Fewer, clearer, and higher , to best drive effective policy and - - PowerPoint PPT Presentation

Fewer, clearer, and higher, to best drive effective policy and practice; Aligned with college and work expectations, so that all students are prepared for success upon graduating from high school; Inclusive of rigorous content and application of knowledge through high-

• rder skills, so that all students are prepared for the 21st century;

Internationally benchmarked, so that all students are prepared for succeeding in our global economy and society; and Research and evidence-based.

Standards for Mathematical Practice  Recurring throughout the grades  Describes habits of mind for the mathematics student  Integrated into instruction Standards for Mathematical Content  K-8 standards presented by grade level  Organized into domains that progress over several grade levels  Grade introductions give 2-4 focal points per grade level  High school standards present concepts and focus on widely applicable prerequisites

Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

• 1. Focus: Focus strongly where the standards focus
• 2. Coherence: Think across the grade levels, and link to major topics
• 3. Rigor: In major topics, pursue conceptual understanding, procedural

skill fluency, and application

Move away from “mile wide, inch deep” curricula Teach less, learn more “Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.”

• Ginsburg et al., 2005

Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. “The Standards are not so much build from topics as they are woven out

• f progressions.”

Structure is the Standards, Publishers’ Criteria for Mathematics.

Understand ratio concepts and use ratio reasoning to solve problems. Analyze proportional relationship and use them to solve real- world and mathematical problems. Understand the connections between proportional relationships, lines, and linear equations.

The CCSS require a balance of the following: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving situations Pursuit of all of the above requires equal intensity in time, activities, and resources

Before: NJCCCS (2004) 1. Understand and apply the Pythagorean Theorem. After: CCSS (2010) 1. Explain a proof of the Pythagorean Theorem and its converse. 2. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 3. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives. Students are able to see math as more than a set of mnemonics or discrete procedures. Conceptual understanding supports the other aspects of rigor (fluency and application).

Traditional Approach to Conceptual Understanding (Grade 6) CCSS-Aligned Approach to Conceptual Understanding (6.EE.A)

Provide tasks that require students to solve problems independently. Give students time to analyze a problem intuitively. Resist the urge to tell students how to solve a problem when they become frustrated. Ask students questions that will prompt their thinking. Encourage students to ask probing questions of themselves and of their peers. Establish a classroom climate in which students feel comfortable sharing their mathematical arguments.

Students must understand and be able to explain the structural underpinning of mathematics reasoning. It was enough to memorize formulas and patterns to achieve the right answers. Emphasis on solving math word problems, or “constructed response”

• problems. Sometimes these questions ask children to undo, then fix a

problem that has been incorrectly solved. There is a change from focusing on computation to focusing on problem solving strategies. The expectation now is that there is less “teacher talk” with more student practice and exploration for deeper understanding.

Administered in two components:

• A performance-based assessment (PBA) component, administered after

approximately 75% of the school year. (March 2nd – 27th)

• PBA component will have two sessions approximately 50 minutes

each

• An end of year assessment (EOY) component, administered after

approximately 90% of the school year. (April 27th – May 22nd)

• EOY component will have two sessions approximately 55 minutes

each

The Performance Based Assessment (PBA) will contain all three types of tasks.

• Assessing concepts, skills and procedures
• Assessing expressing mathematical reasoning
• Assessing modeling/applications

The End-of-Year (EOY) will contain only type 1 tasks.

• Assessing concepts, skills and procedures

www.corestandards.org/ www.parcconline.org www.state.nj.us/education/ www.achievethecore.org http://www.cgcs.org/Page/244 http://www.pta.org/parents/ www.engageny.org Parent Resource Site for Connected Mathematics https://connectedmath.msu.edu/families/

“No other decision that a teacher makes has a greater impact on students’ opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics.”

Glenda Lappan Michigan State University

Students in Kindergarten to grade 5 have been instructed in the area

• f mathematics using the Pearson enVisionMATH program since 2010.

Chatham Middle School mathematics resources were not aligned to the Common Core State Standards. In order to support the implementation of these new standards, the district needed to purchase materials and resources for mathematics teachers to use in grades 6, 7 and 8.

Identified Best Practices in Discipline Related Pedagogy

• Fosters student engagement (problem-centered, inquiry based

instruction)

• Aligns to the Common Core State Standards
• Intertwines conceptual knowledge with procedural knowledge
• Maintains an appropriate balance between being student-centered and

subject -centered Student Centered Subject Centered

Focus on the growth and development of learners Emphasis on the logical

• rder of the

discipline

Identified and Examined Potential Resources

• Programs aligned with best practices
• Programs used in other districts
• Explored resources and gathered teacher input to identify the top

resource Examples of districts that use the Connected Mathematics resource: Millburn School District Colts Neck School District Ridgewood School District Paramus School District Washington Township School District

Further Investigated the Connected Mathematics Program (CMP3)

• Conferred with consultant in the area of mathematics
• Conducted site visits to school districts to observe CMP being utilized

Implementation of the CMP3 Program

• 2013-2014 grades 6 and 7
• 2014-2015 grade 8
• Provided professional development for teachers prior to and during the

implementation

• Focused meetings on articulation to further support the consistent

implementation of the program

“In the first phase, the teacher launches the Problem with the whole class. Launches include connecting to prior knowledge, as well as presenting the challenge

• f

the Problem” (Lappan, Phillips, Fey, & Friel, 2014, p. 17). “As students work, they gather data, share ideas, look for patterns, make conjectures, and develop problem-solving strategies” (Lappan, Phillips, Fey, & Friel, 2014, p. 17). “In this phase, students present and discuss their solutions and the strategies they used to understand the Problem,

• rganize the data, and find the solution.”

(Lappan, Phillips, Fey, & Friel, 2014, p. 17).

Bagging Snacks: Choosing Common Multiples or Common Factors Focus Question: How can you decide when finding common factors is useful in solving a problem? How can you find the greatest common factor of two numbers? Choosing Common Multiples or Common Factors Seven students are going on a trip. Sarah is in charge of buying snacks for the trip. Each person wants two health bars and a juice drink. How many should she buy of each?

Connecting to Prior Knowledge  Teacher uses prior knowledge to position the new Problem.  Teacher clarifies prior definitions, reviews previous concepts, and connects the Problem to previous experiences. Presenting the Challenge  After connecting to prior knowledge, the teacher then helps students to understand the Problem setting, mathematical context, and the challenge. Teacher Planning:

• What prior knowledge do my students need to develop?
• How can I utilize that information to support students in understanding this

Problem?

• What are students expected to know and do?
• What difficulties for students can I foresee?
• How can I support my students without giving them too much of the answer?

Lappan, G., Defanis Phillips, E., Fey, J., & Friel, S. (2014). A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching. New Jersey: Pearson.

The nature of the Problem will help teachers identify which structure is most suitable for learning: individual, partners, small groups,

• r whole class. The teacher’s role during this

process is twofold: Providing for Individual Needs Planning for the Summary Providing for Individual Needs The Explore phase provides an opportunity for a teacher to circulate among the classroom, observing and providing specific feedback to students. During this time, the teacher supports students in persevering by asking appropriate questions and providing direction. Additionally, a teacher may also challenge students of high ability by asking challenging questions related to the problem.

Lappan, G., Defanis Phillips, E., Fey, J., & Friel, S. (2014). A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching. New Jersey: Pearson.

Teacher Planning:

• How will I organize this class for this problem? (Individuals? Pairs? Groups?

Whole Class?)

• What questions and strategies can I use to focus their thinking?

Planning for the Summary As the teacher gathers information from moving about the classroom , he or she makes decisions about how to tailor the summary to meet students’ needs. The teacher will address students’ questions, ideas, or strategy use that was observed and/or discussed during the Explore.

Lappan, G., Defanis Phillips, E., Fey, J., & Friel, S. (2014). A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching. New Jersey: Pearson.

Teacher Planning:

• What strategies are students using? Are they correct?
• What evidence do I have from my observations and discussions with students

that can be used to support student understanding of the Focus Question?

• How will I organize the discussion?

Orchestrating a Discussion Although led by the teacher, students play an integral role in the Summarize. Students will pose conjectures, question another student’s strategy use, and make connections between mathematical concepts. Teachers will also pose a Focus Question to further assess students understanding of the learning goal.

Lappan, G., Defanis Phillips, E., Fey, J., & Friel, S. (2014). A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching. New Jersey: Pearson.

Teacher Planning: How can I organize the discussion to support students in summarizing their thinking about the Problem? What questions, concepts, or strategies can be used to guide this process?

Karen Chase

Assistant Superintendent for Curriculum and Instruction kchase@chatham-nj.org

Seth Korman

Supervisor of Mathematics and Science 5-8 skorman@chatham-nj.org

FOCUS QUESTION For a fixed perimeter, what are the shape and area of the rectangles with the greatest and least area?