7/31/2019 AZ TE 801-E Week 6

1/38

TE 801 Week 6

7/31/2019 AZ TE 801-E Week 6

2/38

LOOKING AT STUDENT WORK

Subject Based Groups

7/31/2019 AZ TE 801-E Week 6

3/38

Make sure that all members of the

group first have a chance to examine

the artifact of student work

7/31/2019 AZ TE 801-E Week 6

4/38

What are two different ways that you

anticipate a child might solve this problem?

How did this student solve this problem? Canyou describe the steps that the student used

to solve this problem?

Why might the child have done this?

What future questions might encourage the

child to consider a more efficient strategy?

On the basis of the childs existingunderstanding, what problem might you pose

next and how might the child solve it?

7/31/2019 AZ TE 801-E Week 6

5/38

Please post a blog

To the Blog of Student Work

What is your analysis?

How might you advance the studentsunderstanding?

This (like the Noticing blog) should be very

interesting for you to read seeing what eachother are seeing

7/31/2019 AZ TE 801-E Week 6

6/38

Looking at transforming some

problems

Please keep this in mind:

At this point, the point is not to learn how to

create the worlds most creative lessons.

In fact, that was never the point.

7/31/2019 AZ TE 801-E Week 6

7/38

Transforming Problems

This is the key skill:

To think about the math

Anticipating student responses What do these responses tells you?

How might you sequence this responses?

These are the key questions fordifferentiation, formative assessment, and

lesson planning.

7/31/2019 AZ TE 801-E Week 6

8/38

SOME EXAMPLES

7/31/2019 AZ TE 801-E Week 6

9/38

Example #1

Remember the Fencing Task:

Find the area and perimeter of a square with

side length 7.

Becomes, Find the side lengths of a

rectangular pen that maximizes the area of a

pen built from 28 ft. of fencing.

7/31/2019 AZ TE 801-E Week 6

10/38

Example #1

Note that you are connecting two procedures(area & perimeter; becomes procedures withconnections)

Note that there are now multiple ways to solvethe problem (you could make a table; draw it out;use algebra)

You need to defend your thinking and your

method. There is nothing to defend when the question

says, Find the area of a square of side length 9.

7/31/2019 AZ TE 801-E Week 6

11/38

Example #2

Teaching two digit subtraction:

E.g., 29 17

Can you think of a good sequence of problems?

Can you think of a good task for this objective?

7/31/2019 AZ TE 801-E Week 6

12/38

7/31/2019 AZ TE 801-E Week 6

13/38

My ideas

Present a problem: e.g., 21-14

Have students solve the problem howeverthey want:

Unifix cubes; writing on paper; usingsubtraction algorithm; counting up

Monitor to see what strategies students are

using Lead a whole class discussion, having students

present their ideas and defend their methods.

7/31/2019 AZ TE 801-E Week 6

14/38

Example #3

Teaching how to measure (e.g., teaching

students how to use a ruler to measure a

book)

Can you think of a good task for this

objective?

7/31/2019 AZ TE 801-E Week 6

15/38

My ideas

Have students measure the same object usingdifferent measurement tools

E.g., have all students measure a pencil (same

length) using whatever tool nonstandard toolthey want: a piece of string, notecards, pieces ofcandy, etc.

Have different student groups compare their

measurements. Talk about the inaccuracy. This leads towards the big idea of why we have

standard measurement tools.

7/31/2019 AZ TE 801-E Week 6

16/38

My ideas

Another measurement activity:

Have students use a ruler to measure a textbook

(purposely vague instructions)

What dimensions of the book do the students

measure (probably length, but which length, and

what vocabulary do they use?)

Have a discussionleads towards the big idea ofone object can have different measurement

dimensions(length, width, height, weight, etc.)

7/31/2019 AZ TE 801-E Week 6

17/38

Example #4

Teaching students how to tell time (e.g.,

identifying how much time has elapsed from

7:00 am to 2:15 pm)

Can you think of a good sequence of problems

for this objective?

Can you think of a good task for this

objective?

7/31/2019 AZ TE 801-E Week 6

18/38

Example #4

Teaching students how to tell time (e.g.,

identifying how much time has elapsed from

7:00 am to 2:15 pm)

Can you think of a good sequence of problems

for this objective?

Can you think of a good task for this

objective?

7/31/2019 AZ TE 801-E Week 6

19/38

My ideas

How much time elapsed between:

7:00 am and 8:00 am

1:00 pm and 2:00 pm 7:00 am and 12:00 am

12:00 am and 2:00 am

7:00 am and 7:15 am Etc.

7/31/2019 AZ TE 801-E Week 6

20/38

My ideas

Now, give students some problems like, howmuch time elapsed between 7:00 am and 8:30pm.?

Allow students to solve however they want(they can draw clocks; count up; use amanipulative clock; make a table)Monitor tosee what strategies students are using.

Have a whole class discussion and havestudents compare and defend strategies.

7/31/2019 AZ TE 801-E Week 6

21/38

Example #5

Teaching student how to round decimals

Can you think of a good sequence of

problems?

Can you think of a good activity that will

provide more entry points?

7/31/2019 AZ TE 801-E Week 6

22/38

My ideas

Sequence of problems

Round 0.2, 0.9.0.01, 0.830.19, 0.71

Make sure to have students share theiranswers to see if they are rounding to the

nearest whole number.

7/31/2019 AZ TE 801-E Week 6

23/38

My ideas

For each problem, make sure that you providestudents with the opportunity to createmultiple representations:

[Using / Creating] A Number line

Drawing a diagram (perhaps a pie chart linkingit to percents)

Writing a story problem (e.g., with money)

There must be more representations than justthe procedure.

7/31/2019 AZ TE 801-E Week 6

24/38

ONE OTHER WAY TO EXPAND

7/31/2019 AZ TE 801-E Week 6

25/38

Classroom Discussions (Vacc)

Factual Questions vs. Reasoning Questions

(Show a shape)

What is the name of Figure X?Teachers asking questions in this category will

find out whether their students know specific

mathematical facts, but they will gain little, if

any, information about whether their students

actually understand the given concept.

7/31/2019 AZ TE 801-E Week 6

26/38

Reasoning

In what ways are Figure X and Figure Y

similar?

Still fairly closed reasoning, but it does require

reasoning, not memorization.

7/31/2019 AZ TE 801-E Week 6

27/38

Open Questions

What do you notice about Figure X?

This presents an opportunity for students todescribe what they know or what they

observe, even if they do not have a proper

name or algorithm for the phenomenon yet.

7/31/2019 AZ TE 801-E Week 6

28/38

Levels of Questions

What is the name of X?

What is the difference between X and Y?

What do you notice about X?

You might analyze your own practice (e.g., byrecording yourself somehow) and noting howoften you ask each type of question (Part of

Project 3). Also try deliberately to incorporate these

higher questions into your lessons?

7/31/2019 AZ TE 801-E Week 6

29/38

And also

Dont just ask these open questions to ask

them.

What do you want to know?!!!

How will it help you to know what students

think about the specific math content?

Do you care?

This is a paradigm shift.

7/31/2019 AZ TE 801-E Week 6

30/38

7/31/2019 AZ TE 801-E Week 6

31/38

The Magic Formula to Good

Curriculum and Instruction

Step 3: Anticipate student thinkingWhat are

some ways / strategies / mistakes that

students might employ?

Step 4: Think about the sequence of these

strategies that leads towards your big idea

Step 5: Ask the students open-ended

questions (What do you notice about?)

7/31/2019 AZ TE 801-E Week 6

32/38

The Magic Formula to Good Formative

Assessment

Step 1: Think about what you want to learn

about your students thinking (think about the

math)

Step 2: Think about how you might get this

information

Step 3: Think about what you might do with

this information once you get it (think of the

math)

7/31/2019 AZ TE 801-E Week 6

33/38

OMG

This principle applies to ALLSUBJECTS

It is a matter of

1) Applying this template

2) Thinking about the content

7/31/2019 AZ TE 801-E Week 6

34/38

SET FEEDBACK

7/31/2019 AZ TE 801-E Week 6

35/38

Feedback

Making the most of a polycom class;

Dawnmaire and I are going to visit

Positive responses to noticing blogs; thats

good, because I feel they are truly valuable.

Well have another assessment later. We are

also trying to find ways to make this course

valuable to your growth as a teacher.

7/31/2019 AZ TE 801-E Week 6

36/38

In your grade-level groups: Talk

about where you are in planning

your unit (after 5 minutes, I will askfor your questions)

Wh f h ifi bi

7/31/2019 AZ TE 801-E Week 6

37/38

What are some of the specific big

ideas in the content that you will

want to look for? What are somestudent responses / misconceptions

you anticipate? What might you

look for specifically in your

formative assessments?

What will this student thinkingsuggest that you do in terms of your

lessons?

7/31/2019 AZ TE 801-E Week 6

38/38

Draft of the Unit Plan

One the wiki, please submit a full draft of your

unit plan

By Saturday nightI read them all on Sunday.