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MATH NIGHT

MATH NIGHT. Dr. Paul Rasmussen Secondary Mathematics Curriculum Leader Fairfield Public Schools. Introduction. Welcome Common Core State Standards ( CCSS ) & Mathematical Practices Smarter Balanced Assessment Consortium ( SBAC ) Concept vs. Skill

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MATH NIGHT

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  1. MATH NIGHT Dr. Paul Rasmussen Secondary Mathematics Curriculum Leader Fairfield Public Schools

  2. Introduction • Welcome • Common Core State Standards (CCSS) & Mathematical Practices • Smarter Balanced Assessment Consortium (SBAC) • Concept vs. Skill • Concrete-Representational-Abstract Instructional Model • Example Instructional Task/Lesson Progression • Closure & Questions

  3. Video Introduction • http://video.msnbc.msn.com/nightly-news/49156028#49156028

  4. Common Core State Standards • National initiative to improve the math instruction and learning in the United States. • Adopted in 46 out of the 50 states. • Fewer Topics taught in various grades and courses. • Benchmarked internationally

  5. CCSS Mathematical Practices • 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.

  6. Grouping the Mathematical Practices HABITS OF MIND 1. Make sense of problems and persevere in solving them. 6. Attend to precision. LOGICAL THINKING AND EXPLAINING 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. REPRESENTATION AND TOOLS 4. Model with mathematics. 5. Use appropriate tools strategically. STRUCTURE AND GENERALIZING 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

  7. SBAC Assessment

  8. SBAC Assessment • New State Assessment System • Replaces the Connecticut Mastery Test (CMT) • Begins in the 2014-2015 school year • Computer Adaptive Assessment • Administered during the last 12 weeks of the school year

  9. Sample SBAC Assessment Question • Parking Lot Problem • How is this problem different than the problems you solved within math class?

  10. Current Data

  11. Recent Scores from the High Schools

  12. CAPT Assessment: Algebra Strand

  13. Grade 8 Strand 25: Math Applications (Problem Solving)

  14. Research to Improve Problem Solving

  15. Concepts vs. Skills • Concept Development before Skill Development helps provide students with the rationale behind the particular skill. • Connecting the procedures to BIG IDEAS allows students to cognitively link to prior knowledge, thus helping augment student learning. • (Stein, Smith, Henningsen, & Silver, 2000)

  16. Classification of Mathematical Tasks

  17. Boaler & Staples (2008) • The success of students in the high-achieving school was due in part to the high cognitive demand of the curriculum and the teachers’ ability to maintain the level of demand during enactment through questioning.

  18. CRA Instructional model • CRA is the Concrete to Representational to Abstract sequence of instruction. • Three stages of learning • C = Learning through concrete tangible/hands-on manipulative objects • R = Learning through pictorial forms of the math skill • A = Learning through work with abstract (Arabic) notation • Based on Bruner’s theory of enactive, iconic and symbolic reasoning (Witzel, 2007)

  19. Instructional Sequence Example

  20. Example: Algebra • Graph the equation: • y = 2x + 1

  21. Traditional Approach to Linear Functions

  22. WHY? Where does this procedure approach come from?

  23. CCSS Approach to Linear Functions • Using a motion detector, walk away from the device at a constant rate (i.e., walk the same speed the entire time). Then, once a graph is generated, use the graphing technology provided by your teacher to find the equation of the line.

  24. What number in the equation changed the slope of the line? • What number in the equation changed how high the graph crossed the y-axis?

  25. CCSS Approach to Linear Functions • Decide how to walk so that you will get the graph for the equation y = 2x + 1. • After the entire team understands how to walk, one member will try to graph the line • by walking in front of the motion detector. • Pay close attention to detail! You only have two tries!

  26. Graphing a Linear Equation Dependent Variable Rate of Change Independent Variable Starting Amount y = mx + b

  27. Now to the ABSTRACT!

  28. THE BIG RACE In the first heat, Leslie, Kristin, and Evie rode tricycles toward the finish line. Leslie began at the starting line and rode at a constant rate of 2 meters every second. Kristin got an 8-meter head start and rode 2 meters every 5 seconds. Evie rode 5 meters every 4 seconds and got a 6-meter head start.

  29. Classification of Mathematical Tasks

  30. CCSS Mathematical Practices • 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.

  31. Myths • My student will learn less if he/she is in a classroom where the teacher uses cooperative learning strategies. According to John Hopkins University (2010), the most effective math programs use cooperative learning strategies. These programs allow all students to challenge their thinking through the use of rigorous tasks.

  32. Myths • The teacher does not do any work during the instructional period. The teacher is constantly monitoring how ALL students are doing throughout the learning process. The teacher’s role is the question student thinking and guide them to proper conceptual and procedural understanding.

  33. Group Work Continued • Myths • The top student is being held back by the slower student in the group. All students will be challenged during the instructional period. If a teacher notices a student is doing all the work, then he/she reserves the right to reassess the various roles they are assigned.

  34. Myths My student will receive a poor grade based upon other students’ work. The teacher assesses what each individual student can do and what they know. Cooperative learning is the vehicle that gets more students engaged in the learning and to perform better on the objective assessments.

  35. Grade Data to Date:Algebra

  36. Closure and Questions

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