*(Bill Hanlon/Hanlon’s Razor)* – Many people equate completing homework assignments with studying, the most effective teachers know this not to be the case. They know studying includes reading, thinking, reflecting, organizing, writing, analyzing, visualizing, reviewing, remembering, and recalling. Too many students think homework is about completion. There are those in education that think it’s about completion and recalling, experienced teachers know there is more to it.

Homework that reflects and reinforces the day’s instruction and the notes taken from that instruction that encourages study is the best way to check for student understanding, address instruction, and increase student achievement. All too often in schools across America, a homework assignment is nothing more than a page in the book with exercises assigned or a worksheet. The best homework assignments reflect what the teacher values. That is, homework that encourages studying.

A typical secondary math assignment in the United States looks like this:

Page 165, 1 – 33 odd

A more appropriate homework assignment that would encourage studying would look more like this:

Read Sec 4.2 Add/Subtract Fractions

Define Fraction

Write the procedure for add/sub fractions

Draw a model to represent adding fractions

Explain the relationship between the algorithms for adding fractions and decimals

Page 165 – 3, 4, 6, 11, 13, 16, 17, 21, 28, and 30

N.B. – fewer exercises were assigned and the exercises were chosen specifically because they took into account all the nuances of the concepts and skills taught that day.

That homework assignment includes components that encourage and reflect studying.

Knowing standard procedures is important in learning math so having it part of the homework assignment will help students complete the exercises assigned as well as being better able to verbalize their knowledge. On subsequent nights’ homework, students might be asked to write the procedure for adding fractions again. Other questions might also be included in subsequent assignments, such as, why aren’t denominators added when adding fractions.

The good news about including these types of questions in the homework is that it increases the probability that students are acquiring the language, read, write & speak, and that it encourages studying. Since teachers typically address these in their instruction, the answers should be contained in student notebooks. Students would have a tough time telling a teacher the reason they did not do their homework was because they did not understand since all they had to do for most of it was revisit their notes to answer the first four or five questions. And, if the students did answer those questions, there would be a much higher probability that they would be able to complete the practice exercises. A good homework assignment reflects and supports student notes and instruction.

Homework assignments vary greatly from school to school. In some algebra classes, students will be routinely assigned thirty to fifty (equations) exercises each night taken directly from the textbook. In another school, students might only be assigned 15 to 20 exercises per night. In the least successful programs, there is a belief that students won’t do the homework, so they don’t assign any, and the students live up to that low expectation. In the most successful programs, homework appears to be assigned more thoughtfully. Those programs view homework assignments as an extension of their instruction. That suggests the time needed to complete the number of exercises assigned along with the reading, writing, thinking, and memorization that increases understanding are all taken into consideration. The most experienced teachers know that homework that encourages studying and supports their instruction is in the students’ best interests.

Parents who feel their understanding of math is suspect can easily ask their own children to define terms, recite procedures or formulas that are part of the homework assignment. And to determine if their kids know the answers, the parent can refer to the student’s notebook. Simply stated, if students were being asked to find the distance between two points and they don’t know the distance formula, there is no way they will be able to do the exercises.

From a parental standpoint they could help their student achieve, students who do not know the formula could repeat or write the formula a number of times, then have them explain how the numbers are substituted into the formula. That creates the knowledge base to be successful and increases their probability of successfully completing that night’s homework assignment.

Nothing increases proficiency more than practice. When students compute, solve equations or graph, they initially have to think/concentrate on the procedure. As they practice the computing, solving or graphing, those skills should almost become automatic. If they are not, more practice might have to be done in class and/or more exercises might need to be assigned for homework.

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