The State of Mathematics in the State of Massachusetts<br />NEAP (National Assessment of Educational Progress)<br />Massachusetts had the highest scores in the Nation for the last three years in math performance for grades 4 and 8<br />TIMSS (Trends in International Math and Science Study)<br />Massachusetts outscored all other states in mathematics<br />Grade 4 Students ranked 4th worldwide<br />Grade 8 students ranked 6th worldwide <br />
AYP Yearly Targets<br />for 100% Proficiency in 2013<br />100<br />95.1<br />100<br />90.2<br />90<br />92.2<br />85.4<br />80.5<br />84.3<br />80<br />ELA<br />75.6<br />Composite Performance Index (CPI)<br />76.5<br />70.7<br />70<br />68.7<br />60<br />60.8<br />Math<br />ELA<br />Math<br />53.0<br />50<br />2001 & 02<br />2003 & 04<br />2005 & 06<br />2007 & 08<br />2009 & 10<br />2011 & 12<br />2013 & 14<br />Ten years ago, only 24 % of the state’s 10th graders scored proficient or higher on the math MCAS exam. <br />
The State of Mathematics in North Middlesex<br />
Research on Best Practices in MathematicsNational Mathematics Panel 2008<br />Elementary and middle school mathematics programs should focus on proficiency with key topics/core concepts. Any approach that continually revisits topics year after year without closure is to be avoided.<br />A major goal for K-8 mathematics should be conceptual understanding of and proficiency with fractions, decimals, percents and negative fractions, for such proficiency is foundational for algebra. <br />The curriculum must simultaneously develop conceptual understanding, computational fluency and problem-solving skills<br />Computational proficiency is dependant on:<br />automatic recall of addition, subtraction, multiplication and division facts <br /> conceptual understanding of operations and properties of operations <br /> fluency with standard algorithms<br />
Research on Best Practices in MathematicsNational Mathematics Panel 2008<br /><ul><li>A mix of student centered and teacher centered approaches is desired
Teachers’ use of formative assessment , especially when additional guidance is provided to teachers to help them individualize instruction improves student learning
Technology based drill and practice and tutorials can improve student automaticity
Calculator use should be limited until students develop automaticity and fluency with basic facts, as well as estimation skills and conceptual understanding
Estimation skills should be expanded beyond rounding to multiple strategies for a single problem
Struggling students should receive explicit instruction that ensures that they develop foundational skillsand conceptual understanding. This instruction should include opportunities for students to ask</li></ul> and answer questions and think aloud about the decisions they make while solving problems<br /><ul><li>Gifted students should be offered opportunities for enrichment and acceleration.</li></li></ul><li>Research on Best PracticesNCTM 2008<br /><ul><li>A coherent curriculum effectively organizes and integrates important mathematical ideas so that students can see how the ideas build on or connect with other ideas.
Problem solving, reasoning, connections, communication, and conceptual understanding are all developed simultaneously along with procedural fluency.
Students should have frequent opportunities to formulate, grapple with, and solve complex problemsthat require a significant amount of effort. They should then be encouraged to reflect on their thinking. Problem solving is an integral part of all mathematics learning.
Being able to reason is essential to understanding mathematics. By developing ideas, exploring phenomena, justifying results, and using mathematical conjectures in all content areas and at all grade levels, students should recognize and expect that mathematics makes sense.
Communicating mathematical thinking and reasoning is an essential part of developing understanding. </li></li></ul><li>Research on Best PracticesNCTM 2008<br /><ul><li>Students must demonstrate understanding of numbers and relationships among numbers with a focus on the place-value system. Students must develop understanding of number operations and how they relate to one another.
Students should become proficient at using mental math shortcuts, performing basic computations mentally, and generating reasonable estimates for situations involving size, distance, and magnitude.
Algebraic concepts and skills should be a focus across the pre-K–12 curriculum.
Geometry is a natural place for the development of students’ reasoning and justification skills
Students should have experience in formulating questions, designing simple surveys and experiments, gathering and representing data, and analyzing and interpreting these data in a variety of ways.
Basic ideas of probability form the underpinnings of statistical inference.
Alignment and coherence of curriculum, standards, and assessment—are critically important foundations of mathematics education. </li></li></ul><li>Massachusetts DESE Curriculum Frameworks<br />Guiding Philosophy<br />Problem Solving is an essential part of the curriculum.<br /> Students need many opportunities to formulate questions, model problem situations in a variety of ways, generalize mathematical relationships and solve problems in both mathematical and everyday contexts.<br />Communicating<br /> Students develop this skill and deepen their understanding of mathematics when they use accurate mathematical language to talk and write about what they are doing.<br />Reasoning and Proof<br /> From the early grades on, students develop their reasoning skills by making and <br /> testing mathematical conjectures, drawing logical conclusions, and justifying their <br /> thinking in developmentally appropriate ways.<br />Making Connections<br /> Encouraging students to explore the connections that exist within mathematics, with <br /> other disciplines, and between mathematics and students’ own experiences.<br />
Massachusetts DESE Curriculum Frameworks<br />Guiding Principles<br /> To achieve mathematical understanding, students should be actively engaged in doing meaningful mathematics, discussing mathematical ideas, and applying mathematics in interesting, thought provoking situations.<br /> Mathematical problem solving is the hallmark of an effective mathematics program.<br /> Technology enhances the mathematics curriculum in many ways. Tools such as measuring instruments, manipulatives(such as base ten blocks and fraction pieces), scientific and graphing calculators, and computers with appropriate software, if properly used, contribute to a rich learning environment for developing and applying mathematical concepts.<br />Assessment of student learning in mathematics should take many forms to<br />inform instruction and learning.<br />
Massachusetts DESE Curriculum Frameworks<br />Strands<br />Number Sense and Operations<br /> Patterns, Relations and Algebra<br /> Geometry<br /> Measurement<br /> Data Analysis, Statistics and Probability<br />
Learning Standards for Grades PreK–K<br />Number Sense and Operations<br /> Understand patterns, relations, and functions<br /> Represent and analyze mathematical situations and structures using algebraic symbols<br /> Use mathematical models to represent and understand quantitative relationships<br /> Analyze change in various contexts <br />Massachusetts Frameworks<br />
DESE Characteristics of a Standards Based Mathematics Classroom<br /><ul><li>Learning standards being addressed are evident and clear to students.
Connections are made to previous and subsequent learning standards.
Students have access to exemplars that represent mastery of the standards.
Students havedescriptorsof what constitutes a high quality product.
All components of the lesson contribute to the learning objectives.
The majority of the lesson involves students actively engaged in mathematics rather than passively receiving instruction about mathematics.
Multiple grouping strategies are used to achieve the lesson objectives.
Student learn and practice mathematical skills, facts, procedures/algorithms.</li></li></ul><li>DESE Characteristics of a Standards Based Mathematics Classroom<br />Student s discuss mathematical concepts using correct mathematical vocabulary, support their reasoning with evidence and articulate their mathematical reasoning.<br />Students use multiple problem solving strategies.<br />Students with special needs are supported.<br />Students learn mathematics in the context of real-world problems and applications<br />Math concepts are presented in multiple ways pictures, words, symbols, diagrams, tables, graphs.<br />Questions are scaffolded progression to higher levels of mathematical thinking.<br />Use of manipulatives and technology are connected to the lesson objectives.<br />Presentation is responsive to various learning styles. <br />Assessment is used to inform instruction.<br />Multiple forms of assessment are employed.<br />
Is a textbook the solution?<br />The teacher provides the greatest impact<br />The teacher provides the greatest impact on students.<br />
“Content Knowledge” is not enough to teach effectively; a good textbook is just the beginning. <br /><ul><li>To interpret student work to give student-appropriate feedback
Provide mathematical explanation that is student friendly
Connect present math to future math courses and understandings
Based on committee recommendations one or two textbooks will be piloted in the 2010-2011 school year.
Ongoing evaluations of the strengths and weaknesses of each series will be monitored throughout the pilot year by teachers and administrators who are using the pilot materials
Recommendation for series adoption will be made to Dr. Brady and Dr. Marshall for adoption in the 2011-2012 school year</li></li></ul><li>Committee Assignments<br />
Administrivia<br />Presentations will be scheduled for Wednesday afternoons whenever possible.<br />Everyone is invited to all presentations, but those reviewing each series should plan to attend the presentation that is specific to the series that they are responsible to review .<br />Everyday Math Presentation – December 16 - 3:30 – High School ILC<br />School visits will be scheduled for Wednesdays whenever possible.<br />Committee members reviewing each series should plan to attend the school visit that is specific to the series that they are reviewing.<br />Textbook samples are located in central office.<br />Please view sample materials at central office.<br />If it is necessary to review the materials at a different location (i.e., over a weekend), please make sure to sign the materials out and return them promptly.<br />Math program evaluation rubric will be available online or in hard copy<br />