Moving to Action: Effective Mathematics Teaching Practices in the Middle Grades Michael D. Steele University of Wisconsin-Milwaukee Elizabeth Cutter Whitnall (WI) School District
Session Overview NCTM s Principles to Actions: Background, Rationale and Development Supporting the Development of Effective Mathematics Teaching Practices Engaging in Sample Activities: The Hexagon Task Using the Materials with Teachers and Districts Questions and Discussion
A 25-year History of Standards-Based Mathematics Education Reform 1989 Curriculum and Evaluation Standards for School Mathematics 2000 Principles and Standards for School Mathematics 2006 Curriculum Focal Points 2009 Focus in High School Mathematics 2010 Common Core State Standards for Mathematics
Standards have led to higher achievement 4th grade NAEP 8th grade NAEP Mean SAT- Math Mean ACT- Math 1990 13% proficient 15% proficient 501 19.9 2012-2013 42% proficient 36% proficient 514 21.0
but challenges remain. The average mathematics NAEP score for 17year-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.
From Standards to Pedagogy High-quality standards are necessary for effective teaching and learning, but not sufficient. The Common Core does not describe or prescribe the essential conditions required to make sure mathematics works for all students.
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.
Organization of P2A Guiding Principles for School Mathematics 1. 2. 3. 4. 5. 6. Teaching and Learning Access and Equity Curriculum Tools and Technology Assessment Professionalism For each principle Productive and Unproductive Beliefs are Listed Obstacles to Implementing the Principle are Outlined Overcoming the Obstacles Taking Action o Leaders and Policymakers o Principles, Coaches, Specialists, Other School Leaders o Teachers
Teaching and Learning Principle Eight High-Leverage 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 The challenge: How to support meaningful change in classrooms around these eight practices?
A set of professional development resources SUPPORTING DEVELOPMENT OF THE MATHEMATICS TEACHING PRACTICES
The case for content-focused professional development Teachers must see aspects of their own teaching in new practices Case-based professional development allows teachers to generalize about teaching from the particulars of practice Seeing the mathematics teaching practices in action is a critical component to foster meaningful change
The case for content-focused professional development The typical US teacher receives less than 2 days per school year of content-specific professional development. Steele et al. (2015). Learning about new demands in schools: considering algebra policy environments
Principles to Actions Professional Development Modules High-quality classroom video from the University of Pittsburgh Institute for Learning Focus on one or more of the P2A Mathematics Teaching Practices High cognitive demand mathematical task Designed to be used by departments, districts, and cross-district teacher professional learning communities
Sixth Grade Exploring the Hexagon Pattern Task THE CASE OF PATRICIA ROSSMAN Developed by Michael D. Steele at the University of Wisconsin- Milwaukee. Video courtesy of PiPsburgh Public Schools and the InsRtute for Learning.
The Hexagon Task Trains 1, 2, 3, and 4 are the first 4 trains in the hexagon pattern. The first train in this pattern consists of one regular hexagon. For each subsequent train, one additional hexagon is added. For the hexagon pattern: 1. Compute the perimeter for the first 4 trains. 2. Determine the perimeter for the tenth train without constructing it. 3. Write a description that could be used to compute the perimeter of any train in the pattern. (Use the edge length of any pattern block or the length of a side of a hexagon as your unit of measure.)
Hexagon Task: Some Possible Solutions 1 2 1 2 1 2 1 2 1 2 1 2 3 4 3 4 3 4 3 4 3 4 3 4 A Tops & BoPoms, plus 2 ends y = 4x + 2 B Insides and Outsides y = 4(x 2) + 10 C Shared sides subtracted y = 6x 2(x 1) The two outside hexagons each contribute 5 sides The inside hexagons each contribute 4 Number of inside hexagons is train number minus 2 Each hexagon contributes 6 sides For each new hexagon past train 1, there is a pair of inside sides that have to be subtracted The number of shared pairs is the train number minus 1
The Hexagon Task Video School: Austin Independent School District Teacher: Ms. Patricia Rossman Class: 6th grade Many of the students in the classroom have recently arrived to the United States. The students are in a dual language program. This task is an introduction to a unit titled Number Sense, Patterns, and Algebraic Thinking. It is the first time students have been asked to engage in a task that requires them analyze and look for patterns in a visual diagram.
Ms. Rossman s Mathematics Learning Goals Students will: 1. Create a generalization that describes the relationship between the train number and the perimeter of the train and explain how the different components of their generalization can be seen in the visual pattern 2. Identify a constant rate of change between the quantities in the relationship -- as the train number increases by one, the train's perimeter increases by four 3. Understand that the rate of change between the quantities can be seen in a table as the first difference, in a graph as the slope of the line, and in an equation as a the coefficient of the input quantity
Connections to the CCSS Content Standards Expressions and EquaRons 6.EE.6 Represent and analyze quantitative relationships between dependent and independent variables. 9. Use variables to represent two quantities in a real-world problem that change in the relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Connections to the CCSS Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
The Hexagon Task: Video Context Prior to this clip: Ms. Rossman launched the task, ensuring that students understood the words in the task Ms. Rossman communicated that all students in a group should understand the methods they discuss In this clip, we see a small group working on their explanation and interacting with Ms. Rossman, followed by an excerpt of the whole-class discussion in which the same group shares their method.
Lens for Watching the Video: Time 1 As you watch the video, make note of what the teacher does to support student learning and engagement as they work on the task. In particular, identify any of the Effective Mathematics Teaching Practices that you notice Mrs. Rossman using. Be prepared to give examples and to cite line numbers from the transcript to support your claims.
Effective 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.
Effective 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.
Facilitate Meaningful Mathematics Discourse Discourse in math classrooms should: Analyze and compare student approaches and arguments; Make use of student thinking in ways that keep key mathematical ideas prominent; Build students responsibility and agency as knowers and doers of mathematics Students who learn to articulate and justify their own mathematical ideas, reason through their own and others mathematical explanations, and provide a rationale for their answers develop a deep understanding that is critical to their future success in mathematics and related fields. (Carpenter, Franke, & Levi, 2003, p. 6)
Lens for Watching the Video: Time 2 As you watch the video this time, pay attention to discourse moves the teacher makes. As you do, consider: In what ways did the teacher s discourse move support moving her mathematical goals forward? In what ways did the teacher s discourse move support students developing mathematical identities as learners?
What have you learned and how do these ideas apply to your classroom work?
REFLECTING ON THE EXPERIENCE
Principles to Actions Professional Development Modules High-quality classroom video from the University of Pittsburgh Institute for Learning Focus on one or more of the P2A Mathematics Teaching Practices High cognitive demand mathematical task Designed to be used by departments, districts, and cross-district teacher professional learning communities
Reflections and Questions on the Effective Teaching Practices? on the Principles to Action document? on Principles to Action Professional Development modules? Principles to Action webpage: http://www.nctm.org/ PrinciplestoActions/
Getting Started with P2A Learn more about the effective teaching practices from reading the book, exploring other resources, and talking with your colleagues and administrators. Engage in observations and analysis of teaching (live or in narrative or video form) and discuss the extent to which the eight practices appear to have been utilized by the teacher and what impact they had on teaching and learning. Co-plan lessons with colleagues using the eight effective teaching practices as a framework. Invite the math coach (if you have one) to participate. Observe and debrief lessons with particular attention to what practices were used in the lesson and how the practices did or did not support students learning.
Getting Started with P2A PD modules Learn more about the effective teaching practices from reading the book, exploring other resources, and talking with your colleagues and administrators. Engage in observations and analysis of teaching (live or in narrative or video form) and discuss the extent to which the eight practices appear to have been utilized by the teacher and what impact they had on teaching and learning. Co-plan lessons with colleagues using the eight effective teaching practices as a framework. Invite the math coach (if you have one) to participate. Observe and debrief lessons with particular attention to what practices were used in the lesson and how the practices did or did not support students learning.
Using the Principles to Actions Professional Development Modules Book Clubs around P2A: Teachers can read about an effective teaching practice, then meet to engage in a PD module highlighting that practice. On-line access to videos and PD materials: Enable collaboration between teachers in different districts and geographic locations. Optimize use of limited face-to-face meeting time (though we recommend face-to-face interaction for solving the task, when possible).
Using the Principles to Actions Professional Development Modules Provide PD materials for teacher-based groups within or across schools and districts: For school-based teams during common meeting time. To support a District-wide focus on a specific effective teaching practice. For vertical groups: Teachers across different gradelevels could read and discuss an effective teaching practice, then engage with the PD materials for their specific grade-band. For horizontal groups: Teachers in common gradebands or subjects (across schools or districts) could collaborate in face-to-face or on-line groups.
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.
The Title Is Principles to Actions