That Red Dot On My Driver's License

There are a few people living better lives because of my brother's death several years ago.  One family still has their father because he has my brother's heart.

Sometimes, though, people donate their bodies to science after they die.  Dissecting cadavers has been, and continues to be, a valuable training exercise.  I can't imagine that a future doctor could get equivalent experience in a simulation (at least, not until Star Trek-like holodecks are created).

Do we want students to learn biology, or do we want them to learn about biology?  There's more than just a subtle difference between the two, and the line is being crossed by the Idiots In The Big White Building Downtown:

Dissecting frogs and cats — a common assignment for kids in California biology classes — could soon be a thing of the past.

A bill from Assemblyman Ash Kalra, D-San Jose, would prohibit animal dissections in K-12 schools, both public and private.

People for the Ethical Treatment of Animals is a strong supporter of the bill. The animal rights organization has documented methods used by companies that supply schools with birds, cats and amphibians for classroom dissections. PETA argues the practice is “miserably cruel.”

Cats used for dissection tend to be euthanized animals acquired from shelters; frogs and other amphibians are often gathered in the wild.

Students (or their parents) can already request alternate assignment if they don't want to participate in dissection.  This bill proves that satisfying one person's personal political belief is worth sacrificing the science education of an entire state's worth of students.

But you can still donate your body to science if you want.  But cats or frogs?  No way, dude.  Not in Cali-unicornia.

College-level Temper Tantrum

If they held their collective breath until they turned blue and passed out, that would be a better outcome:

Middlebury College’s Student Government Association has thrown down the gauntlet: Give us our demands or we go away.

Huh?

In a campuswide letter Tuesday, student leaders promised that most of them will resign, “effectively dissolving” the Senate, if the administration doesn’t make “tangible plans to implement” the SGA’s 13 demands. They demanded President Laurie Patton address their demands at a Tuesday town hall...

It wants to subject invited speakers to the scrutiny of the administration’s and its own diversity organizations. Academic departments and other organizations would have to fill out a “due diligence form” that would let the diversity organizations “determine whether a speaker’s beliefs align with Middlebury’s community standards, removing the burden of researching speakers from the student body"...

Students leaders are also demanding a blacklist of “faculty, staff, or administration members who do not participate in bias training,” so that students can “make informed decisions on courses and interactions.”

They sure are good little fascists, aren't they?

Britain, the New California

In this post from a few weeks ago I point out how California meets its energy needs--by being the largest electricity importer of all the 50 states.  Replies Britain, hold my beer:

Britain has a fracking industry–or could have one, anyway, if it weren’t for the Greens’ political clout. It finally became too much for Natascha Engel, Britain’s “fracking czar,” who quit with a blistering letter of resignation...

The United States is the only country to reduce significantly its CO2 emissions; we did it by substituting natural gas for coal in power generation. But Britain’s Greens won’t let that country develop its considerable natural gas reserves...

Given the Greens’ intransigence, how does Britain generate electricity? It simply imports gas that was produced elsewhere, thus increasing CO2 emissions and outsourcing jobs and tax revenues to other countries. It also commits the ultimate environmental folly by burning “biomass,” i.e., low-quality trees from the southern U.S. that are shipped to Britain at considerable expense. I wrote about the biomass folly, which is imposed on Britain by environmentalists, here and here. The last link is especially informative if you are interested in the details of the biomass fiasco.

Britain’s Greens want to substitute renewable energy sources for the natural gas that can be produced by fracking.

These people are Cuckoo for Cocoa Puffs.

Do We Believe Data, Or Don't We?

Or do we only believe it when it supports our views?

For context, 5.3 times as many people (8,109) are murdered in the United States with "knives or cutting instruments" than with rifles, and 2.3 times as many people (3,574) are murdered in the United States with "hands, fists, [and] feet" than with rifles, according to FBI data.

The gun-grabbers will deflect and ignore, and will scream "AR-15!" until the cows come home.

The Snake Tightens Its Hold

First, the background:

Parents have been complaining about a question on the SAT their children took recently.

Two parents reported a question about a speech given by Bernie Sanders that was asked on the SAT. 
The first parent asked on social media:

1) Why was there an Essay Question on my daughter’s SAT test asking her to explain why Bernie Sanders speech was effective?? 

Regardless of any political beliefs this is underhanded and just wrong.

2) The whole country takes mandatory SAT’s yesterday and my daughter was one of them….she told me that the last question was critiquing a speech that Bernie Sanders made on not privatizing the post offices. His arguments/opinions put out there without any opposing views. 

It’s a good time to remind you that David Coleman, one of the Chief Architects of the Common Core Standards, is now the President of the College Board. Since he was elevated to this position there has been much controversy surrounding the SAT/ACT and Advanced Placement Program.

Keep this story in mind and consider that California is considering replacing its 11th grade standardized tests with the SAT.

Racist Teachers?

What other possible conclusion can be drawn except that America's teachers have been, and continue to be, rabid racists?

Contrary to other research, the socioeconomic achievement gap has remained unchanged over the past 50 years, according to a new study published by Education Next.

I mean, someone must be keeping non-Asian students down, right?  Right?

Wait, what's this?

However, Sawhill did not place all the blame on schools. Other factors, such as the increase in the numbers of single-family households and widening of wage gaps between upper-income households and middle- and lower-income households may also neutralize the progress.

So, our culture has an effect?  Who knew?!

Maybe, though, the problem is worse than this study claims:

The study findings run counter to other research, including some by Sean Reardon, of Stanford Graduate School of Education, which found that the socioeconomic achievement gap has grown significantly over the past three decades. Reardon used family income and student scores on standardized tests from other studies, including the National Education Longitudinal Study, for his research.

Maybe all those unionized teachers are racists after all.

Feminists I Support

I don't support that modern feminism that posits women as victims.  I support the feminism of strength and intelligence and independence and truth.

Too many lefties don't like it, though, when women leave the plantation, but at least one university president has stood up to the mob of crybullies:

Camille Paglia is an outspoken critic of modern feminism and some of the far-left trends that have taken hold on many college campuses of late so it’s probably not surprising that she would eventually become the target of student activists caught up in those same trends. A group of students at University of the Arts, where Paglia has been on the faculty since the 1980s, launched a protest aimed at getting her fired or, if that wasn’t possible, de-platforming her...

As a result of these and other statements [made by Paglia], the petition demands that Paglia be fired and replaced by “a queer person of color.” If that’s found to be impossible because of her tenure, the activists want someone else hired to teach Paglia’s classes so students aren’t exposed to any dangerous opinions. In addition, the petition demands Paglia stop being given platforms to speak and sell books on campus. In short, Paglia must be silenced as much as possible.

In response to these demands, the school’s president, David Yager wrote a letter defending the right to free speech. 

Wouldn't want to be exposed to any different ideas, would we?  You can't think here, this is a university!

I attended West Point.  We read The Communist Manifesto there, in a required philosophy class.

Paglia, and Christina Hoff Sommers, are feminists I admire:

Sommers also spoke about her multiple experiences of being shouted down and protested at other schools, criticizing the culture of shouting down speakers students find disagreeable.

“When you heckle and shout down speakers, you prevent other students from listening,” Sommers said. “I think that shouting down a speaker that other students want to hear is sort of like going up to somebody who’s reading a book and grabbing it from their hand and going, ‘You can’t read that.’”

“How can a movement that’s associated with liberation have gone in the direction of hyper-protection and trigger warnings and censorship?” Sommers later added.

Another topic Sommers addressed was social activism.

“Men and women are best served by the truth,” she said, adding later that repeatedly reinforcing the idea that women are oppressed sends the wrong message to young women. “Smart activism requires a grasp of reality.”

Sommers also took issue with the controversial statistic that one in five women will be sexually assaulted during their time on a college campus, claiming that the number is actually closer to one in 40 or one in 50.

It's not a controversial statistic, it's an obvious falsehood, but let's continue.  Here's what I mean about strength and truth:

Sommers responded to the assertion about activism by saying she understands how the narrative that women are oppressed can be motivating, but also argued that feminism has become too extreme and too divisive in pushing these narratives.

“Even though it excites a group of people, there is a group of people who are being turned away,” Sommers said.

Lies and whining have a way of doing that.

The Poster Child For Meritocracy

I love seeing high schoolers do well:

A senior in New Orleans has been accepted into 115 colleges and universities and offered nearly $3.8 million in scholarships.

Antoinette Love, who attends the International High School of New Orleans (IHSNO), was still awaiting responses from 12 more universities...

“Antoinette began her freshman year as a shy girl, and she has grown into a hard-working scholar who is eager to help her fellow students with their academics,” said Sean Wilson, Head of School for IHSNO.

She was inducted into the National Senior Beta Club, the National Honor Society, the National English Honor Society and Rho Kappa National Social Studies Honor Society in her four years at the school, administrators said.

Love, who plans to major in elementary education, said she will be busy over the next few weeks visiting several colleges that have awarded her scholarships.

Great job!

Letting Inmates Run The Asylum

What do these idiots think will change behavior, holding hands and singing Kumbayyah?

It could soon be illegal in California for schools to suspend students for being disruptive.

A bill banning that practice for K-12 students, in both public and charter schools, sailed to passage in the California Senate on Monday, 30-8. The bill moves on now to the Assembly.

“An overwhelming body of research confirms that suspending students at any age fails to improve student behavior and greatly increases the likelihood that the student will fail, be pushed out of school and/or have contact with the juvenile justice system,” wrote Sen. Nancy Skinner, D-Berkeley, who is the primary author of Senate Bill 419. “SB 419 helps keep students in school, increases student success rates, and increase high school graduation rates.”

See, they're only interested in graduation rates. They aren't interested in the quality of learning at all.

But behavior isn't changed by suspensions, either, you might say.  OK, I'm willing to concede that.  But suspensions are remarkably effective at providing a better education for the rest of the students when a disruptive student is removed.  Supporters of stupid bills like this are willing to sacrifice the education of good students so that they can pretend to show they care about "students of color, with disabilities or who are part of the LGBTQ community" who are supposedly suspended at higher rates.  But you know who's penalized by having to be in class with disruptive students?  Other students of color, with disabilities, or who are part of the LGBTQ community in the same class.

The question I don't see answered:  are "students of color", etc., suspended at higher rates than Asians (who are not considered "students of color" in education) for the same offense, or do they commit a disproportionate number of offenses?  Doesn't anyone think that is important?

Read more here: https://www.sacbee.com/news/politics-government/capitol-alert/article229645389.html#storylink=cpy

The Very Definition of Hypocrisy

This is rich, coming from someone who illegally used a mail server located in her bathroom:

Hillary Clinton: Anyone other than Trump would have been indicted for obstruction

Doing Everything Except What We're Paid To Do

Teaching is difficult.  Mrs. Barton made it look easy, but it's not.  You have to know what works, and do what works.

Too many teachers want to "change the world" or whatever.  It's easier to turn (someone else's) kids into "agents of change" or "members of The Resistance" than it is to teach them to read, write, and calculate.

Yet, teaching them to read, write, and calculate is what the public expects of us.  We should do that before we put on our amateur psychologist or community organizer hats:

Nearly half of U.S. children have experienced childhood trauma, according to the National Survey of Children’s Health. “Adverse childhood events” or ACEs, include parental divorce or separation, as well as poverty, racial/ethnic bias, witnessing violence, living with an alcoholic, addict or suicidal person and having a parent in jail. Twenty-two percent have experienced two or more ACEs, one in 10 three or more...

With the rise of social-emotional learning, we are in danger of pathologizing childhood, writes Rick Hess in Education Week. He cites Fordham fellow Robert Pondiscio, who warns that “trauma-informed” education “can push us to view children as trauma victims and teachers as therapists.”

Pondiscio worries about teachers devoting their time and energy to social work rather than  academics.

If you view half your class—and in impoverished areas the vast majority of your class—as trauma victims, as struggling or vulnerable, it’s almost inevitable that low or reduced expectations will take root.

The "soft bigotry of low expectations", anyone?

I agree with this comment on Joanne's post:

Ann in L.A. says

April 19, 2019 at 12:05 pm

Teachers are not psychologists. It takes about 7+ years to become a psychologist: college, grad school, apprenticeship, etc. Teachers are simply not qualified and should not be tasked with being psychologists.

We should do what we're paid to do.

Misunderstandings About Understanding In Math

When Barry Garelick sent me his article about understanding in math class, I had every intention of quoting from it.  However, by the time I finished reading it I decided it would just be better if I cut and pasted the entire thing here (and I have his permission to do so).  Some of his images and other text in MS Word didn't translate to blogger well, so I've added two screenshots where necessary.

Misunderstandings about Understanding in Math Education

Conceptual understanding in math has served as a dividing line between those who teach in a conventional or traditional manner (like myself), and those who advocate for progressive techniques. The progressives/reformers argue that understanding of a procedure or algorithm must precede the procedure/algorithm itself; failure to do this results in what some call “math zombies”.

For many concepts in elementary math, understanding builds from procedures. The student practices the procedure until it is realized conceptually through familiarity and tactile experience that forges pathways and connections in the brain. (Furst, 2018).  Daniel Ansari (2011), maintains that procedures and understanding provide mutual support. Rittle-Johnson (2001) supports the push-pull relationship between understanding and practice of procedure.

Or to put it more plainly, Steve Wilson, a math professor from Johns Hopkins University at a conference on math education held in Winnipeg in 2011 stated that “The way mathematicians learn is to learn how to do it first and then figure out how it works later.” 

While this came as a surprise to some who were on Wilson’s panel, this is a fairly accurate description of how most of us gain understanding in math: through familiarity with and practice of procedures.  Nevertheless, the prevailing belief is summarized in statements made by teachers or school administrators such as “In the past students were taught by rote; we teach understanding.”

The result of such belief is a teaching approach in which understanding and process dominate over content. Students are frequently required to use inefficient methods and to draw pictures, reciting their understanding at every step.  Students who cannot solve problems in more than one way are believed to lack understanding.  A student unable to explain in writing how they solved a problem—even in early grades—is taken as evidence of lack of conceptual understanding. Some students may be held up when they are clearly ready to move forward and mathematical proficiency is often sacrificed in the name of understanding.

Levels of Understanding

We are not born as experts—we have to start out as novices. There are levels of understanding—the level of one’s understanding depends on where the person is on the spectrum of novice to expert. As students advance along the spectrum from novice to expert, they acquire more knowledge which is assimilated and connected as the definition says.  The “why” of the procedure is generally easier to navigate once students are fluent in the particular procedure. 

Anyone who has worked with young students you has seen that they gravitate to the “how” or the procedural. Though we may teach the “why”, it is not always grasped at that stage.  There is a reason for this “Just tell me” response, given in large part through Cognitive Load Theory (Sweller, et al, 1994, and 2006).

Working memory is where thinking takes place: It is where incoming new information is connected with prior knowledge, and where both are manipulated. It is new information’s “entry ticket” to the long term memory storage. While it plays an important role in thinking, working memory gets overloaded quickly. This is particularly true when trying to juggle many things at once before achieving automaticity of certain procedures leading to information loss. You may have experienced this when someone tells you directions when you’re new to a city. They decide to also tell you some shortcuts and you may say “No, I’m fine, I got it, thanks!”

Learning a procedure or skill is a combination of big picture understanding and procedural details. Deliberate practice of the procedure is essential for learning. Repetition brings about automaticity and with that, a less cluttered working memory. With less clutter, there is more capacity to make new connections and, ultimately, to understand. Depending on the procedure, requiring young students to retrieve understanding while mastering the method can often result in cognitive overload and impede efficiency.

Misunderstandings and Beliefs

The most common misunderstandings about understanding that I hear include that students should not be taught standard algorithms before they have the conceptual understanding—it prevents full understanding of why it works. I also hear that “Getting answers does not support conceptual understanding.”

Lastly, if a student cannot transfer prior knowledge to solve never-seen-before problems, that is taken as evidence of a lack of understanding.

In my experience, a key reason for these misunderstandings is a tendency to view the world with an adult lens. As adults, we are experts who are better problem solvers than our students. We have a large amount of knowledge.  We sometimes forget that what we are teaching is all new to the students.

Also, one doesn't need to 'deeply understand' a procedure to do it and do it well. Just as football players and athletes do numerous drills that look nothing like playing a game of football or running a marathon, the building blocks of final academic or creative performance are small, painstaking and deliberate. According to Robert Craigen, a math professor at University of Manitoba, at the novice level “functional fluency with effective procedures is the level of understanding that really matters.”

Drilling Understanding—and the Result

Those who believe that understanding must come before learning a standard algorithm or problem solving procedure frequently posit that such conceptual understanding helps students. There is some truth to this belief—namely, it is helpful when the conceptual underpinning is part and parcel to the procedure. For example, in algebra, understanding the derivation of the rule of adding exponents when multiplying powers can help students know when to add exponents and when to multiply.

When the concept or derivation is not as closely attached, however, such as with fractional multiplication and division, insisting on students showing understanding of the derivation does not provide an obvious benefit. Nevertheless, a prevailing belief in education remains that not understanding the concept renders the procedure as a “rule or trick” with no connection of what is actually going on mathematically. This belief has led to making students “drill understanding”. 

For example, multiplying the fractions  is done by multiplying across so we obtain  or But before students are allowed to use this algorithm, there are some textbooks that require students to draw diagrams for each and every problem to demonstrate and reinforce the conceptual understanding.

For example, the problem of   is demonstrated by first dividing a rectangle into three columns and shading two of them, thus representing 2⁄3 of the area of the square.

Then the shaded part of the rectangle is divided into five rows with four shaded.  This is  of the shaded area; i.e,  of (or times). 

This pictorial method of fraction multiplication then represents the area of a rectangle that is by units. This intersection yields  or eight little boxes shaded out of a total of  or 15 little boxes: thus  of the whole rectangle. This explains the reasoning—the conceptual understanding—behind multiplying numerators and denominators. 

Such diagrams have been used in many textbooks—including mine from the 60’s as shown below—to introduce the conceptual underpinning for multiplying fractions.  

In my particular book, students used the area model for, at most, two fraction multiplication problems. Students were then let loose to solve more problems using the algorithm. But many textbooks claiming alignment with the Common Core, require students to draw these type of diagrams for a full set of problems—in essence drilling understanding.

While the goal of drilling understanding is to reinforce concepts, it generally leads to what I call “rote understanding”—exercises that become new procedures to be memorized. Such drilling forces students to dwell for long periods of time on each problem and holds up students’ development when they are ready to move forward.

On the other hand, there are levels of conceptual understanding that are essential—foundational levels. In the case of fraction multiplication and division, students should know what each of these operations represent and what kind of problems can be solved with it. For example: Mrs. Green used  of  pounds of sugar to make a cake. How much sugar did she use? 

Given two students, one who knows the derivation of the fraction multiplication rule, and one who doesn’t, if both see that the solution to the problem is  and can do the operation correctly, I cannot tell which student knows the derivation, and which does not. And at this stage of learning, I am more concerned with their foundational level of understanding.

Further Questions

In wrapping up this discussion about misunderstandings about understanding in math, I want to address two statements that for me raise many questions. 

I have heard people say “Calculation is the price we used to have to pay to do math. It's no longer the case. What we need to learn is the mathematical understanding.”

And often on the heels of this statement I will hear that they had done well in math all through elementary school, but when they got to algebra in high school they hit a wall.  Or, similarly, they did great in high school, and hit a wall with calculus. 

There is much information that we do not have from such statements. 

·        Was the education they received really devoid of any kind of understanding; that is, was it all rote?  

·        Are there people who get A’s in math in high school who are really math zombies and cannot progress to the next level?

·        Are these complaints limited to those who were educated in the era of traditional or conventionally taught math? 

·        And of those, how much of what they experienced is due to concepts not explained well, emphasis on procedures only, and grade inflation? 

·        And to what extent are these problems the result of the obsession over understanding?

I would be curious to see any research that has been done on this—either verifying or disproving such notion. In addition, I would also like to see research conducted in the following areas:

·        For successful math students in high school and college what did they do that’s different than those who were successful in math in high school but did not do well in college math courses

·        What effect has the emphasis on understanding been on students who have been identified as having a learning disability? 

·        And a more difficult question: is there evidence that such emphasis has resulted in students being labeled as having learning disabilities?

·        Finally, people have told me that those students in lower grades who were “taught understanding” do better in the long-term than those students for whom the focus was procedural fluency. Are there studies that support or disprove this?

Based on what I see in the classroom, research that I have read (see references), and people in the field with whom I have spoken I believe that attaining procedural fluency and conceptual understanding is an iterative process of which practice is key. I also strongly believe that whether understanding or procedure comes first ought to be driven by subject matter and student need — not by educational ideology.

References:

Ansari, D. (2011). Disorders of the mathematical brain : Developmental dyscalculia and mathematics anxiety. Presented at The Art and Science of Math Education, University of Winnipeg, November 19th 2011. http://mathstats.uwinnipeg.ca/mathedconference/talks/Daniel-Ansari.pdf

Furst, E. (2018) Understanding ‘Understanding’  in blog Bridging (Neuro)Science and Education https://sites.google.com/view/efratfurst/understanding-understanding?authuser=0

Geary, D. C., & Menon, V. (in press). Fact retrieval deficits in mathematical learning disability: Potential contributions of prefrontal-hippocampal functional organization. In M. Vasserman, & W. S. MacAllister (Eds.), The Neuropsychology of Learning Disorders: A Handbook for the Multi-disciplinary Team, New York: Springer

Morgan, P., Farkas, G., MacZuga, S. (2014). Which instructional practices most help first-grade students with and without mathematics difficulties?; Educational Evaluation and Policy Analysis Monthly 201X, Vol. XX, No. X, pp. 1–22. doi: 10.3102/0162373714536608

National Mathematics Advisory Panel. (2008). Foundations of success: Final report. U.S. Department of Education. https://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

Rittle-Johnson, B., Siegler, R.S., Alibali, M.W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, Vol. 93, No. 2, 346-362. doi: 10.1037//0022-0063.93.2.346

Sweller, P. (1994) Cognitive load theory, learning difficulty, and instructional design.  Leaming and Instruction, Vol. 4, pp. 293-312

Sweller, P. (2006). The worked example effect and human cognition. Learning and Instruction, 16(2) 165–169