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Toward Greater Focus and Coherence
The MAISA CCSS Mathematics Curriculum Materials are designed to support districts as they work to implement the Common Core State Standards for Mathematics. A primary purpose of these materials is to provide resources to help teachers create opportunities for students to build connections within and among mathematical ideas in increasingly sophisticated ways. The MAISA CCSS Mathematics Curriculum Materials are not intended or designed to replace research-based instructional materials but rather to support shifts in teachers instructional practices consistent with the intent of the CCSS. As such, these materials extend well beyond providing teachers a checklist of content expectations or lessons.
The curriculum materials are designed to:
be professional learning tools to improve educators understanding of the CCSS;
organize the CCSS into mathematically coherent and sequenced units of study that make visible connections among mathematical ideas. They are not designed to prescribe a single pathway through a particular unit; and
provide a context for conversations among colleagues (e.g., Professional Learning Communities) within and across grades. Lesson and assessment topics within the units of study are selected to highlight content that might be new, different, or challenging for teachers and students. This highlighted content may be used to spark important planning and problem solving discussions related to the CCSS implementation.
Included in each unit of study:
Unit Overview
A conceptual organization of related mathematical ideas that includes an overarching question, graphic organizer, questions to focus assessment and instruction, intellectual processes (a.k.a. Standards for Mathematical Practice), key concepts, unit abstract, applicable CCSSM and unit level/bridging standards, and instructional and professional resources. The CCSS and these units view mathematics as a set of connected ideas that are developed over time. Therefore, standards may be repeated in multiple units to support the development of mathematical connections.
Highlight Lesson
A fully articulated lesson designed to provide a model for effectively engaging students with a rich mathematical task. Each highlight lesson has been written using the Thinking Through a Lesson Protocol (TTLP), a research-based tool to help teachers prepare for lesson enactment. Questions taken from the TTLP appear in the left-hand column of each highlight lesson. These questions are intended to be used to scaffold teachers planning of additional lessons using their instructional resources (e.g., textbooks).
Formative Assessment
An assessment designed around the notion of re-engaging students in content and practices based on students understanding of mathematical ideas at a particular point in time. These assessments are intended to provide data to guide teachers instructional decisions. They suggest that teachers provide feedback to students in a manner to advance and deepen students understandings as opposed to simply evaluate their answers. It is important to note that the formative assessments are designed to be used at some point within the unit. The formative assessments may or may not directly connect to the highlight lesson.
Artifacts
A growing body of professional learning activities developed to support teachers understanding of and implementation of the unit. These materials could include, but are not limited to, samples of student work, student interviews, teacher reflections, and video of classroom instruction. The artifact cover sheet suggests focus questions for collegial conversations (e.g., professional learning community meetings).
Professional and Instructional Resources
These are a selected repertoire of high quality resources to further equip a teacher to teach a particular unit. This section could include, but is not limited to, web sites for student activities, childrens literature connections, assessment activities, and professional learning resources for educators.
Frequently Asked Questions (FAQ):
Is it appropriate to re-order these units of study within a grade and/or course?
The order of units has evolved over time to attend to existing research and inherent connections between and among mathematical ideas. While they can be re-ordered, the user needs to be aware that there are assumptions made in later units about students prior mathematical experiences in earlier units. As such, reordering units is likely to have additional implications for instruction.
Why does the unit contain just one highlight lesson and one formative assessment?
The highlight lesson and formative assessment serve as a model to support shifts in teachers instructional practices consistent with the intent of the CCSS. Therefore, teachers should use these models to develop or enhance the remaining lessons and formative assessments required for the unit.
Why arent all 8 Standards for Mathematical Practice listed in every unit and/or lesson?
Attending to all 8 Standards for Mathematical Practice constantly could mean that none of the standards are ever explicitly a focus of instruction. The project has made the decision to identify particular practices for focus within the units and lessons. The mathematical features of the content informed these decisions. This does not mean that additional practices are not or should not be part of instruction in any given unit.
How are the unit overview and the highlight lesson template connected? Why are some components grayed-out on the highlight lesson?
The highlight lesson focuses on a subset of the mathematical ideas in the whole unit. When components in the lesson appear in lighter font, it is to indicate that these ideas are in the unit but not a focus of the particular highlight lesson. The intent is to help teachers keep the overall unit ideas in mind when considering the mathematics in a lesson.
Why are some standards identified with an asterisk and/or listed as unit level standards?
Standards identified with an asterisk and/or listed as unit level standards are intended to be bridging standards to strengthen the connections and coherence within and between grades/courses. They are not to suggest additional topics to be taught but to strengthen mathematical connections for teachers and students. Often these standards are modified from how they appear in the CCSSM to be grade/course appropriate.
Are key concepts meant to be vocabulary?
Key concepts are intended to highlight mathematical ideas that are to be developed and/or used extensively within a particular unit. While the key concepts often include formal mathematical vocabulary that students should learn to use over time, the use of the formal mathematical language may or may not be expected of students at the grade in which it appears as a key concept.
Are the focus questions in the unit and lesson templates meant for students or teachers?
Both, the focus questions that appear in the unit and lesson templates (note: not in the artifacts) are meant to be used by teachers with students. Teachers should use these questions to guide their instructional and assessment decisions toward the mathematical goals of the overall unit of study and, as such, the highlight lesson.
Bridging/Unit Level Standards are noted with an asterisk in the units and lessons.
For more information on the Thinking Through a Lesson Protocol (TTLP) and its use as a professional learning tool see: Smith, M.S., Bill, V., & Hughes, E.K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14, 132-138.
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