118 Chapters
Medium 9781942496427

Chapter 6 Measurement

Juli K. Dixon Solution Tree Press ePub

In grades 3–5, topics central to measurement include concepts related to perimeter, area, volume, elapsed time, angles, and conversion within systems. Contexts related to measurement offer opportunities for students to engage in problem solving.

The initial task in this chapter (figure 6.1) provides an opportunity for you to engage in problem solving related to measurement. This task involves the use of the geoboard and geoboard dot paper. If you do not have access to a geoboard, the activity can be completed using virtual geoboard manipulatives or the geoboard dot paper provided.

Make nine different (simple) polygons, each with an area of four square units. Record them on geoboard dot paper so that each polygon is on its own board.

Figure 6.1: Geoboard polygons task.

Visit go.solution-tree.com/mathematics for a free reproducible version of this figure.

In order to solve this task, you also need to define different in terms of the problem. In this problem, different means not congruent. Therefore, the polygons in figure 6.2 would not qualify as different because they are transformations of one another. In figure 6.2, you can see that the second figure was just a translation of the first, and the third figure was a rotation of the first figure. Polygons are the same if they are congruent, regardless of their location or orientation on the geoboard (see chapter 5 for more on polygons).

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Medium 9781947604049

Chapter 1

Dixon, Juli K.; Brooks, Lisa A.; Carli, Melissa R. Solution Tree Press PDF


Best Practices in Small-Group Instruction

Most of the elementary educators we have worked with view small-group instruction as an essential part of their mathematics block. Why? What are the benefits of small-group instruction that make it a priority in the school day? Typically, teachers consider it essential because they believe that they can fill gaps in student learning and meet students’ individual needs during this time. However, based on a wealth of research on effective mathematics education, we can assume that small-group instruction that is focused solely on correcting errors in procedural computations rarely serves its intended purpose (NCTM, 2014).

In this chapter, we explore best practices and effective strategies for working with small groups, and we discuss how teachers can use the time as a powerful means to advance and deepen mathematical understanding for each and every learner, including those who have met the initial learning goal. We begin by analyzing a video that depicts several best practices for small-group mathematics instruction in the classroom, allowing you to consider the lesson’s learning goal, the roles of the teacher and students, and the tools the teacher uses to support learning. Throughout the chapter we will discuss the teacher’s role, effective teaching strategies, the students’ roles, and how the teacher can help students negotiate those roles. We conclude by discussing management of the pulled small group.

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Medium 9781936763689

Chapter 1 Why Mathematics Education Needs to Improve

Matthew R. Larson Solution Tree Press ePub

We are systematically underestimating what our kids can do in math.


Since the 1990s, efforts to improve mathematics teaching and learning have focused on state adoption and implementation of increasingly more rigorous K–12 mathematics standards. These state standards represent the guaranteed and viable curriculum that every student should learn—what we expect students to know and be able to do in each grade level and course. In addition, each state implemented accountability measures attached to attainment of those standards.

The standards movement was kick-started by the National Council of Teachers of Mathematics (NCTM) in 1989, when it published Curriculum and Evaluation Standards for School Mathematics. This document and the subsequent edition, Principles and Standards for School Mathematics (NCTM, 2000), as well as Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics (NCTM, 2006), served as the blueprints for various state mathematics standards produced over a two-decade period beginning in the early 1990s. NCTM presented a new sense of rigor in terms of both the what and the how of learning school mathematics.

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Medium 9781935543558

Seven - Working with Families

Tinothy D. Kanold Solution Tree Press ePub



Families are their children's first teachers and are in prime position to have an important influence on their children's academic development. Through the values they communicate about education, effort, persistence, and responsibility, parents influence their children's mathematics achievement.

A meta-analysis of seventy-seven studies involving approximately 300,000 students found a positive relationship between amount and type of family involvement and student achievement (Jeynes, 2005): “The academic advantage for [students whose] parents were highly involved in their education averaged about 0.5-0.6 of a standard deviation for overall educational outcomes, grades, and academic achievement” (p. 2). Specifically, parental expectations, parenting style, reading to children, and participation in school-related activities influenced students' achievement, with parental expectations being particularly important. These results held for minority and low-income students as well as for the population in general.

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Medium 9781936764938

Chapter 10: Effectiveness Indicator 10 District Support

Dunsworth, Mardale; Billings, Dawn Solution Tree Press PDF



Effectiveness Indicator 10

District Support

I learned that courage was not the absence of fear, but the triumph over it. The brave man is not he who does not feel afraid, but he who conquers that fear.

— Nelson Mandela

The board and district determine the context within which schools function and the culture within which they operate. Effective districts are committed above all else to setting and supporting goals for high levels of student learning, and the board and superintendent work together to emphasize this priority.

From this principle, we derive Effectiveness Indicator 10. An on-site school review evaluates the district’s leadership in aligning curriculum, instruction, and assessment between and within grade levels, districtwide.

It also examines the district’s performance in committing resources to its goals and in using data to evaluate progress toward those goals.

Six characteristics define Effectiveness Indicator 10: District Support:

10A. The roles and responsibilities of the board, the district, and the schools are clear and communicated to stakeholders.

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