Promoting Learning and Understanding for Students in MathematicsPromoting Learning and Understanding for Students in Mathematics

High Quality Teaching and LearningHigh Quality Teaching and LearningLeadership forLeadership for

Kim Estes, GRREC Math Consultant

Gary Houchens, WKU Department of Ed. Admin., Leadership, & Research

Other new faces

1. Review of MathPLUS grant components2. Goals for Leadership Session/Big Picture3. Data Collection/Debrief homework

assignment4. Explore the scope, audience, and

purposes of student assessment - Concept Maps

5. Review research findings on the role of assessment in supporting student learning - Jigsaw Reading

6. Consider formative assessment practices that benefit student learning - Partner Quiz

Lunch 12:00-12:307. Reflecting on Assessment Feedback8. Homework

Set cell phones to vibrate.Check email during lunch.Participate and contribute fully.Create safe environment for

sharing.Respect ideas of others.Use rule of two feet

1. Content PD through new common standards

23 days of content and standards-based PD around Common Core and content needs as determined by PRAXIS II

2. Authentic learning communities

Lenses on LearningOne-On-One CoachingSchool level PLC

3. Thinking strategies

PD via the Denver-based Public Education & Business Collaborative

4. Coaching Teachers and leadership teams

Planning/Pre-briefObservationReflecting/Debrief

5. Demonstration sitesSchools will become demonstration labs for high-quality math instruction and assessment

For participants, individually, to expand their notions of:

The mathematical knowledge and dispositions students need to have to be mathematically literate in today’s worldhe learning opportunities that need to be created in order to make significant mathematics accessible to all students

For building teams to move their educational systems and classrooms forward in a state of continuous improvement in mathematics instruction and achievement and support the work of teachers engaged in the teacher portion of the MathPLUS grant.

Learning about the characteristics of high-quality math instruction

Learning the NCSM PRIME Leadership framework for leading high-performing math programs in your schools

Increasing administrator confidence regarding instructional leadership of the school’s math program

Assembling a collaborative building/district-level team for leading math improvements.

Building team capacity for using data to inform instruction and develop a meaningful, long-term math improvement plan.

All this facilitated through face-t0-face sessions at GRREC, team work back home, and on-site coaching.

PRIME Leadership Framework

PRinciples and Indicators for Mathematics Education Leaders

Based upon four essential principles of leadership:

1. Equity2. Teaching and Learning3. Curriculum4. Assessment

Day 1 – Content (Algebra)

Day 2 - Characteristics of High Quality Instruction

Sources of data for evaluating your school’s math program

Team-based approach to observing math lessons- each team’s DATA assignment includes an observation of a math lesson

When observing lesson, goal is not to judge.

Intent of observation is to consider how students were making sense of the mathematics and how the teachers worked with student ideas and thinking processes in these lessons.

Explain to teacher that you are conducting this observation as part of an assignment for a seminar in which you are enrolled.

Teams are taken through a structured process for collecting, analyzing and interpreting data for the purpose of identifying current strengths and weaknesses in their mathematics program.

1. Take intellectual risks when needed to explore complicated issues, new ideas, and new mathematics.

2. Complete the individual and team assignments between each session.

3. Meet as a mathematics leadership team between each session to discuss team DATA assignment.

1. Observe a mathematics lesson (using the Secondary Lenses on Learning Observation and Reflection Guide), then reflect with the others who observed the same lesson.

2. Obtain a copy of any problem/task used during the lesson.

3. Meet as a team to discuss the lesson and to identify the cognitive demand of tasks used during the lesson.

Among the tasks collected:1.Identify the cognitive demand of each

task. 2.Categorize each task along a scale from

1 to 4 where 1= low level & 4= high level. (Note that all tasks could be the same level.) Write level of each task on separate post-it note.

3.Place each of the post-it notes at the appropriate position on the chart paper along the horizontal axis (cognitive demand)

Identify the following:• One or two areas of strength that

became evident when your team considered your classroom observations

• One or two areas that will be important to develop

• Which component of instruction will be especially important for your mathematics program improvement plan to address.

How Can Assessment Support Learning and Instruction?

This session offers participants the opportunity to:

• Explore the scope, audience, and purposes of student assessment

• Review research findings on the role of assessment in supporting student learning

• Consider formative assessment practices that benefit student learning.

Discuss at your table the various assessments typically used in education.

A technique for visualizing the relationships among different concepts.

A diagram showing the relationships among concepts.

A technique development by Joseph Novak at Cornell University as a means of representing the science knowledge of students.

Create a concept map, list, or outline that summarizes the range of student assessments used in your school.

Include information about the purposes of, and audiences for, each type of assessment.

Share maps, lists, and outlines with other building team members.

Make revisions (using a different color writing tool) based on comparisons and discussion of how various assessments are used in your building setting and who the audience is for the information.

Meta-analysis of 250 studies from several countries.

Concluded that formative assessment, properly used, leads to significant learning gains (.4 to .7 SD gain) 25 percentile points on the ITBS 4 ACT score points

Questions posed1.Is there evidence that improving

formative assessment raises standards? YES

2.Is there evidence that there is room for improvement? YES

The assessment methods teachers use are not effective in promoting good learning

Grading practices tend to emphasize competition rather than personal improvement

Assessment feedback often has a negative impact, particularly on low-achieving students, who are led to believe they lack “ability” and so are not able to learn

3.2 pg. 102 – 115 Number 1 – 7#1 – Questioning#2 – Feedback through Grading#3 – Peer Assessment and Self-

Assessment#4 – Formative Use of Summative Tests#5 – Underlying Issues#6 – The Big Idea#7 – What You Can Do

Black, et. al (2004) Define formative assessment:

“An assessment activity can help learning if it provides information that teachers and their students can use as feedback in assessing themselves and one another and in modifying the teaching and learning activities.”

The target audience for data from formative assessment is both the teacher and the student.

The information gleaned from data must be “actually used to adapt the teaching work and to meet learning needs.”

QuestioningFeedbackPeer Assessment & Self-AssessmentThe Formative Use of Summative

Assessments

Lengthen wait timeAllows for more complex questions

and for students to express provisional thinking

Use questions that make visible student thinking – answer and explanation

Redirect and extend student thinking

Make opportunities for peer- and self-assessment a regular part of instruction.

Use clear learning targets and rubrics available to students for judging their own work.

Use targets to guide all phases of instruction and encourage students to monitor their own progress.

Allow students to develop their own test questions and solutions.

Through peer and self assessment, let students identify how their work might be improved and revise their answers.

“A student’s lack of learning at any given point is never the end, but rather the

starting point for the next level of learning.”

Shift toward descriptive, non-evaluative feedback: Use written tasks and oral questions that

make student thinking visible Offer comments that let students know

what was done well, what still needs improvement, and guidance on how to make improvements

Give opportunities for students to improve

10 minute BREAK

During this activity you will: Engage in a partner quiz as a student

Analyze the task for its algebra Analyze the experience of participating in a partner quiz for what students and teachers can learn about students’ knowledge of algebra.

1. Select partners.2. Work Question 1 of the task

individually.3. Discuss Question 1 with partner.4. Make revisions (as needed)

based on your partner conversation.

5. Complete Question 2 with your partner.

The task shows a drawing of a single supermarket cart and of as et of 12 nested supermarket carts. The drawings are 1/24 the real size.

1.Create a rule that will tell you the length of the storage space needed when all you know is the number of supermarket carts to be stored. Show how you built your rule: explain which data you used and tell how you used it.

2.Now show how you can figure out the number of carts that can fit in a space s meters long.

See handout 3.j

1. What could a teacher learn about a student’s knowledge of linear patterns from this quiz? How could this activity help a teacher adjust instruction?

2. How could this partner quiz enhance student learning? How would you rate its cognitive demand?

3. How does this activity make the learning goals and performance expectations clear to students?

4. How does the partner quiz shift assessment from assessment OF learning to assessment FOR learning?

5. How would a student who has struggled with math in the past feel about his or he chances of success on this type of assessment?

LUNCH12:00 – 12:30

Assume the role of a teacher who is reviewing student papers from the Supermarket Carts partner quiz. Draft feedback of the type described on pages 99-116. In deciding what feedback to offer Student C, consider the goals of the task and identify the following:

What math skills or concepts does this student seem to understand? What evidence can you point to?

What math skills or concepts does this student still need to learn? What evidence can you point to?

When you have completed your comments on the student paper, consider the following questions:

1.How is this approach to providing feedback similar or different from your understanding of current practices?

2.How might a student, particularly one who has struggled with math in the past, feed about his or her chances to be successful given this type of feedback?

Based on the ideas just discussed, make revisions to your concept map, list, or outline to reflect the changes in your thinking

about your school and district assessment practices.

This session offered the chance to do the following:

1.Explore the scope, audience, and purposes of student assessment.

2.Review research findings on the role of assessment in supporting student learning.

3.Consider formative assessment practices that benefit student learning.

Review the concept map, list, or outline you created today and identify any more revisions you would recommended for your school assessment plan, based on today’s discussion. Synthesis your individual maps into one common school map.

Individual Assignment:

Read 4.2 The Case of the Rafter School District pg. 143-147

Optional Readings and Discussions:Individual or divide as team:

4.1 Making Math Work for All Children4.3 It Doesn’t Add Up – African American Students’ Math Achievement

4.4 Learning from Teaching4.5 Bilingual Math Learners

As a team:Observe algebra lesson and collect data

on formative assessment pg. 366-370 Gather samples of assessment types pg.

371 Select a time and place for your team to

review the collected assessment samples & respond to the questions on page 387 of Participant Book.

Collect info about math course pathway pg. 372-378

Interview students pg. 379-382

1. Pick an idea that came up today that you found particularly interesting. What is your current thinking about this idea?

2. Where are you, and where is your school, with regard to this idea?

3. What are one or two things that you will go back and pursue in order to move yourself and your school along with this data?

4. With whom would you work on this, and what role would they play (or what support would they give?)

Please complete an evaluation form.

Your honest feedback will help guide the planning of our next meeting

See you on December 6, 2011

Contact your facilitators:

kim.estes@grrec.ky.govgary.houchens@wku.edu