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Nate Franz Supervisor of Mathematics November 19, 2013

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Nate Franz

Supervisor of Mathematics

November 19, 2013

Instructional Leadership in Mathematics:

Promoting Understanding

What type of feedback does Austin receive on his butterfly?

- The specific changes in his drawings can be linked to very specific feedback from peers, illuminating the need for critique to be targeted and specific.
- An inspirational model of the power of perseverance and revision to improve quality

On what specific features - the ones that really make a difference in how students come to view mathematics and what they ultimately learn - of a math classroom should we target our feedback?

What are ways that instructional leaders can create an environment that expects and supports this type of feedback?

- Goals
- Effort to go beyond cross-national achievement data to focus on the underlying processes that produce achievement

- Scope of Project
- Germany, Japan, Australia, Hong Kong, Czech Republic, Netherlands
- 638 randomly selected, eighth grade lessons throughout the entire year.

- What do you see?
- Gather as much information as possible from the data
- Identify where observations are being made – e.g., “One page one in the second column…”
- Avoid judgments about quality or interpretation

Types of Math Problems

Teacher Implementation of Making Connections Problems

- What does the data suggest? What are the assumptions we can make about features of math classrooms?
- Make sense of what the data says and why.
- Find as many interpretations as possible and evaluate them against the kind and quality of evidence.
- Think broadly and creatively. Assume that the data, no matter how confusing, makes sense to some people, your job is to see what they may see.

Types of Math Problems

Teacher Implementation of Making Connections Problems

Making Sense: Teaching and Learning Mathematics with Understanding (Hiebert, 1997)

- High Level Tasks
- Task predicts performance; if we increase the cognitive demand of the work students are engaged in, their learning will increase.

- Fluency
- All students need to compute knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.

- Conceptual Models and Tools
- Leverage vertical coherence; the connections in math will strengthen understanding and allow for reason and intuition.

- Lower-level demands (memorization)
- Lower-level demands (procedures without connections)
- High-level demands (procedures with connections)
- High-level demands (doing mathematics)

Selecting and Creating Mathematics Tasks: From Research to Practice (Smith and Stein, 1998)

- Working as a table, sort the cards into the four groups.
- Develop criteria for each category.
- Record your thoughts on Demand/Criteria slip.
- Be prepared for discussion and reflection.

Tasks sorted into the four levels of cognitive demand

Criteria identified for each level of demand

Note or Post-It with the tasks for each group.

- Does a particular feature indicate that the task has a certain level of cognitive demand?
- Can you think of other factors that might make a task appear to be high level on the surface but that actually only require recall of memorized information?

Lower-Level Demands (Memorization)

Mathematical Tasks as a Framework for Reflection (Smith and Stein, 1999)

Lower-Level Demands (Procedures without Connections)

Mathematical Tasks as a Framework for Reflection (Smith and Stein, 1999)

High-Level Demands (Procedures with Connections)

Mathematical Tasks as a Framework for Reflection (Smith and Stein, 1999)

High-Level Demands (Doing Mathematics)

Mathematical Tasks as a Framework for Reflection (Smith and Stein, 1999)

On what specific features - the ones that really make a difference in how students come to view mathematics and what they ultimately learn - of a math classroom should we target our feedback?

What are ways that instructional leaders can create an environment that expects and supports this type of feedback?

- Lower-level demands (memorization)
- Lower-level demands (procedures without connections)
- High-level demands (procedures with connections)
- High-level demands (doing mathematics)

Selecting and Creating Mathematics Tasks: From Research to Practice (Smith and Stein, 1998)

ConcretePictorialAbstract

0.123 __ 0.13

Janet picked 3 daisies and 2 sunflowers from her garden. How many total flowers did Janet pick from her garden?

Janet picked a total of __________ flowers.

D

D

D

S

S

?

Janet’s flowers

A total of 438 people were at the concert. There were 213 children and the rest were adults. How many adults were at the concert?

There were _______ adults at the concert.

A

C

People at concert

213

?

438

Ling put 3 photos on each page of her album. If there were 6 pages, how many photos did Ling put in her album?

Ling put a total of _______ photos in her album.

pg.

pg.

pg.

pg.

pg.

pg.

Ling’s photos

3

3

3

3

3

3

?

Itty and Bitty each did jumping jacks. Itty did 8 jumping jacks. Bitty did 4 times as many jumping jacks as Itty. How many jumping jacks did Itty and Bitty do altogether?

Itty and Bitty each did _______ jumping jacks altogether.

Itty’s jumping jacks

8

?

Bitty’s jumping jacks

8

8

8

8

Simon arranged chairs in the gym for an assembly. He put 42 chairs into 6 equal rows. How many chairs were in each row?

There were _______ chairs in each row.

Chairs in rows

?

42

Abu earned $30 mowing lawns on Saturday. He spent half of the money on a new CD, and he spent 1/3 of the remaining money on lunch. Does he have enough money to also buy a bike attachment that costs $12.98?

Abu has _______ left.

CD

Abu’s Money

$30

$5 $5 $5

The ratio of Ty’s books to Ling’s books is 3 : 4. Ty has 60 books. If Ty buys another 5 books, what will be the new ratio of Ty’s books to Ling’s books?

The new ratio of Ty’s books to Ling’s books is _______.

60

Ty’s Books

20

20

20

Ling’s Books

20

20

20

20

First Draft

Final Draft

On what specific features - the ones that really make a difference in how students come to view mathematics and what they ultimately learn - of a math classroom should we target our feedback?

What are ways that instructional leaders can create an environment that expects and supports this type of feedback?

Identify one instructional lever that you are interested in improving

Collect artifacts (protocols, templates…) that you are using

- Review curricular resource
- Deep dive into the content – progressions, standards, connections
- Plan tasks, make instructional decisions and determine student outcomes
- Execute lesson
- Reflect on student thinking and work

Overview

Grade 2

Grade 3

What features of the task provide students to make connections?

What features might you add to this task to give all students a chance to use reason and intuition to meet the objective?

Grade 4 Module 3 Lesson 1 Problem Set

Student A

Student B

Student C

Student D

- Was there opportunity for the students to learn? Why and why not?
- What evidence was there that the mathematics was in fact learned?
- What worked and was worthy of praise?
- What didn’t work and why?
- What opportunities were missed?
- What growth nugget can I end with or leave with the teacher?

Tilling the Soil for the CCSSM: Ten Essential Math Leader Mindsets (Steve Leinwand, 2012)

- Become Aware of Cultural Routines
- We can only change teaching by using methods known to change culture. Primary among these methods is the analysis of practice, which brings cultural routines to awareness so that teachers can consciously evaluate and improve them. A recent study by Hill and Ball (in press) of a large-scale professional development program found that analysis of classroom practice was one of three factors predicting growth of teachers' content knowledge.
- Analysis of classroom practice plays several important roles. It gives teachers the opportunity to analyze how teaching affects learning and to examine closely those cases in which learning does not occur. It also gives teachers the skills they need to integrate new ideas into their own practice. For example, by analyzing videotaped examples of other teachers implementing making connections problems, teachers can identify the techniques used to implement such problems, as well as the way in which teachers embed these techniques within the flow of a lesson.
- Attempts to implement reform without analysis of practice are not likely to succeed.

- Focus on the Details of Teaching, Not Teachers
- Most current efforts to improve the quality of teaching focus on the teacher: how the profession can recruit more qualified teachers and how we can remedy deficiencies in the knowledge of current teachers. The focus on teachers has some merit, of course, but we believe that a focus on the improvement of teaching—the methods that teachers use in the classroom—will yield greater returns.
- A focus on teaching must avoid the temptation to consider only the superficial aspects of teaching: the organization, tools, curriculum content, and textbooks. The cultural activity of teaching—the ways in which the teacher and students interact about the subject—can be more powerful than the curriculum materials that teachers use. As Figure 2 shows, even when the curriculum includes potentially rich problems, U.S. teachers use their traditional cultural teaching routines to transform the problems and reduce their instructional potential. We must find a way to change not just individual teachers, but the culture of teaching itself.

- Sherin and van Es (2005) have proposed three key components of teachers’ ability to notice classroom interactions:
- identification of what is important in teaching situations
- connection of specific classroom interactions with the broader concepts and principles of teaching (e.g., equity, classroom norms, mathematical topics)
- use of knowledge about the teaching context (e.g., public school, grade eight mathematics) to reason about the situation.