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Strategies for Mathematics Instruction and Intervention, 6-8

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Build a solid mathematics program by emphasizing prioritized learning goals and integrating RTI into your curriculum. Prepare students to move forward in mathematics learning, and ensure their continued growth in critical thinking and problem solving. With this book, you’ll discover an RTI model that provides the mathematics instruction, assessment, and intervention strategies necessary to meet the complex, diverse needs of students.

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Chapter 1 Prioritized Content in Mathematics

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There is, perhaps, no greater obstacle to all students learning at the levels of depth and complexity necessary to graduate from high school ready for college or a skilled career than the overwhelmingly and inappropriately large number of standards that students are expected to master—so numerous, in fact, that teachers cannot even adequately cover them, let alone effectively teach them to mastery. Moreover, students are too often diagnosed with a learning disability because we have proceeded through the curriculum (or pacing guide or textbook) too quickly; we do not build in time for the remediation and reteaching that we know some students require. We do not focus our efforts on the most highly prioritized standards and ensure that students learn deeply, enduringly, and meaningfully (Lyon et al., 2011). In short, we move too quickly trying to cover too much.

We distinguish between prioritized standards and supporting standards. We must focus our content and curriculum, collaboratively determining which standards are must-knows (prioritized) and which standards are nice-to-knows (supporting). This does not mean that we won’t teach all standards; rather, it guarantees that all students will learn the prioritized, must-know standards. To those who suggest that all standards are important or that nonteachers can and should prioritize standards, we respectfully ask, “Have teachers not been prioritizing their favorite standards in isolation for decades? Has prioritization of content not clumsily occurred as school years conclude without reaching the ends of textbooks?” Other colleagues contend that curricular frameworks and district curriculum maps should suffice. But we ask, “Will teachers feel a sense of ownership if they do not participate in this process? Will they understand why standards were prioritized? Will they stay faithful to first ensuring that all students master the must-knows, or will teachers continue, as they have for decades, to determine their own priorities and preferences regarding what is taught in the privacy of their classrooms?”

 

Chapter 2 Designing Conceptual Units in Mathematics

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This chapter is about what we want students to learn and how we can determine whether they have learned it (DuFour et al., 2011). Subsequent chapters describe strategies and pedagogies—the how. In this chapter, we will expand beyond the initial prioritization of mathematics content that we shared in the previous chapter to detail the deeper understandings that all middle school students must possess. Deeper understandings are most likely when we have designed rich, focused, and conceptually cohesive units of instruction. After revisiting the prioritization process, briefly describing how to build a unit of instruction, and describing the unwrapping and unpacking of standards, we will begin with the end in mind, with common assessments. Common assessments are an absolutely vital part of the unit design process and represent a key decision-making moment within an RTI process; they establish the target toward which students and staff are working and provide the evidence that can be used to extend learning for some and intervene with others. In the first part of this chapter, we build the case for common assessments and describe how to craft them. In the second half of the chapter, we provide examples of units for grades 6–8.

 

Chapter 3 Instructional Practices for Application-Based Mathematical Learning

ePub

After educators have identified essential outcomes or big ideas and designed conceptual units that promote the interrelated nature of mathematics, they must focus their attention on the instructional practices that promote authentic, application-based learning. Application-based learning is an instructional mindset that shifts the focus from ensuring students can use mathematics to compute answers to ensuring conceptual understanding and procedural competency applied to real-world problems. This chapter will provide guidance related to the three interrelated elements of highly effective Tier 1 instruction: (1) teachers’ knowledge of the mathematics, (2) the integration of mathematical practices (habits of the mind), and (3) effective instructional practices. In addition, the chapter will provide a sample structure to organize mathematics instruction that focuses on application-based mathematics learning.

The complexity of mathematical learning is such that students must master concepts and skills with an understanding that is fluid enough to allow them to apply these concepts and skills in a variety of contexts. In addition, students must be able to communicate and model mathematics, and explain and justify their solutions. Students must also master and apply related academic language and mathematical tools. For teachers to design and implement instruction that ensures such rich learning, they must be able to weave evidence-based instructional strategies with mathematical practices and apply those elements strategically within engaging, real-world contexts. Effective instruction includes those instructional decisions that positively impact student learning and engagement. The NMAP (2008) identifies these practices as follows:

 

Chapter 4 Tiers 2 and 3 Approaches to Foundational Conceptual Understandings and Mathematical Practices

ePub

Most middle school mathematics teachers understand mathematics deeply and thoroughly. In our conversations with grades 6–8 teachers, however, they are candid about the challenges of meeting the instructional needs of students who are missing foundational skills. Teachers find it quite challenging to address these early skills within the context of their classrooms or even to identify how to model those concepts and skills simply because they are so far removed from the grade-level content.

In this chapter, we first describe how middle school teacher teams may organize and deliver Tier 2 supports for students. We provide examples of common formative assessment results that would identify the need for Tier 2 supports and examples of how a few prioritized middle school concepts may be taught differently. We then examine how middle school leadership and RTI teams may organize and deliver Tier 3 supports for students. We will provide examples of universal screening evidence that may reveal significant deficits in foundational mathematics skills as well as examples of the types of intervention strategies that would explicitly target diagnosed needs.

 

Chapter 5 Integrating Assessment and Intervention

ePub

Success in mathematics is a moral imperative and “algebra is a civil right” (Moses, 2001, p. 5). If educators do not believe in each student’s ability to master mathematics concepts and procedures, then we would have to consider why we are bothering to intervene. We must accept that some students will simply require alternative strategies to learn, that not every student will learn the same way, and that some students will require additional time. We must also believe in our ability to teach every student. A teacher’s sense of self-efficacy significantly predicts the achievement of students, and middle school teachers’ beliefs in their abilities to teach mathematics lag far behind their beliefs in teaching reading well (Ashton & Webb, 1986; Bandura, 1993; Coladarci, 1992; Dembo & Gibson, 1985). We must also believe, and communicate to students, that mathematics achievement is not dependent on innate ability; work ethic, effort, perseverance, and motivation exert a significant impact on learning (Duckworth, Peterson, Matthews, & Kelly, 2007; Dweck, 2006; Seligman, 1991).

 



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