AZ TE 801-E Week 6
Transcript of AZ TE 801-E Week 6
-
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.