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  1. Classroom Resource Materials
  2. Bridges | The Math Learning Center
  3. Pick of the week
  4. Looking for other ways to read this?

We now move to a more detailed exploration of teaching and learning in three disciplines: history, mathematics, and science. We chose these three areas in order to focus on the similarities and differences of disciplines that use different methods of inquiry and analysis. A major goal of our discussion is to explore the knowledge required to teach effectively in a diversity of disciplines. We noted in Chapter 2 that expertise in particular areas involves more than a set of general problem-solving skills; it also requires well-organized knowledge of concepts and inquiry procedures.

Different disciplines are organized differently and have different approaches to inquiry. For example, the evidence needed to support a set of historical claims is different from the evidence needed to prove a mathematical conjecture, and both of these differ from the evidence needed to test a scientific theory. Discussion in Chapter 2 also differentiated between expertise in a discipline and the ability to help others learn about that discipline. Pedagogical content knowledge is different from knowledge of general teaching methods. In short, their knowledge of the discipline and their knowledge of pedagogy interact.

But knowledge of the discipline structure does not in itself guide the teacher. For example, expert teachers are sensitive to those aspects of the discipline that are especially hard or easy for new students to master. These conceptual barriers differ from discipline to discipline. An emphasis on interactions between disciplinary knowledge and pedagogical knowledge directly contradicts common misconceptions about what teachers need to know in order to design effective learning environments for their students.

The misconceptions are that teaching consists only of a set of general methods, that a good teacher can teach any subject, or that content knowledge alone is sufficient. Some teachers are able to teach in ways that involve a variety of disciplines. However, their ability to do so requires more than a set of general teaching skills. Consider the case of Barb Johnson, who has been a sixth-grade teacher for 12 years at Monroe Middle School.

By conventional standards Monroe is a good school. Standardized test scores are about average, class size is small, the building facilities are well maintained, the administrator is a strong instructional leader, and there is little faculty and staff turnover. What happens in her classroom that gives it the reputation of being the best of the best?

After the students list their individual questions, Barb organizes the students into small groups where they share lists and search for questions they have in common. After much discussion each group comes up with a priority list of questions, rank-ordering the questions about themselves and those about the world.

Classroom Resource Materials

The students had the opportunity to seek out information from family members, friends, experts in various fields, on-line computer services, and books, as well as from the teacher. Sometimes we fall short of our goal.

Build Number Sense Through Counting

At the end of an investigation, Barb Johnson works with the students to help them see how their investigations relate to conventional subject-matter areas. They create a chart on which they tally experiences in language and literacy, mathematics, science, social studies and history, music, and art.

Students often are surprised at how much and how varied their learning is. It would not work to simply arm new teachers with general strategies that mirror how she teaches and encourage them to use this approach in their classrooms.

Bridges | The Math Learning Center

Unless they have the relevant disciplinary knowledge, the teachers and the classes would quickly become lost. At the same time, disciplinary knowledge without knowledge about how students learn i.

In the remainder of this chapter, we present illustrations and discussions of exemplary teaching in history, mathematics, and science. The three examples of history, mathematics, and science are designed to convey a sense of the pedagogical knowledge and content knowledge Shulman, that underlie expert teaching. Most people have had quite similar experiences with history courses: they learned the facts and dates that the teacher and the text deemed relevant.

This view of history is radically different from the way that historians see their work. Students who think that history is about facts and dates miss exciting opportunities to understand how history is a discipline that is guided by particular rules of evidence and how particular analytical skills can be relevant for understanding events in their lives see Ravitch and Finn, Unfortunately, many teachers do not present an exciting approach to history, perhaps because they, too, were taught in the dates-facts method.

In Chapter 2 , we discussed a study of experts in the field of history and learned that they regard the available evidence as more than lists of facts Wineburg, The study contrasted a group of gifted high school seniors with a group of working historians. Both groups were given a test of facts about the American Revolution taken from the chapter review section of a popular United States history textbook. The historians who had backgrounds in American history knew most of the items, while historians whose specialties lay elsewhere knew only a third of the test facts.

Pick of the week

Several students scored higher than some historians on the factual pretest. In addition to the test of facts, however, the historians and students were presented with a set of historical documents and asked to sort out competing claims and to formulate reasoned interpretations. The historians excelled at this task. Most students, on the other hand, were stymied. Despite the volume of historical information the students possessed, they had little sense of how to use it productively for forming interpretations of events or for reaching conclusions.

Different views of history affect how teachers teach history. Consider the different types of feedback that Mr.

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Barnes and Ms. Kelsey gave a student paper; see Box 7. Overall, Mr. Barnes saw the papers as an indication of the bell-shaped distribution of abilities; Ms. Kelsey saw them as representing the misconception that history is about memorizing a mass of information and recounting a series of facts. These two teachers had very different ideas about the nature of learning history.


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Those ideas affected how they taught and what they wanted their students to achieve. For expert history teachers, their knowledge of the discipline and beliefs about its structure interact with their teaching strategies. Rather than simply introduce students to sets of facts to be learned, these teachers help people to understand the problematic nature of historical interpretation and analysis and to appreciate the relevance of history for their everyday lives.

One example of outstanding history teaching comes from the classroom of Bob Bain, a public school teacher in Beechwood, Ohio. Historians, he notes, are cursed with an abundance of data—the traces of the past threaten to overwhelm them unless they find some way of separating what is important from what is peripheral.

The assumptions that historians hold about significance shape how they write their histories, the data they select, and the narrative they compose, as well as the larger schemes they bring to organize and periodize the past. Often these assumptions about historical significance remain unarticulated in the classroom. Bob Bain begins his ninth-grade high school class by having all the students create a time capsule of what they think are the most important artifacts from the past.

In this way, the students explicitly articulate their underlying assumptions of what constitutes historical significance. At first, students apply the rules rigidly and algorithmically, with little understanding that just as they made the rules, they can also change them. But as students become more practiced in plying their judgments of significance, they come to see the rules as tools for assaying the arguments of different historians, which allows them to begin to understand why historians disagree. Leinhardt and Greeno , spent 2 years studying a highly accomplished teacher of advanced placement history in an urban high school in Pittsburgh.

The teacher, Ms.

BOX 7. When the French and Indian war ended, British expected Americans to help them pay back there war debts. If I had the choice between being loyal, or rebelling and having something to eat, I know what my choice would be. I think a lot of people also just were going with the flow, or were being pressured by the Sons of Liberty. By the end of the course, students moved from being passive spectators of the past to enfranchised agents who could participate in the forms of thinking, reasoning, and engagement that are the hallmark of skilled historical cognition.

For example, early in the school year, Ms. Remember that your reader is basically ignorant, so you need to express your view as clearly as you can. Try to form your ideas from the beginning to a middle and then an end. In the middle, justify your view. What factors support your idea and will convince your reader? By January his responses to questions about the fall of the cotton-based economy in the South were linked to British trade policy and colonial ventures in Asia, as well as to the failure of Southern leaders to read public opinion accurately in Great Britain.

Elizabeth Jensen prepares her group of eleventh graders to debate the following resolution:.