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.

We now turn our attention to what it takes to develop proficiency in teaching mathematics. Proficiency in teaching is related to effectiveness: Proficiency also entails versatility: Teaching in the ways portrayed in chapter 9 is a complex practice that draws on a broad range of resources.

Despite the common myth that teaching is little more than common sense or that some people are just born teachers, effective teaching practice can be learned. In this chapter, we consider what teachers need to learn and how they can learn it.

First, what does it take to be proficient at mathematics teaching? If their students are to develop mathematical proficiency, teachers must have a clear vision of the goals of instruction and what proficiency means for the specific mathematical content they are teaching.

They need to know the mathematics they teach as well as the horizons of that mathematics—where it can lead and where their students are headed with it. They need to be able to use their knowledge flexibly in practice to appraise and adapt instructional materials, to represent the content in honest and accessible ways, to plan and conduct instruction, and to assess what students are learning.

Helping Children Learn Mathematics. The National Academies Press. If you can interweave the two things together nicely, you will succeed….

Believe me, it seems to be simple when I talk about it, but when you really do it, it is very complicated, subtle, and takes a lot of time. It is easy to be an elementary school teacher, but it is difficult to be a good elementary school teacher.

Used by permission from Lawrence Erlbaum Associates. Teaching requires the ability to see the mathematical possibilities in a task, sizing it up and adapting it for a specific group of students. In short, teachers need to muster and deploy a wide range of resources to support the acquisition of mathematical proficiency.

In the next two sections, we first discuss the knowledge base needed for teaching mathematics and then offer a framework for looking at proficient teaching of mathematics.

In the last two sections, we discuss four programs for developing proficient teaching and then consider how teachers might develop communities of practice.

The Knowledge Base for Teaching Mathematics Three kinds of knowledge are crucial for teaching school mathematics: Page Share Cite Suggested Citation: In our use of the term, knowledge of mathematics includes consideration of the goals of mathematics instruction and provides a basis for discriminating and prioritizing those goals.

Knowing mathematics for teaching also entails more than knowing mathematics for oneself. Teachers certainly need to be able to understand concepts correctly and perform procedures accurately, but they also must be able to understand the conceptual foundations of that knowledge.

In the course of their work as teachers, they must understand mathematics in ways that allow them to explain and unpack ideas in ways not needed in ordinary adult life. Knowledge of students and how they learn mathematics includes general knowledge of how various mathematical ideas develop in children over time as well as specific knowledge of how to determine where in a developmental trajectory a child might be.

Knowledge of instructional practice includes knowledge of curriculum, knowledge of tasks and tools for teaching important mathematical ideas, knowledge of how to design and manage classroom discourse, and knowledge of classroom norms that support the development of mathematical proficiency.

Teaching entails more than knowledge, however. Teachers need to do as well as to know. For example, knowledge of what makes a good instructional task is one thing; being able to use a task effectively in class with a group of sixth graders is another.

Understanding norms that support productive classroom activity is different from being able to develop and use such norms with a diverse class. Knowledge of Mathematics Because knowledge of the content to be taught is the cornerstone of teaching for proficiency, we begin with it.

Many recent studies have revealed that U. The mathematical education they received, both as K students and in teacher preparation, has not provided them with appropriate or sufficient opportunities to learn mathematics.

As a result of that education, teachers may know the facts and procedures that they teach but often have a relatively weak understanding of the conceptual basis for that knowledge. Many have difficulty clarifying mathematical ideas or solving problems that involve more than routine calculations.

Many have little appreciation of the ways in which mathematical knowledge is generated or justified. Preservice teachers, for example, have repeatedly been shown to be quite willing to accept a series of instances as proving a mathematical generalization.

Although teachers may understand the mathematics they teach in only a superficial way, simply taking more of the standard college mathematics courses does not appear to help matters. The evidence on this score has been consistent, although the reasons have not been adequately explored.

For example, a study of prospective secondary mathematics teachers at three major institutions showed that, although they had completed the upper-division college mathematics courses required for the mathematics major, they had only a cursory understanding of the concepts underlying elementary mathematics.

For the most part, the results have been disappointing: Most studies have failed to find a strong relationship between the two. Many studies, however, have relied on crude measures of these variables.Title - Be A Food Critic By - Madeline McDougal Primary Subject - Language Arts Grade Level - Concept / Topic To Teach: Writing a Comparison Essay Standards In this lesson, students write a comparative essay from the perspective of a food critic.

Subject: Students can work in groups of four. 4. Students will describe cookies and. Teaching Math: (Task 2) Explain how to teach fourth -grade students the concept of equivalence when working with fractions with unlike denominators.

List at least three prerequisite skills to working with fractions . Comments (8) Natalie C (Seventh Street Elem, North Little Rock, AR) Subject taught: Grade: K Enjoyed this article I would like to use this article in a paper that I am writing about the benefits of teaching addition and subtraction through word problems with elementary aged students.

Printable Fourth Grade (Grade 4) Worksheets, Tests, and Activities. Worksheets labeled with are accessible to Help Teaching Pro subscribers only. Become a Subscriber to access hundreds of standards aligned worksheets. Jump to: Arts;. Writing a compare and contrast essay is hard for upper elementary students.

Scaffolding the compare and contrast essay can help students be successful. How to Scaffold Writing A Compare and Contrast Essay. This leaves out a very important step – the scaffolded essay.

All of my 3rd grade students – even my more advanced and gifted. Teaching the Concept of Equivalence for Grade Four Students Essay Sample There are actually a lot of ways that you can teach grade four students and let them understand the concept of equivalent fractions.

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Printable Fourth Grade (Grade 4) Tests, Worksheets, and Activities