Changing the Course of High School Mathematics Classrooms: More than One

Teacher at a Time

Mary Mooney Laura Maly

Mathematics Teaching Specialists, Milwaukee Public Schools

www.mmp.uwm.edu

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation.

In this session participants will:

Examine the system of support a large urban school district is using in order to improve teaching and learning in high school mathematics.

Consider implementation strategies for advancing classroom instruction, improving content knowledge, and deepening understanding of a discovery approach.

Distributed Leadership

Student Learning Continuum

Teacher Learning Continuum

Mathematics Framework

How it all began…

Textbook Selection Committee for 9th and 10th grade

RubricWisconsin StandardsDistrict Learning TargetsAdditional ResourcesComprehensive Math Framework

Comprehensive Mathematics Framework

Put your student hat on…

Describe as many ways as you can to multiply 34 by 34.

Laying the Groundwork Partnering with Key Curriculum Press

Curriculum Pacing Guides Discovering Algebra Discovering Geometry

Train the Trainer

Moodle

UWM Credit Option

And they’re off…

We had in place…

Algebra and Geometry Labs All day PD sessions designed to familiarize

teachers with the content and pedagogy of the Discovering Series

MPS and UWM collaborative session Any teacher could attend

Math Teacher Leader meetings All day PD for MTL’s involving content,

assessment and leadership pieces

In December, we got snowed…

It snowed…a lot Wind, snow, and cold, cold temps

Publisher visits (from Texas) Three days of classroom visits Lessons learned

How do we dig ourselves out?

Mandatory PD for all high school MTL’s

PD offered to all Administrators

Classroom Visit Template

Classroom Visit Template

Designed with MTLs in mind

Communication tool to use with teachers

 Data collection to help design meaningful PD based on teacher needs

Students are: Teachers are:

Engaging in the exploration or investigation

Using investigation

Gathering, organizing, and analyzing data

Using technology

Using technology tools Employing cooperative learning

Sharing with their groups Moving among groups

Sharing results with the class Asking reflective questions

Asking pertinent questions Prompting and redirecting

Making conjectures Asking inquiry-type questions

Testing conjectures Highlighting mathematical content objectives

Analyzing results Offering encouragement

Explaining reasoning Using ample wait time

Justifying conclusions Informally assessing

Modifying instruction

Highlighting appropriate vocabulary

On target with curriculum pacing guide

Using CABS

Using resources from district-selected Discovering Mathematics

Working with Resistors

MTL request for PD on … ”everything”

Really?

Making Coherence

Fidelity with Discovering Mathematics Program

MMP Learning Team Continuum

MPS School Improvement Plan(SIP)

Stage 1Learning Targets

Stage 2Alignment of

State Framework & Math Program

Stage 3Common Classroom

Assessments

Stage 4Student Work

on CABS

Stage 5Descriptive Feedback

on CABS

Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.

Develop meaning for the math embedded in the targets and alignment to state standards and descriptors and to the school’s math program.

Provide a measure of consistency of student learning based on standards/descriptors and targets.

Examine student work to monitor achievement and progress toward the targets and descriptors.

Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback.

School Professional Work• Teachers develop an awareness of district learning targets for each mathematics strand.• Teachers discuss what each learning target means and can articulate the math learning goals students are to reach.• Teachers examine the development of mathematical ideas across grade levels.

School Professional Work• Teachers examine alignment of state descriptors to targets.• Teachers identify the depth of knowledge in the descriptors.• Teachers study how the mathematical ideas in the descriptors are developed in the school’s math program.• For each lesson, teachers inform students of the math learning goals in terms that students understand.

School Professional Work• Teachers select and study common CABS that will be used within a grade level.• Teachers identify math expectations of students assessed through the CABS.• Teachers identify potential student misconceptions revealed through the CABS.• Learning Team and teachers examine student WKCE and Benchmark Assessment data to identify areas of strengths and weaknesses for focusing teaching and learning.

School Professional Work• Teachers collaborate in grade-level meetings to discuss student work and implications for classroom practice.• Teachers meet in cross grade-level meetings to discuss common expectations of student math learning and implications for school practice.• Learning Team monitors and discusses student learning on CABS results from across the school, shares observations with staff, and uses data for Educational Plan.

School Professional Work• Teachers collaborate to write students descriptive feedback on Benchmark Assessments and on common CABS from the curriculum guides.• Students use descriptive feedback to revise their work and improve learning. • Teachers use descriptive feedback to continuously adjust and differentiate instruction.• Learning Team monitors the successes and challenges of writing descriptive feedback and identifies professional learning needs of teachers.

Tools• Grade level lists of 9-11 big ideas per grade (the targets)• Horizontal list of targets by content across grades

Tools• Target-descriptor alignment worksheets• WKCE Depths of Knowledge Framework• Curriculum Guides

Tools• Curriculum Guides • District Model CABS• Depths of Knowledge worksheet• CABS Assessment Overview worksheet• WKCE and Benchmarks student data

Tools• MMP Protocol for Analysis of Student Work• DVD of MMP Protocol• CABS Class Summary Report form• School Educational Plan

Tools• Types of Feedback sheet • Descriptive feedback worksheets• CABS Class Feedback Summary worksheet

What to do with all that snow?

What does it look like?

How do we package it?

How do we market it?

Talk a Mile a Minute

CONSTANT

PRODUCT

TERM

QUADRATIC EQUATION 

TRINOMIAL

Talk a Mile a Minute

BINOMIAL  EXPRESSION    VARIABLES  POLYNOMIAL

SQUARED

Sharing Learning Intentions

We are learning to use a rectangle diagram to model multiplication.

We know we are successful when we can recognize and use properties of a perfect square.

“…children are more motivated and task oriented if they know the learning intention of the task, but they are also able to make better decisions about how to go about the task. “

Shirley Clark, 2001

What is the area of each of the inner rectangles?

What is the sum of the rectangular areas?

What is the area of the overall square?

What conclusions can you make?

Back to the Mathematics…

Draw a rectangle diagram for each expression. Combine any like terms and express as a trinomial.

a. (x+5)2

b. (x-3)2

Just Do It!

Make a rectangle diagram for each expression. How did you decide on the dimensions?

a. x2 + 14x + 49

b. x2 - 18x + 81

Let’s “Undo”!

Which of these trinomials are perfect squares? How do you know?

a. x2 + 14x + 49

b. x2 - 18x + 81

c. x2 + 20x + 25

d. x2 - 12x - 36

Perfect Squares

Tasks that require students to perform a memorized procedure in a routine manner lead to one type of opportunity for student thinking; tasks that demand engagement with concepts and that stimulate students to make purposeful connections to meaning or relevant mathematical ideas lead to a different set of opportunities for student thinking. (Stein et al., 2009)

Questioning & Cognitive Demand

We are learning to use a rectangle diagram to model multiplication.

We know we are successful when we can recognize and use properties of a perfect square.

Check for Understanding

Examine the system of support a large urban school district is using in order to improve teaching and learning in high school mathematics.

Consider implementation strategies for advancing classroom instruction, improving content knowledge, and deepening understanding of a discovery approach.

Check for Understanding

Changes we’ve made Teacher-driven PD sessions Collaborative lesson planning

Changes we want to make Meaningful and timely follow-up after PD More explicit support for professionals who

support math classrooms

Looking Back and Looking Forward

Lesson Planning with Formative Assessment Principles Date: ______________ Grade: ______________ Lesson: ______________

Part 1: Selecting and Setting Up a Mathematical Task This part contains four critical components that need to be considered when selecting and setting up a mathematical task.

Part 2: Supporting Student Exploration of the Task In this section, construct three questions that will develop the mathematics of the lesson. Be sure to consider the Depth of Knowledge to develop the questions. These questions could be used with students individually or in small groups.

Part 3: Summarizing the Mathematics In this section, construct a question that focuses on orchestrating a whole group discussion of the task that uses different solution strategies produced by the students that highlight the mathematics of the lesson.

1. Important Mathematics to Develop: 2. Learning Target & Descriptors: 3. Lesson Objective in Student Friendly Language: We are learning to… 4. Success Criteria: We know we are successful when…

Q1. Access background knowledge: Q2. Develop understanding of the mathematics by pushing student reasoning: Q3. Summarize the important mathematics in the lesson. This should tie back to the success criteria.

Q. Summarize the important mathematics in the lesson as a whole class discussion. This should tie back to the success criteria.

“Labs refresh my motivation to be creative and to create higher level thinking activities and lesson plans that are interesting and engaging. They have helped me be a better teacher! I now know and have experienced the potential of a classroom environment.”

Quotes from Lab Participants

“Labs have given me different ways of approaching lessons, connections with fellow colleagues (sharing lesson plans, ideas, etc.), and a chance to actually do the lesson plans prior to the students. Gives me good insights!”

Quotes from Lab Participants

Personal Reflections

An idea that squares with my beliefs. . .

A question or concern going around in my head. . .

A point I would like to make. . .

Resources Black, P., & Wiliam, D. (1998). Inside the black box:

Raising standards through assessment. Phi Delta Kappan, 80(2), 139-148.

Brookhart, S.M., (2007). Feedback that fits. Educational Leadership, 65(4), 54-59.

Clarke, S. (2001). Unlocking formative assessment: Practical strategies for enhancing pupils’ learning in the primary classroom. Abingdon, UK: Bookpoint LTD.

Stein et al. (2009). Implementing Standards-Based Mathematics Instruction. Columbia University: Teachers College Press.

Stiggins, R.J., Arter, J., Chappuis, J., & Chappuis, S. (2005). Assessment for learning: An action guide for school leaders. Portland, OR: Assessment Training Institute.

Wiggins, G., & McTighe, J. (1998). Understanding by design. Alexandria, VA: Association for Supervision and Curriculum Development.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation

www.mmp.uwm.edu

Mary Mooney: mooneyme@milwaukee.k12.wi.usLaura Maly: guzmanlm@milwaukee.k12.wi.us