Kathleen Cramer Learning about fractions is one of the most difficult tasks for middle and junior high school children. The results of the third National Assessment of Educational Progress NAEP show an apparent lack of understanding of fractions by nine- thirteen- and seventeen-year-olds. Similar trends were observed in the first, the second, and the recently completed fourth National Assessments Carpenter et al.
There is some overlap among these topics, so I recommend reading the whole page. Ultimately, what are the sources of errors and of misunderstanding? What kinds of biases and erroneous preconceptions do we have? Two of my favorite historic discoveries are Einstein's discovery of relativity and Cantor's discoveries of some of the most basic rules of infinities.
These discoveries are remarkable in that neither involved long, involved, complicated computations. Both are fairly simple, in retrospect, to anyone who has studied them.
But both involved "thinking outside the box" par excellence -- i. As philosopher John Culkin said, "We don't know who discovered water, but we are certain it wasn't a fish. Errors in Communication Some teachers are hostile to questions. That is an error made by teachers. Teachers, you will be more comfortable in your job if you try to do it well, and don't think of your students as the enemy.
This means listening to your students and encouraging their questions. A teacher who only lectures, and does not encourage questions, might as well be replaced by a book or a movie. To teach effectively, you have to know when your students have understood something and when they haven't; the most efficient way to discover that is to listen to them and to watch their faces.
Perhaps you identify with your brightest students, because they are most able to appreciate the beauty of the ideas you are teaching -- but the other students have greater need of your help, and they have a right to it.
A variant of teacher hostility is teacher arrogance. Actually, most of the errors listed below can be made by teachers, not just by students. However, most teachers are right far more often than their students, so students should exercise great caution when considering whether their teachers could be in error.
If you're a student with a hostile teacher, then I'm afraid I don't know what advice to give you; transfer to a different section or drop the course altogether if that is feasible.
The remarks on communication in the next few paragraphs are for students whose teachers are receptive to questions.
For such students, a common error is that of not asking questions. When your teacher says something that you don't understand, don't be shy about asking; that's why you're in class! If you've been listening but not understanding, then your question is not a "stupid question.
Think of yourself as their spokesperson; you'll be doing them all a favor if you ask your question.This page lists recommended resources for teaching number topics at Key Stage 3/4.
Huge thanks to all individuals and organisations who share teaching resources. Common Core Eureka Math for Grade 2, Module 8. Created by teachers, for teachers, the research-based curriculum in this series presents a comprehensive, coherent sequence of thematic units for teaching the skills outlined in the CCSS for Mathematics.
Division word problems The number is of course , but to find it, do a quick division of 26, by You can also think of the problem above as a linear equation Basic math word problems.
Division word problems. Recent Articles. Modeling Multiplication. Nov 15, 18 PM. Also, the interactive style and scoring method for the students are great.K Math & English · Adaptive & Individualized · Immediate Feedback · Standards-based LearningCourses: Math, English, Science, Social Studies, Spanish.
This page is a collection of math links for children, teachers, and lausannecongress2018.com are based on the curriculum for Kindergarten through grade four,although many pages will be of interest to older students.
I’ve been meaning to let you know about the Illustrative Mathematics blog, which launched a few weeks ago. It has blog posts by members of the IM community about our grades 6–8 curriculum and about teaching practice, including a whole series on the 5 practices framework of Smith and Stein.