Assessing students using the KCASM/CCSSM

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

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

List 3 examples of formative assessment….

Formative Assessment

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.

Formative AssessmentEvidence 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 Discuss1. 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.

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Leon’s method

15

Gianna’s method

16

Ava’s method

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Is this task a formative assessment?

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

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

Formative AssessmentReview the NCTM Research Brief : What does research Say the Benefits of Formative Assessment Are?

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 Oneof 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

Re-teaching Re-engagementTeach 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

Knowledge Targets Reasoning TargetsPerformance 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

Assessing the TargetsTarget

• 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.

So…Do these assess the standard?

Standard Cake

“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…

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

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?

Thanks for your participation today.

Katrina SloneKVEC Regional Mathematics

Content Specialist Kentucky Department of Education

Office of Next Generation LearnersKatrina.slone@education.ky.gov

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Debbie WaggonerCKEC Regional Mathematics

Content Specialist Kentucky Department of Education

Office of Next Generation LearnersDebbie.waggoner@education.ky.gov