanding. Here are a couple of possibilities. First, doing so may level the range of apparent abilities in a class of twenty-something children. Parents might think their children are ahead academically, but if they don’t really understand what they are doing, there’s less pressure to provide them with an accelerated curriculum. There’s also less of an apparent achievement gap to be troubled by.

Underestimating comprehension may also serve to avoid or postpone teaching harder material that, frankly, can be a pain in the neck to teach. Believing that children don’t understand place value, for example, gives you an excuse not to teach those pesky standard algorithms of arithmetic. Why? Because if children don’t understand place value, then they can’t understand borrowing and carrying (regrouping), let alone column multiplication and long division. And unless they understand how these procedures work from the get-go, educators claim (though mathematicians disagree), using them will permanently harm their mathematical development.

What’s particularly striking about this underestimation is how much it seems to have permeated the establishment’s take even on those children it itself identifies as “gifted.” For example, at the recent New England Conference on the Gifted and Talented, most of the math talks either expressed concerns about children’s comprehension of place value, and/or advocated the use of manipulatives in place of abstract math. The mathematically gifted kids I know, however, grasp place value and other aspects of arithmetic with only minimal exposure to manipulatives, and quickly advance to higher levels of abstraction by the time they hit first or second grade. 

So, indeed, do children in other developed countries around the world (see examples on my blog, Out in Left Field here, here and here)–whether or not we’d consider them “mathematically gifted.”

To stop holding our students back relative to their international peers, we need to stop asking them the wrong questions. Sometimes, indeed, no questions are necessary. If a child enjoys reading a particular book, then even if she fails to tell you what it’s about, she probably has a reasonable understanding of its content.  If his multi-digit calculations are error-free, then even if he can’t clearly explain his steps in words, he probably has a reasonable understanding of his calculations. Comprehension may not be perfect—when is it ever so? — but the fact that it may need refinement is reason to encourage a child forward, not to stand in his or her way.

 

Math Myth Put to Rest

by Robert Pondiscio
October 28th, 2010

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Posted in Parents, Teaching | 7 Comments »

A meta-analysis of studies of math aptitude shows no substantial difference betwen the sexes, e! Science News reports.  Janet Hyde, a professor of psychology and women’s studies at the University of Wisconsin-Madison looked at 242 articles that assessed the math skills of over 1.2 million people over nearly 20 years.  She also examined results from the National Assessment of Educational Progress (NAEP) and found the difference between the two sexes “was so close as to be meaningless.”

“The idea that both genders have equal math abilities is widely accepted among social scientists, Hyde adds, but word has been slow to reach teachers and parents, who can play a negative role by guiding girls away from math-heavy sciences and engineering. ‘One reason I am still spending time on this is because parents and teachers continue to hold stereotypes that boys are better in math, and that can have a tremendous impact on individual girls who are told to stay away from engineering or the physical sciences because “Girls can’t do the math.’”

Hyde notes there is strong evidence that stereotype threat holds women back in math. “If, before a test, you imply that the women should expect to do a little worse than the men, that hurts performance. It’s a self-fulfilling prophecy,” she says.  ”Parents and teachers give little implicit messages about how good they expect kids to be at different subjects,” Hyde adds, “and that powerfully affects their self-concept of their ability. When you are deciding about a major in physics, this can become a huge factor.”

Less School, Higher Scores in Finland

by Robert Pondiscio
April 9th, 2010

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Posted in No category | 24 Comments »

Children in Finland spend fewer hours in school than any other country in the developed world so how do they consistently turn in top international scores in reading, science and math?  A BBC report focuses on the relaxed atmosphere of the nation’s schools, lack of political interference, as well as the country’s approach to schooling.

“The Finnish philosophy with education is that everyone has something to contribute and those who struggle in certain subjects should not be left behind.  A tactic used in virtually every lesson is the provision of an additional teacher who helps those who struggle in a particular subject. But the pupils are all kept in the same classroom, regardless of their ability in that particular subject.”

The report makes much of the contributions of Finnish home life to student achievement.  “There is a culture of reading with the kids at home and families have regular contact with their children’s teachers,” notes the BBC’s Tom Burridge, who also points out that teaching is a prestigious career in Finland. “Teachers are highly valued and teaching standards are high,” he says.

Education Minister Henna Virkkunen is now looking to boost the performance of Finland’s brightest pupils.  ”The Finnish system supports very much those pupils who have learning difficulties but we have to pay more attention also to those pupils who are very talented. Now we have started a pilot project about how to support those pupils who are very gifted in certain areas,” she says.

“Math of Least Resistance”

by Robert Pondiscio
March 26th, 2010

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Posted in accountability, Assessment and Testing, Curriculum, Educational Policy | 16 Comments »

At Teacher in a Strange Land, Nancy Flanagan tells a fascinating story of a Michigan community college that received a big grant to build a wind turbine and create a green energy careers program.  Education! 21st century careers! In Michigan, no less.   Just where we need to be headed, right?  There was just one problem. 

“They received over 500 applications. The minimal prerequisite for application was successfully completing Algebra II–but the 16 candidates selected for the prestigious pilot program all had top-flight math coursework credentials, including success in national AP math exams. When they got into the actual hands-on learning in the program, however, the selected students had great difficulty in applying the mathematics content they had aced the previous year.”

In short, these looked-good-on-paper students couldn’t integrate and utilize what they knew. Flanagan sees in this story a problem with what grades and test scores tell us about student preparedness–and a cautionary tale for ed reformers.  The disconnect between the students’ credentials and what they could actually do with what they supposedly learned ”can’t be traced back to lack of market-based schooling options, teachers who didn’t get merit pay, or the fact that none of their teachers came from Teach for America,” she notes.  “Their troubles are directly tied to curriculum and instruction–the way they learned to ‘be successful’ in math.

“Education wonks and armchair pundits hate this kind of traditionalist thinking. Curriculum and instruction are dull and unsexy, and push wide-scale policy-lever solutions to the periphery of the discourse. This is why we hear lots of pontificating about recruiting and rewarding quality teachers–including those break-the-mold whiz kids who cut their teeth in the country’s toughest classrooms–but almost nothing about consistent, quality teaching.

Flanagan puckishly headlines her story “The Math of Least Resistance,” which is clearly a comment on ed reform’s tendency to take on the “easy” challenges of structures and incentives while ignoring the much harder task of getting curriculum and instruction right.  Take the lessons from Flanagan’s fascinating anecdote that you will.  But when students that our schools deem successful–those who would almost certainly meet any current definition of “college and career ready”–struggle in situations in which they should have been well-prepared, something’s clearly not right.

Legislator Proposes Banning Calculators From Classrooms

by Robert Pondiscio
January 27th, 2010

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Posted in Education Practice | 3 Comments »

A West Virginia state legislator, apparently frustrated by the inability of retail clerks to make correct change, has proposed a radical solution:  ban calculators in the state’s schools from kindergarten to eighth grade. 

This is a bit like noticing that people can’t swim and banning life jackets.  That said, I’m deeply sympathetic to the notion that de-emphasizing automatic grasp of math facts and ease with basic calculations does more harm than good.   “It’s like giving them a crutch. I don’t like using that term, but that’s essentially what it is,” state delegate Ray Canterbury tells the Charleston Daily Mail. “They really don’t learn math the way they once did.  A lot of things just need to be learned by practice and rote memorization,” he added. 

At Teacher in a Strange Land, now in its new home at Teacher Magazine, Nancy Flanagan rolls her eyes.  “I think we should require kids to memorize their times tables, too. Who doesn’t? I also think that there’s no point in not using cheap, ubiquitous technologies to solve diverse mathematical problems encountered in daily life.”

“I think in this age of technology that it’s wrong not to teach children how to use calculators in an appropriate way,” says House Education Chairwoman Mary Poling, echoing Flanagan.  ”They should not be used to avoid learning how to do basic calculations, but they certainly should be used as tools for learning.”

 

 

 

 

 

“It seems like everywhere I go, people, particularly young people, can’t even make change,” he said.

So Canterbury, a University of Chicago graduate with a bachelor’s degree in mathematics, decided to do something about that and drafted House Bill 3235.

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