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Assessing students using the KCASM/CCSSM Minute-by-minute Day-by-day Katrina Slone, KDE Regional Math Consultant – KVEC Debbie Waggoner, KDE Regional Math Consultant - CKEC Kentucky Council of Teachers of Mathematics Bowling Green, KY - October 8 th, 2011

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Todays Targets I can define formative assessment. I can describe examples of formative assessments. I can classify formative assessments by their types. I can explain why each type of formative assessment is critical to both assessment and further learning.

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Diagram #1 Listen to the following directions. Without talking to anyone, sharing work with anyone or asking any questions, draw the figure described.

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Diagram #2 Listen to the following directions and draw the figure described.

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List 3 examples of formative assessment….

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Formative Assessment

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Formative assessment can and should be done BY STUDENTS as well as by teachers. The key to improvement is how students and teachers use assessment information.

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Formative Assessment Evidence of Learning Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students achievement of intended instructional outcomes. KDE, 2010

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Student Responses to Discuss 1.Describe the problem solving approach the student used. You might, for example: Describe the way the student has colored the pattern of tiles. Describe what the student did to calculate a sequence of numbers. 2.Explain what the student needs to do to complete his or her solution. 14

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Leons method 15

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Giannas method 16

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Avas method 17

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Is this task a formative assessment?

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Formative Assessment Long-cycle Medium- cycle Short- cycle Review the NCTM Research Brief : What does research Say the Benefits of Formative Assessment Are?

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Typology of Kinds of Formative Assessment TypeFocusLength Long-cycleAcross marking periods, quarters, semesters, years 4 weeks to 1 year Medium-cycleWithin and between instructional units 1 to 4 weeks Short-cycle day-by-day minute-by- minute Within and between lessons hours 5 seconds to 2 hours

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Why Now?

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Lack of Engagement in Math Lack of student engagement in learning is the greatest problem in many math classrooms. The Mathematics Practice Standards present a way to leverage discourse. Formative assessment or Assessment for Learning as learning activity for teachers and students.

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Traditionally Teachers Choose One of Three Options 1. Go back and re-teach the topic with the entire class. 2. Identify the students needing remediation and find some time/opportunity to re-teach the topic while the rest of the class continues on. 3. Feeling the pressure of the over packed curriculum the teacher ventures on to the next topic.

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Re-teaching vs. Re-engagement Re-teachingRe-engagement Teach unit againRevisit student thinking Address missing basic skillsAddress conceptual understanding On the same or similar problems Examine task from different perspective Practice moreCritique student approaches Cognition lowerCognition higher

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Generalizing Patterns: Table Tiles Projector Resources

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How does the Table Tiles task require this kind of thinking?

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CCSSM/KCASM ~ Content Cluster CLUSTER: Building a function that models a relationship between two quantities

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Knowledge TargetsReasoning Targets Performance Skills Targets Product Targets Define explicit function and recursive process. Write a function that describes a relationship between two quantities by determining an explicit expression, a recursive process, or steps for calculation from a context. Combine two functions using the operations of addition, subtraction, multiplication, and division Evaluate the domain of the combined function. Given a real-world situation or mathematical problem: -build standard functions to represent relevant relationships/ quantities, -determine which arithmetic operation should be performed to build the appropriate combined function, and -relate the combined function to the context of the problem Identify arithmetic and geometric patterns in given sequences. Generate arithmetic and geometric sequences from recursive and explicit formulas. Given an arithmetic or geometric sequence in recursive form, translate into the explicit formula. Given an arithmetic or geometric sequence as an explicit formula, translate into the recursive form. Use given and constructed arithmetic and geometric sequences, expressed both recursively and with explicit formulas, to model real-life situations. Determine the recursive rule given arithmetic and geometric sequences. Determine the explicit formula given arithmetic and geometric sequences. Justify the translation between the recursive form & explicit formula for arithmetic and geometric sequences. CLUSTER: Building a function that models a relationship between two quantities

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Assessing the Targets Target Define explicit function and recursive process. Determine the recursive rule given arithmetic and geometric sequences. Identify arithmetic and geometric patterns in given sequences. Evaluate the domain of the combined function Formative Assessment Exit Slip: Define explicit function. Entrance Slip: Find the recursive rule for this sequence. Thumbs UP if you think this is an arithmetic pattern for this this sequence. Thumps DOWN if you think it is a geometric pattern. Evaluate the domain of this combined function on your white board.

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So…Do these assess the standard?

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Standard Cake

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I thought that if I taught them all the bits, [students] could put them together. FAL Trial Teacher CCSSM/ KCASM Learning Deconstruction was like sand-blasting to see each part: each skill & concept students need to build on.., Now we need students to make a Mosaiac seeing how the targets & standards fit together to make clusters & BIG IDEAS in mathematics…

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Linking to Research: The QUASAR Project Low-Level Tasks memorization procedures without connections to meaning (e.g., Marthas Carpeting Task) High-Level Tasks procedures with connections to meaning doing mathematics (e.g., The Fencing Task)

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Research – based Conclusions Not all tasks are created equal -- they provided different opportunities for students to learn mathematics. High level tasks are the most difficult to carry out in a consistent manner. Engagement in cognitively challenging mathematical tasks leads to the greatest learning gains for students. Professional development is needed to help teachers build the capacity to enact high level tasks in ways that maintain the rigor of the task. Based on QUASAR & TIMSS Video Study

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Formative Assessment Lessons, or Mathematics FALs, are based on the research about formative assessment and about implementing high level tasks

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Todays Targets I can define formative assessment. I can describe examples of formative assessments. I can classify formative assessments by their types. I can explain why each type of formative assessment is critical to both assessment and further learning.

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How Can We Support You? Thanks for your participation today. Katrina Slone KVEC Regional Mathematics Content Specialist Kentucky Department of Education Office of Next Generation Learners 48 Debbie Waggoner CKEC Regional Mathematics Content Specialist Kentucky Department of Education Office of Next Generation Learners

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