Transcript part 2 - Silicon Valley Mathematics Initiative

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Administrative Tools
• Comparison of Grade Level
• Graphs for Ethnicity, Home Language, Parent
Education, Gender, Language Fluency
• Description of test by standards, graphs by
tasks
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Shape of the Data
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Appendices
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NSLP Performance Levels
Comparison of CST Levels to MARS Levels
Correlations of STAR Scores to MARS Scores
Correlations of CST Clusters to MAC Tasks
Status of the Data
Comparison of Raw Scores by District
Audit Report by task and District
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Trends in Data
Using Formative Assessment
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Embedded formative assessment
So the model that says learn while you’re in
school, while you’re young, the skills that you
will apply during your lifetime is no longer
tenable. The skills that you can learn when
your at school will not be applicable. They will
be obsolete by the time you get into the
workplace and need them, except one skill.
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Embedded formative assessment
The one really competitive skill is the skill of
being able to learn. It is the skill being able
not to give the right answer to questions
about which you were taught at school, but
to make the right response to situations that
are outside the scope of what you were
taught in school. We need to produce people
who know how to act when they’re faced
with situations for which they were not
specifically prepared. Seymour Papert (1998)
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Teacher Effect
It doesn’t matter very much which school you
go to , but it matters very much which
classrooms you’re in. In the US, the
classroom effect appears o be at least four
times the size of the school effect (PISA,
2007)
The greatest impact on learning is the daily
lived experiences of students in classrooms,
and that is determined much more by how
teachers teach.
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Variety of styles/strategies
“teachers should not try to fit their teaching to
each child’s style, but rather that they should
become aware of different styles and help
students also become aware of different styles
and then encourage all students to use as wide
a variety of styles as possible.
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Use of Formative Assessment
Research suggested that attention to the use of
assessment to inform instruction particularly at
the classroom level in many cases effective
doubled the speed of student learning.
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Five elements of using assessment to
inform learning
• The provision of effective feedback to students
• The active involvement of students in their
own learning
• The adjustment of teaching to into account the
results of assessment
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Five elements of using assessment to
inform learning
• The recognition of the profound influence
assessment has on the motivation and selfesteem of students, both of which are crucial
influences on learning
• The need for students to be able to assess
themselves and understand how to improve
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The teacher’s job is not to transmit knowledge. It is to engineer
effective learning environments for students. The features of
effective environments are that they create student engagement and
Allow teachers, learners, and their peers to ensure that learning is
Proceeding in the intended directions.
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An important technique for helping students
understanding learning intentions and
success criteria is asking them to look at
samples of other students’ work and to
engage in a discussion about the strengths
and weaknesses of each.
Students are much better at spotting errors and
weaknesses in the work of others than they
are in their own.
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Questions that give us insight into student learning
are not easy to generate and often do not look like
traditional test questions.
In the U.S. most teachers spend a majority of their
lesson preparation time grading student work, and
almost invariably doing so alone. In other
countries much, if not the majority of lesson
preparation time is spent planning how new topics
can be introduced and which contexts and
examples will be used, and teachers work in
groups to devise questions to find out whether
their teaching has been successful.
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Only 8% of the questions asked by teachers
required the students to analyze, to make
inferences, or to generalize. Less than 10%
of the questions that were asked by teachers
actually caused any new learning.
Only two good reasons to ask questions in
class: to cause thinking and o provide
information for the teacher about what to do
next.
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How to provide constructive written feedback
on the mathematics homework produced by
their students - feedback included specific
comments on errors, suggestions to students
about how to improve and at least one
positive remark. Students receiving
constructive feedback learned twice as fast
as control-group. Students given only
comments scored on average 30% higher on
work done in the next lesson than that done
in the first.
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Students working logo enabled them to get a
solution with little mental effort. For those
using pencil and paper, working out the
effect of a single rotation was much more
time consuming, giving students an
incentive to think carefully, and this greater
“mindfulness” led to more learning.
Students given the scaffolded response
learned more and retained their learning
longer than those given full solutions.
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Putting Principals into Practice
Mathematical Practices
• Attend to precision. -use clear definitions
• Construct viable arguments and critique the
reasoning of others.
Briefly: Think of a definition for perimeter.
Share with a neighbor.
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Marco thinks
Plan C has a
larger perimeter
than Plans A
and B. Explain
why Marco is
wrong.
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Look at sample work and engage in
discussion about strengths and
weaknesses
“Marco probably counted. But he
counted wrong.”
“How could this explanation be improved?
What is missing to make it convincing?”
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Getting students engaged
“Plan A and B have bigger areas,
so they have bigger perimeters.”
Do you agree or disagree? Is this sometimes true,
always true, or never true?
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Understanding Learning Trajectory and
a Variety of Strategies
Jade sold only Peanut Butter Cookie
Dough. She raised $32. How many
Tubs did she sell?
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What do you think the student is doing?
What do the lines represent? What do
the numbers represent? Does it make
sense?
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This helps lay the foundation for
proportional reasoning at later grades,
for understanding input/output tables,
for making graphs.
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Understanding Learning Trajectory
Situating the mathematics of the task in the learning
trajectory for number and data: At earlier grade
levels students have been learning about data
collection and representation in the form of bar
graphs. At this grade level students are extending the
ways of displaying data to include line plots. In
second and third grade students have been
successfully thinking about most and least and using
comparison subtraction to find the how many more.
Also at third grade students have started to expand
their ideas about number to include fractions, as parts
of a whole, and use rulers to measure with fractions.
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Understanding Learning Trajectory
At this grade level students are starting to
decompose a fraction into a sum of its parts
and add and subtract fractions. At later grades
students will learn algorithms for adding and
subtracting fractions. Students will perform
more complex analysis of data to look at mean,
median, mode and range.
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Asking a Question that gives Insight
into learning
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Promote learning/ push thinking
“As teachers we are not interested in our
students’ ability to do what we have taught
them to do. We are only interested in their
ability to apply their newly acquired
knowledge to a similar but different situation.”
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Asking a Question that gives Insight
into learning
How much longer was the longest wingspan from the shortest?
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Understanding Place Value and
Subtraction
What does a student need to understand to use this process?
What principals remain in place from subtraction with whole
numbers?
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Understanding Place Value and
Subtraction
What principals about subtraction doesn’t the student understand?
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Understanding Place Value and
Subtraction
What is going on in the diagram? Where do the numbers come
from? Does this make sense?
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Attention to the Use of Assessment
Consider the following from 5th grade:
She used 5/8 of the cooking oil.
and
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Extending Multiplicative Situations to
Include Fraction Multipliers and
Quantities
NCTM 2002 Yearbook - Making Sense of
Fractions, Ratios, and Proportions - gives
tables on comparing whole-number
multipliers and fractional multipliers.
Teachers need to ensure that they provide a
variety of problem types.
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6th Grade - Rising to Meet CCSS
• Only 38% of the students met standards
• Task 1 - 38% scored 0 or 1 point (Rate
Concentrate) pick the juiciest for 1 point
• Task 2 - 18.5% scored 0 or 1 (Freezing in Fargo)
could identify the lowest temperature
• Task 3 - 44% scored 0 or 1 (Fraction Match)
complete addition equation
• Task 4 - 29% scored 0 or 1 (Lattice Fence) count
the rhombi in a picture
• Task 5 - 51% scored 0 or 1 (Unfolding a Box)
draw the unfolded box
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Preparing Students Who Think
No test can capture what is important for future
progress: A fourth grade teacher who spends a
great deal of time developing skills of independent
and collaborative learning, who ensures that her
students at solving problems, may find that her
student scores on math are not as high as those
who have emphasized only what is on the test.
And yet, the teacher who inherits this class will
look very good because of the firm foundations
that were laid in place.
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Quantitative Reasoning
Which is the fruitier concentration?
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What do you think this student is doing?
What label could we attach to the division
problem? How does this help us think
about relationships?
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What is this student doing? Does it make
sense? Why or why not?
10 > 6
Does this make sense? Why or why not?
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Other Tools - FALs
If teachers and teaching make the difference:
then this tool is one of the most effective for
changing practice. Lessons now available for
sixth grade through geometry and can be
placed into units of instruction.
http://map.mathshell.org
Lessons, video, professional development
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Match to Assessments
• 7th Grade - Similar Figures - Evaluating
Statements about Length and Area
• 8th Grade - 200 Freestyle - Interpreting Time
Distance Graphs
• Geometry - Flip Sliding Away - Representing
and Combining Transformations
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Use of Formative Assessment
Research suggested that attention to the use of
assessment to inform instruction particularly at
the classroom level in many cases effective
doubled the speed of student learning. So, I
sincerely hope that you take what we’ve
learned, the tools we developed, and do the
tasks this year to inform instruction.
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Eighth Grade
• Test to CCST Standards – Have all 8th graders
take 8th grade exam?
• Policy for 7th and 6th graders to match Smarter
Balance and state?
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