One of the recommendations is for teachers to teach students at the grade level they are at even if they are missing a few skills. If you put students in a lower mathematical level they might resent it especially if placement is based on test results. There are ways to help students manage grade level material such as allowing the use of a calculator when combining like terms if they have difficulty with integers. The calculator does the arithmetic while they work on learning the more advanced concept rather than getting stuck on the arithmetic they struggle with.
It is also important to show students how certain things relate across the curriculum. For instance, in elementary math, students learn that fractions must have a common denominator for adding or subtracting and the same applies to rational express that are being added or subtracted. In addition, multiplying binomials can be done in the same way as two digit times two digit numbers. Most textbooks do not take time to show the connectivity so students see each topic or concept as unique rather than connected.
Most textbooks come with assessments built in. The series I use have a quiz scheduled about half way through the chapter and a test at the end. This is very traditional but it doesn't give the teacher much data and it is better to carry out mini assessments throughout the chapter. Mini assessments give both the teacher and student a chance to check understanding.
The assessment doesn't have to be formal like a quiz. Instead it might be something like a thumb up or thumb down to show yes or no, or a showing of fingers indicating 1 finger says I don't know to 5 which says I could teach another student.These type of assessments give the student a chance to self assess because they have to determine their level of understanding in order to share it with the teacher.
For something a bit more formal, exit tickets and journal entries provide a nice amount of information without being a "quiz". Its also possible to give students a "quiz" made up of a couple of questions. I like giving five questions at the beginning of the week and letting students retake the quiz to work on only the questions they missed. When they have done all five questions correctly, they are done with the quiz for the week.
It is suggested that students be allowed to work together on assignments and other activities. Research shows that students who work together in collaborative groups tend to achieve more. In addition, it appeals to the social nature of students and students are less likely to get stuck. Any collaboration among students must be monitored otherwise one person does all the work while the other copies.
On Wednesday, I'll address what is needed to create an effective mathematical environment in the classroom. The classroom environment is important to helping students be successful. Let me know what you think, I'd love to hear. Have a great day.
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