The Mathematics Vision Project structures the teacher and student role quite differently than in 'traditional' mathematics instruction. The following information comes from this document on the MVP Website. Some edits have been made for clarity.
Each course in the Mathematics Vision Project materials is composed of two main parts, the classroom experience, which is designed around the implementation of a specific type of task and the aligned “Ready, Set, Go!“ homework assignment. Each task is accompanied by a set of teacher notes. The teacher notes identify the purpose of the lesson and then describe the steps the teacher can take during the classroom experience to ensure that students engage in a rich learning event. Tasks are to be done in class and should not be assigned as homework. There is an aligned “Ready, Set, Go!“ homework assignment for each task. It is the independent practice. Homework serves the student as a type of formative assessment. It is while doing the homework that the student can discern for himself if the mathematics done in class can be performed independently.
The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students’ ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems. These strategies are eventually solidified into a body of practices and mathematical habits that belong to the students, because, they were developed by the students, as an outcome of their own creative and logical thinking. This is how students learn mathematics. They learn by doing mathematics. They learn by needing mathematics. They learn by verbalizing the way they see the mathematical ideas connect and by listening to how their peers perceived the problem. Students then own the mathematics because it is a collective body of knowledge that they have developed over time through guided exploration.
This process describes the Learning Cycle, an instructional framework that allows students to build mathematical knowledge over time. This framework is flexible. Every task in the curriculum is identified as one of the following:
Every lesson does not follow the pattern of develop, solidify, practice. For instance, the first module on quadratics begins with a Develop Understanding Task. Many aspects of the definition of a quadratic, surface in that task. Five solidify tasks follow the first task. Each of the Solidify tasks extends one of the key concepts that surfaced in the beginning Develop Task. The module ends with a Practice task that pulls all of the key concepts together into a complete definition of quadratic.
Each type of task serves a different purpose in moving a student’s mathematical knowledge from a foundation of conceptual understanding to that of procedural fluency. Paying attention to the type of task will help teachers know if they have accomplished the goal of the lesson.
Each module in the MVP educational program has been carefully designed and sequenced with rich mathematical tasks that have been formulated to generate the mathematical concepts within the core curriculum. Careful attention has been placed upon the way mathematical knowledge emerges, is extended, and then becomes efficient, flexible, and accurate. Some tasks are developmental tasks while others are for solidifying or practicing the concepts. The sequencing of the tasks encourages students to notice relationships and make connections between the concepts. In this way, students perceive mathematics as a coherent whole.
While the classroom experience is predominantly geared towards improving students’ reasoning and sense-making skills, MVP regards mathematical understanding and procedural skill as being equally important. Hence, the “Ready, Set, Go!” homework assignments are focused on students practicing procedural skills and organizing principles to add structure to the ideas developed during the classroom experience. As in any discipline, practice is the refining element that brings fluency and agility to the skills of the participant. The Ready and the Go sections of the homework assignments have been designed to continue to spiral a review of content, while the Set section focuses on consolidating the mathematics addressed in class that day. Each day when a student engages in the homework assignment, it is expected that he or she will have the opportunity to reflect on the new learning from class and will practice the retrieval of ideas from the body of learning that has been growing over the school year, and even prior to the current school year. Recent research on learning has identified reflection and retrieval practice as being two key ingredients for durable learning. True learning should be long lasting and should grow out of previous understandings, extending over years of study. Hence, the “Go!” sections of the “Ready, Set, Go!” homework assignments will contain topics from previous lessons and prior years of mathematics instruction. Together the classroom experience and the “Ready, Set, Go!” homework assignments offer a powerful blend of new learning and maintained proficiency.
The Learning Cycle depicts how students become proficient in the mathematics overtime. Each task represents at least one day of instruction. Therefore, a Learning Cycle may extend over several days or weeks of classroom instruction, however, each day the teacher is expected to frame the lesson around The Teaching Cycle. This cycle also has three components: Launch, Explore, and Discuss.
The Teaching Cycle may seem to be simple, but it involves careful preparation and then deliberate implementation by the instructor.
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