Florida’s K – 3 Mathematics Formative Assessment System

Introduction to Formative Assessment and Research Findings

Laura Lang, Principal InvestigatorMark LaVenia, Methodologist2012 FCR-STEM Conference St. Petersberg, FL

Overview of presentationIntroductionDefinition and processResearch OverviewResults of MFAS studiesEffect on the gender gap in 3rd grade FCAT mathematics

scoresDiscussion

The importance of K-3 math• Researchers have documented

that student knowledge and achievement in mathematics in preschool and the earliest grades predicts later school success in elementary years and even through high school.

• Scientists typically score at the 90th percentile or above in mathematics in high school.

The importance of K-3 math

• Based on an analysis using the Early Childhood Longitudinal Study of the Kindergarten Class of 1998-99 through 5th grade, boys in kindergarten do better at the top of the distribution and worse at the bottom.

• By third grade, boys do better than girls across the distribution.

Gender Achievement Gap in Grade 3 Mathematics

Reflection and Discussion

1. What are the biggest challenges facing your teachers in elementary mathematics teaching and learning?

2. What tools do you foresee as essential to remove roadblocks for students?

Florida’s definition of formative assessment

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.

(McManus, 2008, p. 3)

Summative assessmentvs. formative assessment• Summative is an assessment

OF learning.

• Formative is an assessment FOR learning.

(Black, Harrison, Lee, Marshall, & Wiliam, 2004)

What is formative assessment?

• A process, not a test• Reveals student thinking in addition to whether

or not the answer is correct• Embedded within a learning activity• Reveals gaps in knowledge and understanding

that derail student progress• Targets instruction to strengthen the core

concepts and processes essential for mathematics learning

• Used not only to “inform” instruction, but more importantly to “form” instruction.

How does formative assessment work?Formative assessment elicits students’ thinking,

helping teachers to:• Diagnose critical misconceptions and errors.• Identify students’ progress toward standard mastery.• Differentiate instruction based on students’

understanding (i.e. individualize interventional strategies and regroup students for optimal learning opportunities).

• Provide students the deep understanding needed for future mathematics learning.

K-3 MFAS - CCSS tasks and rubrics

For each K-3 Mathematics Common Core State Standard, there will be a minimum of four formative assessment tasks and rubrics.

Sample MFAS task

Materials

Instructions

Background on Task

Sample MFAS rubricMisconception or Error

Student Work Examples

Questions Eliciting Thinking

Instructional Implications

Engage Students• Provide pencil, paper, base ten blocks, and number

line.

• Ask each student to solve the following problem:

38 + 13

Eliciting evidence of student understandingStudent solution: 38 + 13 = 51• T: How did you get that solution?

S: I added 3 and 1 to get 40. Then, I added 8 and 3 to get 11. With 40 and 11, I have 51.

• T: Is there any other way that you could have solved the problem?S: I don’t know, maybe.T: Will you show me what you are thinking?S: [explains another possible route]

When to implement formative assessment?

•Before introducing a topic, essentially identifying students’ prior knowledge

•After introducing a topic, with additional instructional time on the horizon

Basic formative assessment process

Select benchmark to teach

Draft a sequence of tasks related to the benchmark.

Implement MFAS task with student.

Take notes describing each student’s response(s)—identifying gaps in knowledge.

Provide descriptive feedback to students; encourage self- and peer- assessment.

Develop a thorough understanding of the benchmark and related MFAS task(s).

Become familiar with selected MFAS task and associated rubric.

Discuss results with your team and develop a plan to differentiate instruction, targeting gaps in the student’s knowledge of the benchmark.

Implement instructional plan targeted to the needs of individual students.

MFAS Process Detail

DECISIONSelect a new benchmark to teach

OrImplement another MFAS task related to the benchmark

OrContinue instruction for student(s) who has not demonstrated mastery.

Research shows that when students take an active role in “monitoring and regulating their learning, then the rate of their learning is dramatically increased,” in fact in some instances doubled.

(NCTM, 2007, p. 3)

Research: Self-Assessment

In non-threatening, collaborative classroom environments:

• Students trust their teacher as well as their peers.• Differences in ideas and opinions are respected

and appreciated. • Teachers exhibit model behaviors and

demonstrate how to provide appropriate feedback.

(Wiliam & Thompson, 2007; CCSSO, 2008)

Research: Collaboration

• Evaluating peer work and providing productive feedback allows students to practice and build skill in improving their own work.

• Effective peer assessment requires two critical elements:

– Students must work as a group not just in a group.

– Each student must be held accountable for his or her contribution to the group.

(Slavin, Hurley, & Chamberlain, 2003)

Research: Peer Assessment

Research: Descriptive FeedbackHelps the student answer three basic questions: 1. Where am I going? 2. Where am I now? 3. How can I close the gap?

Feedback should also force students to engage cognitively:4. Find errors themselves5. Reflect on teacher and peer feedback6. Act on that feedback

(CCSSO, 2008)

Research: Quality Feedback Provide students evidence-based feedback that is directly linked to

the learning outcome and criteria for success.

Effective feedback needs to focus on the quality of student learning rather than on the student or the accuracy of the student’s response.

• Verification tells students whether or not their answers are correct.

• Elaboration provides information to guide students towards the correct answer.

Research indicates that quality feedback should include elements of both types of feedback.

(Shute, 2008)

Research: Comparative Effects

Research indicates that well-designed and implemented formative assessment is an effective strategy for enhancing student learning.

InterventionExtra Months of Learning Gained per Year

Class-size reduction by 30% (for example, from 30 to 20 students) 3

Increase teacher content knowledge from weak to strong (2 standard deviations) 1.5

Formative assessment 6 to 9

(Wiliam, 2007)

Relation between Classroom Practice and Grade 2 Student Achievement

Classroom observation protocol subscale

Estimate (SE) p-value Effect Size

Clarifying and sharing learning intentions

0.48 (0.11)

< .001 0.61

Eliciting evidence of learning and providing feedback

0.36 (0.13)

.006 0.45

Student self- and peer-assessment

0.25 (0.15)

.089 0.29

MFAS Efficacy Trials

Three randomized controlled trials have been conducted on MFAS: 1. a nine-week pilot study in 2010 with K-3 teacher

teams using tasks aligned with Florida’s NGSSS; 2. a semester-long pilot study in 2012 with grade 2-3

teacher teams using tasks aligned with Florida’s NGSSS; and

3. a year-long study currently underway in 2012-13 with K-1 teacher teams using tasks aligned with the CCSS.

Study Samples

• 2010 nine-week pilot study– 14 schools from one district– 169 K-3 teachers – 1939 students

• 2012 semester-long pilot study– 21 schools across three districts– 160 grade 2-3 teachers– 2756 students

2010 MFAS - NGSS Pilot Study

2010 MFAS - NGSSS Pilot Study: Implementation Data

Other Findings from the 2010 MFAS – NGSSS Pilot Study• Teachers’ knowledge of mathematics moderated the student

mathematics outcomes • Principal support is critical in the implementation of formative

assessment. • Many of the treatment group teachers initially rejected the

tasks because they believed the tasks to be too difficult for students. – After implementing the tasks and seeing that their students learned

to successfully solve the problems when instruction targeted the gaps in their knowledge, these teachers reported major changes in beliefs and increased expectations for students in mathematics (Lang, Schoen, Howell, & Davis, 2010).

2012 MFAS - NGSSS Pilot Study: Effect of MFAS Task Usage on Grade 2 and Grade 3 Math Performance

2012 MFAS – NGSSS Pilot Study: Effect of MFAS on Grade 3 Mathematics Achievement by Gender

MFAS-CCSS Project 2011 - 2013• Development of at least 376 formative

assessment tasks aligned to the CCSS for K-3 Math.

• Produce four introductory modules in CPALMS, three for teachers and one for school leaders.

• Create 18 lesson study toolkits aligned to the domains of the CCSS for K-3 Math.

• Test the effect of the use of MFAS on K-3 student achievement and teacher knowledge of content and pedagogy.

• Updates to CPALMS.• All components will be available June 30, 2013.

Closing

• MFAS leaves teachers to decide whether tasks are implemented in one-on-one interviews, small groups, or whole class.

• MFAS is focused on formative assessment occurring day-to-day and minute-to-minute.

• MFAS is focused on teacher collaboration around student thinking and instruction.

• MFAS is designed to support differentiated instruction.

The 2011 – 2013 MFAS-CCSS Team• Laura Lang, Principal Investigator

• Robert Schoen, Co-Principal Investigator• Maureen Oberlin, Project Manager• Michael Anderson (Pinellas)• Charity Bauduin (Okaloosa)• Zachary Champagne (Duval)• Michelle Robinson (Seminole)• Linda Walker (Walton)• Andy Reeves (Pinellas)• Mark LaVenia, Methodologist• Anabelle Andon, ELL Support

Questions and Contact information

Laura Lang, Principal Investigatorllang@lsi.fsu.edu