Elements of a Mathematically Powerful Classroom

Robert PrestonCUSD Mathematics Coach

Yesterday . . .

• Identified 7 essential shifts in classroom practice

• Made connections between mindsets, shifts and SMPs

• Began to process the importance discourse plays in all 3

• So, for today . . .

If you had 5 things to focus on inorder to improve mathematicsteaching, what would they be?

And,How would you know they’re

the right things?

Why 5?(or fewer; no more that 7 or 8)?

Difficult to focus on more than that . . .

Think of the CA standards, with 40+ things to focus on at each grade level. How did we do?

What properties should those 5things have?

• They should be all you need• They should have a certain integrity on

there own and should be able to be worked on in meaningful ways

• They should be supported by research (opinion not enough) and professional development

So, what do you think are the main (5-ish) dimensions of

mathematically powerful classrooms?

120 seconds -- Quiet think time; generate your list of the 5 most important elements/dimensions.

4 minutes -- Turn and Talk with a neighbor about what made your list and why?

So, what did someone else have on their list that you wish you had

listed?

According to Alan Schoenfeld

• The Mathematics• The Cognitive Demand• Access to the Mathematical Content (Equity)• Agency, Authority and Identity• Uses of Assessment

Teaching for Robust Understanding of Mathematics (TRU Math) scheme

According to Alan

• The Mathematics• The Cognitive Demand• Access to the Mathematical Content (Equity)• Agency, Authority and Identity• Uses of Assessment

Teaching for Robust Understanding of Mathematics (TRU Math) scheme

According to Alan

• The Mathematics• The Cognitive Demand• Access to the Mathematical Content (Equity)• Agency, Authority and Identity• Uses of Assessment

Teaching for Robust Understanding of Mathematics (TRU Math) scheme

(A tool for capturing classroom practice)

Our Target

What might this look like in a/your classroom?

Our Target

What might this look like in a/your classroom?

Our Target

What might this look like in a/your classroom?

Are These Elements Connected to . . .• Mindsets?• SMPs?• Shifts in practice?

As with the CCSS content, is coherence to these elements vital for their development over time?

How coherent are we, as a district, with:- the mathematics- cognitive demand- access to math content- agency, authority and identity- uses of assessment

How Do We Get Our Classrooms Here?

• Start with one or two of the elements; assess where you are an try to move forward

• Start with the one that you believe to be your strength

• Start simple and expand from there• Select one or two as a PLC focus

– Use in planning– Use peers’ strengths as resources– Evaluate student work through its lens

Teach Through Units, Not Lessons

• Teach through the Mathematical Big Ideas• Identify connections within lessons to Big

Ideas of the unit– Make them explicit for all to see

e.g. (Grade 1, Lesson 9.7)Rufus has 2 dogs. He has taken them for a walk in the rain and needs to clean all of their paws. How many paws will he clean altogether?

Grain size is a major issue

• Mathematics is simplest at the right grain size. • “Strands” are too big, vague e.g. “number”• Lessons are too small: too many small pieces

scattered over the floor, what if some are missing or broken?

• Units or chapters are about the right size (8-12 per year)

• Districts:– STOP managing lessons – START managing units

Phil Daro

Before a unit, you can ask:• How can I use the five dimensions toenhance my unit planning?

After a unit, you can ask:• How well did things go? What can I dobetter next time?

Planning next steps, you can ask:• How can I build on what I’ve learned?

To do either of these, we need to start with the core questions.

Before a lesson, you can ask:• How can I use the five dimensions toenhance my lesson planning?

After a lesson, you can ask:• How well did things go? What can I dobetter next time?

Planning next steps, you can ask:• How can I build on what I’ve learned?