# Homework 2004 Ford

If you walk into a typical teachers’ workroom and ask the question, “What’s the purpose of homework?” you’ll likely find that most teachers have a definite opinion.

- Homework teaches students responsibility.
- Homework gives students an opportunity to practice and refine their skills.
- We give homework because our parents demand it.
- Our community equates homework with rigor.
- Homework is a rite of passage.

But ask them what research says about homework, and you’ll get less definitive answers. What does research really say about homework as a strategy to improve student achievement?

When I was reviewing the research prior to writing *Classroom Instruction that Works, 2 ^{nd} ed*

*.,*I looked at a wide review of the effects of homework on student achievement. It became clear that the effects of homework on student achievement are not entirely clear. A number of factors, such as degree of parental involvement and support, age of the student, homework quality, students’ learning preferences, and structure and monitoring of assignments can affect the influence of homework on achievement (Hong, Milgram, & Rowell, 2004; Minotti, 2005).

One synthesis of research on the relationship between homework time and achievement showed some gains at the middle and high school levels, but less so at the elementary school level (Cooper, Robinson, & Patall, 2006). Others have found that homework can help students strengthen their self-regulation skills such as managing time, setting goals, self-reflecting on their performance, and delaying gratification (Ramdass & Zimmerman, 2011).

On the flip side, there’s some research highlighting negative aspects of homework, including disruption of family time, stress, conflicts between student and parent, and restricted access to community and leisure time (e.g., Coutts, 2004; Warton, 2001).

So what’s the best approach to take? In Cathy Vatterott’s 2009 book, Rethinking Homework: Best Practices That Support Diverse Needs, she outlines practices she refers to as her “New Paradigm for Homework”:

- design quality homework tasks;
- differentiate homework tasks;
- move from grading to checking;
- decriminalize the grading of homework;
- use completion strategies; and
- establish homework support programs.

If you take Vatterott’s recommended practices along with the research-based recommendations found in Classroom Instruction That Works, 2nd ed., you can begin to view homework differently, as an extension of practice and a chance to deepen understanding of a topic. Consider these tips:

- Always ask, “What learning will result from this homework assignment?” The goal of your instruction should be to design homework that results in meaningful learning.
- Assign homework to help students deepen their understanding of content, practice skills in order to become faster or more proficient, or learn new content on a surface level.
- Check that students are able to perform required skills and tasks independently before asking them to complete homework assignments.
- When students return home, is there a safe and quite place for them to do their homework? I have talked to teachers who tell me they know for certain the home environments of their students are chaotic at best. Is it likely a student will be able to complete homework in such an environment? Is it possible for students to go to an after school program, possibly at the YMCA or a Boys and Girls Club. Assigning homework to students when you know the likelihood of them being able to complete the assignment through little fault of their own doesn’t seem fair to the learner.
- Consider parents and guardians to be your allies when it comes to homework. Understand their constraints, and, when home circumstances present challenges, consider alternative approaches to support students as they complete homework assignments (e.g., before-or after-school programs, additional parent outreach).

Because the research on homework is mixed, teachers should think carefully about what tasks they assign for homework, and what the purpose of that homework truly is. Remember that it’s essential for students to receive feedback on their homework so that they know what they did correctly, what they did incorrectly, and what they need to do next to improve.

One final note – students should not be able to pass, nor should they fail a class based on homework. I have seen some course syllabi indicating homework comprised 30% or more of the final grade. A course grade should be based almost entirely on how well a student has mastered the content. If a student earns all A’s and B’s on tests and in-class assignments, they shouldn’t be punished with an overall D because of missing homework. On the flip side, if a student has mostly D’s and C’s but turns in all homework, they shouldn’t earn a B in the course. If you feel you must include homework on the final report, consider a grade for responsibility or citizenship. An A grade in Math and a D in responsibility gives students and parents a more clear view of the student’s true progress.

*Howard Pitler is a dynamic facilitator, speaker, and instructional coach with a proven record of success spanning four decades. Pitler is an ASCD Faculty member and the author of several ASCD publications including Classroom Instruction That Works, 2nd edition, Using Technology with Classroom Instruction That Works, and A Handbook for Classroom Instruction That Works, 2nd edition. Contact Pitler at hpitler@gmail.com or on his website.*

### CLAIM

A student mistook examples of unsolved statistics problems for a homework assignment and solved them.

True### RATING

True### ORIGIN

A legend about the “unsolvable math problem” combines one of the ultimate academic wish-fulfillment student not only proves himself the smartest one in his class, but also bests his professor and every other scholar in his field of study — with a “positive thinking” motif which turns up in other urban legends: when people are free to pursue goals unfettered by presumed limitations on what they can accomplish, they just may manage some extraordinary feats through the combined application of native talent and hard work:

A young college student was working hard in an upper-level math course, for fear that he would be unable to pass. On the night before the final, he studied so long that he overslept the morning of the test.

When he ran into the classroom several minutes late, he found three equations written on the blackboard. The first two went rather easily, but the third one seemed impossible. He worked frantically on it until — just ten minutes short of the deadline — he found a method that worked, and he finished the problems just as time was called.

The student turned in his test paper and left. That evening he received a phone call from his professor. “Do you realize what you did on the test today?” he shouted at the student.

“Oh, no,” thought the student. I must not have gotten the problems right after all.

“You were only supposed to do the first two problems,” the professor explained. “That last one was an example of an equation that mathematicians since Einstein have been trying to solve without success. I discussed it with the class before starting the test. And you just solved it!”

And this particular version is all the more interesting for being based on a real-life incident!

One day In 1939, Dantzig, a doctoral candidate at the University of California, Berkeley, arrived late for a graduate-level statistics class and found two problems written on the board. Not knowing they were examples of “unsolved” statistics problems, he mistook them for part of a homework assignment, jotted them down, and solved them. (The equations Dantzig tackled are more accurately described not as unsolvable problems, but rather as unproven statistical theorems for which he worked out proofs.)

Six weeks later, Dantzig’s statistic professor notified him that he had prepared one of his two “homework” proofs for publication, and Dantzig was given credit on another paper several years later when another mathematician independently worked out the same solution to the second problem.

George Dantzig recounted his feat in a 1986 interview for the *College Mathematics Journal*:

It happened because during my first year at Berkeley I arrived late one day at one of [Jerzy] Neyman’s classes. On the blackboard there were two problems that I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework — the problems seemed to be a little harder than usual. I asked him if he still wanted it. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o’clock, [my wife] Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: “I’ve just written an introduction to one of your papers. Read it so I can send it out right away for publication.” For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard that I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them.

A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.

The second of the two problems, however, was not published until after World It happened this way. Around 1950 I received a letter from Abraham Wald enclosing the final galley proofs of a paper of his about to go to press in the

Annals of Mathematical Statistics.Someone had just pointed out to him that the main result in his paper was the same as the second “homework” problem solved in my thesis. I wrote back suggesting we publish jointly. He simply inserted my name as coauthor into the galley proof.

Dr. Dantzig also explained how his story passed into the realm of urban legendry:

The other day, as I was taking an early morning walk, I was hailed by Don Knuth as he rode by on his bicycle. He is a colleague at Stanford. He stopped and said, “Hey, was visiting in Indiana recently and heard a sermon about you in church. Do you know that you are an influence on Christians of middle America?” I looked at him, amazed. “After the sermon,” he went on, “the minister came over and asked me if I knew a George Dantzig at Stanford, because that was the name of the person his sermon was about.”

The origin of that minister’s sermon can be traced to another Lutheran minister, the Reverend Schuler [sic] of the Crystal Cathedral in He told me his ideas about thinking positively, and I told him my story about the homework problems and my thesis. A few months later I received a letter from him asking permission to include my story in a book he was writing on the power of positive thinking. Schuler’s published version was a bit garbled and exaggerated but essentially correct. The moral of his sermon was this: If I had known that the problem were not homework but were in fact two famous unsolved problems in statistics, I probably would not have thought positively, would have become discouraged, and would never have solved them.

The version of Dantzig’s story published by Christian televangelist Robert Schuller contained a good deal of embellishment and misinformation which has since been propagated in urban legend-like forms of the tale such as the one quoted at the head of this page: Schuller converted the mistaken homework assignment into a “final exam” with ten problems (eight of which were real and two of which were “unsolvable”), claimed that “even Einstein was unable to unlock the secrets” of the two extra problems, and erroneously stated that Dantzig’s professor was so impressed that he “gave Dantzig a job as his assistant, and Dantzig has been at Stanford ever since.”

George Dantzig (himself the son of a mathematician) received a Bachelor’s degree from University of Maryland in 1936 and a Master’s from the University of Michigan in 1937 before completing his Doctorate (interrupted by World ) at UC Berkeley in 1946. He later worked for the Air Force, took a position with the RAND Corporation as a research mathematician in 1952, became professor of operations research at Berkeley in 1960, and joined the faculty of Stanford University in 1966, where he taught and published as a professor of operations research until the 1990s. In 1975, was awarded the National Medal of Science by President Gerald Ford.

George Dantzig passed away at his Stanford home at age 90 on 2005.

This legend is used as the setup of the plot in the 1997 movie . As well, one of the early scenes in the 1999 film *Rushmore* shows the main character daydreaming about solving the impossible question and winning approbation from all.

FeedbackSources

Fact Checker:David Mikkelson

Published:4 December 1996

Updated:20 August 2017

Albers, Donald J. and Constance Reid. “An Interview of George B. Dantzig: The Father of Linear Programming.”

*College Mathematics Journal.* Volume 17, Number 4; 1986 (pp. 293-314).

Brunvand, Jan Harold. *Curses! Broiled Again!*

New York: W. W. Norton, 1989. ISBN 0-393-30711-5 (pp. 278-283).

Dantzig, George B. “On the Non-Existence of Tests of ‘Student’s’ Hypothesis Having Power Functions Independent of Sigma.”

*Annals of Mathematical Statistics*. No. 11; 1940 (pp. 186-192).

Dantzig, George B. and Abraham Wald. “On the Fundamental Lemma of Neyman and Pearson.”

*Annals of Mathematical Statistics*. No. 22; 1951 (pp. 87-93).

Pearce, Jeremy. “George B. Dantzig Dies at 90.”

*The New York Times*. 23 May 2005.

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