|
Elementary for Day 1 – Sept 28 |
|
|
|
Practicum |
|
How well is your
current school practice addressing this principal? How important is equity?
After reading the
many modifications available, what are three strategies you would recommend
to classroom teachers to meet students’ needs? Explain.
What are the
implications for students who do not grasp this fundamental concept of
equality?
In what ways is
algebra woven into the other content strands at each level?
|
·
|
|
Middle School for Day 1 – Oct 5th |
|
|
|
Practicum |
|
What are the things
that distinguish the behavior of students doing geometry at different levels
of the Van Hiele Framework?
1.What are some things you have seen (or
wish you had seen) in classrooms that exemplify this principle? 2.What impact will this principle have on
you as a trainer and/or in a classroom?
|
|
|
High School for Day 1 – Oct 26 |
|
|
|
Practicum |
|
Compare and
contrast the five main question types in the “taxonomy of questioning
intention” on p.173-74. What are some other types?
Which of the 4
practical issues (p.180-81) for teachers related to assessment in a problem based
classroom do you think will require the most difficult adjustment for high
school mathematics teachers in your area? Others?
There are 3 main
points made in the description of the Equity Principle. How is each of these key points about
equity reflected, or not, in mathematics classrooms in your area?
According to these
readings, what is the teacher’s role in identifying and using multiple
representations in mathematics classes?
|
|
|
Elementary for Day 2 - |
|
|
|
Practicum |
|
How well is your
current school practice addressing this principle? How important is using
technology?
What do you think
is meant by “we (teachers) hear what we understand not understand what we
head”? How can we become better
listeners to our children? Teaching Mathematics Through Problem Solving Grades PreK-6 chapter 12 p.107-121 According to these
readings, what is the teacher’s role in developing reasoning and proof in
geometry?
|
· Choose a task you judge at either the doing math or procedures with connections level. Explain why you think it is at that level. · Teach a lesson and collect samples or observation notes of student work that reflect the range of ability in the classroom. · Try to determine the level of understanding the sample students have of the topic. What new insights can you gain from the students’ work or discussion that this approach allowed to surface? |
|
Middle School for Day 2 – Nov 9 |
|
|
|
Practicum |
|
Why are
visualization, spatial reasoning, and modeling skills important to the study
of geometry?
How can the use of
technology impact how mathematics is taught? How can the use of technology impact what mathematics is taught?
How can
visualization, spatial reasoning, and geometric modeling be used to solve
problems?
1. At each level of the van Hiele model, describe what the student can do and
something they cannot do. 2. At each level of the van Hiele model, identify one or two types of activities and
questions that will help students develop to another level. |
·
|
|
High School for Day 2 – Dec 7 |
|
|
|
Practicum |
|
Take the assessment “Some Problems About Graphs” yourself and administer to students prior to the reading. Compare article to your assessment and results of students.
Compare the
questioning techniques presented in this article to the questioning you
observe in a high school geometry class.
www.qca.org.uk/293_3233.html download PDF from site According to these
readings, what is the teacher’s role in developing connections in mathematics
classes?
There are 3 main points made in the description of the Technology Principle. What is an example of each point that you have seen in mathematics classrooms?
What are some
activities from Day 1 that provide examples of points made in this reading?
What additional points were made in Day 1 that complement or extend the points
made in this reading?
|
· Find a teacher to work with that teaches geometry · Agree to enrich a lesson in the spring · Observe a class and describe at least 1 example of effective questioning and 1 that could be improved (bring to day 2 ready to share) · Administer the assessment “some problems About graphs” to an ALGEBRA class. Collect, analyze and bring student data with to day 2 |
|
Elementary for Day 3 - |
|
|
|
Practicum |
|
Teaching
mathematics according to the six teaching standards can seem
overwhelming. If you were to change just
10% of how you teach math now, what aspect recommended in the standards for
teaching mathematics will you focus on?
If you are not teaching now, what would you recommend teachers focus
on first? Why?
What key
characteristics of effective mathematics teaching in your opinion were found
in this article? Which ones are the
most difficult to master?
Why do you think
students have difficulty with measurement concepts? What kind of experiences would help
students with them?
|
|
|
Middle School for Day 3 – Feb 1 |
|
|
|
Practicum |
|
How does Every
Student Counts promote the Teaching Principle?
What coordinate geometric concepts do middle
school students generally understand when they leave elementary school? What types of activities will help extend
the middle school students’ understanding of coordinate geometry?
|
Do ONE of the following · Teach a middle school geometry PBIT – either one done in the workshops or one out of the Navigations in Geometry book. Bring samples of student work from the lesson showing high, middle, and low levels of achievement. · Interview 3 or 4 middle school students about geometric understandings. You can just choose one of the geometric topics. Have the students tell or show you what they know about that topic – List student comments and/or work activities that illustrate students working at the different van Hiele levels. |
|
High School for Day 3 – Feb 15 |
|
|
|
Practicum |
|
Take the assessment “Some Problems About Graphs” yourself and administer to students prior to the reading. Compare article to your assessment and results of students.
There are three
main points made in the description of the Teaching Principle. What is an
example of each point that you have seen in mathematics classrooms?
According to these readings, what is the teacher’s role in fostering communication in mathematics classes? Be prepared to analyze the day 3 activities
What are some
activities from Day 2 that provide examples of points made in these readings?
What additional points were made in Day 2 that complement or extend the
points made in these readings? ·
PSSM pp.42 “Specify
locations and describe spatial…” ·
PSSM pp.313-314
“Specify locations and describe spatial…” |
· Enriching Lessons Assignment – Consult with your cooperating teacher to identify a geometry lesson to be enriched. The enriched lesson will be taught sometime between the Day 3 and Day 4 workshops. Bring the lesson to the Day 3 workshop, at which time we will work on enriching the lesson · Assessment for Learning Assignment – Work with your cooperating teacher to find at least one example of interesting student work on geometry. This could be work on a quiz or test, on homework, or other written work that is part of a lesson. The student work will be analyzed on Day 3 in terms of assessment for learning. |
|
Elementary for Day 4 – |
|
|
|
Practicum |
|
How can these
principles enhance student engagement?
Choose a couple of
strategies from pg. 62-63 and explain the reasoning behind your choice.
How can teachers’
knowledge, beliefs and goals and their problem solving behaviors influence
students?
Why is measurement
so important to mathematics curriculum?
|
·
|
|
Middle School for Day 4 – April 12 |
|
|
|
Practicum |
|
What are the
important ideas in the transformations and symmetry section of the geometry
standard? What are some things that might cause problems to students in this
area?
How can these
principles enhance student engagement?
What impact does
this article suggest for curriculum being taught? What impact does this
article suggest for instruction?
Slavit,
David. “Above and beyond AAA: The
Similarity and Congruence of Polygons.” under section called “More
Readings.” What can you gain
from listening to students when they are working in groups?
How does this
promote formative use of summative assessment?
|
·
Observe
a teacher teaching a PBIT 1.
List any questions that were asked in class 2.
Who asked the questions? 3.
Describe the ways the lesson was like a PBIT and the
ways it was not 4.
How did the teacher assess the students? |
|
High School for Day 4 – April 19 |
|
|
|
Practicum |
|
|
·
|