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Chapter 3: Geometry

Nolan, Edward C.; Dixon, Juli K.; Safi, Farshid; Haciomeroglu, Erhan Selcuk Solution Tree Press ePub

CHAPTER 3

Geometry

Geometry often provides the first opportunity for a formal exploration of proof. Students make sense of and apply both inductive and deductive reasoning in this exploration. Inductive proof could be thought of as connecting to recursive thinking in the study of arithmetic sequences in algebra, while deductive thinking links more closely to determining explicit rules for those sequences. Thinking back to the bridges problem from chapter 2 (see figure 2.5, page 42), the recursive rule would be that the number of beams in the next bridge is equal to the number of beams in the current bridge with four additional beams added. The number of beams in each subsequent bridge is based on the previous example. An explicit rule for the number of beams in any bridge is not based on the number of beams in a prior bridge but is rather determined using the length of the bridge.

Specifically, inductive reasoning is using observations and examples to reach a conclusion. For example, when you recognize a pattern in a number of different isosceles triangles that the base angles are congruent, you may inductively conclude that base angles of isosceles triangles are congruent. However, this type of reasoning is always subject to finding an example that does not follow the pattern. For example, in the bridges problem if you only examine a bridge of length 4 (see figure 2.6, page 43), you might conclude that a rule for the number of beams in a bridge of any length is 3 + n(n − 1). However, upon further examination, you would see that this rule cannot be generalized to bridges of other lengths.

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Medium 9781936764686

Chapter 1 Setting the Stage for Curriculum Building

Susan Udelhofen Solution Tree Press ePub

To begin the curriculum-building process we needed to first create a broader “systems” viewpoint as to what foundational pieces were necessary for a sound, effective, mutually understood curriculum. I knew that by taking the time at the beginning to develop common goals and learning expectations, we would have a stronger curriculum, better teacher understanding, and ultimately higher student achievement.

K–12 Director of Instruction

• The role and responsibilities of administrators in the curriculum-building process

• The rationale for having meaningful, focused conversations about teaching and learning, called map and talk sessions

• An overview of assessment definitions and practices to guide the curriculum-building process

To build a curriculum that is meaningful, commonly understood, used, and sustained over time, three specific structures and practices need to be in place: (1) administrators need to be actively involved with the curriculum-building process, (2) teachers and administrators must have opportunities to engage in focused conversations about their work, and (3) everyone should have the knowledge and skills to effectively assess students to maximize learning. This chapter describes these three practices and offers strategies and tools for implementation that can be referred to throughout the curriculum-building process and beyond.

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Medium 9781936764723

Chapter 8: Proverb Pairs

Bailey, Kim Solution Tree Press ePub

Standardizing reasoning

Evaluating deductive conclusions

Asking questions to challenge assumptions

Pairs of proverb and syllogism cards (see pages 184–194 and online reproducibles)

Copies of summary sheet (one per student per round; see reproducible on page 195)

Pen or pencil for each student

Timer (optional)

In Proverb Pairs, students discover the premises and conclusions behind common sayings and proverbs and then evaluate them for validity and truth.

For this game, you will need enough pairs of proverb and syllogism cards so that each student will have one card (for example, in a class of thirty, you would need fifteen pairs of cards). In each pair, one card states a common saying or proverb, and the other card lists an underlying syllogism—that is, two premises and a conclusion—for the saying or proverb. This chapter includes premade pairs of proverbs and syllogisms (see pages 184–194; for reproducible cards with the proverbs and syllogisms, visit marzanoresearch.com/activitiesandgames), but teachers may also elect to create their own. Shuffle the set of cards and randomly distribute one card to each student. Each student should also receive copies of the summary sheet (see reproducible on page 195) that he or she can use to evaluate the proverb-syllogism pairs. Each student will need one copy of the organizer for each proverb-syllogism pair he or she evaluates (see the next section).

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Medium 9781574411713

2: Impact of Federal Bilingual Education Policy

Guadalupe San Miguel Jr. University of North Texas Press PDF

T H E E X P A N S I O N O F B I L I N G U A L E D U C AT I O N , 1 9 6 8 – 1 9 7 8

37

Lau Remedies Compliance Reviews, 1975–78

In addition to these procedures, the federal government also developed an elaborate civil rights enforcement mechanism and pressured local school districts to develop bilingual education programs. Although there were programmatic and interpretational problems and even opposition to the Lau Remedies, the Office for Civil Rights used it to negotiate compliance plans with over 500 local school districts in the late 1970s. Coercion or the threat of coercion and the withdrawal of federal school funds served as the basis for the development of bilingual education programs.38

IMPACT OF FEDERAL BILINGUAL EDUCATION POLICY

The origins of and changes in federal bilingual education policy had a significant impact on various aspects of American political and educational life. For instance, this policy significantly impacted state and local governments, the political fortunes of minority groups, and language use. More importantly, it encouraged a political opposition to voice its opinion and to speak out against this policy.

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Chapter 6 Designing Engaging Opening and Closing Activities

James H. Stronge Solution Tree Press ePub

Planning the opening and closing activities for lessons reminds teachers to think about the priorities of the lesson and how they can best engage all students. Opening and closing activities are opportunities for students to attach personal meaning and relevance to what they learn. These activities can help structure learning and create what psychologists call the primacy-recency effect; that is, during a lesson, learners remember best that which comes first and that which comes last. They remember least that which comes just past the middle (Sousa, 2011). Therefore, the amount of information that students are likely to retain depends on what is presented during the lesson and when. Figure 6.1 shows how the primacy-recency effect influences retention during a forty-minute lesson (Sousa, 2011). The first ten minutes and the last ten minutes of a lesson are the optimal times for learning.

Figure 6.1: Primacy-recency effect.

The primacy-recency effect has important implications for instructional planning and design. It is common for teachers to introduce a lesson objective and then move on to taking attendance, distributing the day’s homework, collecting the previous day’s homework, and making announcements. By the time new learning finally rolls around, more than ten minutes have lapsed, and students are already beyond optimal learning time. At the end of a lesson, some teachers allow students to do anything they want as long as they keep quiet and stay busy, thus, wasting a learning opportunity. Designing engaging opening and closing activities for instruction provides opportunities for learning as productively and effectively as possible.

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