Middle Years Math on the Move!

Promoting Confident and Capable 21st Century Math Learners

Teaching to the Big Ideas

Marian SmallJanuary 2010

explore

Show &Share

connect

Reflect

practice

• Students DO Math• Builds on prior

knowledge• Accommodates a

variety of levels and learning styles

• Highlights the mathematical target – without solving the Explore!

• Focuses the learning for students, teachers, and parents

• Clarifies, refines, and applies learning to new situations

Math Makes Sense

Distinctives • Teaching

through Problem Solving

Learning – PD, readings

Big Ideas- Develop your understanding through discussion and application

Develop Essential Questions

Leadership: (Teacher to Teacher)Share your understanding of the Big Ideas (Smart Notebook)

Instruction: (Teacher to Students)Design explore activities to engage and support student learning

Complete Smart Notebook (Teacher Resource):

• In lab/board room, finish creating the Notebook (a tool to share understanding of the big ideas)

• Write script for notebook lesson: with your slides in front of you talk about the big ideas in your concept area

• Once the script is completed, return to board room to compete voice recording

Our primary goal is to complete the big ideas resource for teachers today!

• What is a problem?• Questioning to learn• How do we build stamina

What is Math

Reasoning

• Negotiating meaning• Clarify understandings

The Role of

Definition

Professional Learning Focus

Teaching students to expect, and excel at, paint-by-number class work, robs students of a skill more important than solving problems: formulating them.

Math Reasoning

Skills

Math Class Needs a Makeover

Dan Meyer

Computation

- We tend to forget how to do it

Easy to relearn if strong grounding in

reasoning

Reasoning

Applications to math problems in the world around us

-hard to teach- needed to solve

problems

Math Reasoning• The ability

to apply process to problems in the real world

5 symptoms that you are doing math reasoning wrong

1. Lack of initiative- don’t self start

2. Lack of perseverance

3. Lack of retention- need to re- explain and re-teach

4. Aversion to word problems- 99% of students

5. Eagerness for formula

Are we shaping neural pathways to expect

easy problems?

...creating

impatience with

irresolution?

• What real-life problem have you ever come across where all the information is given?

We are doing the thinking!4 layers that create impatient problem

solving: 1. Visual2. Mathematical Structure- grid, labels,

measurements3. Sub-Steps4. Question

• Traditionally, textbooks, not students do the thinking and pave the path to success.

Process to Rebuild Problems 1. Eliminate given information

2. Start with the Visual- use pictures/video and ask the question

3. Encourage discussion and debate- know when you have baited the hook

4. Invite students to Identify what would make it easier or what is needed to solve

the problem

5. Then offer the structure: Labels and measurement

The math serves the conversation the conversation does not serve the math!

6. Let students create the sub-steps if needed

Supporting Patient Problem-solvers• Every student is on a even playing field• Refining what math is and what a problem is• Increases student engagement and discussion• Use multi-media• Encourage student intuition• Ask the shortest question you can• Let students build the problem- because

Einstein said so• Be less helpful

How Do We Teach Math Reasoning?

NCTM Professional Standards suggests that the students’ role is to “initiate problems and questions; make conjectures and present solutions” (p. 45).

Math is the vocabulary for your own intuition!

When students make public conjectures and reason with others about mathematics, ideas and knowledge are developedcollaboratively, revealing mathematics as constructed by human beings within an intellectual community.

(NCTM 1991, 34)

• What is a problem?• Questioning to learn• How do we build stamina

What is Math

Reasoning

• Negotiating meaning• Clarify understandings

The Role of

Definition

Professional Learning Focus

Dan Meyer

Jane Keiser, NCTM

Exploring Angles

What is an angle?

All these have angles.

What is an angle? Does a ball have an angle?

Does a rainbow have an angle?

Define Angle

• Write your own definition of what is an angle. • Share and discuss in triad.

The Role of Definition• Anticipation Guide

Re-Designing Textbook Problems

Tower 2

Tower 1

Tower 3

How can you report the directions from each tower to locate the fire?

Process to Rebuild Problems 1. Eliminate given information

2. Start with the Visual- use pictures/video and ask the question

3. Encourage discussion and debate- know when you have baited the hook

4. Invite students to Identify what would make it easier or what is needed to solve

the problem

5. Then offer the structure: Labels and measurement

The math serves the conversation the conversation does not serve the math!

6. Let students create the sub-steps if needed

Tower 2

Tower 1

Tower 3

How can you report the compass directions from each tower to locate the fire?

North

North

Golf Irons and the

Shot

• Golf clubs are made to hit the ball different distances. Irons have different loft angles--the angle between the face of the blade and the shaft--to hit the ball different distances. The loft of a typical pitching wedge is about 45 degrees, but this can vary with different manufacturers.

Irons have different loft angles to hit different distances.

Board passhttp://www.jes-hockey.com

Learn to use the Boards and the Glass:The boards and the glass are your friends, not only when practicing but in game situations. Try to learn how to make passes off the boards and incorporate these moves into your skills. Try to pass the puck off the boards and then pick it up on the other side of the defender

Your Turn…