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Grades K-8 – Eureka Math—also known as EngageNY—“is a complete, curriculum that carefully sequences the mathematical progressions into expertly crafted modules. Eureka Math was written by a team of teachers and mathematicians who took great care to present mathematics in a logical progression from grade PK—12. This coherent approach allows teachers to know what incoming students already have learned and ensures that students are prepared for what comes next. When implemented faithfully, Eureka Math will dramatically reduce gaps in student learning, instill persistence in problem-solving, and prepare students to understand advanced math. Eureka Math connects math to the real world in ways that take the fear out of math and build student confidence—helping students achieve true understanding lesson by lesson and year after year.
It’s not enough for students to know the process for solving a problem; they need to understand why that process works. Teaching mathematics as a "story," Eureka Math builds students’ knowledge logically and thoroughly to help them achieve deep understanding. While this approach is unfamiliar to those of who grew up memorizing mathematical facts and formulas, it has been tested and proven to be the most successful method in the world.” from https://greatminds.org/math/about-eureka
Depth of Knowledge (DOK)
What is DOK? Depth of Knowledge also referred to as D.O.K., is the complexity or depth of understanding required to answer or explain an assessment related item or a classroom activity. The concept of depth of knowledge was developed through research by Norman L. Webb in the late 1990’s.
DOK-1: What is the knowledge? At this level, students are asked to acquire and gather the information they need to develop deeper knowledge and thinking. They are asked mostly factual questions (who, what, where, when) about the texts and topics they are reading and reviewing. They might also be asked to recall or reproduce how or why a concept or procedure works or is used. The answers to these good questions are either correct or incorrect. Good questions at this level ask students to describe what are the ideas and information presented in texts and explain how concepts and procedures work.
DOK-2: How can the knowledge be used? At this level, students are asked to demonstrate and communicate conceptual and procedural knowledge. They are asked analytical questions that challenge them to examine and explain how can the concepts and procedures they are learning be used to answer questions, address problems, accomplish tasks, or analyze texts and topics. They also begin to show and tell self-knowledge and personal understanding of how can and could they (or you) use what they (you) are learning. They also begin to think critically about how would you use the concepts and procedures to answer a question, address a problem, accomplish a task, or analyze a text or topic. Good questions at this level ask students to show and tell how concepts and procedures are used. The emphasis is more on the application of ideas and information rather than the item being addressed.
DOK-3: Why can the knowledge be used? Students learning at this level are still demonstrating and communicating conceptual and procedural understanding. However, the instructional focus and assessments shift from applying to analyze and evaluating how and why concepts and procedures can be transferred and used to attain and explain certain scenarios, settings, situations, and solutions. Students are also asked hypothetical questions that prompt them to think strategically and creatively about how could you use what they are learning. They are also asked argumentative questions that engage them to think reasonably about the credibility and validity of ideas and theories, critique different perspectives and points of view, and defend or refute conclusions and decisions.
DOK-4: How else can the knowledge be used? At this level, students are encouraged to extend their thinking deeper within the subject they are learning, across the curriculum, and even beyond the classroom. These learning experiences focus heavily on developing and demonstrating metacognition - specifically, conditional and contextual knowledge and self-knowledge. Students are asked to think critically about the impact, implications, and influence ideas and information have on a much grander scale. They are also encouraged to express and share their own perspectives and points of view about a text or topic using oral, written, creative, or technical communication. These learning experiences are time and thought-intensive and are typically presented and provided as active and authentic learning experiences such as project-based or problem-based learning that require in-depth research, examinations, investigations, and demonstrations of learning through design. http://edge.ascd.org/blogpost/what-exactly-is-depth-of-knowledge-hint-its-not-a-wheel