If you work in ink, use "white-out" to correct mistakes. If you run out of room at the end of a problem, continue onto the next page; do not try to squeeze lines together at the bottom of the sheet.
Effective discourse happens when students articulate their own ideas and seriously consider their peers’ mathematical perspectives as a way to construct mathematical understandings." In an article from the National Council of Mathematics Teachers (NTCM) September 2015, titled Making the Most of Going Over Homework, authors Samuel Otten, Michelle Cirillo, and Beth A.
Herbel-Eisenmann argue that teachers should "Reconsider typical discourse strategies when discussing homework and move toward a system that promotes the Standards for Mathematical Practice." Their research focused on the contrasting ways to have students engage in discourse-the use of spoken or written language as well as other modes of communication to convey meaning—in going over homework in class.
They acknowledged that an important characteristic of homework is that "it provides each individual student with the opportunity to develop skills and to think about important mathematical ideas." Spending time in class going over homework also gives students the "opportunity to discuss those ideas collectively." With homework dominating all other categories of math instruction, the researchers argue that the time spent going over homework can be "time well spent, making unique and powerful contributions to students’ learning opportunities" In talking over homework problems, the tendency is the focus is on the mechanics of one problem rather than the big mathematical ideas.
The examples from the published research show how discourse can be limited in talking over homework problems.
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Studies on math homework in secondary classrooms from 20 indicate an average of 15% -20% of class time daily is spent reviewing homework.
Do not squeeze the problems together, with one problem running into the next.
Use sufficient space for each problem, with at least one blank line between the end of one problem and the beginning of the next. This means showing your steps, not just copying the question from the assignment, and then the answer from the back of the book.
Show everything in between the question and the answer.
Use complete English sentences if the meaning of the mathematical sentences is not otherwise clear.