Successfully Implementing High-Level Math Tasks

Presented by

Jennifer Montgomery

and Grace Greenleaf

Opener Sometimes when we subtract one number

from another number we “regroup”, and sometimes we don’t. For example, if we subtract 8 from 375, we can “regroup by converting a ten to 10 ones:

Opener Find a 3-digit number to subtract

from 375 so that:a. You don’t have to use regrouping (decompose).

b. You would naturally use regrouping from the tens to the ones place.

c. You would naturally use regrouping from the hundreds place to the tens place.

d. You would naturally use regrouping in all places.

In each case, explain how you chose your numbers and complete the problem.

4.NBT.B.4 (Numbers and Operations in Base Ten) – Fluently add and subtract multi-digit whole numbers using the standard algorithm.

A good teacher makes you think even when you don’t want to.

(Fisher, 1998, Teaching Thinking)

Objectives Participants will….

Use the thinking through a lesson protocol to successfully plan for and implement a high-level math task to all students, including English Learners to bridge to CCSS implementation.

Create an implementation site plan for Fall 2013

Agenda

Opener The CCSS for Mathematics Example of a Problem Solving Lesson:

A Pencil and a Sticker Problem Thinking Through a Lesson Protocol Group Practice PLC Process Reflection

Common Core State Standards

For Mathematics

Common Core State Standards

Emphasize the 21st Century Learning Skills

Full implementation in 2014-15 with a new assessment

Students in grades 3-8 and grade 11 will be tested in 2014-15

Test includes constructed and selected response questions focused mostly at DOK levels 3 and 4

Common Core State Standards

Mathematics has two set of standardsStandards for Mathematical

Practice which occur throughout all grade levels

Content Standards that are specific for each grade level

Standards for

Mathematical Practice

Student Friendly Language

CCSS for Mathematical Practice Student-friendly Language

Make sense and persevere in solving problems.

I can try many times to understand and solve a math problem.

Reason abstractly and quantitatively. I can think about the math problem in my head, first.

Construct viable arguments and critique the reasoning of others.

I can make a plan, called a strategy, to solve the problem and discuss other students’ strategies too.

Model with mathematics. I can use math symbols and numbers to solve the problem.

Use appropriate tools strategically. I can use math tools, pictures, drawings, and objects to solve the problem.

Attend to precision. I can check to see if my strategy and calculations are correct.

Look for and make use of structure. I can use what I already know about math to solve the problem.

Look for and express regularity in repeated reasoning.

I can use a strategy that I used to solve another math problem.

Math Solutions-Look Fors as Classroom Indicators

What students should be doing for each practice

What teachers should be doing for each practice

Understanding Language:Judit Moschokovich

University of CA, Santa Cruz

Language Functions in the Standards for

Mathematical Practice Read, locate and highlight language

functions in the standards for mathematical practice.

Use the margins to make any inferences you make.

• Note: A language function refers to the purpose for which speech or writing is being used.

Standards for Mathematical Practice

What standards for mathematical practice did you use as you solved the opening problem? Explain your thinking.

How are the standards

for mathematical practice

helpful for English Learner’s?

Content Standards

The standards for mathematics:Are focused, coherent, and rigorousAim for clarity and specificityStress conceptual understanding of

key ideasBalance mathematical understanding

and procedural skillAre internationally benchmarked

Reading the Content Standards

Content standards define what students should understand and be able to do.

Clusters are groups of related content standards. Domains are larger groups of related content

standards that progress across grade levels.

StandardfromGrade 3

Problem Solving

High-Level Math Tasks as the Center of All

Instruction

Problem Solving

“When students do computation, their thinking should be high-level, critical thinking--- including the same math strategies that many adults in the United States employ in their daily lives.”

“Small Steps, Big Changes: Eight Essential Practices for Transforming Schools Through Mathematics” Chris Confer and Marco Ramirez”

Try Solving This Problem

“You are shopping at a grocery store. You have a twenty-dollar bill in your pocket. You find a frozen pizza for $10.00, a bag of apples for $5.55, and a box of cereal for $4.65. Do you have enough money to buy everything?”

“Problem Solving requires a degree of intellectual struggle. Good math problems make students want to do that kind of mental exercise. Good math problems encourage students to think back to similar problems they’ve done in the past, and try out tools and models that could help them. Most important of all, intellectual struggle develops persistence.”

“Small Steps, Big Changes: Eight Essential Practices for Transforming Schools Through Mathematics” Chris Confer and Marco Ramirez”

Math Task – A Pencil and a Sticker

Solve the problem in as many ways as you can.

A Pencil and a Sticker

A pencil costs 59 cents, and a sticker costs 20 cents less. How much do a pencil and a sticker cost together?

Thinking Through a Lesson Protocol

Focused Lesson Planning

Thinking Through a Lesson Protocol (TTLP) Provides a framework for

developing lessons that uses students’ mathematical thinking as the critical ingredient in developing their understanding of key disciplinary ideas.

Helps teachers anticipate what students will do and generate questions to ask that will promote student learning.

Why Lesson Planning?

The effectiveness of a lesson depends significantly on the care with which the lesson plan is prepared.

(Brahier, 2000)

Good planning “shoulders much of the burden” of teaching by replacing “on-fly-decision making” during a lesson with careful investigation into the what and how of instruction before the lesson is taught.

(Stigler & Hiebert, 1999, p.156)

Why Lesson Planning?

“During the planning phase, teachers make decisions that affect instruction dramatically. They decide what to teach, how they are going to teach, how to organize the classroom, what routines to use, and how to adapt instruction for individuals”

(Fennema & Franke, 1992, p. 156).

Thinking Through a Lesson Protocol (TTLP)

Divided into three sessions:Part 1: Selecting and Setting Up

a Mathematical TaskPart 2: Supporting Students’

Exploration of the Task Part 3: Sharing and Discussing

the Task

Part 1: Selecting and Setting Up A Mathematical Task

Teachers will… Identify the mathematical goals Select a high-level math task Anticipant student solutions Locate tools or resources that students will

use Discuss how the task will be introduced and how they know that all students understand the context of the task

Part 2: Supporting Students’ Exploration of the Task

Teachers will..Monitor students (no telling)Anticipate questions that they will ask

to get a group started or make progress on the task

Generate questions that will focus students’ thinking on the key math ideas in the task

Part 3: Sharing and Discussing the Task Teachers will..

Strategically select and sequence students to present their ideas in an order that allows access for all

Make connections between the presentations and to the math goals for the lesson

Thinking Through a Lesson Protocol Planning Template Sample Standards and Goals

Challenges for ELL’s Task and Possible Solutions and

Strategies Questions the teacher may ask Ideal order of presentations and why Next Steps

Group Practice

In a small group begin to practice using the Thinking Through a

Lesson Protocol You will be given a grade level

standard and an optional corresponding task that you can choose to use or you may use your own materials.

Be prepared to share your experience with the process, your questions and thoughts with the large group.

Seven Stages of Teacher Collaboration

Seven Stages of Teacher Collaboration

Stage # Title

1 Filling the time

2 Sharing personal practice

3 Planning, planning, planning

4 Developing common assessments

5 Analyzing student learning

6 Adapting instruction to student needs

7 Reflecting on instruction

Common Core Mathematics in a PLC at work: Leaders Guide Tim Kanold and Matt Larson

Seven Stages of Teacher Collaboration

In what stage do you think using the Thinking Through a Lesson Protocol would most appropriately fit? Why?

What stages are the PLC teams typically functioning at your site? Why? What could be done to push them to the next stage?

Reflection As a team discuss the following related to today’s training and be prepared to share:

What will you personally use next school year?

What are the math needs at your site?Where should your site begin? Create an implementation plan for the

thinking through protocol with as many details as possible, such as dates and topics for training, planning time, etc.