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Alabama College- and Career-Ready Standards for Mathematics. Thinking Through A Lesson Protocol (TTLP), Part II. Quarterly Meeting #4. Alabama Quality Teaching Standards (AQTS). Standard 1: Content Knowledge Standard 2: Teaching and Learning Standard 5: Professionalism.
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Alabama College- and Career-Ready Standards for Mathematics Thinking Through A Lesson Protocol (TTLP), Part II Quarterly Meeting #4
Alabama Quality Teaching Standards (AQTS) Standard 1: Content Knowledge Standard 2: Teaching and Learning Standard 5: Professionalism
As professionals, we should take ownership of our professional growth and continued improvement This is an opportunity to do just that!
Outcomes Participants will: • Reflect and discuss previous learning (QM 1 – 3) (10 – 15 minutes) • Identify and evaluate strategies that provide effective instructional support (part II of TTLP – explore) – for the targeted standards and use of precise and accurate mathematics
Worthwhile tasks alone are not sufficient for effective teaching. Teachers must also decide what aspects of a task to highlight, how to support students without taking over the process of thinking for them and thus eliminating the challenge, what questions to ask to challenge those with varied levels of expertise, and how to organize and orchestrate the work of students. NCTM, 2000
Escalator Video http://www.youtube.com/watch?v=uVN-7h4YiAs&feature=related
Thinking Through a Lesson ProtocolBackwards Planning What will you see or hear that lets you know students are developing understanding of the concepts? What questions will you need to ask to build mathematical understanding? What mathematical concepts will be developed in the implementation of this task? What do you expect your students to do as they engage in the lesson? Share, Discuss, and Analyze Set Up Explore
K – 5 Tasks K- 2 Task: Write two math story problems where both the answers would be 100. Write the equation that goes with each of your stories and show your computation. Put an “E” by the easy problem and an “H” by the hard problem and explain what makes the easy problem easy and the hard problem hard. 3 – 5 Task: Comparing is in the Cards Place the following cards into the blanks to make the greatest number and the smallest number. Write these two numbers on a piece of paper with a <, >, or = to make a true statement. (Cards are 8, 3, 5, 1, and 7) ____ ____ . ____ ____ ____
6 – 12 Tasks 6 – 8 Task: Orange Juice Jungle: Which Tastes Juicier? If all orange concentrates are the same strength, which recipe would you expect to have the strongest orange taste? 1) Oscar’s Juice: 2 cups concentrate, 3 cups water. 2) Orangeade: 5 cups concentrate, 8 cups water 3) Outrageous Orange: 3 cups concentrate, 4 cups water 4) Julius’ Juice: 4 cups concentrate, 7 cups water Work with a partner. Share reasoning and solution strategies. 9 – 12 Task: Administrative Assistant’s Wages What measure of central tendency would most closely represent the potential pay of a new administrative assistant if there are ten administrative assistants who all make about the same amount and a supervisor who makes ten times as much? In your group, discuss and justify why this would be the best choice.
Task In your table group… • Review and Solve the task • Complete the TTLP – Part II
Teacher’s Support In your table group… • Using the TTLP – Part II, discuss and chart out what instructional supports teachers could use to support students’ exploration of the task without reducing the cognitive demands of the task
“During the planning phase, teachers make decisions that affect instruction dramatically. They decide what to teach, how they are going to teach, how to organize the classroom, what routines to use, and how to adapt instruction for individuals.” Fennema & Frank, 2007
Job-a-Like Reflection How can we help teachers improve their capacity to anticipate and provide instructional supports for the difficulties students are likely to have with a particular task?
Session II Participants will: Discuss and reach a consensus on what is observable evidence of the degree to which students can independently demonstrate the targeted CCRS standards (hear, see, model, write) (Practice Standards)
Formative assessment is… • Questioning rather than explaining. • Listening rather than talking. • Centered on student learning. • Assessment for learning. The instruction must change as a result of the assessment for it to be formative.
Why Formative Assessment? “Research reported shows conclusively that formative assessment does improve learning.” - Assessment in Education 1998 “Reports conclude that formative assessment will improve student learning, even when not done ‘perfectly’.” - James Popham, Ed.D (2011)
K – 5 Tasks K- 2 Task: Write two math story problems where both the answers would be 100. Write the equation that goes with each of your stories and show your computation. Put an “E” by the easy problem and an “H” by the hard problem and explain what makes the easy problem easy and the hard problem hard. 3 – 5 Task: Comparing is in the Cards Place the following cards into the blanks to make the greatest number and the smallest number. Write these two numbers on a piece of paper with a <, >, or = to make a true statement. (Cards are 8, 3, 5, 1, and 7) ____ ____ . ____ ____ ____
6 – 12 Tasks 6 – 8 Task Orange Juice Jungle: Which Tastes Juicier? If all orange concentrates are the same strength, which recipe would you expect to have the strongest orange taste? 1) Oscar’s Juice: 2 cups concentrate, 3 cups water. 2) Orangeade: 5 cups concentrate, 8 cups water 3) Outrageous Orange: 3 cups concentrate, 4 cups water 4) Julius’ Juice: 4 cups concentrate, 7 cups water Work with a partner. Share reasoning and solution strategies. 9 – 12 Task Administrative Assistant’s Wages What measure of central tendency would most closely represent the potential pay of a new administrative assistant if there are ten administrative assistants who all make about the same amount and a supervisor who makes ten times as much? In your group, discuss and justify why this would be the best choice.
Formative Assessment Using your task: • How will you orchestrate the class discussion so that you accomplish your mathematical goals? • How will you formatively assess? • What data will you collect? • How should we use this data? • How will this change the rest of your class and future classes? • How will you consider learning supports in your assessment?
A key challenge mathematics teachers face in enacting current reforms is to orchestrate discussions that use students’ responses to instructional tasks in ways that advance the mathematical learning of the whole class. Stein, Engle, Hughes, & Smith, 2006
Equity begins with an understanding of how the selection of tasks, the assessment of tasks, the student learning environment creates great inequity in our schools… Timothy Kanold, February, 2010
Job-a-Like Reflection • Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain • Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain. • Final thoughts comments?
