Task Selection PARTNERS for Mathematics Learning 1 PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 2 Grades 6 – 8 Questioning and Task Selection Partners for Mathematics Learning

On the paper provided, list… 2 Putting It To Practice On the paper provided, list…  The lesson(s) and learning targets shared  The methods of sharing with students and parents  Any impact you noticed within your students, yourself, and/or your classroom from this sharing Be sure to look at your colleagues pages at the break Partners for Mathematics Learning

 Module 1: Learning Targets 3 Overview of Modules  Module 1: Learning Targets  Module 2: Questioning and Task Selection  Module 3: Inferences and Feedback  Module 4: Making Students Active Partners  Module 5: Decisions about Next Steps  Module 6: Collaboration Around Assessment Partners for Mathematics Learning

Teaching-Learning Cycle Clear Learning Targets Decisions About Next Steps Student Self- Assessment & Responsibility Questioning & Instructional Tasks Making Inferences & Giving Feedback Partners for Mathematics Learning Collaboration Around Assessment

Why Focus on Tasks?  Classroom instruction should be organized 5 Why Focus on Tasks?  Classroom instruction should be organized around mathematical tasks  The tasks in which students engage determine what they learn about mathematics and how they learn it  “Not all tasks are created equal, and different tasks provoke different levels and kinds of student thinking.” (Stein, Smith, Henningsen & Silver, 2000) Partners for Mathematics Learning

Why Focus on Tasks?  How do you use mathematical tasks in your class? 6 Why Focus on Tasks?  How do you use mathematical tasks in your class?  Currently, how do you decide on the tasks for your class? Partners for Mathematics Learning

Task Selection “One of the most important and yet difficult 7 Task Selection “One of the most important and yet difficult aspects of designing a lesson is choosing or creating the worthwhile mathematical task a teacher wants students to engage in.” Lappan & Friel, 1993 Partners for Mathematics Learning

 To learn how to select tasks that allow for 8 Module Learning Targets  To learn how to select tasks that allow for the greatest opportunity for student learning, while being aligned with lesson learning targets  To ask questions at higher levels to support those tasks in order to engage, deepen, and assess mathematical understanding in our students Partners for Mathematics Learning

C haracteristics of M athematical T asks 9 C haracteristics of M athematical T asks  Look at the two tasks on the next slides and think about:  How would you go about solving them?  What would be a possible learning target you would have for selecting these tasks? Which of the two tasks requires students to do more in-depth thinking and causes them to be more intellectually engaged? Partners for Mathematics Learning

Task 1  You are carpeting a room that is 3 yards 10 Task 1  You are carpeting a room that is 3 yards long and 4 yards wide. How many square yards of carpeting do you need to purchase? Partners for Mathematics Learning

 Our class will raise chickens for the 11 Task 2  Our class will raise chickens for the science fair and can use 24 feet of fencing to build a rectangular pen  How long are the sides that give the chickens as much room as possible?  How long are the sides if only 16 feet of fencing is used?  How would you determine the pen with the most room for any amount of fencing? Partners for Mathematics Learning

Comparisons  How are the two tasks alike?  How are they different? 12 Comparisons  How are the two tasks alike?  How are they different?  For each task…  How/when would you implement this task?  What is the role of the teacher and students?  What skills were employed during the task?  What kinds of information about a student’s thinking can be gathered through each task? Partners for Mathematics Learning

1 2 4 5 Difficulty vs. Intellectual Engagement 13 Difficulty vs. Intellectual Engagement 1 2 + = 4 5  This problem would be difficult for a first grader to solve but not for a sixth grader that has the mathematical understanding  The math is the same and the intellectual engagement is the same for any grade level  The level of difficulty changes depending on the student’s mathematical understanding Partners for Mathematics Learning

NAEP Levels Of Complexity 14 NAEP Levels Of Complexity  Low Complexity- recall, recognition, calls for some procedure or algorithm  Moderate Complexity- more flexibility of thinking than the low-complexity, beyond the habitual, more than a single step, methods of reasoning and problem-solving strategies  High Complexity- more abstract reasoning, planning, analysis, judgment, and creative thought Partners for Mathematics Learning

Task Sort  Sort the task cards into piles 15 Task Sort  Sort the task cards into piles  One pile you consider to contain low complexity tasks  One pile you consider to contain moderate  One pile you consider to contain high  Remember: Difficulty ≠ intellectual engagement! Partners for Mathematics Learning

 When is the appropriate time and place for 16 Turn and Talk  When is the appropriate time and place for lower complexity tasks?  How should tasks relate to learning targets? Partners for Mathematics Learning

 Sufficient time allowed for exploration – not 17 Maintaining Higher Complexity Tasks  Sufficient time allowed for exploration – not too much or too little  High level performance modeled by teacher or capable students  Task builds on prior knowledge  Teacher draws on frequent connections  Teacher presses for justifications, explanations, and meaning through questioning, comments, and feedback Partners for Mathematics Learning

Good Math Questions  Good math questions engage students 18 Good Math Questions  Good math questions engage students  Students do more than recall known facts  Students have opportunities to make connections  Good math questions promote development of higher levels of thinking and reasoning in students Partners for Mathematics Learning

Good Math Questions  Requires more than remembering a fact or 19 Good Math Questions  Requires more than remembering a fact or reproducing a skill  Students can learn from answering the question and teachers learn about each student from their attempts at solutions  There may be several possible answers Relate good questions to tasks that require greater intellectual engagement Partners for Mathematics Learning

Math Task, Question, or Problem? 20 Math Task, Question, or Problem?  These terms are being used interchangeably throughout our modules, though different authors may use different definitions  Sometimes a task has only one question, and other times, it’s a scenario with multiple questions Partners for Mathematics Learning

 Explain why the first question is routine 21 Recognizing “Good” Questions  Explain why the first question is routine  What is the mean of 6, 7, 5, 8, and 4?  The average of five different numbers is 6. What might the numbers be?  After five games, the goalie had averaged blocking 6 goals per game. What might be the number of goals he blocked in each game?  How do the 2 nd and 3 rd questions challenge student thinking of the same learning target? Partners for Mathematics Learning

Transforming a Routine Question 22 Transforming a Routine Question  Learning Target: Solve multi-step inequalities  Routine Question: Solve 3 x + 1 < 28 NOW…  Write a possible non-routine question that is likely to stimulate student interest and encourage a greater depth of understanding Partners for Mathematics Learning

Transforming a Routine Question 23 Transforming a Routine Question Learning Target 1: Add and subtract integers Learning Target 2: Use ratios to solve a problem  Write a routine question  Write 2 new non-routine questions  Record your examples in your journals and be ready to share with others Partners for Mathematics Learning

Talk at Your Tables  Why is it okay for students to struggle with 24 Talk at Your Tables  Why is it okay for students to struggle with a task or a good question?  Write your response in your journal Partners for Mathematics Learning

The Role of Questioning 25 The Role of Questioning “During the course of a school day, teachers ask many questions. In fact, something like 60% of the things said by teachers are questions and most of these are not planned.” Good Questions for Math Teaching , Sullivan & Lilburn, 2002  Discuss with a partner kinds of questions you routinely ask and write examples in your journal Partners for Mathematics Learning

Ways Teachers Use Questions 26 Ways Teachers Use Questions  Engaging Questions  Refocusing Questions  Clarifying Questions Dynamic Classroom Assessment , Bright and Joyner, 2005 Partners for Mathematics Learning

 Invite students into a discussion, 27 Engaging Questions  Invite students into a discussion,  Keep students engaged in conversations  Invite them to share their work or get answers “on the table” Examples: What strategies might we use to solve this problem? What do you know that will help you answer this question? Partners for Mathematics Learning

Find The Perimeter  Engaging  “How can we find 3 cm 4 cm 1 cm 28 Find The Perimeter  Engaging questions are questions that invite students into a conversation 4 cm 3 cm 1 cm  “How can we find the missing measurements?” Modified from Dynamic Classroom Assessment , Bright and Joyner, 2005 Partners for Mathematics Learning

Refocusing Questions  Helps students get back on track or walk 29 Refocusing Questions  Helps students get back on track or walk away from “dead end” strategies  Reopens conversation to the group if only one or two students are answering Examples: How is this problem similar to the one we just did? What quantities are you comparing? Partners for Mathematics Learning

Find The Perimeter  Refocusing questions  “If the figure is a large 30 Find The Perimeter  Refocusing questions help students get back on track or move away from a dead-end strategy 4 cm 3 cm 1 cm  “If the figure is a large rectangle with a piece cut out, what do you know about the large rectangle?” Partners for Mathematics Learning

Clarifying and Probing Questions 31 Clarifying and Probing Questions  Help students clarify their own thinking  Help teachers understand students’ thinking  Help students understand each other’s ideas Example Questions How did you figure out your answer? Why did you start with that number? Nika, can you explain, in own words what Maria just shared? Partners for Mathematics Learning

Find The Perimeter  Bob said that the missing 3 cm 4 cm 1 cm 32 Find The Perimeter  Clarifying questions help students explain & teachers understand their thinking  Bob said that the missing measurements are 1 cm and 2 cm, and the teacher asks, “Bob, can you explain to Mary how you got those answers?” Partners for Mathematics Learning 4 cm 3 cm 1 cm

Integrating Purposes of Questions 33 Integrating Purposes of Questions  Engaging questions can help thread a discussion by involving many students in the conversation  Refocusing questions can help keep a discussion from going off on a tangent  Clarifying or probing questions can help others understand student responses and can help students self-check the relevance of their contributions Partners for Mathematics Learning

How to Ask Good Questions 34 How to Ask Good Questions  From research on questioning we know  Waiting for answers is important  Questions may need to be rephrased for clarity  More probing questions need to be asked, not just factual questions  Ask only one question at a time  Be flexible with expected answers  So much of questioning is contextual Partners for Mathematics Learning

 Once your learning targets have been 35 Making It A Habit  Once your learning targets have been determined and the appropriate tasks have been chosen, think about important questions to ask students during the lesson  Engaging, Refocusing, Clarifying and Probing • Specific to the content For students who are struggling For students who are on track For students ready for more  Copy them on index cards to keep with you throughout the lesson Partners for Mathematics Learning

When selecting tasks, think about…  What are your learning targets? 36 In Summary When selecting tasks, think about…  What are your learning targets?  What background knowledge is needed for the task?  What are ways the task can be solved? (misconceptions/errors students may have)  What are your expectations for students?  How will you communicate and assess your expectations?  Are there any challenges for EC/ELL students? Partners for Mathematics Learning

Selecting and Supporting Tasks 37 Selecting and Supporting Tasks  What questions will you ask – engaging, refocusing, and clarifying?  How will you orchestrate a classroom/group discussion around a task?  How will you assess student mastery of the learning target?  What will you do tomorrow to build on this lesson? Partners for Mathematics Learning

Why Focus on Tasks?  Revisiting journal questions: 38 Why Focus on Tasks?  Revisiting journal questions:  What questions do you still need answered on mathematical tasks from your list from earlier in this module?  In summary, what makes a good mathematical task? Partners for Mathematics Learning

Homework: Putting It To Practice 39 Homework: Putting It To Practice  Take a task you have used frequently in class and change it to increase the level of complexity associated with that task  Create a list of questions - engaging, refocusing, and clarifying and probing - you might ask about this altered task Partners for Mathematics Learning

Partners for Mathematics Learning is a Mathematics-Science 40 DPI Mathematics Staff Chief Consultant Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell Carmella Fair Johannah Maynor Amy Scrinzi Partners for Mathematics Learning is a Mathematics-Science Partnership Project funded by the NC Department of Public Instruction. Permission is granted for the use of these materials in professional development in North Carolina Partner school districts. Partners for Mathematics Learning

PML Dissemination Consultants 41 PML Dissemination Consultants Julia Cazin Ruafika Cobb Anna Corbett Gail Cotton Jeanette Cox Lisa Davis Ryan Dougherty Tricia Essick Tery Gunter Barbara Hardy Kathy Harris Rendy King Rene Lemons-M atney Tina McSwain Marilyn Michue Kayonna Pitchford Ron Powell Susan Riddle Alisan Royster Judith Rucker P enny S hockley Pat Sickles Nancy Teague Jan Wessell Dan Wicks Carol Williams Stacy Wozny Partners for Mathematics Learning

2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich 42 Partners Staff Jeane M. Joyner, Co-PI & Project Director Freda Ballard, Webmaster Anita Bowman, Outside Evaluator Meghan Griffith, Administrative Assistant Tim Hendrix, Co-PI and Higher Ed Ben Klein , Higher Education Katie Mawhinney, Co-PI and Higher Ed Catherine Schwartz, Higher Education 2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich Nancy Teague Stacy Wozny Please give appropriate credit to the Partners for Mathematics Learning project when using the materials. Permission is granted for their use in professional development in North Carolina Partner school districts. Partners for Mathematics Learning

Task Selection PARTNERS for Mathematics Learning 43 PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 2 Grades 6 – 8 Questioning and Task Selection Partners for Mathematics Learning