CORESAI Leadership Team Meeting

CCSS Math Dive

What’s to Come

1. The Challenge

2. Some tools for the classroom

3. Some Tools for Professional Development

1. The Challenge

To borrow from Charles Dickens:

It was the best of times,

It was the worst of times.

Why the Best of Times?

Thanks to CCSSM, SBAC, etc., we will have the opportunity to pursue the goals we’ve wanted to pursue since the 1989 NCTM Standards.

Why the worst of Times?

It’s HARD.People don’t realize how hard.

And, It’s going to demand

sustained planning and effort.

What’s the shift?

Consider what happens when we move from the CST to SBAC.

Here are two typical release items from CST:

They’re skill-oriented.

(To put it mildly)

No thinking required, none of the CCSSM practices called for.

Compare the task demands with what this task asks for:

Distance (meters)

Time (seconds)

This is a rough sketch of 3 runners’ progress in a 400 meter hurdle race.Imagine that you are the race commentator. Describe what’s happening as carefully as you can. You do not need to measure anything accurately.

Hurdles Race

Think of the Content involved:

• Interpreting distance-time graphs in a real-world context

• Realizing “to the left” is faster

• Understanding points of intersection in that context (they’re tied at the moment)

• Interpreting the horizontal line segment

• Putting all this together in an explanation

Think of the Practices involved:

• Make sense of problems and persevere in solving them.

• Reason abstractly and quantitatively.• Construct viable arguments…• Model with mathematics…

25% Sale, Part 1

In a sale, all the prices are reduced by 25%.

Julie sees a jacket that cost $32 before the sale. How much does it cost in the sale?

25% Sale, Part 2In the second week of the sale, the prices are reduced by 25% of the previous week’s price.

In the third week of the sale, the prices are again reduced by 25% of the previous week’s price.

In the fourth week of the sale, the prices are again reduced by 25% of the previous week’s price.

Alan says that after 4 weeks of these 25% discounts, everything will be free. Is he right? Explain your answer.

Again: Core content, central practices.

But Will they Count?

YES, because SBAC will return 4 scores:

1.Concepts and Procedures

2.Problem Solving

3.Producing & Critiquing extended chains of reasoning

4.Modeling and data analysis

Want to see more?

Check out Consortium specs;

look at the

Mathematics Assessment Project (google the name);

Ask David Foster or Phil Tucher for MARS tasks.

How do we prepare kids to do well on assessments like the

these assessments?

(I thought you’d never ask!)

2. Tools to help in the classroom

A Tool:

The formative assessment lesson, or FAL:

A rich “diagnostic” situation

and

Things to do when you see the results of the diagnosis.

Rev up the engines, Scotty…

We’re going at warp speed… I just want you to know they exist.

A Challenge:

We know that students have many graphing misconceptions, e.g., confusing a picture of a story with a graph of the story in a distance-time graph.

Here’s one way to address the challenge.

Before the lesson devoted to this topic, we give a diagnostic problem as homework:

Describe what may have happened. Is the graph realistic? Explain.

We point to typical student misconceptions and offer suggestions about how to address them…

The lesson itself begins with a diagnostic task…

Students are given the chance to annotate and explain…

Follow-up Task: Card SortThe students make posters.

Students work on converting graphs to tables:

Tables are added to the card sort…

And the class compares solutions together.

This kind of lesson can:

• be embedded in a curricular unit;

• help the teacher know what kids have gotten, and where they need help; and,

• help them, develop the skills they need for SBAC.

Here’s another FAL:

Shape Statement 1

Shape Statement 2

Shape Statement 3

There are more great tasks, e.g.,

And, the students develop critiquing skills. The task:

They discuss the task, and sort out the mathematics. Then…

They’re given other (hypothetical) students’ work…

And helped to critique it.These are central skills called for in CCSSM.

The Mathematics Assessment Project’s goals are to:

• Help students grapple with core content and practices in CCSSM, and prepare them for the rich assessments they should (and it looks like, will) experience;

• Support formative assessment; and

• Do so in “curriculum-embeddable” ways (cf. BUSD, OUSD; Ask Phil Tucher).

We’re building 20 FALs at each grade from 6 through 10.

They’re FREE, at http://map.mathshell.org/materials. Just

google

Mathematics Assessment Project

Look for resources at:

• Mathematics Assessment Project (google it)

• The Gates Math Design Collaborative: http://collegeready.gatesfoundation.org/Learning/MathDesignCollaborative

• The inside mathematics web site, http://www.insidemathematics.org

3. Some Tools for Professional Development

Here are the things the literature says are important dimensions of classrooms that produce kids who are powerful mathematical thinkers.

Key Dimensions• How rich is the mathematics that’s

discussed?

• Do students engage in “productive struggle,” or are things dumbed down to the point where they don’t?

• Who has the opportunity to engage? A select few, or everyone?

• Who has a voice? Did students get to say things, explain, develop ownership?

• Does instruction find out what students know, and build on it?

Put everything together:

and you have the dimensions of a general framework for assessing lesson quality.

That means that these are the things you have to work on in

professional development:1. Rich Mathematics

2. Cognitive Demand

3. Equitable Opportunities to Engage

4. Opportunities to talk mathematics

5. Building on Student thinking

These are what Phil Daro has called the “backbone” of

Professional Development – if you don’t attend to all of them,

your efforts may be in vain.

And there’s a lovely tool for working on classroom discourse,

known as “the 5 by 8 card”

After flashing it up on the screen, I’ll turn to Phil Tucher to discuss it.

(First, I’ll note we have a tool for supporting conversations between teachers about the 5 dimensions. Just ask…)

We’re building ways to talk about these...…

The “question version” of TRU Math –

A tool for teachers, coaches, lesson study groups, to reflect on their teaching.

Think about sets of questions for each dimension that

stimulate conversation and reflection…

- Pre-lesson

- After the lesson

- When planning next steps

You might start with these questions:• How do mathematical ideas from this

unit/course develop in this lesson/lesson sequence?

• What opportunities do students have to make their own sense of mathematical ideas?

• Who does and doesn’t participate in the mathematical work of the class, and how?

• What opportunities do students have to explain their own and respond to each other’s mathematical ideas?

• What do we know about each student’s current mathematical thinking, and how can we build on it?

And think about expanding them:

But, each of these is hard, and takes time to work on!

So, where do you start?

How about dimensions 1 and 4,

1.Rich mathematics

4. Opportunities to talk mathematics

(a.k.a. “discourse)

Here’s where Phil Tucher can tell you about OUSD’s efforts

with the “5 by 8 card.”