By: Marcy Myers. Developing Math Tasks. http://answergarden.ch/view/63462. Answer Garden. Performance Tasks.
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By: Marcy Myers Developing Math Tasks
http://answergarden.ch/view/63462 Answer Garden
Performance tasks challenge students to apply their knowledge and skills to respond to complex real-world problems. They can best be described as collections of questions and activities that are coherently connected to a single theme or scenario. These activities are meant to measure capacities such as depth of understanding, writing and research skills, and complex analysis, which cannot be adequately assessed with traditional assessment questions. (Smarter Balanced, 2012) Definition of Performance Task
DEPTH OF Knowledge (Rigor) Retrieved from: Smarter Balanced
Type I tasks include a balance of conceptual understanding, fluency, and application. These tasks can involve any or all mathematical practice standards. Type I: Tasks assessing concepts, skills and procedures
Type II tasks call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP. 3, 6). These tasks can also involve other mathematical practice standards. Type II: Tasks assessing expressing mathematical reasoning
Type III tasks call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards. Type III: Tasks assessing modeling / applications
Standards • Mathematical Practices (Begin Here) 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 Common Core
Begin with Real World and use factual data • Then move to abstract or symbolic • Do not use distracting graphs, pictures, etc. • Non Math vocabulary 1 grade level below Keys to Performance Tasks
Concise Questions • Time for Exploration • creating conjectures and understanding • perplexity or wonder • Photos or videos are useful Creating the Tasks
Allow time for Communication • MP 3 Construct viable arguments and critique the reasoning of others • Develop roles in small group (facilitator, recorder, manager, reporter) • Allow think time begin with individual time • Anticipate Questions • Group asks question guide thinking “no answers” • Set Clear Expectations (consistent) • Some problems short (opener type) • Open with a literacy passage to introduce Implementation of Math Tasks
Task Name • Grade Level • Task Description • Standards • Mathematical Practices • Create a Rubric or Scoring Developing a Task
What standard are you trying to address? • What are some real life situations for this age group that is relevant? • Cell Phones/Mobile devices • Games • Sports • Music Downloads • Ask for a survey at beginning of year what they enjoy. Brain Storm
Beginning of Year Task Example What do you see?
Beginning of Year Task Example Now what do you notice?
Beginning of Year Task Example What do you see on this picture?
Beginning of Year Task Example What do you think?
Beginning of Year Task Example Now ask them how much they think these items might cost for 1 student?
Beginning of Year Task Example Notebook: $1.00 Pack of Paper: $0.50 Colored Pencils: $1.50 Scissors: $2.00 Eraser: $1.00 Ruler: $0.50 Pack of Pencils: $0.50 Folders: $3.00 Now ask them how much do these items cost for 1 student based on the information provided? How much would these supplies cost for our class? How did you calculate that?
Beginning of Year Task Example Notebook: $1.00 Pack of Paper: $0.50 Colored Pencils: $1.50 Scissors: $2.00 Eraser: $1.00 Ruler: $0.50 Pack of Pencils: $0.50 Folders: $3.00 How much would these supplies cost for 10 students? How much would these supplies cost for 100 students? How much would these supplies cost for 500 students? How did you calculate each of the above?
This could be appropriate for any grade one way to make it accessible for a 1st grader is to change it to just calculating how much the supplies are that are dollar amounts. • Then focus on 1 item that might be $1.00 to find how much for 10 students or the class question. • You might want to give them actual play money to represent the money. Beginning of the Year Task
Does the tool provide a meaningful model to support the mathematics? • Does the tool extend students’ thinking and support their learning of the given mathematical topic? • Is the tool necessary? • Is the tool easy to use? • Does the tool provide support for students to engage in and solve a problem? 5 Questions to Ask for Tool Selection
Virtual Manipulative Library • http://nlvm.usu.edu/en/nav/vlibrary.html • Illuminations • http://illuminations.nctm.org/Activities.aspx?grade=1&grade=2 • Shodor • http://www.shodor.org/interactivate/activities/ Virtual Manipulatives
Close to 20, 100, 1000 (from pearson) • Wings (see quick images and comparing) • Brainbow (fun for teachers and challenging) • Hungry Fish (good for addition/subtraction starts off easy and gets challenging) • Hands On Equations • Math Kid (very basic addition, subtraction, multiplication, and division) Apps for Ipads
Meaningful and has purpose • Read Alouds, small group reads • Teach how to write in math • Begin Day 1 • Model Math and Literacy
http://teacher.scholastic.com/products/math-concepts-skills/math-reads/webinar.htmhttp://teacher.scholastic.com/products/math-concepts-skills/math-reads/webinar.htm • Webinar from Marilyn Burns • http://teacher.scholastic.com/products/math-concepts-skills/math-reads/math-books-topics.htm • List of books from Math Reads by grade level • http://www.slideshare.net/ismes/one-is-a-snail-ten-is-a-crab • This is the book Marilyn uses Math Literature
Mental Math (5-7 minutes) • Today’s Number • On carpet • Not writing down possibly • Math Review (5-7 minutes) • Lesson (10-15 minutes) • Whole group • Problem solving • Flexible Groups (50-60 minutes) • Individuals • Technology (computers, smart board, Ipad, etc.) • Groups of no more than 4 • Key is students need to have direction!!!!!! • Closure (5-7 minutes) • Bring students back to carpet • Journal Writing Balanced MathKey is Standards based and Student Centered
Establish Procedures or routines • Accountability (students) • Data Driven Instruction • (MAPs, anecdotal notes, observations, common assessments) What Now
Blomberg, A. (May, 2013). Math Tasks in a Common Core Curriculum Alignment. Master's Paper for University of Wisconsin. Retrieved from minds.wisconsin.edu/bitstream/handle/1793/65896/AdamBlomberg.pdf?sequence=1 • Rothman, R. (July/August 2012). Nine Ways the Common Core Will Change Classroom Practice. Harvard Education Letter. Retrieved from: http://hepg.org/hel/article/543 • Ramirez, G. Gunderson, E.A., Levine, S.C., Beilock, S.L. Math Anxiety and Working Memory in Elementary School. Journal of Cognition and Development. Retrieved from http://home.uchicago.edu/~lizgunderson/Publications/Ramirez%20et%20al%20%28in%20press%29%20-%20math%20anxiety.pdf Reference Page
CMS Math- https://elementarymathematics.org/ • Marcy’s Wiki- http://marcymyers.cmswiki.wikispaces.net/ • My Blog- http://mmyers44.weebly.com/blog.html • Pearson for investigations- https://www.pearsonsuccessnet.com/snpapp/login/login.jsp?showLoginPage=true Few Important Information