Saturday, May 25, 2019

So Few Students

Yesterday was Senior Cut Day, also known as Senior "Have mommy call in so it's not really a cut" Day. My 4th period class has no seniors, and 6th period has only 1 senior. 1st, 3rd, and 5th periods are overwhelmingly seniors.

Only 1 student in my 1st period class showed up. Only 1 student in 3rd, and 1 student in 5th. My one senior in 6th period didn't show--should I make her make-up quiz exponentially harder? :-)

It was a pretty easy day for me.

Thursday, May 23, 2019

"The Most Important Quiz Of My High School Career"

I've taught no new material in my statistics classes this month.  I've devoted the month mostly to review, with a lot of emphasis on doing statistics on an advanced calculator.  The days of using tables are over for my students, and this month they've honed their skills on the ancient-but-still-useful TI-83 (yes, I'd prefer 84's, but at over $100 apiece...).

Today was the TI-83 Quiz, the last graded exercise prior to the final exam.  It was the last chance my students had prior to the final exam to test their knowledge under exam conditions.  One student said to me that this quiz was the most important quiz of his high school career.  Why, you might ask?

I excuse from taking the final those students who have 97% or above going into the final.  This student had 97.3% going into this quiz.  This quiz was the decider.

He will not be taking the final exam :-)

What's Your Solution To This, Lefties?

Instapundit quotes Larry Elder paraphrasing Thomas Sowell:
LARRY ELDER: The Left’s Battle Against ‘Inequality’ Leaves Out One Critical Factor. “In his book Discrimination and Disparities, economist Thomas Sowell notes that a disproportionate percentage of first-born siblings become National Merit scholars compared to siblings born later, presumably because the first-born starts life with no sibling competition for parental attention. This, says Sowell, illustrates the absurdities of expecting equal results when equal results do not even occur within the same family among siblings raised under the same roof with the same parents.”

I Never Did Like Common Core

Years ago I anticipated this would be the problem, at least in math:
With irresistible prodding by Gates and then-President Obama, the Common Core national standards were adopted by the vast majority of states, which have also adopted tests and curricula aligned with those standards.

But a new large-scale study by the federally funded Center for Standards, Alignment, Instruction, and Learning (C-SAIL) has found that since the adoption of Common Core there has been a decline in key test scores.

C-SAIL researchers analyzed changes in student performance on the National Assessment of Educational Progress, or NAEP, from 2010 to 2017.

They had assumed that Common Core would raise student performance on the NAEP exam, but they were in for a surprise.

“Contrary to our expectation,” they reported, the data revealed that the Common Core standards produced “significant negative effects on 4th graders’ reading achievement during the 7 years after the adoption of the new standards.”

When analyzing the results of a selected group of states, fourth-grade reading achievement would have improved more “had the states continued with their old standards, thus reflecting negative effects of the new [Common Core] standards.”

In other words, if those states had ignored the entreaties by Gates, Obama, et al., they would have been better off.

In addition to the decline in reading performance among fourth graders, the C-SAIL study also found that Common Core “had a significant negative effect on 8th graders’ math achievement.”

What’s more, the performance of students declined significantly in specific reading and math categories, such as literacy experience and numbers properties, the longer Common Core was in effect.

Study co-author Mengli Song said: “It’s rather unexpected. The magnitude of the negative effects [of Common Core] tend to increase over time…”

…Some blame the failure of Common Core on process issues, such as lack of adequate teacher training, but the key culprits are the standards themselves and the type of teaching promoted by Common Core.

When Common Core was first being adopted by states, James Milgram, a Stanford math professor who served on a key Common Core committee, warned that by the end of the fifth grade the material covered by Common Core’s math standards “was more than a year behind the early grade expectations of high-achieving countries,” and that “by the end of the seventh grade, [Common] Core standards are roughly two years behind.”

By high school, “Common Core — in its fullness — does not prepare students even for a full pre-calculus class,” notes Ze’ev Wurman, a former senior education policy advisor under President George W. Bush.
It wasn't hard to look at the standards and see the difference.

Held Accountable

A couple days ago I linked to a video showing a snowflake getting arrested for a sign with which she didn't agree.  The look on her face is precious as it transforms from innocent to defiant to confused to shocked to mortified as she realizes, as the interaction with the police officer continues, that her ridiculous left-wing excuses, eyelash-batting, and eventual tears won't keep her from being held accountable for her actions.

A couple days ago another leftist--a teacher this time, rather than a college student--was held accountable for her execrable behavior:
In a case in which he described Antifa activist Yvette Felarca's legal claims "entirely frivilous," California District Judge Vince Chhabria recently ordered her to pay the $22,000 in legal fees incurred by Judicial Watch, and the $4,000 in litigation costs.

Felarca, a middle school teacher in the Berkeley Unified School District (BUSD), and two co-plaintiffs, had sued the BUSD to try to prevent it from turning over to Judicial Watch their communications mentioning Felarca, Antifa, and BAMN, By Any Means Necessary...

“This is a huge victory for Judicial Watch against Antifa and the violent left,” said Judicial Watch President Tom Fitton. “Ms. Felarca attacked Judicial Watch without basis and the court was right to reject her ploy to deny our ‘right to know’ because we don’t share her violent left views.”
I've mentioned Felarca in other posts.  Real gem, that one.

Wednesday, May 22, 2019


I signed my evaluation form today.  It was 13 pages long.  And I had to do most of the writing.  What a waste of my time and energy.  Things like that frustrate me to no end.

See, it's not so much an "evaluation" anymore as it is a "system of professional growth".  Yawn.  Just tell me if I'm doing a good job, or not.  In case of disagreement, have an appeal process in place.  Seems reasonable to me.

13 pages that I had to write on.  How many trees died unnecessarily for that?

I'm up for another "growth" in 5 years.  If the current program stays in place, that will be my last "growth", as I plan to retire in 9 years.

Tuesday, May 21, 2019

I Wasn't Even A Marketing Major

There's a strip mall on my route to work.  Having worked at the same school for 16 years now, I've passed that strip mall twice a day times 185 days times 16 years...and there was a store in there that would periodically make me wonder.

Dress Barn.

Now, I'm no marketing genius, but in what way is Dress Barn a good name?  No, it's not a "western" clothing store.  It is, as one of my students described it today, a "mom store".  So it seems to me like the name of the store implies that cows shop there--not the image I think they'd want to convey to their female clientele.  It's a name that I always thought was just darned odd.

Oddly enough, it's not in that strip mall anymore.  I didn't notice when the store closed and the sign came down--clearly it didn't captivate my attention--but dang, what a name.

What brings up a post about the name of a women's clothing store?  I saw a headline today:

 I am not shocked at this, not shocked at all.

Monday, May 20, 2019

An Argument For Vouchers

Do you support vouchers for K-12 education, or not?  Why or why not?

Here are a couple points from DC:
Washington, D.C. voucher students did no better in reading and math than students who applied for vouchers but lost the lottery, a new study shows. However the voucher students felt safer and had better attendance, reports Andrew Ujifusa in Education Week.
Arguments for both sides there, but what about this?
Choice provides the same academic outcomes at one-third the cost, concludes Corey DeAngelis in the Washington Examiner. “Public schools in D.C. spend around $28,000 per student each year, while the average private school voucher amount is only around $9,600 per student each year in D.C.”
That's significant.

Sunday, May 19, 2019

Interesting Constitutional Clash

I find Texas' argument compelling:
Texas is asserting its sovereign immunity against Congress, telling Democrats on two congressional committees this week that the state has no obligation to comply with their investigative demands.

Attorney General Ken Paxton’s office says that as a state with sovereign powers under the Constitution, Texas can’t be treated like a federal agency or Cabinet secretary who can be compelled to comply.

“Texas does not draw its authority from the United States or the United States Constitution, but from its status as a dual sovereign within the union,” Jeffrey C. Mateer, first assistant attorney general, wrote in a letter Monday to the House Oversight and Reform Committee.

Mr. Mateer fired off a similar letter Wednesday to the House Ways and Means Committee rebuffing its attempts, saying the state wouldn’t stand to be treated like a “subdivision of the federal government or a private citizen.”

“Granting Congress the power to exercise ‘oversight’ over the constitutional officers of a state engaged in the lawful exercise of that state’s core authority would undermine the fabric of our system of dual sovereignty,” Mr. Mateer wrote.
If a court ordered the turnover of documents, that would be a different story, I think.

Thief Shocked She Is Arrested For Theft

As the article says:
The most amazing thing is the girl’s reaction when she realizes she will be held accountable for her behavior. She is stunned to learn that her outrage over this issue doesn’t override the law. Watch the whole thing below, strong language warning:

Maybe if more students were held responsible for their behavior in this way, we would see fewer students acting out on campus like angry children.
Exactly.  Your feeeeeeeeelings don't excuse your criminal act.

Do you find her excuses as pathetic as I do?

Hometown Story Makes International News

From the UK's Daily Mail:
A pair of bungling vandals tried to key a Tesla car but unknowingly got caught out when its inbuilt security cameras captured their grinning faces in action.

The video, taken by the Tesla Model 3's Sentry Mode, shows the duo walk towards the car with their faces in full view in Sacramento, California.

The car's security system adds a layer of protection and acts like a home alarm system by continuously monitoring its environment when it is left unattended.

The car's cameras show the two men wearing caps walk to the side of the Tesla to a Ram pickup truck parked next to it.

After inspecting the truck's handle and pointing out some marks, one of the men takes out his keys and appears to drags it along the side of the Tesla Model 3 which costs around $49,000.

It is not known if there was a prior incident which caused the men to target the car.

The pair then return to the front of the car to admire their handiwork, blissfully unaware they have given the camera another full view of their faces.

Saturday, May 18, 2019

The Fighting Snowflakes

Maine bans all Native American mascots in public schools:
On the heels of changing the Columbus Day holiday to “Indigenous People’s Day,” the state of Maine has now banned the use of Native American names and mascots in public schools and colleges.

Maine is the first, and thus far only, state to forbid such imagery.

Governor Janet Mills signed the bill into law yesterday. The vote on the bill was divided along party lines, with the Democratic-controlled legislature ultimately prevailing.
I'm sure this solves many non-existent problems and fails to solve any real problems.

Thursday, May 16, 2019

Test Re-takes

In the vast majority of cases, I'm against test re-takes--for the reasons outlined in my school math department's document on why we don't give re-takes in lower level math classes:
What does a grade represent? It’s a difficult question. Some might say that a grade represents student achievement, how much a student has learned in relation to the course content standards—but that’s not exactly accurate. If it were, a student’s grade would be his/her grade on the final exam. So, in reality, a grade is sort of a weighted average of how much a student has learned in relation to the course content standards as well as how well they were able to “stay caught up” in that learning—periodic test and quiz grades, for example. Some say that if a student didn’t know the material last week, but knows it this week, the student’s grade should reflect that. Again, the logical conclusion of that line of thinking is that a semester grade should reflect what a student knows at the end of the semester—it should be the final exam grade.

1. We found test retakes to be detrimental to student learning, as well as an inefficient use of time. Students did not properly prepare for tests and an increase in re-takes became the norm. Students that were both able and willing would come in after or before school and take a retest; those that were unable to were unable to change their grades. This practice promotes inequity (or a similar experience for students, as described by WASC) in the math program.

2. Retakes can artificially inflate a student’s grade but don’t reflect any improvement in student achievement. Students whose grades rely on retakes haven’t truly mastered the material, their grade doesn’t truly reflect the information the grade is designed to convey, and the new inflated grade gives both student and parent a false sense of the student’s math abilities.

3. In response to the drive towards equity, towards interventions (and test retakes count as interventions) during the school day, we have opted to give bonus problems on each test. These bonus problems are key standards, or frequently-missed standards, from the previous chapter’s test—thus, a student who didn’t know the material when the last chapter test was given can, if they know the material now, demonstrate knowledge of that material and earn an extra 10% on the current test. As most teachers capped retest grades at 10% higher than the original test score anyway, this system has several advantages:
a. It doesn’t require additional work, for teachers or for students, outside of the school day. It allows slower students to demonstrate mastery, and earn a higher grade after demonstrating that mastery, during the school day.
b. It requires students to put forth extra effort to learn the material, and it gives them plenty of time (a chapter usually takes a few weeks to cover) to actually master the material before the next chapter test.
c. It eliminates the effect of not being able to ascertain from a student’s grade what the student’s capabilities are. Is the student truly prepared for follow-on math classes, or not?
d. Unforeseen pitfalls of students having re-takes include limiting opportunities to build authentic, academic executive functioning skills. As a result, some students who receive re-take accommodations may be deprived of instructional opportunities to build test taking and study-skills. Teachers, parents, students, and school administrators need to focus on teaching and learning study skills prior to testing as a starting ground. Post-secondary transitions can improve from fading off those accommodations that limit a student’s ability to test according to typical higher-education expectations. (Basically – re-takes eliminate the behavioral parameters that lead to authentic study skills improvement.)
Thus, while retakes, in our minds, are both inefficient and not academically defensible, our own system has the advantages of retakes without the pitfalls.

4. We are not noticing more students failing math classes now that we have eliminated retakes. Students know in advance when tests are given, they are given reviews and even practice tests, and are prepared by their teachers to demonstrate their grasp of the material. Students have had multiple opportunities to demonstrate their knowledge (homework, quizzes, and then a test)—a test is not truly a “one time” shot at demonstrating knowledge and mastery of material.
As they say on social media, "change my mind."

Wednesday, May 15, 2019

Like A Bad Penny

Haven't heard from Jackie Goldberg in awhile, but then her name turns up again:
Jackie Goldberg, a veteran politician and educator who served on the Los Angeles school board three decades ago, will once again have a voice in the nation’s second-largest school district after a resounding win Tuesday for a seat in a special election...

Goldberg was the front-runner, having collected 48% of primary votes, just short of the majority needed to win outright. She had high name-recognition thanks to her previous experience on the school board, the L.A. City Council and in the California Assembly.
All that so-called experience, and nothing of value ever came from it.

When Good Intentions Are Not Enough

Alex Trebek:  "Being a one-party state, believing in unicorns, thinking that the productive members of society will stay in California even if they're taxed to death, being progressive to the point where too many people are so open-minded that their brains fall out."

Jeopardy contestant:  "Why does California have the highest rate of poverty in the US?"
So how is it that California, which has spent nearly $1 trillion on antipoverty programs, has the highest poverty rate in the nation?

Jackson, a fellow at the Pacific Research Institute, suggests that the state’s war on poverty is one of the causes of California’s impoverished state, and why it is home to about one-third of the nation’s welfare population despite having just 12 percent of the population.

It turns out that state and local bureaucrats who administer California’s antipoverty programs have proven stubbornly resistant to pro-work reforms that have been effective at spurring individuals to pull themselves out of poverty. It’s a phenomenon familiar to those who have read the scholarship of economist Robert Niskanen, whose model of bureaucratic behavior suggested that bureaucrats tend to “maximize their own utility” rather than the interests of their constituents.
There's much more at the link.

Tuesday, May 14, 2019

Math and the Electoral College

Whenever liberals don't get the election results they want, they scream about the electoral college.  They want to get rid of it, and pack the Supreme Court, while screaming how it's conservatives who are trashing constitutional values.  Consistency isn't a strong suit of the left, that's for sure.

Anyway, Math With Bad Drawings provides some information about the Electoral College, along with some math problems that even a social studies teacher should be able to follow :-)
The formula for your state’s number of Electors is roughly this: Population/700,000 + 2, rounded to the nearest whole number. Assume that the winner within each state gets all of its Electors.
1. Compute the number of electors for Alaska (737,000 people), South Dakota (882,000 people), Mississippi (2,986,000 people), and Alabama (4,887,000 people).
2. Now, compute the number of electors per capita for Alaska, South Dakota, Mississippi, and Alabama.
3. Under this system, which sorts of states will have the most Electors per capita?
4. Which will have the fewest?
5. Who do you think is more powerful – voters in small states, voters in big ones, or does it not matter? Explain.
Let’s imagine the country were made of 2 states: Megastate, with a population of 1.4 million, and the State of Moe, with a single resident named Moe.
6. How many Electors does each state receive?
7. How many Electors per capita does each state have?
8. Whose vote has a better chance of swinging the election: Moe’s, or a voter’s in Megastate? Think carefully, and explain!
9. What does this two-state scenario tell us about the usefulness of “Electors per capita” as a measure of power?
10. What is another way we could measure a voter’s power?

Currently, 48 out of 50 states apportion their Electors on an all-or-nothing basis: the winner of the statewide vote gets all of the Electors.
Imagine if states switched to a proportional system, whereby if you win X% of the vote in a state, you get X% of the Electors (rounded to the nearest whole number).
1. Suppose that Minnesota votes 68% for A, 30% for B, and 2% for C. How should it apportion its 10 electors? Explain.
2. Suppose that Minnesota votes 53% for A, 44% for B, and 3% for C. How should it apportion its 10 electors? Explain.
3. How would the effect of this change be different for big states like California (with 55 electors) than for small states like Vermont (with 3 electors)?
4. Imagine going to Hawaii (which usually votes Democrat) and asking a Democrat and a Republican whether they support this change. What do you think they would say, and why?
Imagine if states switched to a district-by-district system. For example, if a state has 5 electors, it breaks its voters into 5 districts, and assigns an elector to the winner of each.
5. Suppose that in Massachusetts, this has no effect on the electors. What does that tell us about Massachusetts? Be specific.
6. Suppose that in New Hampshire, this has a big effect: instead of winning all 4 electors, the Democrat now wins only 2. What does this tell us about New Hampshire? Be specific.
7. Suppose a Republican and a Democrat in New Hampshire are each asked to divide the state into districts. Do you think they’d make similar divisions? Why or why not?

Monday, May 13, 2019

A Potemkin State

We have some very real problems in Cali-unicornia:
A plan by California’s biggest utility to cut power on high-wind days during the onrushing wildfire season could plunge millions of residents into darkness. And the vast majority isn’t ready.

The plan by PG&E Corp. comes after the bankrupt utility said a transmission line that snapped in windy weather probably started last year’s Camp Fire, the deadliest in state history. While the plan may end one problem, it creates another as Californians seek ways to deal with what some fear could be days and days of blackouts…

"I’m worried," Newsom said Thursday during a budget briefing in Sacramento. "We’re all worried about it for the elderly. We’re worried about it because we could see people’s power shut off not for a day or two but potentially a week."
Our governmental officials like to tout that we're the world's 5th (or so) largest economy, and that may be so, but we're getting more and more like a Third World country.

You know, there are places in the country with extreme weather where the power doesn't go out.  Just sayin'.

Sunday, May 12, 2019

How The Cool Kids Spend Saturday Night

The Robert and Margrit Mondavi Center for the Performing Arts is a rather nice venue at UC Davis.  Before last night I'd been there twice before, once to see Margaret Cho perform and once to see a student of mine play concert piano.  Last night, though, I was there for a different reason:

That's right, there was a special screening of Star Trek II: The Wrath of Khan followed by an hour talk/Q&A with Shatner and the UC Davis chancellor, who is also a Star Trek fan.

It wasn't a convention, but there was certainly some of the convention vibe. Some people even showed up in uniform. Others of us just represented:

When the opening credits began, there was clapping and cheering as each actor's name appeared on the screen. And later in the film when Kirk cried out his iconic "Khaaaaaaaaaaaaaaan!", the auditorium erupted.

After the movie the chancellor and the Captain had a one-hour talk up on the stage. Shatner likes to tell stories, and he overacts when telling stories as much as he does on screen. He has a wit about him, but I wish they'd talked a little more about Star Trek in general and Wrath of Khan in particular, though.

When the talk was over, those of us who'd signed away our firstborn children took our VIP passes and were led backstage, where we got a picture with the Captain. There was no time for chit-chat or autographs or anything like that--just stand next to him, take the picture, and go. There were 2 women in front of me in line, so when I approached Shatner I said, "All these good-looking women, and now you get me." He smiled at that, we took the picture, and just before I walked off he looked me in the eyes and said, very quietly so that it seemed a personal moment only between us, "Thank you." Just as quietly I said, "Thank you", and that was it.

This morning I got to download my picture with him:

While he doesn't look bad for 88 years old, he's still 88 years old.  I can't imagine it'll be too much longer before he joins so many of his crew already in the cosmos.  That's why I paid extra for my less than 10 seconds with him--10 seconds, and those few words that passed between us.

Saturday, May 11, 2019

A Nice Way To Recognize Students

I see nothing wrong, and quite a lot that's good, in this:
High schools across the country are highlighting their soon-to-be graduating students' intentions to join the military.

Similar to college or athletic "signing days" — in which high school students officially or ceremonially declare the place of higher education they've committed to — schools are increasingly hosting "military signing days."

The Very Definition of Heinlein's "Crazy Years"

Liberals pretend to believe that it's perfectly reasonable for boys to compete in girls' sports, and that you are the horrible person for thinking that's crazy:
When two high school athletes who were born male but identify as female took first and second place at Connecticut’s girls indoor track championship this year, it wasn’t just a local news story.

To some, it was a story of triumph and courage. The winner, a junior from Bloomfield High School, set a girls state indoor record of 6.95 seconds in the 55-meter dash, and went on to win the New England titles in both the 55-meter dash and the 300-meter dash.

To others, it was a story of shock and disappointment: Is this the end of women’s sports?

To Selina Soule, a 16-year-old runner from Glastonbury, it was personal.

A junior, Selina missed qualifying for the 55-meter in the New England regionals by two spots. Two spots, she said, that were taken by biological boys.

Had the boys who identify as girls not been allowed to compete, Selina would have placed sixth, qualifying to run the 55 in front of college coaches at the New England regionals.

Instead, she placed eighth, watching the 55 from the sidelines after qualifying in only the long jump, an event in which the transgender athletes didn’t compete.

“It’s very frustrating and heartbreaking when us girls are at the start of the race and we already know that these athletes are going to come out and win no matter how hard you try,” Selina told The Daily Signal. “They took away the spots of deserving girls, athletes … me being included.”

While the debate over transgender athletes and fairness is complex, the situation in Connecticut has brought forth another complicating layer: Plenty of parents and high school girls appear to object to the participation of biological boys in girls sports, but fearing public bullying and backlash, they’re not speaking out.

Publicly, at least.
As I said, the Crazy Years.

Thursday, May 09, 2019

Don't Like It? Don't Eat There.

The pro-abortion crowd likes to trumpet, as if they're being witty, "If you don't like abortion, don't have one."  Those of us who are pro-life don't think it's asking too much to insist that you not kill an innocent child.  Abortion for us isn't about "controlling women", which is the straw man lefties like to make and tear down, it's about the killing.

But the same type of person who says "If you don't like abortion, don't have one" can't even live by their own stupid sound bite.  They don't like a company run by an avowed Christian, so they don't want to let anyone eat there:
Cal Poly will not remove Chick-fil-A from its San Luis Obispo campus, despite renewed calls to do so by faculty and students who criticize the company’s public and vocal support for anti-LGBTQ groups and causes.

Student, faculty and community groups say they want to remove the restaurant because the company’s values are contrary to those of Cal Poly, which has made efforts to be more inclusive of marginalized groups.

On Tuesday night, Cal Poly’s Academic Senate overwhelmingly voted to urge the university to terminate its contract with Chick-fil-A, according to KCBX.

But Cal Poly administrators say that to remove the fast food chain from campus “would be its own form of censorship and intolerance.”
By the way, I hadn't heard of Chick-fil-A 20 years ago.   Now it trails only Starbucks and McDonald's as the country's 3rd-largest restaurant chain.

Read more here:

Read more here:

Demonstrating Liberal Hypocrisy

Seen on social media:

Wednesday, May 08, 2019

Some Will Be Happy It's A Majority

I won't be happy until it's a 90+% supermajority:
A majority of respondents say that socialism is incompatible with American values, a Monmouth University poll released Monday says.  link

I've Long Been A Fan of Bjorn Lomborg

My favorite gay leftie Danish vegetarian statistician continues to be dead right about global warming.

Here's more about him.

Tuesday, May 07, 2019

Abysmal, But Stereotypical, Behavior

While I've had one or two minor encounters with individual union reps, I've never had negative experiences with my local union itself.  Don't these people know they're going to lose, and don't they care how this makes them look?
A California educator is battling a state teachers' union over his problems leaving the organization, in what his attorneys say could be a precedent-setting legal case that ultimately forces labor unions across the country to reimburse billions in back dues to their members.

Tommy Few, a special education teacher at Sepulveda Middle School in Los Angeles’ San Fernando Valley, filed suit late last year against the United Teachers of Los Angeles – along with the Los Angeles Unified School District and California Attorney General Xavier Becerra – claiming his First Amendment rights to freedom of speech and association were violated when he tried to leave the UTLA following last summer’s Supreme Court ruling in Janus v. AFSCME.
I'd ask if they have no shame, but we already know the answer to that question.

Monday, May 06, 2019

"Algorithms of Suppression"

In an article entitled Algorithms of Suppression, the Claremont Institute tells us:
The Claremont Institute has launched a campaign to engage our fellow citizens in discussion and debate about what it means to be an American. As part of that effort, we have begun to point out the increasingly existential danger of identity politics and political correctness to our republic. As if to prove our point, Google has judged our argument as wrongthink that should be forbidden. They are now punishing us for our political thought by refusing to let us advertise to our own readers...

Google, either its algorithm or some individual, had a look at my essay launching our new campaign for a unifying Americanism, “Defend America—Defeat Multiculturalism.” They decided it to be in violation of their policy on “race and ethnicity in personalized advertising” and shut down our advertising efforts to American Mind readers. We weren’t “advertising” anything in the essay, of course, but the relevant section of their policy lists “racially or ethnically oriented publications, racially or ethnically oriented universities, racial or ethnic dating” as examples of violations.

Somebody must have determined we were offering “racially or ethnically oriented publications.” This is news to us. The Claremont Institute has spent forty years teaching all who are willing to listen that the meaning of the proposition that all human beings are created equal is the central, animating principle of American political life.
Google later admitted to "a mistake", but I can't help but wonder why all such mistakes lean one way politically. 

Too many people, mostly our friends on the Left, like to make reference to President Eisenhower's Farewell Address in which he warned about the "military-industrial complex".  Those same people, though, should read the entire address, as Eisenhower also warns us:
[I]n holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientific-technological elite. 
He was prescient, that Eisenhower fellow.

I Am Absolutely Against This

Our service academies exist for one reason and one reason only:  to provide junior officers for their parent services.  West Point exists to provide army lieutenants, the Naval Academy exists to provide naval ensigns, and the Air Force Academy exists to provide air force lieutenants.  These academies do not exist to provide talent for professional sports:
President Donald Trump presented the Army Black Knights with the Commander-in-Chief's Trophy Monday, calling the group "star athletes and stars in every way."

The President then made some news, saying he's looking at "doing a waiver for service academy athletes who can get into the major leagues," adding that those players can serve in the military after they play professionally. 
"I think it's a great idea, I think it's really fair, too," he said.
You might wonder why West Point has a football team if the academy's purpose is to produce army officers.  The purpose is to produce good officers. 

"Every cadet an athlete."  That is one of the foundations of a West Point education.  General George Marshall, Chief of Staff during World War 2, is quoted as saying, "I want an officer for a secret and dangerous mission.  I want a West Point football player."  Obviously every cadet cannot participate in intercollegiate athletics, but those who don't do so will participate in intramurals.  This is in addition to required PE classes and more-than-a-couple-times-a-year physical fitness tests of one sort or another.  Individual sports (boxing, swimming, wrestling, martial arts) build fitness, and team sports build leadership and teamwork.  That these are attributes we want in young military officers should go without saying. 

Our sports programs exist to help produce better junior officers.  The men and women who attend our service academies are supposed to be there to serve the country.  They can serve their country first and then "get into the major leagues" if they so desire.  Reversing that, as the president has suggested, encourages "self" over the military and the country.  That is not what our academies should be promoting.

Saturday, May 04, 2019

Math Humor

CO2 Is Good For Humans And Other Living Things :-)

If nothing else, you've got to enjoy the thought of all these congresspeople getting their panties in a bunch upon hearing this:
Climate statistician Dr. Caleb Rossiter from the CO2 Coalition hijacked the Democratic Rep. Alexandra Ocasio-Cortez and the Democrats (sic) climate hearing on Capitol Hill on April 30. Dr. Rossiter upended the House Oversight Committee Environment subcommittee hearing on “The Public Effects” of climate change when he declared “CO2 emissions have had a positive and modest impact on Americans’ health.” Rep. Ocasio-Cortez saw her message “hijacked” by the skeptical scientist.
My favorite line:
Climate Statistician Dr. Caleb Rossiter: ‘We are trying to save the people of the planet from the people ‘saving the planet.'”

School Discipline

These same people wouldn't put up with the ridiculous crap for 5 minutes that they want me to put up with for the next 9 years:
American adults surveyed about improving school discipline tended to favor supportive solutions, like school climate efforts and additional training for teachers, over stricter practices like detentions or suspensions.

The poll, conducted by Gallup on behalf of Communities in Schools, found that 43 percent of respondents believe most teachers are "prepared" or "very prepared" to handle discipline issues in the classroom. And 54 percent of respondents said most teachers are "unprepared" or "very unprepared" to handle discipline...

Of the survey respondents, 90 percent said that, in addressing discipline issues, it would be "very effective" or "somewhat effective" to provide more training for educators on appropriate discipline practices.  link
At least 90% of teachers would like more parents to get more training on effective discipline practices at home.  That way, we wouldn't have to discipline their kids so much.

Thursday, May 02, 2019

George Washington Is Traumatizing

I doubt the people claiming to be traumatized even notice George when they pull out a buck and a quarter, so forgive me if I find their claims to be a little, uh, manufactured.  But here we go in Cali-unicornia, where every culture is valued except the one that made us the greatest place to live in the world:
A high school in Northern California — George Washington High School, to be specific — is mulling over a push to remove two 83-year-old murals from its hallways. Critics advocating for their removal say they are offensive to Native Americans and African-Americans. They say the pair of panels “traumatizes students and community members.”
Former US Secretary of Education Margaret Spellings once said what I consider to be the appropriate response to these people, whether they're actually traumatized or not:  "Put your big girl panties on and deal with it."

Credit Recovery

A summary for the uninitiated:  "credit recovery" is a way for students who don't have enough credits to graduate to earn beaucoup credits in a very short time, and thus graduate.  Most credit recovery schemes are online programs that allow a student to earn credit for a course in just a few weeks--even though that student failed the course when offered 18 or 36 weeks (a semester or school year) to complete the course.

Allow me to be blunt:  credit recovery is a scam.  It's a huge money-maker for the online companies who offer the programs, and it's a lie to the taxpayers who are supposed to celebrate when graduation rates go up (even as learning goes down).  It's very name, credit recovery, tells you where the emphasis is, and it's certainly not on education.  We in this field should stand against this blatant lying--lying to the taxpayer, to the employer who thinks a high school graduate has some minimal learning, to the student him/herself--but our administrators worship at the altar of credit recovery as if it were the Golden Calf itself.  What should be a disgrace to our profession is instead given a perverse place of honor as a savior of the very students it is purported to help.

Perhaps you're not in the education field, perhaps you think I'm exaggerating.  I'm not:
Many other districts stopped short of outright fraud, opting to juice the graduation rate by expanding credit recovery programs with exceptionally low standards, allowing students to sit in front of a computer and effectively shotgun enough credits to be granted a diploma.

This fakery and inflation has significant, if unmeasurable, costs. Off record, teachers speak of its depressing effects on the classroom: students who try hard become demotivated when they see slackers receiving equal credit, and slackers put forth even less effort when they realize they don’t have to. Students lose respect for the school when they realize that whether they learn enough to graduate matters less than whether adults can take credit for their graduation.

Second, graduation inflation does significant harm to students who – despite all the standard-lowering – don’t graduate. Education advocates argue that students need a high school diploma to be employable in the 21stcentury. But this is a self-fulfilling policy driven by credentialism, not skill acquisition.

In a city where 50 percent of students graduate, employers would not automatically stigmatize half of its young adult workforce. But in a city where 90 percent of students graduate, employers would have good reason to suspect that there is something wrong with the 10 percent who don’t. Shut out of the labor market, those young adults will have few opportunities other than crime. Unless schools are actually equipping at-risk students with more skills, graduation inflation will streamline the “school-to-prison pipeline.”

Third, graduation inflation allows activists to pass off destructive policies as effective reforms. Putting students in front of screens all day may do nothing to boost academic achievement even as it makes them more depressed and anxious-- but graduation rates are up so it worked! Reducing suspensions may harm academic achievement and make classrooms more chaotic– but graduation rates are up so it worked! As American schools implemented the Common Core and test-based teacher evaluations, academic achievement for low-performing students saw an unprecedented drop– but graduation rates are up so it worked!

Graduation inflation is an excellent case study in what some call “structural oppression” or “institutional racism.” Self-interested politicians, privileged advocates, and lazy journalists all have their own status incentives to promote and cheerlead graduation inflation. They’re all, perhaps, largely unconscious of how their policies and rhetoric perpetuate racial inequity.

Adding To The Cost of a College Education...

Textbooks are ridiculously expensive, and probably will get more so:
Now experts worry the challenges students face in order to pay for course materials are about to get worse. McGraw-Hill and Cengage CNGO, +109.68% two major textbook publishers, announced Wednesday that they would merge, creating the second-largest supplier of textbooks and higher-education materials. Right now, five companies control about 80% of the textbook market and, if the merger is approved by regulators, that number could go down to four.

“The textbook market is already highly concentrated and this just takes it and puts it into fewer hands,” said Nicole Allen, the director of Open Education at the Scholarly Publishing and Academic Resources Coalition (SPARC), which advocates for more open sharing of educational materials. “Students are already captive consumers in this and this would just make it worse.”

Dessert Social Comment

One of the events I look forward to as the school year ends each year is the AVID Dessert Social.  The juniors in our AVID program bring desserts and other snackies for the senior AVID students as well as the teachers--as a sort of "farewell" to the seniors and a "thank you" to the teachers.  Today there were cookies, cakes, pies, chips, ice cream, etc.  It's a great way to spend a lunch :-)

What really got my attention was the comment of one of the seniors in line in front of me.  After remarking on the voluminous goodies arrayed in front of us he said, with obvious relish, "Good-bye, Michelle Obama."

Made my day!

Wednesday, May 01, 2019

I Know How To Solve The College Cost Problem!

First, the problem:
When it comes to preaching financial savvy to college students forking over considerable cash for school, the “back in my day” argument doesn’t apply.

Working hard and living at home can only go so far in staving off debt for today’s students because of steep fee increases that have unfolded over the past 40 years, according to the California Budget and Policy Center determined in a recent data analysis.

The center adjusted 1979 college tuition and fees for inflation and found the cost of attending a University of California school is six times greater than 40 years ago. A year at UC today costs $14,400, up from an inflation-adjusted $2,200 in 1979.
Let's look at administrative bloat.  Let's look at the cost of "diversity" initiatives.  Here in California, let's factor in illegal immigrants, just for fun.  Let's look at the amenities that schools generally didn't have in 1979 that they have today--the ever-popular rock-climbing walls, the buffet meals, "free" wi-fi.  Do the dorms look anything like what they looked like in 1979?

I'm not convinced that "inflation-adjusted dollars" captures the entire issue.  But I'll play along, let's start cutting the diversity offices and so-called Bias Response Teams.  Oh, and students?  Quit voting for higher fees! (I'm talking to you, UC Davis Aggies, who have voted yourselves the highest fees in the UC system.)  And maybe schools shouldn't accept students who need remedial math or English work--so those students won't have to worry about the cost of a CSU/UC degree and can go to community college instead (where lesser-prepared students belong).

Any other ideas?

Did People Ever Take These Seriously?

From the very beginning the idea of "traffic school" was a scam, a racket.  I'm supposed to be upset now because the scam is online?
Just when you thought things could not get any worse for the California Department of Motor Vehicles, the beleaguered bureaucracy sinks even lower into disrepute.

This time, the DMV has been caught asleep at the wheel in its duty to provide oversight for the traffic schools California drivers must “attend” in order to clear speeding tickets from their official driving records.

“A few owners of online traffic schools in California have taken advantage of loose oversight by the Department of Motor Vehicles to stifle competition and boost their share of customers among the roughly 670,000 ticketed drivers who enroll in the schools every year,” according to a news story by The Sacramento Bee’s State Worker reporter Wes Venteicher.

Once upon a time, drivers had to attend actual traffic schools in classrooms to clear minor infractions from their records. Over the past two decades, the schools morphed into an online industry. In order to compete for business, these “schools” bear names like No Study Traffic School, Easy Daddy Traffic School and Five Dollar Traffic School.

Clearly, the owners of many of California’s 3,000 traffic “schools” do not pick their names in an effort to convey seriousness or competency. The ridiculous naming trend persists despite rules barring any name that “implies that the school offers inducements or premiums which derogate or distort the instruction intent of the traffic violator school program.”

Idiots Traffic School and 4 Lazy Traffic School seem in clear violation of the DMV’s solemn principles.
"DMV" and "solemn" in the same sentence? I wonder if that's ever happened before.

Tuesday, April 30, 2019

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.

Monday, April 29, 2019

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.


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.

Sunday, April 28, 2019

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.

Saturday, April 27, 2019

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.

Thursday, April 25, 2019

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!

Wednesday, April 24, 2019

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:

Monday, April 22, 2019

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
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.

Sunday, April 21, 2019

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.


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.

Furst, E. (2018) Understanding ‘Understanding’  in blog Bridging (Neuro)Science and Education
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.

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