June 2011 Archives

It's important when demonstrating mathematical procedures to stress the mathematics behind those procedures (i.e., the "why" behind the "what" or "how"), since failing to do so can cause or reinforce students' misconceptions. Take, for example, multiplying fractions such as 3/5 x 5/8, where teachers commonly--and correctly--note that "the fives cancel out," leaving 3/8 as the product. But unless students understand why the fives cancel out, they see it as something that happens magically rather than mathematically. Some students figure they can then wave their magic wands and also cancel out when adding or subtracting fractions--such that ...


In my last post I declared cold calling the hands down winner over hand raising when it comes to engaging and assessing students, and preparing them for future endeavors. Now cold calling takes on another challenger in the quest for the best questioning strategy: choral response. Choral response is a good choice when all students will benefit from responding aloud and in unison, as when early childhood/primary and foreign language teachers ask students to repeat a new word or sound. Another possible example is when teachers want students to call out arithmetic facts in an effort to build computational ...


A lot of students shrugged their shoulders when I called on them to answer questions at the beginning of the year. Others mumbled, "I don't know." Then there were those kids who let me have it: "Man, I don't know. Stop calling on me!" But I never did stop calling on them. And after a few weeks, most of those shruggers and shouters were earnestly answering my questions. That's how long it took them to adjust to my questioning policy: only raise your hand when you want to ask a question, not when you want to answer one. It was ...


Forget about standardized tests. Forget about weekly quizzes. Forget about homework. The most critical time for assessment is during daily in-class practice, when you can see sooner rather than later what students are struggling with and why they're struggling with it. It's only then that you can provide timely, differentiated feedback and remediation. (See Differentiated Instruction: A Practical Approach.) Unfortunately, teachers often miss the chance to do this because they're assisting a few students at the expense of assessing all students. At the end of typical math lessons, for example, teachers assign practice problems for students to try on their ...


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