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 8th, 2011

Today’s 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.

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

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

List 3 examples of formative assessment….

Formative Assessment Some things you may have identified as Formative Assessments and are now using: Exit Slips entrance slips bell ringers Thumbs up/down Common Assessments Are these really Formative Assessments? Answer: It depends!

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. The key to formative assessment—the use of the information to move students forward—has not changed.

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

http://map.mathshell.org/materials/lessons.php

Student Responses to Discuss 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.

Leon’s method

Gianna’s method

Ava’s method

Is this task a formative assessment? http://map.mathshell.org/materials/lessons.php Is this task a formative assessment?

http://www. insidemathematics. org/index http://www.insidemathematics.org/index.php/tools-for-teachers/problems-of-the-month

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

Typology of Kinds of Formative Assessment Type Focus Length Long-cycle Across marking periods, quarters, semesters, years 4 weeks to 1 year Medium-cycle Within and between instructional units 1 to 4 weeks Short-cycle day-by-day minute-by- minute Within and between lessons 24-48 hours 5 seconds to 2 hours

Why Now?

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.

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.

Re-teaching vs. Re-engagement Teach unit again Revisit student thinking Address missing basic skills Address conceptual understanding On the same or similar problems Examine task from different perspective Practice more Critique student approaches Cognition lower Cognition higher

Generalizing Patterns: Table Tiles Projector Resources

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

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

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

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

CLUSTER: Building a function that models a relationship between two quantities Knowledge Targets Reasoning 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.

Assessing the Targets Target Formative Assessment 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 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. Possible student work (even faked?)

So…Do these assess the standard? Can you convict students guilty of achieving the standard based on each piece of information about the targets?

Standard Cake Ingredients/cake analogy to targets/standards

CCSSM/ KCASM Learning “I thought that if I taught them all the bits, [students] could put them together.” FAL Trial Teacher Explain acronym KCASM CASL helped us to take apart the standards into the bits necessary to teach and learn them. Short-cycle FA helps us to know if students get the bits. Medium-cycle FA, in the guise of FALs, help us to know if they can put the bits together to really understand and utilize the standard. 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…

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

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

From Smarter Balance

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

Today’s 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.

How Can We Support You? Katrina Slone KVEC Regional Mathematics Content Specialist Kentucky Department of Education Office of Next Generation Learners Katrina.slone@education.ky.gov Debbie Waggoner CKEC Regional Mathematics Content Specialist Kentucky Department of Education Office of Next Generation Learners Debbie.waggoner@education.ky.gov PLEASE CONTACT US FOR SUPPORT!! Thanks for your participation today. 48