Principles to Actions: Ensuring Mathematical

Principles to Actions: Ensuring Mathematical
Spring 2015 Principles to Actions: Ensuring Mathematical Success For All NC DPI Mathematics Department

Welcome “Who’s in the Room”
Survey participants: first timers, math coaches, classroom teachers, central office, principals, etc… This will allow us to modify presentation accordingly.

Norms Listen as an Ally Value Differences Maintain Professionalism
Participate Actively Thumbs up if you agree with these norms. Are there other norms we need to add so that we have the best possible learning experience for all?

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 The percent of 8th graders scoring proficient or above on NAEP rose from 15% in 1990 to 36% in 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-eigth grade NAEP Mathematics Average Scores

North Carolina NAEP Trends in Mathematics
Grade Source 1990 2013 Change 4 NC 223 254 Up 31 US 227 250 Up 23 8 286 Up 36 262 284 Up 22 NAEP Scale Score 1990 –First year NAEP reported NC Scores 2013 – Latest NC NAEP Test Data

NC EOG/EOC Percent Solid or Superior Command (CCR)
Grade 3 46.8 48.2 4 47.6 47.1 5 47.7 50.3 6 38.9 39.6 7 38.5 39.0 8 34.2 34.6 Math I 42.6 46.9 Common Core State Standards

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 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 and 2012, the U.S. mean score declined. Significant learning differentials remain.

Brainstorm Students Media Community Teachers Family
Beliefs about Teaching and Learning Administrators & Leadership Students Media Community Teachers Family Brainstorm

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.

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

Effective Mathematics Programs
Teaching and Learning Access and Equity Curriculum Tools and Technology Assessment Professionalism Although such teaching and learning form the nonnegotiable core of successful mathematics programs, they are part of a system of essential elements of excellent mathematics programs. Consistent implementation of effective teaching and learning of mathematics, as previously described in the eight Mathematics Teaching Practices, are possible only when school mathematics programs have in place— a commitment to access and equity; a powerful curriculum; appropriate tools and technology; meaningful and aligned assessment; and a culture of professionalism.

Teacher Beliefs “Teachers’ beliefs influence the decisions they make about the manner in which they teach mathematics.” Pass out books Principles to Actions, p. 10 Principles to Actions pg. 10

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 Principles to Actions pg. 10

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

For Each of the Six Principles
Obstacles to Implementing the Principle Productive and Unproductive Beliefs Overcoming the Obstacles Illustration Moving to Action

Effective Mathematics Programs
Teaching and Learning Effective Mathematics Programs Teaching and Learning Access and Equity Curriculum Tools and Technology Assessment Professionalism

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

5 Interrelated Strands Constitute Mathematical Proficiency
National Research Council, 2001

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.

Eight High-Leverage Instructional Practices
Establish mathematics goals to focus learning Implement tasks that promote reasoning and problem solving Use and connect mathematical representations Facilitate meaningful mathematical discourse Pose purposeful questions Build procedural fluency from conceptual understanding Support productive struggle in learning mathematics Elicit and use evidence of student thinking

Not to be confused with…

What do you notice?

Overview of the Eight Mathematics Teaching Practices

1. 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. Principles to Actions pg. 12

Problems Discussed Math Problems
Morgan wants to buy the next book in her favorite series when it is released next month. So far, she has saved $15. The book will cost $22. How much more money does Morgan need to save so that she can buy the book? (Problem type: Add to/ Change Unknown) George and his dad are in charge of blowing up balloons for the party. The package had 36 balloons in it. After blowing up many balloons, George’s dad noticed that the package still contained 9 balloons. How many balloons had they blown up? (Problem type: Take from/Change Unknown) Lou and Natalie are preparing to run a marathon. Lou ran 43 training miles this week. Natalie ran 27 miles. How much farther did Lou run than Natalie? (Problem type: Compare/Difference Unknown) Principles to Actions pg. 14

Need 3 Volunteers per group for Role Playing
Choose a puzzle piece from the center of the table. Find your group members. In your group, role play the scenario on pgs What do you notice about the dialog? Use puzzle pieces/tickets to break into group of 6. 3 read and 3 observe

What did you notice about the dialog?
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
Now, let’s think about the standards for mathematical practice. What do you notice? Principles to Action – pg. 16

What is the Teacher Doing? What are the Students Doing?
Key Words Teaching Practice What is the Teacher Doing? What are the Students Doing? Establish mathematics goals to focus learning. Clear goals, learning progression, purpose, guide Discussion of goals, focus on progress, where math is going, Implement tasks that promote reasoning and problem solving. Use and connect mathematical representations. Facilitate meaningful mathematical discourse. Pose purposeful questions. Build procedural fluency from conceptual understanding. Support productive struggle in learning mathematics. Elicit and use evidence of student thinking.

1. Establish Mathematics Goals to Focus Learning
Learning progressions or trajectories describe how students make transitions from prior knowledge to more sophisticated understandings Both teachers and students need to be able to answer these crucial questions: What mathematics is being learned? Why is this important? How does it relate to what has already been learned? Where are these mathematical ideas going? Situating learning goals within the mathematical landscape supports opportunities to: Build explicit connections See how ideas build and relate to one another Develop a coherent and connected view of the discipline

2. 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. Principles to Actions pg. 17

High or Low Cognitive Demanding Task?

Cognitive Demand Jigsaw/Sort
Everyone grab a puzzle piece from your table. Move to the designated spot in the room for your color. Green: Memorization Yellow: Procedures without Connections Blue: Procedures with Connections Red: Doing Mathematics Read page 18 and summarize the description associated with your cognitive demand task type. Come to a shared understanding of the demand task and be prepared to share back at your table. At your table, use the contents of the envelope to sort the tasks by cognitive demand.

Low Cognitive Demand Tasks High Cognitive Demand Tasks
Memorization Tasks Involve either reproducing previously learned facts, rules, formulae, or definitions OR committing facts, rules, formulae, or definitions to memory Cannot be solved using procedures because a procedure does not exist or because the time frame in which the task is being completed is too short to use a procedure. Are not ambiguous-such tasks involve exact reproduction of previously seen material and what is to be reproduced is clearly and directly stated. Have no connection to the concepts or meaning that underlie the facts, rules, formulae, or definitions being learned or reproduced. Procedures with Connections Tasks Focus students’ attention on the use of procedures for the purpose of developing deeper levels of understanding of mathematical concepts and ideas. Suggest pathways to follow (explicitly or implicitly) that are broad general procedures that have close connections to underlying conceptual ideas as opposed to narrow algorithms that are opaque with respect to underlying concepts. Usually are represented in multiple ways (e.g., visual diagrams, manipulatives, symbols, problem situations). Making connections among multiple representations helps to develop meaning. Require some degree of cognitive effort. Although general procedures may be followed, they cannot be followed mindlessly. Students need to engage with the conceptual ideas that underlie the procedures in order to successfully complete the task and develop understanding. Procedures without Connections Tasks Are algorithmic. Use of procedure is either specifically called or its use is evident based on prior instruction, experience, or placement of the task. Require limited cognitive demand for successful completion. There is little ambiguity about what needs to be done and how to do it. Have no connection to the concepts or meaning that underlie the procedures being used. Are focused on producing correct answers rather than developing mathematical understanding. Require no explanations, or explanations that focus solely on describing the procedure that was used. Doing Mathematics Tasks Require complex and non-algorithmic thinking (i.e., there is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instructions, or a worked-out example). Require students to explore and understand the nature of mathematical concepts, processes or relationships. Demand self-monitoring or self-regulation of one’s own cognitive processes. Require students to access relevant knowledge and experiences and make appropriate use of them in working with the task. Require students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions. Require considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required. Stein, Smith, Henningsen, & Silver (2000)

What are the attributes of a mathematically strong task?
Table Talk What are the attributes of a mathematically strong task?

Task Implementation Student Learning
High Low High Low Moderate

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.

Yeah – K-2 NCDPI - page 21 Go Kitty! Go Denise!

Look on page 21 NCDPI – Task

Principles to Action - page 24

Key Words Teaching Practice What is the Teacher Doing? What are the Students Doing? Establish mathematics goals to focus learning. Implement tasks that promote reasoning and problem solving. Use and connect mathematical representations. Facilitate meaningful mathematical discourse. Pose purposeful questions. Build procedural fluency from conceptual understanding. Support productive struggle in learning mathematics. Elicit and use evidence of student thinking.

Which Math Practices would students be engaged in?
Make a connection to the SMPs and the student actions in the parallel charts.

2. Implement tasks that promote reasoning and problem solving
Effective math teaching and learning uses carefully selected tasks as one way to motivate student learning and build new knowledge. Research on math tasks over the past two decades has found: Not all tasks provide the same opportunities for student thinking and learning. Student learning is the greatest in classrooms where tasks consistently encourage high-level student thinking and the least in classrooms where tasks are routinely procedural in nature. Tasks with high cognitive demands are the most difficult to implement well and are often transformed into less demanding tasks. To ensure that students have the opportunity to engage in high- level thinking, teachers must regularly select and implement tasks the promote reasoning and problem solving.

3. Use and connect mathematical representations
Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving. Principles to Actions pg. 24

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? Principles to Actions pg. 27

Use and connect mathematical representations.
Illustrate, show, or work with mathematical ideas using diagrams, pictures, number lines, graphs, and other math drawings. Use concrete objects to show, study, act upon, or manipulate mathematical ideas (e.g., cubes, counters, tiles, paper strips). Record or work with mathematical ideas using numerals, variables, tables, and other symbols. Solve the problem How did you solve the problem? Find the type of representation and gather Compare your work with your group. Find someone from another group and compare how you each solved it What do you notice about how most people solved it? Situate mathematical ideas in everyday, real-world, imaginary, or mathematical situations and contexts. Use language to interpret, discuss, define, or describe mathematical ideas, bridging informal and formal mathematical language.

Principles to Actions pg. 29

3. Use and Connect Mathematical Representations
Effective mathematics teaching includes a strong focus on using varied mathematical representations. Using a variety of representations helps students examine a concept through more than one lens. Selected representations could include: Visual representations Physical representations Symbolic representations Contextual representations Verbal representations When students learn to represent, discuss, and make connections among mathematical ideas in multiple forms, they demonstrate deeper mathematical understanding and enhanced problem-solving skills. (Fuson, Kalchman, & Bransford, 2005; Lesh, Post, and Behr, 1987)

4. Facilitate meaningful mathematical discourse
Effective teaching of mathematics facilitates discourse among students in order to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments. Principles to Actions pg. 29

“What students learn is intertwined with how they learn it
“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) Teachers need to develop a range of ways of interacting with and engaging students as they work on tasks and share their thinking with other students.

5 Practices for Orchestrating Productive Mathematics Discussions
Anticipating Monitoring Selecting Sequencing Connecting Group jigsaw Reference page 30

Table Talk Think back to the Band Concert Task
Review the student work samples. As a table, determine the mathematical goal for the task. Determine which students should present a solution, and in what order the solutions should be presented. What questions should be asked to connect solutions? Goal: Order and Reasoning: Connections: Refer to example on pg 27 showing students moving through representations

Let’s Do Some Math One bag of cat food will feed 3 cats for 40 days. If I buy 2 more cats, how long will one bag of cat food last? Do the task individually. Becoming a Problem Solving Genius, Zaccaro, pg. 5

3 cats x 40 days = 120 servings per bag
Number of Cats Equation Number of Days 120 ÷ 1 = 120 120 120 ÷ 2 = 60 60 120 ÷ 3 = 40 40 120 ÷ 4 = 30 30 120 ÷ 5 = 24 24

Table Talk During the cat food task, how did you use discourse to build shared understanding?

4. Facilitate Meaningful Discourse
Effective mathematics teaching engages students in discourse to advance the mathematical learning of the whole class. Smith and Stein (2011) describe five practices for effectively using student responses in class discussions: Anticipating student responses prior to the lesson Monitoring students’ work on engagement with tasks Selecting particular students to present their mathematical work Sequencing students’ responses in specific order for discussion Connecting different students’ responses and connecting responses to key mathematical ideas Students must have opportunities to talk with, respond to, and question one another as part of the discourse community, in ways that support the mathematics learning for all students in class

5. Pose purposeful questions
Effective teaching of mathematics uses purposeful questions to assess and advance student reasoning and sense making about important mathematical ideas and relationships. Principles to Actions pg. 35

Types of Questions-Four Corners
Gathering Information Probing Thinking Making the mathematics visible Encouraging reflection and justification Each corner is a question type Provide participants with cards: description, examples…. Participants locate correct corner

Types of Questions In your table group, sort the question descriptions and examples. Create at least 1 additional question that fits each description. Are these types of questions important in the classroom? Principles to Actions pg

Funneling vs Focusing Read pg 37, last two paragraphs
Review Figure 16 on pg 39-40 Using chart paper, illustrate funneling vs focusing questioning patterns. What are some barriers that might prevent teachers from moving from funneling to focusing questions? All four types of questions are important in our questioning pattern however it’s the way in which we use the questions that develops or leads to understanding. From NCTM’s PtA Reflections Guide: Teachers use a variety of questions in their instruction (see fig. 14, pp. 36–37), including questions that should elicit mathematical reasoning and justification. Unfortunately, teachers too often employ these questions in a “funneling” manner (see fig. 16, pp. 39–40). Brainstorm with your team to identify barriers that might prevent teachers from moving from “funneling” to “focusing” questions. Learning involves a cognitive reorganization of individual beliefs. This reorganization demands some degree of dissonance. How do funneling questions discourage dissonance and how do focusing questions encourage dissonance? In questioning small groups of students working on a problem, a teacher noticed that when she asked a “focusing” question, the students continued to look at their work and continued to engage in their own dialogue. When she asked a “funneling” question, the students looked up at the teacher. Comment on these observations. Identify a math task that you might give to your students. State the learning goal, and then use the task to create a list of related questions using the framework in figure 14 (pp. 36–37). It will be helpful to first anticipate likely student responses and misconceptions (see Smith & Stein’s practice 1, p. 30). If your district uses a specific framework for questioning (e.g., Bloom’s Taxonomy or Webb’s Depth of Knowledge), compare that framework with the framework of types of questions shown in figure 14 (pp. 36–37). Discuss any connections.

Expectation of Knowledge
Funneling vs Focusing Expectation of Knowledge Question 1 Question 2 Question 3 Question/Clarification Questioning pattern dialog to compare strategies….pg

5. Pose Purposeful Questions
Effective mathematics teaching relies on questions that encourage students to explain and reflect on their thinking as an essential component of meaningful discourse. Commonalities exist across a number of questioning frameworks. Key cross cutting aspects of a number of frameworks that are particularly important within mathematics instruction include: Gathering information Students recall facts, definitions, or procedures Probing thinking Students explain, elaborate, or clarify their thinking, including articulating the steps in solution methods or the completing of a task Making the mathematics visible Students discuss mathematical structures and make connections among mathematical ideas and relationships Encouraging reflection and justification Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work

6. Build procedural fluency from conceptual understanding
Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. Principles to Actions pg. 42

Form two lines… How does computational fluency relate to conceptual understanding? How do we move from conceptual understanding to computational fluency? Where do we use computational fluency in mathematics? Why are algorithms necessary? Standard algorithms are to be understood and explained and related to visual models before there is any focus on fluency. (Page 44)

How could Anna’s reasoning help David understand his mistake?
Look at David and Anna’s work. David’s application of the multiplication algorithm leads to and incorrect answer, and he doesn’t recognize that it’s not reasonable. Students need procedures that they can use with understanding on a broad class of problems. Principles to Actions pg. 43

How Are these Methods Interrelated?
Principles to Actions pg. 45

Principles to Action - page 47

6. Build Fluency from Conceptual Understanding
Effective mathematics teaching focuses on the development of both conceptual understanding and procedural fluency. Both NCTM and CCSS-M emphasize that procedural fluency follows and builds on a foundation of conceptual understanding, strategic reasoning, and problem solving. Students who use math effectively do much more than carry out procedures. Such students must also know: Which procedure is appropriate and most productive for a given situation, What a given procedure accomplishes, and What kind of results to expect “Mechanical execution of procedures without understanding their conceptual basis often leads to bizarre results” (Martin, (2009), p.165)

7. Support productive struggle in learning mathematics
Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships. Principles to Actions pg. 48

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. Principles to Actions pg. 50

Shopping Trip Task Joseph went to the mall with his friends to spend the money that he had received for his birthday. When he got home, he had $24 remaining. He had spent 3/5 of his birthday money at the mall on video games and food. How much money did he spend? How much money had he received for his birthday? Principles to Actions pg. 51

Table Talk Using the chart on pg 49, analyze the scenario on pg 51.
Discuss how you see expectations for students, teacher support, and indicators for success.

Principles to Actions pg. 49, 51
Expectations for students Teacher actions to support students Classroom- based indicators of success Most tasks that promote reasoning and problem solving take time to solve, and frustration may occur, but perseverance in the face of initial difficulty is important. Use tasks that promote reasoning and problem solving; explicitly encourage students to persevere; find ways to support students without removing all the challenges in a task. Students are engaged in the tasks and do not give up. The teacher supports students when they are “stuck” but does so in a way that keeps the thinking and reasoning at a high level. Correct solutions are important, but so is being able to explain and discuss how one thought about and solved particular tasks. Ask students to explain and justify how they solved a task. Value the quality of the explanation as much as the final solution. Students explain how they solved a task and provide mathematical justifications for their reasoning. Everyone has a responsibility and an obligation to make sense of mathematics by asking questions of peers and the teacher when he or she does not understand. Give students the opportunity to discuss and determine the validity and appropriateness of strategies and solutions. Students question and critique the reasoning of their peers and reflect on their own understanding. Diagrams, sketches, and hands-on materials are important tools to use in making sense of tasks. Give students access to tools that will support their thinking processes. Students are able to use tools to solve tasks that they cannot solve without them. Communicating about one’s thinking during a task makes it possible for others to help that person make progress on the task. Ask students to explain their thinking and pose questions that are based on students’ reasoning, rather than on the way that the teacher is thinking about the task. Students explain their thinking about a task to their peers and the teacher. The teacher asks probing questions based on the students’ thinking. Principles to Actions pg. 49, 51

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 Principles to Actions pg. 50

Struggling to Learn What is the central message in this video about productive struggle and student learning? Carol Dweck, Psychologist Growth Mind-set Research The Teaching Channel How does having a growth mindset relate to embracing and supporting student struggle?

Emergentmath.com

7. Support Productive Struggle in Learning Mathematics
Effective mathematics instruction supports students in struggling productively as the they learn mathematics. Teacher actions to support students in productive struggle include: Students engage in problems that take time to solve Teachers select tasks that promote reasoning and problem solving; explicitly encouraging students to persevere; finding ways to support students without removing challenges in a task. Students explain and discuss how they thought about and solved tasks Teachers ask students to explain and justify how they solved a task, and value the quality of the explanation as much as the final solution. Students have a responsibility and obligation to make sense of the math Teachers give students the opportunity to discuss and determine the validity and appropriateness of strategies and solutions. Students use important tools in making sense of the task Teachers give students access to tools that will support their thinking process. Students communicate one’s thinking during a task Teachers ask students to explain their thinking and pose questions based on students’ reasoning, rather than on the way the teacher is think about the task.

8. Elicit and use evidence of student thinking
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning. Principles to Actions pg. 53

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.” Principles to Actions pg. 53

“My Favorite No: Learning From Mistakes”
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? 1. Give each student an index card and ask them to individually answer the following problem. Create an array for 4 x 12 and then show the math sentences that could be used to solve it. 2. Each student responds on an index card. 3. Quickly collect the cards and sort by Yes (correct) and No (incorrect) answers. Don't let the students see how others did but announce each yes and no. Select an incorrect response that can promote a strong discussion about the problem. 4. Copy the problem on the board or on another card under the document camera. 5. Ask the children to find what is right about what this person did. Discuss. 6. Ask the children what did this person do incorrectly? Discuss. Both discussions should form a review of the meaning of multiplication, as well as give you further information on who may struggle with this problem

8. Elicit and Use Evidence of Student Thinking
Effective mathematics teaching elicits evidence of student’s current mathematical understanding and uses it as the basis for making instructional decisions. A focus on evidence includes: Identifying indicators of what is important to notice in students’ mathematical thinking Planning for ways to elicit that information Interpreting what the evidence means with respect to students’ learning Deciding how to respond on the basis of students’ understanding Using assessment for learning means that: Students are revealing their mathematical understanding, reasoning, and methods in classroom discourse and written work. Students reflect on mistakes and misconceptions to improve their understanding Students ask questions, responding to, and giving suggestions to support the learning of their classmates Students assess and monitor their own progress towards math learning goals, and identify areas they can improve

Unproductive Beliefs Sort the Beliefs
Check your arrangement on Principles to Actions pg. 11

Beliefs About Teaching and Learning Mathematics
These beliefs should not be viewed as good or bad. Beliefs should be understood as unproductive when they hinder the implementation of effective instructional practice or limit student access to important mathematics content and practices. Principles to Action – pg. 11

Essential Elements of Effective Mathematics Programs
Teaching and Learning Access and Equity Curriculum Tools and Technology Assessment Professionalism

Start Small, Build Momentum, and Persevere
The 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.

What action are you taking?
Principles to Actions What action are you taking? Your role: Leaders and policymakers pgs Principals, coaches, specialists, other school leaders pgs Teachers pgs Choose at least one action that you plan to implement as a result of today’s session. Turn and share your plan with a shoulder partner.

What questions do you have?

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DPI Mathematics Section
Kitty Rutherford Elementary Mathematics Consultant Denise Schulz Lisa Ashe Secondary Mathematics Consultant Vacant Dr. Jennifer Curtis K – 12 Mathematics Section Chief Susan Hart Mathematics Program Assistant 119

For all you do for our students!

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