Informational Math Night Grades 6-9 Reading Public Schools December, 2013
� Shift in Standards � New Math Sequences � Options for Sequence Changes � Placement for Grade 7 � Curriculum Resources & Information
Key Instructional Shifts in Mathematics • The new Massachusetts Curriculum Frameworks emphasize coherence at each grade level – making connections across content and between content and mathematical practices in order to promote deeper learning. • The standards focus on key topics at each grade level to allow educators and students to go deeper into the content. • The standards also emphasize progressions across grades, with the end of progression calling for fluency – or the ability to perform calculations or solving problems quickly and accurate. • The Standards for Mathematical Practice describe mathematical “habits of mind” or mathematical applications and aim to foster reasoning, problem solving, modeling, decision making, and engagement among students. • Finally, the standards require students to demonstrate deep conceptual understanding by applying them to new situations.
Massachusetts Curriculum Framework for Mathematics “These standards are not intended to be new names for old ways of doing business. They are a call to take the next step.”
� Students should be actively engaged in doing meaningful mathematics, discussing mathematical ideas, and applying mathematics in interesting, thought-provoking situations. � Student understanding is further developed through ongoing reflection about cognitively demanding and worthwhile tasks. � Tasks should be designed to challenge students in multiple ways. � Activities should build upon curiosity and prior knowledge, and enable students to solve progressively deeper, broader, and more sophisticated problems.
The new standards state that “educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: � conceptual understanding , � procedural skill and fluency � applications .”
Standards for Mathematical Practice It's not that I'm so smart, it's just that I stay with problems longer. Albert Einstein
“The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.” (From the Massachusetts Curriculum Framework for Mathematics )
Math Educator Perspectives on the New Practice Standards “A large majority of middle school math teachers say the common core is more • rigorous than their state's prior mathematics standards. The teachers surveyed seemed especially upbeat about the math practice standards . In all, 71 percent of teachers agreed or strongly agreed that the focus on math practices is the ‘biggest innovation’ of the standards, with 95 percent saying that participating in those practices is essential for students to learn math.” Ed Week / July 29, 2013 / “Math Teachers Find Common Core More Rigorous Than Prior Standards” " The practice standards are exquisite . . . .” • Philip Uri Treisman, professor of math and public affairs at the University of Texas "The common-core standards and assessments put us in a different game. . . Of • course, the content counts. I'm a mathematician. You've got to get it right, and get it right in the right ways. But the real action is in the mathematical practices . . .” Alan Schoenfeld, NCTM member and professor of mathematics, University of California, Berkeley "It's going to be more challenging . . . more rigorous . . . And I'm here to tell you • that's a good thing, because we've been lying to ourselves and everybody else . . . We've inflated our levels of proficiency." Matthew Larson, math specialist in Lincoln, Nebraska and a board member for NCTM Ed Week / April 24, 2013 / “What Do Math Educators Think About the Common Core?”
Preparing for College Mathematics “To acquire the mathematical background you need, . . . you should study mathematics every year in secondary school. But simply taking mathematics is not enough. You should acquire the habit of puzzling over mathematical relationships. When you are given a formula, ask yourself why it is true and if you know how to use it. When you learn a definition, ask yourself why the definition was made that way. It is the habit of questioning that will lead you to ���������� mathematics rather than merely to remember it, and it is this understanding that your college courses require. In particular, you should select mathematics courses that ask you to solve hard problems and that contain applications (‘word problems’). The ability to wrestle with difficult problems is far more important than the knowledge of many formulae or relationships.” Harvard’s Thoughts on Mathematics
Grade 7 Courses Math 7 and Math 7 Enhanced • Students develop an understanding of and applying proportional relationships; develop an understanding of operations with rational numbers and working with expressions and linear equations; work with two- and three- dimensional shapes to solve problems involving area, surface area, and volume; and draw inferences about populations based on samples Math 7/8 • Students develop a deep unified understanding of rational numbers; study algebraic functions focusing on problem solving with linear functions and systems of equations, statistics topics including comparing data sets, random sampling and bivariate data; and problem solve involving two and three dimensional geometry concepts
Grade 8 Courses Math 8 and Math 8 Enhanced • In-depth study of linear relationships and equations, with the addition of functions, the exploration of irrational numbers, geometric graphing to algebra, statistics and the connection linear relations with the representation of bivariate data. Many more algebra standards are evidenced in these courses than in the previous Framework. Algebra I • The Algebra 1 course of the new Framework progresses from the Grade 8 algebra topics, expanding the study of functions to exponential and quadratic relationships, as well as other topics previously taught in Algebra II and high school courses.
Grade 6 Criteria for placement in Grade 7 � Unit assessments from 6 th grade curriculum � Spring cumulative assessment in May (will include open-response and novel application questions) � IOWA Algebra readiness assessment (for 7/8 acceleration option) or Skills assessment (for Enhanced option)
Algebra: Not 'If' but 'When' By NCTM President Linda M. Gojak December 3, 2013 “One of the questions I am frequently asked by teachers, parents, and reporters is, ‘When should students take algebra?’ Let’s assume that we’re talking about a college preparatory Algebra 1 course. The content and instruction must be designed to develop both conceptual and procedural understanding. For students to be considered successful in first-year algebra, the expectation must be that reasoning and making sense will be priorities of both teaching and learning.” “Requirements for taking algebra in the middle grades should be clear and must not be compromised. Successful completion of a rigorous algebra course requires students to have prerequisite mathematical understandings and skills as well as a work ethic that includes the tenacity to stick with a problem or concept until it makes sense and the willingness to spend more time on assignments and class work.”
Algebra: Not 'If' but 'When' By NCTM President Linda M. Gojak (excerpts continued) . . . “Furthermore, a key characteristic of students who are successful in algebra, no matter when they take it, is a level of maturity that includes a readiness to understand abstract mathematical definitions, to work with abstract models and representations, and to understand and make connections among mathematical structures—and this readiness should extend to making abstract generalizations.” “My experience, both as a student and as a teacher, leads me to believe that we do more harm than good by placing students in a formal algebra course before they are ready . . . .” http://www.nctm.org/about/content.aspx?id=40258
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