Tag Archives: matematica


Reforma uitată (o scurtă descriere)
La începutul anilor ’80 a avut loc o amplă reformă a predării matematicii în România, cu efecte negative asupra capacităţii elevilor de a înţelege şi folosi noţiunile predate. Din dorinţa de a ridica nivelul performanţei olimpice, sistemul şi-a confruntat elevii cu un mod de predare a matematicii mult peste puterea de înţelegere vărstei. Ca urmare, tot mai mulţi elevi au absolvit şcoala cu deficienţe serioase în înţelegerea noţiunilor de bază din matematică, dar şi de gândire în general. A urmat un lung şir de încercări de remediere a situaţiei, prin noi reforme şi noi programe.

Oare cum de am priceput şi iubit geometria noi, cei care am învăţat înainte de 1980 din manualele profesorului Hollinger, atunci când scriam ∢A = 60˚ în loc de mult mai riguroasa scriere m(∢A) = 60˚? Noi nu am învăţat despre congruenţă, dar am înţeles geometria. La noi intersecţa a două drepte, de exemplu a diagonalelor unui trapez, se scria AC ∩ BD = O, pe când ca profesor, după 1990, nu aveam voie să scriu decât varianta AC ∩ BD = {O} corectă prin prisma teoriei mulţimilor.

Pentagonia – Arta predării matematicii
Orice meserie îşi are artiştii săi, cei care o practică atât de bine încât rezultatul muncii lor să devină o încântare. Chiar şi predarea matematicii poate fi practicată ca o artă, făcută să încânte, iar beneficiarul acestei încântări va fi elevul. Predarea la ora de matematică trebuie să aducă bucurie elevilor: cât mai des şi cât mai multor elevi!

Racial Equity Requires Teaching Elementary School Teachers More Mathematics
The understanding of the area of a rectangle and its relationship to multiplication underlies an understanding not only of the multiplication algorithm but also of the commutative law of multiplication, the distributive law, and the many more complicated area formulas. Yet in my first visit in 1986 to a K-6 elementary school, I discovered that not a single teacher knew how to find the area of a rectangle.
“What is the area of a rectangle that is x high and y wide?” I asked. There was no response, so I asked the question again. “What is the area of a rectangle that is x by y?” The teachers were very friendly people, and they know how frustrating it can be when no student answers a question. “x plus y?” said two in the front simultaneously. “What?!!!” I said, horrified. Then all fifty of them shouted together, “x plus y.” Apparently my nonverbal reaction had not been a sufficient clue that the original answer was wrong.
American Methematical Society

The Math Question That Went Viral
So what makes Singapore so good at a subject with which America’s students have routinely struggled? Singapore’s math instruction focuses heavily on mastery over rote memorization. Math students on the small island nation perform well because they understand the material deeply—not because they are studying for a specific test. Thus, they react well when “curveballs” are thrown at them in the form of confusing math questions.
And even though the “Cheryl’s Birthday” question may be atypical of the average Singaporean classroom, perhaps it’s still worth asking: Are you smarter than a (Singaporean) 10th-grader?
The Atlantic

The Common Core makes simple math more complicated. Here’s why.
This math is frustrating to parents and to some students — with good reason. Elementary school math has become more complicated since the introduction of the Common Core state standards, which require that elementary school kids not just know how to subtract, multiply and divide, but understand what they’re doing and why.
Arithmetic has usually been taught like it’s a recipe: Take the raw ingredients (the numbers), follow a series of steps, and end up with a result (the answer). While an experienced baker knows why you cream butter and sugar before adding eggs, then add flour last, a beginner just following the steps is in the dark. They might know what to do, but they can’t explain why.

How Elementary School Teachers’ Biases Can Discourage Girls From Math and Science
In math, the girls outscored the boys in the exam graded anonymously, but the boys outscored the girls when graded by teachers who knew their names.
The boys who had been encouraged when they were younger performed significantly better. The girls who had been discouraged by their elementary schoolteachers were much less likely than the boys to take advanced courses.
The researchers also found that discouragement from teachers in math or science wound up lowering students’ confidence in other subjects at school, showing again the potential importance of nods of encouragement.

New York Times

Learn math without fear, Stanford expert says
People with “number sense” are those who can use numbers flexibly, she said. For example, when asked to solve the problem of 7 x 8, someone with number sense may have memorized 56, but they would also be able to use a strategy such as working out 10 x 7 and subtracting two 7s (70-14).
When students are stressed – such as when they are solving math questions under time pressure – the working memory becomes blocked and the students cannot as easily recall the math facts they had previously studied. This particularly occurs among higher achieving students and female students.
Some estimates suggest that at least a third of students experience extreme stress or “math anxiety” when they take a timed test, no matter their level of achievement. “When we put students through this anxiety-provoking experience, we lose students from mathematics.”
Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts

In education-crazy South Korea, top teachers become multimillionaires
This is a society in which you have to get into the right kindergarten, so that you can get into the right elementary school, then into the right middle school and high school, and finally into the right college. Which, of course, gets you the right job and scores you the right spouse. Here, teaching pays: Cha said he earned a cool $8 million last year.
Washington Post