Good morning… Please complete the Survey that can be found on the check in table

Good morning…

Please complete the Survey that can be found on the check in table.

Principles to Actions: Ensuring Mathematical

Success For All

Kitty Rutherford & Denise Schulz

NC DPI Mathematics Section

Fall 2015

Welcome“Who’s in the Room?”

Norms

• Listen as an Ally

• Value Differences

• Maintain Professionalism

• Participate Actively

maccss.ncdpi.wikispaces.net

A 25-year History of Standards-Based Mathematics Education

Reform

Standards Have Contributed to Higher Achievement• The percent of 4th graders scoring proficient

or above on NAEP rose from 13% in 1990 to 42% in 2013.

• The percent of 8th graders scoring proficient or above on NAEP rose from 15% in 1990 to 36% in 2013.

• Between 1990 and 2012, the mean SAT-Math score increased from 501 to 514 and the mean ACT-Math score increased from 19.9 to 21.0.

Trend in fourth-and-eighth grade NAEP

Mathematics Average Scores

http://nces.ed.gov/nationsreportcard/subject/publications/main2013/pdf/2014451.pdf


North Carolina NAEP Trends in Mathematics

Grade Source 1990 2013 Change

4 NC 223 254 Up 31

4 US 227 250 Up 23

8 NC 250 286 Up 36

8 US 262 284 Up 22

NAEP Scale Score1990 –First year NAEP reported NC Scores

2013 – Latest NC NAEP Test Data



NC EOG/EOC Percent Solid or Superior Command (CCR)

Grade 2012-2013 2013-2014 2014-2015

3 46.8 48.2 48.8

4 47.6 47.1 48.5

5 47.7 50.3 51.3

6 38.9 39.6 41.0

7 38.5 39.0 40.0

8 34.2 34.6 35.8

Math I 42.6 46.9 48.5

http://www.ncpublicschools.org/accountability/reporting/

http://www.ncpublicschools.org/accountability/reporting/

Although We Have Made Progress, Challenges Remain• The average mathematics NAEP score for 17-

year-olds has been essentially flat since 1973.• Among 34 countries participating in the 2012

Programme for International Student Assessment (PISA) of 15-year-olds, the U.S. ranked 26th in mathematics.

• While many countries have increased their mean scores on the PISA assessments between 2003 and 2012, the U.S. mean score declined.

• Significant learning differentials remain.

Brainstorm

Principles to Actions pg. 10-11

Beliefs About Teaching and Learning Mathematics

“Students’ beliefs

influence their perception of what it means

to learn mathematics and how they

feel toward the subject.”

Examine the comic strip. What do you see?

“Teachers’ beliefs influence the

decisions they make about the manner in

which they teach mathematics.”

Principles to Actions: Ensuring Mathematical Success for All

“The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.”

NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

“The overarching message is that effective teaching is the non-negotiable core necessary to ensure that all students learn mathematics. The six guiding principles constitute the foundation of PtA that describe high-quality mathematics education.”

Principles to Actions: Ensuring Mathematical Success for All

NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

High-Quality Standards are Necessary, But Insufficient, for Effective Teaching and Learning

“Teaching mathematics requires specialized expertise and professional knowledge that includes not only knowing mathematics but knowing it in ways that will make it useful for the work of teaching.”

Ball and Forzani 2010

Teaching and Learning

“An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.”

Principles to Actions pg. 7

Obstacles to Implementing High-Leverage Instructional Practices“Dominant cultural beliefs about the teaching and learning of mathematics continue to be obstacles to consistent implementation of effective teaching and learning in mathematics classrooms.”


Mathematics Teaching Practices

1. Establish mathematics goals to focus learning

2. Implement tasks that promote reasoning and problem solving

3. Use and connect mathematical representations

4. Facilitate meaningful mathematical discourse

5. Pose purposeful questions

6. Build procedural fluency from conceptual understanding

7. Support productive struggle in learning mathematics

8. Elicit and use evidence of student thinking

Mathematics Teaching Practices

1. Establish mathematics goals to focus learning.

2. Implement tasks that promote reasoning and problem solving.

3. Use and connect mathematical representations.

4. Facilitate meaningful mathematical discourse.

5. Pose purposeful questions.

6. Build procedural fluency from conceptual understanding.

7. Support productive struggle in learning mathematics.

8. Elicit and use evidence of student thinking.

Not to be confused with…

What do you notice?

Establish mathematics goals to focus learning.

“Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses goals to guide instructional decisions.”


Role Play

• Choose a puzzle piece from the center of the table.

• Find your group members.• In your group, role play the

scenario on pgs 14-15.• What do you notice about

the dialog?

What did you notice about the dialog?

“The math coach intentionally shifts the conversation to a discussion of the mathematical ideas and learning that will be the focus of instruction.”


Principles to Action – pg. 16

Reflect On Your Role

• Reflecting on this practice, what would be your role in the implementation of this practice?– Teacher– Administrator– Coach– District Level

Implement Tasks That Promote Reasoning and Problem Solving

“Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and that allow for multiple entry points and varied solution strategies.”


High or Low Cognitive Demanding Task?

High

Low


Cognitive Demand Sort

1. Read page 18 and summarize the description associated with each cognitive demand task type. – Memorization– Procedures without Connections– Procedures with Connections– Doing Mathematics

2. Come to a shared understanding of the demand task.

3. Then, use the contents of the envelope to sort the tasks by cognitive demand.

Table Talk

What are the attributes of a mathematically strong task?

Task Implementation Student Learning

Math Tasks

“There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perception about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in shaping mathematics.”

Lappan & Briars, 1995

http://commoncoretasks.ncdpi.wikispaces.net/

Look on page 21NCDPI – Task

Principles to Action - page 24



Teaching Practices JigsawSelect a ticket from your table.•Green-Use and connect mathematical representations (pg. 24)•Red-Facilitate meaningful mathematical discourse (pg. 29)•Purple-Pose purposeful questions (pg. 35)•Yellow-Build procedural fluency from conceptual understanding (pg. 42)•Pink-Support productive struggle in learning mathematics (pg. 48)•Blue-Elicit and use evidence of student thinking (pg. 53)

1. Read your assigned teaching practice.

2. Find the others in the room with the same color ticket.

3. Come to a shared understanding of the teaching practice.

4. Create a chart with:– Discussion– Illustration – Teacher and student actions

5. Be prepared to share with your table during a gallery walk.

Gallery Walk• With your table group, take a walk to each

practice poster.

• If you are the expert on that practice, explain to your group what the practice is about, pointing out key ideas.

• Take your book with you so you can make notes!

What might be the math learning goals?What might be the math learning goals?Math GoalsMath Goals

What representations might students use in reasoning through and solving the problem?

What representations might students use in reasoning through and solving the problem?

Tasks & Representations

Tasks & Representations

How might we question students and structure class discourse to advance student learning?

How might we question students and structure class discourse to advance student learning?

Discourse & Questions

Discourse & Questions

How might we develop student understanding to build toward aspects of procedural fluency?

How might we develop student understanding to build toward aspects of procedural fluency?

Fluency from Understanding

Fluency from Understanding

How might we check in on student thinking and struggles and use it to inform instruction?

How might we check in on student thinking and struggles and use it to inform instruction?

Struggle & Evidence

Struggle & Evidence

Let’s Do Some Math!The third grade class is responsible for setting up the chairs for the spring band concert. In preparation, the class needs to determine the total number of chairs that will be needed and ask the school’s engineer to retrieve that many chairs from the central storage area. The class needs to set up 7 rows of chairs with 20 chairs in each row, leaving space for a center aisle. How many chairs does the school’s engineer need to retrieve from the central storage area?


What might be the math learning goals?

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Formulating clear, explicit learning goals sets the stage for everything else.

(Hiebert, Morris, Berk, & Janssen, 2007, p. 57)

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Learning Goals should:

•Clearly state what it is students are to learn and understand about mathematics as the result of instruction.

•Be situated within learning progressions.

•Frame the decisions that teachers make during a lesson.

Daro, Mosher, & Corcoran, 2011; Hattie, 2009; Hiebert, Morris, Berk, & Jensen., 2007; Wiliam, 2011

Mr. Harris’s Math Goals

Students will recognize the structure of multiplication as equal groups within and among different representations, focusing on identifying the number of equal groups and the size of each group within collections or arrays.

Student Friendly Version:We are learning to represent and solve word problems and explain how different representations match the story situation and the math operations.

Alignment to the Standards

Standard 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. ------------------------------------------------------------Standard 3.NBT. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

Table Talk

• Think back to the Band Concert Task

• Review the student work samples.• With the mathematical goal in mind,

determine which students should present a solution, and in what order the solutions should be presented.

• What questions should be asked to connect solutions?

Student Work:

Connections:

MR. HARRISThe Case of Mr. Harris and the Band Concert Task

•Read the Case of Mr. Harris and study the strategies used by his students.

•Make note of what Mr. Harris did before or during instruction to support his students’ developing understanding of multiplication.

•Talk with a neighbor about the “Teaching Practices” Mr. Harris is using and how they support students’ progress in their learning.

Group Questions

• As a group, answer the questions regarding Mr. Harris and the teaching practices.

• Be prepared to share with the whole group.

• What were the math expectations for student learning?

• In what ways did these math goals focus the teacher’s interactions with students throughout the lesson?

• Consider Case Lines 4-9, 21-24, 27-29.

Questions

Implement tasks that promote reasoning and problem solving.

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Implement tasks that promote reasoning and problem solving.

Student learning is greatest in classrooms where the tasks consistently encourage high-level student thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature.

(Boaler & Staples, 2008; Stein & Lane, 1996)

Boaler & Staples, 2008; Hiebert et al., 1997; Stein, Smith, Henningsen, & Silver, 2009

Implement tasks that promote reasoning and problem solving.Mathematical tasks should:•Allow students to explore mathematical ideas or use procedures in ways that are connected to understanding concepts. •Build on students’ current understanding

and experiences. •Have multiple entry points.•Allow for varied solution strategies.

Questions• In what ways did the implementation

of the task allow for multiple entry points and engage students in reasoning and problem solving?

• Consider Case Lines 26-30 & 38-41.

Use and connectmathematical representations.

MathTeachingPractice

3

Use and connect mathematical representations.

Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas.

(National Research Council, 2001, p. 94)

Lesh, Post, & Behr, 1987; Marshall, Superfine, & Canty, 2010; Tripathi, 2008; Webb, Boswinkel, & Dekker, 2008

Use and connect mathematical representations.

Different Representations should:

•Be introduced, discussed, and connected.

•Be used to focus students’ attention on the structure of mathematical ideas by examining essential features.

•Support students’ ability to justify and explain their reasoning.

Principles to Actions (NCTM, 2014, p. 25)(Adapted from Lesh, Post, & Behr, 1987)

Important Mathematical Connections between and within different types of representations

What mathematical representations were students working with in the lesson?

How did Mr. Harris support students in making connections between and within different types of representations?

Jasmine Kenneth

Consider Lines 43-48. In what ways did comparing representations strengthen the understanding of these students?

Molly

Consider Lines 48-49. How did comparing representations benefit Molly?

Facilitate meaningful mathematical discourse.

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Facilitate meaningful mathematical discourse

Discussions that focus on cognitively challenging mathematical tasks, namely those that promote thinking, reasoning, and problem solving, are a primary mechanism for promoting conceptual understanding of mathematics.

(Hatano & Inagaki, 1991; Michaels, O’Connor, & Resnick, 2008)

Carpenter, Franke, & Levi, 2003; Fuson & Sherin, 2014; Smith & Stein, 2011

Facilitate meaningful mathematical discourseMathematical Discourse should:

•Build on and honor students’ thinking.

•Let students share ideas, clarify understandings, and develop convincing arguments.

•Engage students in analyzing and comparing student approaches.

•Advance the math learning of the whole class.

“What students learn is intertwined with how they learn it. And the stage is set for the how of learning by the nature of classroom-based interactions between and among teacher and students.”

(Smith & Stein, 2011)

5 Practices for Orchestrating Productive Mathematics Discussions

1. Anticipating

2. Monitoring

3. Selecting

4. Sequencing

5. Connecting

Questions

How did Mr. Harris structure the whole class discussion (lines 52-57) to advance student learning toward the intended math learning goals?

Jasmine Kenneth

Teresa

Consider Lines 52-57. Why did Mr. Harris select and sequence the work of these three students and how did that support student learning?

Structuring Mathematical Discourse

During the whole class discussionof the task, Mr. Harris was strategic in:

•Selecting specific student representations and strategies for discussion and analysis.

•Sequencing the various student approaches for analysis and comparison.

•Connecting student approaches to key math ideas and relationships.

Pose purposeful questions.

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Teachers’ questions are crucial in helping students make connections and learn important mathematics and science concepts.

(Weiss & Pasley, 2004)

Boaler & Brodie, 2004; Chapin & O’Connor, 2007; Herbel-Eisenmann & Breyfogle, 2005


Effective Questions should:

•Reveal students’ current understandings.

•Encourage students to explain, elaborate, or clarify their thinking.

•Make the targeted mathematical ideas more visible and accessible for student examination and discussion.

Questions

In what ways did Mr. Harris’ questioning on lines 33-36 assess and advance student learning about important mathematical ideas and relationships?

Purposeful Questions Lines 33-36

“How does your drawing show 7 rows?”

“How does your drawing show that there are 20 chairs in each row?

“How many twenties are you adding, and why?”

“Why are you adding all those twenties?

Math Learning GoalStudents will recognize the structure of multiplication as equal groups within and among different representations—identify the number of equal groups and the size of each group within collections or arrays.

Math Learning GoalStudents will recognize the structure of multiplication as equal groups within and among different representations—identify the number of equal groups and the size of each group within collections or arrays.



Build procedural fluency from conceptual understanding.

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A rush to fluency undermines students’ confidence and interest in mathematics and is considered a cause of mathematics anxiety.

(Ashcraft 2002; Ramirez Gunderson, Levine, & Beilock, 2013)

Baroody, 2006; Fuson & Beckmann, 2012/2013; Fuson, Kalchman, & Bransford, 2005; Russell, 2006


Procedural Fluency should:•Build on a foundation of conceptual understanding. •Over time (months, years), result in known facts and generalized methods for solving problems. •Enable students to flexibly choose among methods to solve contextual and mathematical problems.

Questions

In what ways did this lesson develop a foundation of conceptual understanding for building toward procedural fluency in multiplying with multiples of ten?

What foundational understandings were students developing at each of these points in the lesson that are critical for moving toward procedural fluency?

Questions

Lines 59-69: Discussion of skip counting.

Lines 70-76: Wrote the multiplication equation.

Lines 78-81: Asked students to compare Tyrell and Ananda’s work.

Tyrell Ananda

Discuss ways to use this student work to develop the understanding that 14 tens = 140 and to meaningfully to build toward fluency in working with multiples of ten.

Tyrell Ananda

Discuss ways to use this student work to develop informal ideas of the distributive property—how numbers can be decomposed, combined meaningfully in parts, and then recomposed to find the total.

Principles to Actions (NCTM, 2014, p. 42)

“Fluency builds from initial exploration and discussion of number concepts to using informal reasoning strategies based on meanings and properties of the operations to the eventual use of general methods as tools in solving problems.”

http://maccss.ncdpi.wikispaces.net/Elementary+Webinars

Support productive struggle in learning mathematics.

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Support productive struggle in learning mathematics.

The struggle we have in mind comes from solving problems that are within reach and grappling with key mathematical ideas that are comprehendible but not yet well formed.

(Hiebert, Carpenter, Fennema, Fuson, Human, Murray, Olivier, & Wearne, 1996)

Black, Trzesniewski, & Dweck, 2007; Dweck, 2008; Hiebert & Grouws, 2007; Kapur, 2010; Warshauer, 2011

Support productive struggle in learning mathematics.Productive Struggle should:

•Be considered essential to learning mathematics with understanding.

•Develop students’ capacity to persevere in the face of challenge.

•Help students realize that they are capable of doing well in mathematics with effort.

Questions

How did Mr. Harris support productive struggle among his students, individually and collectively, as they grappled with important mathematical ideas and relationships?

At which points in the lesson might Mr. Harris have consciously restrained himself from “taking over” the thinking of his students?

“Teachers greatly influence how students perceive and approach struggle in the mathematics classroom. Even young students can learn to value struggle as an expected and natural part of learning.”


Fixed vs. Growth Mindset

• Fixed: those who believe intelligence is an innate trait; believe that learning should come naturally

• Growth: those who believe intelligence can be developed through effort; likely to persevere through struggle because they see challenging work as an opportunity to learn and grow


What is the central message about productive struggle and student learning?

http://www.ted.com/talks/angela_lee_duckworth_the_key_to_success_grit?language=en

Additional Resource on Mindset

http://ww2.kqed.org/mindshift/2015/08/24/growth-mindset-how-to-normalize-mistake-making-and-struggle-in-class/



Elicit and use evidence of student thinking.

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Elicit and use evidence of student thinking.

Teachers using assessment for learning continually look for ways in which they can generate evidence of student learning, and they use this evidence to adapt their instruction to better meet their students’ learning needs.

(Leahy, Lyon, Thompson, & Wiliam, 2005, p. 23)

Chamberlin, 2005; Jacobs, Lamb, & Philipp, 2010; Sleep & Boerst, 2010; van Es, 2010’ Wiliam, 2007

Elicit and use evidence of student thinking.Evidence should:

•Provide a window into students’ thinking.

•Help the teacher determine the extent to which students are reaching the math learning goals.

•Be used to make instructional decisions during the lesson and to prepare for subsequent lessons.

Questions

Identify specific places during the lesson in which Mr. Harris elicited evidence of student learning.

Discuss how he used or might use that evidence to adjust his instruction to support and extend student learning.

Examples of Eliciting and Using EvidenceThroughout the lesson, Mr. Harris was eliciting and using evidence of student thinking.

Lines 33-36: Purposeful questioning as students worked individually.

Lines 43-51: Observations of student pairs discussing and comparing their representations.

Lines 59-74: Whole class discussion.

Lines 78-80: Asked students to respond in writing.

Preparation of each lesson needs to include intentional and systematic plans to elicit evidence that will provide “a constant stream of information about how student learning is evolving toward the desired goal.”


During the video;

•Identify strategies the teacher uses to access, support, and extend student thinking.

•How do these strategies allow for immediate re-teaching?

•What student behaviors were associated with these instructional strategies?

“My Favorite No: Learning From Mistakes”

https://www.teachingchannel.org/videos/class-warm-up-routine



Sort the Beliefs

Unproductive Beliefs

Check your arrangement on Principles to Actions pg. 11

Principles to Action – pg. 11

Beliefs About Teaching and Learning Mathematics

Essential Elements of Effective Mathematics Programs

Start Small, Build Momentum,and PersevereThe process of creating a new cultural norm characterized by professional collaboration, openness of practice, and continual learning and improvement can begin with a single team of grade-level or subject-based mathematics teachers making the commitment to collaborate on a single lesson plan.

Principles to ActionsWhat action are you taking?

•Your role:– Leaders and policymakers pgs

110-112– Principals, coaches, specialists,

other school leaders pgs 112-114– Teachers pgs 114-117

– Group Discussion about next steps

For Next Time (December 1)

• Think about the needs of your school/district.

• Create a plan of action for implementing Teaching Practices.

• Be prepared to share your plan and outcome with this group.

Next Steps As A Group

• What would you like to see evolve in our follow-up session?

NCCTM Fall Leadership ConferenceNovember 4th

Koury Convention CenterFeaturing:

Daniel Brahier, lead author for NCTM’s Principles to Actions

Diane Briars, President of NCTM

Jon Wray, Howard County Public Schools

45th Annual State Math ConferencePrinciples to Actions in Action

November 5th and 6th

Koury Convention Center

Greensboro, NC

Anyone here being honored as their district’s NCCTM Outstanding Elementary Mathematics Educator?

2014 PAEMST Math State Finalists

Elementary– Kayonna Pitchford

Heather Landreth Meredith Stanley

https://www.paemst.org/

https://www.paemst.org/

What questions do you have?

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NC Mathematicswww.facebook.com/NorthCarolinaMathematics

@ncmathematics

http://maccss.ncdpi.wikispaces.net

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http://maccss.ncdpi.wikispaces.net/

DPI Mathematics Section

Kitty RutherfordElementary Mathematics [email protected]

Denise SchulzElementary Mathematics [email protected]

Lisa AsheSecondary Mathematics [email protected]

Joseph ReaperSecondary Mathematics [email protected]

Dr. Jennifer CurtisK – 12 Mathematics Section [email protected]

Susan HartMathematics Program [email protected]

mailto:[email protected]






For all you do for our students!

Documents

Good morning… Please complete the Survey that can be found on the check in table