Strategies for Mathematics Instruction and Intervention, K–5

Strategies for Mathematics Instruction and Intervention, K–5

By: Darlene Crane, Chris Weber

Prepare students to move forward in mathematics learning, and ensure their continued growth in critical thinking and problem solving.

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Strategies for Mathematics Instruction and Intervention, K–5

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, youll discover an RTI model that provides the mathematics instruction, assessment, and intervention strategies necessary to meet the complex, diverse needs of students.

  • Understand how teaching prioritized standards helps students become college and career ready and able to retain mathematics knowledge.
  • Gain strategies to build the RTI framework into your mathematics program.
  • Learn to teach mathematics in a way that helps learners gain conceptual understanding, procedural competency, and the ability to apply mathematics knowledge.
  • Discover how to create assessments for determining students difficulties and appropriate supplemental interventions.
  • Access reproducible tools to support your mathematics program.

Related Topics

Instruction Mathematics Response to Intervention


Additional Information

Product Code: BKF620

ISBN: 9781936763313

Published By: Solution Tree

Page Count: 176

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  • Response to feedback

    First, thank you so much for taking the time to provide your feedback. We serve in the most important profession in the world and are committed to continuous learning and improvement.

    We would like to take a few moments to provide a few thoughts on your feedback.

    Regarding the appropriateness of strategies for whole groups: While we agree that most Tier 1 instruction has historically been provided to whole groups using procedurally-heavy and abstract approaches, it need not be that way. The change is challenging, but we have had success ensuring that Tier 1 learning environments very regularly include opportunities for teachers to meet with small group during which the strategies to which you refer may be more practically possible. But these “alternative” approaches can be used with whole groups as well. We can and should use concrete and pictorial approaches to teaching and learning with all students to complement the more abstract approaches that have, in our experiences, dominated instructional techniques. We can add more conceptually-rich and kinesthetically-rich approaches to our repertoires than we have thus far. We agree that we did not provide as many such approaches as would ultimately be required (we just gave examples), but would love to hear from you if you’d like more ideas (my email address is chi.educate@gmail.com)

    Regarding the recency of research, Dylan Wiliam has taught us that dates are not everything. Please know we strive to find the most current research on a topic, but when a topic has been well-studied, researchers may move on to other critical areas. The very best researchers know that more research is sometimes not needed, nor is conducting it efficient when so many other questions remain unexplored and unresolved, if research on a given topic is clear. As examples, the National Reading and Mathematical Advisory Panels produced their researched-based reports in 2002 and 2008; they have for the most part comprehensively addressed the central research-based questions in these areas. Like many, I am reading Jo Boaler’s wonderful book Mathematical Mindsets, published in 2016. On the first pages of chapters 6 and 7, when Dr. Boaler is making the case for the arguments within the chapter and providing a research base, she cites studies from 1995, 1998, and 2002. Again, we are voracious consumers of the newest research, but some topics, like ability grouping, have been definitively studied.

    About ability grouping: If we have communicated that we favor tracking, grouping, leveling, or any related practice, we have made a grave error. We are vehemently opposed to tracking (particularly prior to 10th grade) and have patiently but persistently attempted to eliminate ability grouping in the schools and districts that we have led. The research is clear that grouping harms all students, including the “highest achieving” students.

    Regarding prioritizing standards or creating power or essential standards: Robert Marzano famously found that the sheer number of standards inhibits learning and mastery of standards. He and Dr. DuFour collaborated to replicate this study after the Common Core era began and drew the same conclusions, as did Mike Schmoker. Researchers who have analyzed international achievement results (such as Bill Schmidt from Michigan State University) encourage us to focus on depth, not breadth. PARCC and SBAC have both developed blueprints or frameworks that describe some standards as priority and some as supporting. (I realize that many states are not using these exams but use them as examples.) The research is clear and, for us, it’s an equity issue. Practically speaking, students who require more scaffolding and differentiated supports to master the most critical grade level content will not be able to “cover” as much and coverage is not the goal. When teachers race through curriculum maps attempting to cover it all, they leave students behind, student do not learn deeply, they do not retain their understanding (for those tests months later), and too many students end the year further behind than when they began.

    States are not requiring that we teach it all; they require that students demonstrate that they have learned. And the research is clear: the worst way to prepare students for a test that assesses everything is to to try to teach everything. This applies to all students – a few examples. During my last principalship, I served in a school in which 20% of students mastered state standards (as measured by end-of-year assessments) the prior year. This had not changed in five years. My first year, we did little else but reduce the number of standards that we prioritized, using our precious learning time to ensure that students truly mastered the most critical standards. Yes, our state (California in the early 2000s) gave guidance on what those priorities ought to be, but we trusted our teachers’ professional judgments. Importantly, teachers collaborated horizontally and vertically in PLCs, creating GVCs (Guaranteed Viable Curricula) that we didn't simply teach but committed to all students learning. This, of course, is one of the three central big ideas of PLCs. What happened? In that first year, student achievement doubled. They were taking the same tests as before that assessed all the standards. In four years, it quadrupled. And we carefully examined the performance of all students, both those who had performed poorly and well the years before. All students improved and the gaps significantly decreased. We next replicated this approach across a 50,000 student school district’s 47 elementary buildings; the district was already a high-performing, award-winning district. The board and superintendent wanted even high levels of achievement. Teachers designed scopes and sequences that focused more time on roughly 80% of the most critical standards. (This 80% number was not a target; it was simply the quantity or outcomes at which quality of learning would not be compromised.) While the message was not that teachers shouldn't teach the other 20%, the focus was on mastery of the priorities. What happened? The number of students scoring advanced on the state tests nearly doubled. The students scoring in the lowest performance band nearly disappeared. They were taking the same tests as before that assessed all the standards.

    We are not advocating that teachers willy-nilly not teach standards. We are advocating that, given that school years and school days are not likely to get any longer, PLCs develop GVCs, by rethinking how we organize standards, the order in which we combine and teach them, and focus on those most critical concepts and skills that student need to be successful next year, in college, in their careers, and in life.

    Please, please reach out to me (chi.educate@gmail.com) if you would like to continue the dialogue. And thanks again for your questions.


  • Strategies for Mathematics Instruction and Intervention, K-5

    First of all, I am a huge fan of Solution Tree products. With my position focusing on providing high-quality professional development opportunities to staff, I heavily rely on Solution Tree resources and love that there resources are based off of current research. This is the first review I've written where I have had a negative experience with a Solution Tree book. The reasons are listed below:

    1. Although the Copyright date says 2015, many of the sources are over 10 years old with quite a few sources leaning to being 20 years old or older.

    2. The concept of Power Standards is not a philosophy supported by the Minnesota Department of Ed., which is the state I am from, or the Department of Education. In fact, they caution teachers that when power standards are used we lose the rigor (quality) of the standards and are doing a disservice with our students.

    3. The concept of prioritizing standards is also not supported by MDE or the Department of Education. Teachers need to show students the relevancy and significance of the standards and how they relate to the outside world in order to promote a growth mindset and provide strategies that counteract the little voice inside our heads that supports a fixed mindset philosophy.

    4. Another reason that MDE does not support prioritizing standards is because all of the math benchmarks on the MCA's are in the MCA Math test. This is found evident in the MCA test specs that MDE provides. As a result, if we prioritize standards we are not preparing our students with the knowledge they need to apply on the MCA's and in the real-world. These same skills should be focused on all year long, not just when students are viewed as "struggling."

    5. More recent research shows that we should not be labeling or categorizing our students into categories of abilities, but should be provide high-level math to all students in heterogeneous groups. This book shows the opposite model. Placing students in ability groups will actually hinder student growth because we are, then, subconsciously thinking that our "low students" will never be students who master math concepts.

    6. This book does not provide a long list of interventions that are applicable in a class-wide format. If 50% of the students, in a class, are struggling with a concept then a whole class intervention needs to occur (not just small groups-which we need to make sure are not ability groups).

    Please know that I am not criticizing the authors of this book. I am, just, wanting future buyers to know what this book is truly about, that it not modeled off of current research, and that the title is misleading. Thank you for your time!


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