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They Can Do It! Creating Successful Students by Changing Beliefs and Building Bridges An overview of the researchbased beliefs, strategies, content resources, teacher work habits, and assessment tools that have contributed to student success in mathematics since reform work began in Georgia in 2001 Big Ideas Student Motivation and Confidence Building Classroom Rituals and Routines Content Resources Teaching Strategies Common Assessments Motivating Students Mindset:The New Psychology of Success by Carol Dweck Fixed Mindsets Believe that basic qualities, like intelligence or talent, are fixed traits. A person is either “smart” or “dumb” and there is no way to change this. Talent alone creates success— without effort. Spend time documenting their intelligence or talent instead of developing them. Shy away from challenges. Tell themselves they can’t. Rationalize failure. Growth Mindsets Believe that basic abilities can be developed through effort and hard work - brains and talent are just the starting point. A person can learn more or become smarter if they work hard and persevere. Learn more and learn it more quickly. View challenges and failures as opportunities to improve learning and skills. Research “We now have decades of research demonstrating that teaching students a growth mindset–the knowledge that ability can be developed–leads to greater student challengeseeking, effort, persistence, & achievement.” Students who learn this mindset show greater motivation in school and have higher grades and test scores. The Perils of Promise and Praise Read the article. List three things that surprised or impacted you most. Intelligence is Malleable Neuroscientists tracking students during their teenage years, found substantial changes in performance on verbal and non-verbal IQ tests. Using neuroimaging, they found corresponding changes in the density of neurons in the relevant brain areas for these students. In other words, an increase in neuronal connections in the brain accompanied an increase in IQ-test performance, while a decrease in neuronal connections in the brain accompanied a decrease in IQ-test performance. Four steps for establishing a growth mindset in your classroom: http://blogs.edweek.org/teachers/classroom_qa_with_la rry_ferlazzo/2012/10/response_classroom_strategies_t o_foster_a_growth_mindset.html Strategies for Building Confidence and Promoting Engagement Creating Experts Crediting Competence Scripting for Success Shaded Triangle The diagram above shows a rectangle, with a shaded triangle inside. Create an expression for the area of the shaded triangle. Shaded triangle “Read the problem to yourself. Try and think of a good starting point for the problem. Share your ideas with your partner. Shaded triangle “Read the problem to yourself. Try and think of a good starting point for the problem.(1 to 2 minutes). Share your ideas with your partner. (2 minutes). Teacher reads the problem aloud. “What is a good way to start the problem?” Promoting Engagement: The Three Read You are a medical assistant in a pediatrician’s office and one of your responsibilities is evaluating the growth of newborns and infants.Your first patient, a baby girl named Ivy Smith, was 21.5 inches long at 3 months old. At 8 months, you measure her at 24 inches long. For your medical records, all measurements must be given both in inches and in centimeters: 1 inch = 2.54 cm The Three Read 1. 2. 3. Read the scenario silently. Be ready to describe the situation. What is this about? Read the scenario silently again. This time, list the information you feel is important in this situation. Let’s read the scenario aloud. Write ____ questions that you feel the textbook, a test writer or your teacher might ask about this situation. The Metacognition of the Three Read: What does it do? Classroom Rituals and Routines Pairing of Students (TKES Standards 1, 3, 4, 7, 8) Arrange room for student engagement and a conducive learning environment Homogenous pairs Struggling students seated front and center of the room Allows for differentiation (scaffolding and extension) Questioning (TKES Standards 3, 5, 6, 8) Limit whole-group questioning Informally assess individual student understanding (white boards, thumbs up or down, etc.) Use on-going formative assessment of individual students to inform instruction Call on students randomly (random number generator, popsicles sticks, name cards, etc) Definitive Standards-Based Classroom Structure (TKES Standards 1, 2,3, 5, 6, 7, 8) Use of a timer Warm up- accesses prior knowledge and leads into the opening Opening- learning targets made clear and connected to prior knowledge Work Session- use standards-based units as primary resource Closing- summary of the day’s Big Ideas Resources and Content Unit development Plan at the unit level Based on GaDOE Frameworks Commitment not to write but to FIND tasks All resources from sites written or endorsed by the writers of CCSS-M Unit Development The Process Examine the standards included in the GaDOE unit. Study the intent of the standards ◦ Transformational Geometry ◦ Untangling Functions and Equations Establish unit goals Work through DOE tasks Accept/reject/revise DOE Tasks Find new tasks and skills practice An Example: Coordinate Algebra Unit 2 CA Overview of Units 1 and 2 Unit goals Task List Planning and Teaching a Lesson: We are still not getting it!!! 1. 2. We should offer math as a learning subject, not a performance subject. Students see their role as answering questions correctly. We need to give students more space to learn. Classrooms should teach multi-dimensional mathematics. One dimensional – Repeat the teacher’s methods. Multidimensional – Students ask their own questions, model, reason, problem solve, communicate and connect ideas. 3. 4. All students should be encouraged to take their mathematics learning to the highest possible levels. (Tracking before the 10th grade is a huge problem.) Math classrooms should encourage more depth and less speed. Jo Boaler: Why Students Need the Common Core www.youcubed.org Mathematics Teaching Practices 1. 2. 3. 4. Establish mathematical goals to focus learning. Implement tasks that promote reasoning and problem-solving. Use and connect mathematical representations. Facilitate meaningful mathematical discourse. Mathematics Teaching Practices 5. 6. 7. 8. Pose purposeful questions. Build procedural fluency from conceptual understanding. Support productive struggle in learning mathematics. Elicit and use evidence of student thinking. NCTM Principles to Actions: Ensuring Mathematical Success for All Solving Systems of Linear Equations by Graphing Bellringer: Graph these two linear equations on the same coordinate plane. 2x + 3y = 16 and x – y = 3. Solving Systems of Linear Equations by Graphing Goals You will be able to find exact or approximate solutions of systems of two linear equations in two unknowns by graphing. You will understand that graphical solutions of systems may be approximate rather than exact. Solving Systems of Linear Equations by Graphing Opening: Discussion of the warm-up. What do you notice about the graphs of the equations? What is the significance of this point? Explain that two or more equations can be considered a system of equations. In this case, we have a system of two linear equations in two unknowns. What do you think it means to find the solution of a system of equations. How many solutions does this system have? What is the solution? How can you be sure your solution is correct? Worktime: 1 – 3,( discussion), 4 - 5 Closing: Presentations. Ask students to discuss Problems 4 and 5. Introduce the terms consistent, inconsistent, dependent, and independent. Why might we need an algebraic way to solve systems of equations in addition to a graphical method? Solving Systems of Linear Equations by Graphing Probing and prompting questions: What do you notice about the graphs of the equations? What is the significance of this point? What is the relationship between a linear equation and its graph? (Students have noticed graphs of the equations are the same line.) What does this tell you about the solution set of the system? Explain. How many points are in the solution set? Does every point in the plane make this system true? (Students have noticed that there are no points of intersection.) What does this tell you about the solution set of the system? Explain. How would you describe the graphs of these two equations? Could you have told that without graphing the equations? Explain. Lesson Planning Work the task alone. Discuss solutions with your colleagues. List the mathematics involved in the task. Decide whether the task is aligned to the indicated standard(s). Determine the Standards for Mathematical Practice addressed. Determine the time required to enact the task. For each lesson Establish the goals of the lesson. (Goals are different from posting or reading the standards.) Identify what students should know and understand. Be as specific as possible. Identify new vocabulary. Determine pre-requisite skills. Develop a bell ringer, opening, work session, and closing. Anticipate student responses to the work and write probing questions to address those responses. An Excellent Assessment Program Ensures that assessment is an integral part of instruction. Provides evidence of proficiency with important mathematics content and practices. Includes a variety of strategies and data sources. Informs feedback to students, instructional decisions and program improvement. Common Unit Assessments Less Like This More Like This This is a rough sketch of 3 runners’ progress in a 400 meter hurdle race. Imagine that you are the race commentator. Describe what’s happening as carefully as you can. You do not need to measure anything accurately. Both PARCC and Smarter Balance will emphasize: Concepts and Procedures (40%) Problem Solving (20%) Reasoning (20%) Modeling with mathematics (20%) Common Unit Assessments Format 40% Selected response 40% Constructed response 20% Extended performance task Goals To raise student achievement in mathematics To increase students’ stamina for taking more rigorous assessments such as the Georgia Milestones, PSAT, SAT, and ACT Two Different Plans Separate tests (Teacher tests and more rigorous tests administered separately) Teacher created items combined with more rigorous items to form one test.(These students did better on EOCT) The Process Teachers meet to develop tests before they begin the unit. (Conversation and choices of items help increase rigor and drive instruction.) Items are chosen from resources created or endorsed by CCSS-M writers and individuals or groups advising PARCC and Smarter Balance All items must meet the CCSS-M Assessment Item Quality Criteria. Assessment is evaluated for alignment to the CCGPS using the CCSS Evaluation Tool The Process Tests are graded using a common rubric. Grades on more rigorous items are scaled so as not to destroy student averages. Unit tests are both summative and formative. Data is aggregated and used to assess strengths and weaknesses of individual students, to identify topics for whole class re-engagement, and to compare and improve instructional techniques of individual teachers.