The power of intensive tutoring

At Chicago Vocational Career Academy, which is desperately trying to raise its test scores and graduation rate, nearly all students come from low-income black families. Most ninth graders are years behind in reading and math. Intensive tutoring provided by MATCH Education is helping students catch up, reports Maya Dukmasova in the University of Chicago Magazine.

On a day in early June, three girls sat face to face with tutors in the Math Lab, which they attend in addition to their normal math class.

They were working on division with unknown variables. “Number 23 is a little curveball but I bet you can do it,” Nichole Jannah, a recent college graduate, told her student.

Math tutor Amelia Hansen works with one student at a time. Credit: Maya Dukmasova

Math tutor Amelia Hansen works with one student at a time. Credit: Maya Dukmasova

Veronica, a freshman, started the year with a D in math. With daily help from a tutor, she finished the year with a high B.

Sarah, also a freshman, raised her math grade from a C to an A with the help of her tutor. “When I go into math class, I fly through work,” she said, snapping her fingers.

“Everything in education policy right now is about getting teachers to do a better job teaching grade-level material,” says Jens Ludwig, who co-directs UC’s Education Lab. But good algebra teaching can’t help students who haven’t mastered third-grade arithmetic.

Being able to successfully teach in the classroom involves years of practice and training in pedagogy and classroom management. . . . To get results as a tutor, he says, requires only knowledge of the material, good rapport with people, and commitment.

MATCH recruits recent college graduates — and a few career switchers — who are willing to work full time for $17,000 a year plus benefits.

Before the school got MATCH tutors in fall 2013, the first-year on-track rate — the percentage of freshman passing all their classes — was in the low 70s. Now 86 percent are on track to graduate.

CVCA was able to cancel its summer credit-recovery classes for failing students, writes Dukmasova. “Instead the school focused on offering higher-level math and honors courses.”

Teen wins $250K for film on relativity

A movie explaining Einstein’s theory of relativity won a $250,000 college scholarship for Ryan Chester, a Ohio 12th grader, reports the Washington Post.

Chester also won $100,000 for a new science lab at his school in the Cleveland suburbs, North Royalton High, and $50,000 for his physics teacher, Richard Nestoff.

“This is awesome,” Chester, 18, said in an interview. “Before, I was worried about graduating with debt, and I don’t have to worry about that now.”

The Breakthrough Junior Challenge asked young people between ages 13 and 18 to create short videos that communicated a big idea in science.

Google’s Sergey Brin, Facebook’s Mark Zuckerberg and other Silicon Valley entrepreneurs created Breakthrough Prizes to reward achievement in physics, life sciences and mathematics.

Show your thinking

Peter from Texas posted this on Tumblir.

The problem with ‘explain your answer’

Once upon a time, math students were told to “show your work.” Now, for some questions on Common Core-aligned tests, they must “explain your answer” in words (or words and pictures). The goal is to test if students understand what they’re doing, but “explain your answer” is misguided, argue Katharine Beals and Barry Garelick in The Atlantic.

Here’s a problem: “A coat has been reduced by 20 percent to sell for $160. What was the original price of the coat?”

A student may show the solution as follows:

x = original cost of coat in dollars
100% – 20% = 80%
0.8x = $160
x = $200

But this isn’t adequate to show understanding — not any more.

They describe a middle school that uses 10 percent of class time to teach students how to explain their solutions to two to three problems each week. The model is called “Need, Know, Do.”

. . . the “Need” would be “What was the original price of the coat?” The “Know” would be the information provided in the problem statement, here the price of the discounted coat and the discount rate. The “Do” is the process of solving the problem.

Students were instructed to use “flow maps” and diagrams to describe the thinking and steps used to solve the problem, after which they were to write a narrative summary of what was described in the flow maps and elsewhere.

. . . in order for their explanation to qualify as “high level,” they couldn’t simply state “100% – 20% = 80%”; they had to explain what that means. For example, they might say, “The discount rate subtracted from 100 percent gives the amount that I pay.”

“While drawing diagrams or pictures may help some students learn how to solve problems, for others it is unnecessary and tedious,” write Beals and Garelick.

Furthermore, “there is no more evidence of ‘understanding’ in the explained solution, even with pictures, than there would be in mathematical solutions presented in a clear and organized way.”

Requiring a verbal explanation to prove understanding handicaps English Learners, students with autism and others whose mathematical talents outpace their verbal skills, they argue.

“If a student can consistently solve a variety of problems, that student likely has some level of mathematical understanding.”

‘She got confused’

Why did Sally count by ones, then by tens and then by ones? “She got confused” sounds like a right answer to me.

The question comes from New York’s EngageNY math, Grade 2 – Module 3, writes Catherine Johnson on Kitchen Table Math, the sequel. It’s supposed to be about “skip counting,” which is one of the things the modern second grader is supposed to master.

Johnson turns it into a story problem:

Sally has pennies and dimes in her pocket.
Her friend Jane sells her a glass of lemonade for $2.14.
Sally gives her $1.77.
How many more pennies and dimes does Sally owe?

I still think someone got confused.

The search for a ‘fair’ math test

The Quixotic Search for a “Fair” Math Test ends in tests cleansed of “idiosyncrasy and irregularity,” writes Ben Orlin on Math With Bad Drawings.

We want our tests to be objective. So we stop testing fuzzy, hard-to-measure things like creativity, insight, and broader perspective.

We want our tests to be consistent. So we stop asking questions with any degree of novelty or surprise.

We want our tests to be fair. But deep and authentic understanding is hard to measure fairly — much harder than procedural fluency — and so in the end we abandon that, too.

A colleague believes “every math test is, at its heart, a Turing test.”

Is there a thinking intelligence behind those answers? Or are they just the mechanical replies of a robot, blindly executing an algorithm? Can the test-taker really reason about mathematics, or can they merely fill a few pages with the right symbols?

Scottish students protested a question about a crocodile’s best strategy in stalking a zebra was too hard, Orlin writes. At least, they didn’t say they were too upset by the zebra’s fate to do the math.

Core confusion? Math scores drop

Math scores are down in grades four and eight on the 2015 National Assessment of Educational Progress, the first decline in 25 years. Only 40 percent of fourth graders and 33 percent of eighth graders were proficient or better.

Fourth-grade reading scores were flat with 36 percent of fourth graders scoring proficient or above. Thirty-four percent of eighth graders were reading at grade level or better, a slight decrease.

The transition to Common Core standards may explain the math decline, education officials told the New York Times. The largest score drops on the fourth-grade math exams were on data analysis, statistics and geometry questions, which are not covered in that grade under the new standards.

In addition, “about a quarter of public school students are Hispanic, compared with fewer than 10 percent in 1990,” notes the Times.  Only 21 percent of Hispanic fourth graders scored proficient or above on reading tests, compared with 46 percent of white students.

The proportion of African-American students in public schools has remained about the same.

Baseball lessons

Juan Lagares scored twice in game 1 of the National League playoffs to help the Mets win. Photo: David J. Phillips, Associated Press

Edutopia links to baseball-themed activities for the World Series.

Statistics is a natural. The National Council of Teachers of Mathematics (NCTM) offers Baseball Statistics Lesson Plans for grades 6-8,  a baseball statistics lesson for grades 3-5 and a geometry lesson for students in grades 6-8.

A star pitcher in the Negro Leagues, Satchel Paige was 43 when he started in the Major Leagues.

A star pitcher in the Negro Leagues, Satchel Paige was 43 when he started for the Cleveland Indians.

There are baseball-linked lessons in other subjects too. The Negro League eMuseum features primary sources, including a timeline and history modules covering various Negro League teams, as well as lesson plans for teachers.

Other lessons include: Narrative, Argumentative, and Informative Writing About BaseballBaseball Economics and The Physics of Baseball.

When I was in school, kids would sneak in transistor radios to follow the World Series, catching each other up during passing periods. Without weeks of playoffs first, the Series was more exciting.

Don’t kill the kitten

Via Curmudgeon.

Perplexing puzzles

Professor Povey’s Perplexing Problems include math and physics problems.