Materials

Beliefs• Cut-up beliefs• Answer key

Adjusting support tool

Tasks activity• Martha’s carpeting problem (on

ppt)• Fencing problem (labels)• 3-5 tasks (6-8 tasks)• Levels of cognitive demand• Answer key• Factors affecting copies

Supporting Implementation of Mathematics Standards

RSD Principals

October 22 and 23, 2014

Sue Larson Nora Ramirez

Outcomes• Become familiar with a tool to adjust support by self

assessing mathematics instruction at a school site

• Increased ability to affect teachers’ beliefs regarding the teaching and learning of mathematics

• Raise awareness of how mathematical tasks differ with respect to their levels of cognitive demand

• Increased understanding of an administrator’s role in supporting teachers as they implement math standards

• Consider expectations of teachers as they implement problem solving (related to the October 31 RSD Professional Development Day)

A Data Collection Tool Adjusting Professional Support

A Data Collection Tool Adjusting Professional Support

Outcome

Become familiar with a tool to adjust support by self assessing mathematics instruction at a school site

Beliefs about Teaching and Learning Mathematics

• Pass out slips of paper in each group

• Sort beliefs as either productive and unproductive beliefs with each person taking a turn to read and determine if the belief is productive or not. The group then reaches consensus on each decision.

• Check answers.

Principles to Actions: Ensuring Mathematical Success for All, NCTM 2014

Beliefs about Teaching and Learning Mathematics

• Count off 1-6. Get into numbered group taking the list of Productive and Unproductive Beliefs with you.

• How might you coach a teacher to address this unproductive belief?

Principles to Actions: Ensuring Mathematical Success for All, NCTM 2014

Reflection

• What unproductive beliefs do you find more prevalent in your school?

• What moves might you make to begin to overcome these unproductive beliefs?

Beliefs about Teaching and Learning

Outcome

Increased ability to affect teachers’ beliefs regarding the teaching and learning of mathematics

Mathematical Tasks

Oct 31 Professional Development Outcomes

To reinforce the foundations of teaching and learning mathematics by enhancing teachers’ ability to:– Use problem solving as a vehicle to teach in a

balanced approach– Select/modify/create tasks with high levels of

thinking

Agenda

• Activate Prior Knowledge

• Problem Solving Introduction

• Tasks and Mathematical Practices

• Problem Solving #1

• Tools for Problem Solving

• Problem Solving #2

• Balanced Approach

• Stations

Independent Work

Begin to solve these two problems individually. Record your work in your packet. •Martha’s Carpeting•Fencing

Martha’s Carpeting TaskMartha is recarpeting her bedroom, which is 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

Fencing TaskMs. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. 1. If Ms. Brown’s students want their rabbits

to have as much room as possible, how long would each of the sides of the pen be?

2. How long would each of the sides of the pen be if they had only 16 feet of fencing?

3. How would you go abut determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Partner Work

Continue to work on the two problems with your partner.

•Martha’s Carpeting•Fencing

Presentations

.

Group Discussion

How are Martha’s Carpeting Task and the Fencing Task the same and how are they different? Do the differences matter?

Consider your own experience in solving the tasks, the “mathematical possibilities” of the tasks, and/or the complexity of the tasks.

Math & Science Collaborative

“There is no decision that teachers make that has a greater impact on students’

opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics.”

Lappan and Briars, 1995

Analyzing Mathematical Tasks

DIGGING INTO TASKS - Categorizing - Characterizing

CategorizingTasks

• Sort Tasks A – P into two categories [high-level and low-level]

• Develop a list of criteria that describe the tasks in each category

Categorizing Tasks

Low HighA, D, E, G,

L, OB, C, F, H,

I, J, K, M, N,

P

Math & Science Collaborative

Discussion

• What are the characteristics of the tasks you categorized as “low” level?

• What are the characteristics of the tasks you categorized as “high” level?

Math & Science Collaborative

Discussion

• Are all high-level tasks the same? Is there an important difference between Tasks J and B?

• Are all procedural tasks the same? Is there an important difference between

Tasks I and O?

CategorizingTasks, Part Two

Further sort the mathematical tasks into four categories:– Memorization tasks– Procedural tasks without connections– Procedural tasks with connections– Doing mathematics tasks

Reflection & Share

• What information can we add to our initial brainstorm:– What are characteristics of high levels of

mathematical thinking and reasoning?

Math & Science Collaborative

Categorizing Tasks

“If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks.”

Stein & Lane, 1996

Stein & Lane, 2012

A.

B.

C.

High High

Low Low

High Low Moderate

High

Low

Task Implementation

Patterns of Set up, Implementation, & Student Learning

Task Set Up

Student Learning

Reflect and share

• What do you now understand about the levels of demands of tasks?

Problem Solving

• Select task considering– Level of cognitive demand– The mathematics students will apply and learn– The accessibility of the task to students

• Anticipate student responses– Possible student misconceptions– Different strategies and tools students might use– Language that indicates understanding

Adapted from Principles to Actions

Problem Solving• Teacher presents problem, facilitates the KFA process and does not

model or suggest a solution process.

• Teacher has tools available for student use.

• Students work individually, then in pairs/groups while the teacher

– Monitors,

– asks guiding questions that promote the SMP,

– assesses students’ understanding, and

– chooses students to present and sequence of presentations.

• Teacher facilitates discourse requiring students to explain, defend, ask questions, clarify, model with equations, use representations and appropriate tools, use precise language, make connections, etc.

• Teacher facilitates a class summary and an individual reflection. Adapted from Principles to Actions

Supporting Teachers What is your role in supporting teachers as they implement problem solving?

Think about • what you can do to help teachers implement problem solving• how you might help them learn what problem solving looks like and sounds

like• how you will scaffold their learning and implementation

What might you tell your teachers that you expect to see in their classrooms?

Think about • how often you expect to see problem solving• the type of problems teachers use• how you might help them persevere• what student engagement might look like• acceptance and acknowledgment of the learning process

Outcomes

• Become familiar with a tool to adjust support by self assessing mathematics instruction at a school site

• Increased ability to affect teachers’ beliefs regarding the teaching and learning of mathematics

• Raise awareness of how mathematical tasks differ with respect to their levels of cognitive demand

• Increased understanding of an administrator’s role in supporting teachers as they implement math standards and specifically problem solving

• Consider expectations of teachers as they implement problem solving (related to the October 31 RSD Professional Development Day)

Evaluation, Feedback and Input

• Complete the project’s evaluation form

• Complete the + / Δ form.