Math is all around us. Helping students understand math is cool. Students gain confidence when they see the "how" of solving math problems.
Getting students to feel the "why" of learning math is the key to keeping students engaged in learning.
Learn the way you want to learn, learn the way you learn best.
__________________________________________________
Use the link below to find the full research on Performance Assessment Strategies. I created a one-page summary which is below the link.
Link:
Performance assessments typically focus on
the process of solving problems or completing complex tasks. The emphasis is on what students can do, not
just what they know.
Performance assessments allow students to
show how they reach their solutions, explain their answers, and demonstrate
their ability to synthesize. This
assessment strategy provides teachers with information about students’ thinking
and reasoning (Parke & Lane, 1996).
Performance assessments can provide
information that is more instructionally relevant than paper-and-pencil
tests. Teachers gain a more complete
picture of students’ understandings and abilities. This in turn leads to better decisions about
student misconceptions and errors, and provides better assessment of the
instructional process (Stenmark, 1991).
In order to understand how to help students
improve their work, teachers need information on the processes that students
use. It is impossible to determine what
elements of a teacher’s instruction lead to which student results. However, teachers can use performance
assessments to develop hypotheses about how their students go about creating an
adequate or superior product or performance (Herman, Aschbacher, & Winters,
1992). Using this information, they can
modify or develop instructional practices to facilitate growth among all
students.
Paper-and-pencil tasks that require
students to show their work or describe their procedures will also give
teachers insights into students’ problem-solving tactics. Teachers can get valuable information about
how to help students improve by analyzing how students complete tasks and
looking for patterns related to outcomes.
Did successful students use a different approach than less successful
students?
*
Full study at: http://educationnorthwest.org/webfm_send/750
1 Assessment Strategies to Inform Science and Mathematics Instruction, It’s Just Good Teaching. Northwest Regional Educational Laboratory, June 1997
________________________________________________
Below are two examples of Performance Assessments I would use for my 7th Grade Math Class. I listed the Standard, Benchmark, etc., and included a short checklist that will help students see what is expected.
Minnesota Mathematics
Standard
Grade 7 Strand:
Geometry & Measurement
Standard: Use reasoning with proportions and
ratios to determine measurements, justify formulas and
solve real-world and mathematical problems involving
circles and related geometric figures.
No. 7.3.1.1
Benchmark: Demonstrate an understanding
of the proportional relationship between the
diameter and circumference of a circle and that the unit rate (constant
of proportionality) is
Pi. Calculate the
circumference and area of circles and
sectors of circles to solve problems in various contexts.
Performance Assessment Type 1
Building a
Landscaped Garden
Your family has decided to
create a beautiful landscaped garden in your backyard. They have asked you to help with ideas and
design for the garden. Your Dad gives
you the yard’s dimensions: 75 feet long by 50 feet wide. A scalloped wood fence runs along the perimeter of the backyard so the design
will need to leave room around the perimeter to allow easy access.
Your Mom has a few ideas
that she runs by you and asks if you have any comments. Her idea is to form a circular area that will house a number of native plant
species. She thinks she wants a short
walkway from the circular garden to another section that will contain an arbor
and wooden bench. You like her idea of
the circular garden but suggest that it should also contain seating. She asks you how big the circular garden
should be but then realizes she doesn’t know how to figure out its dimensions.
You tell your Mom not to
worry and that you can explain how to figure it out. You start by throwing out some measures for
circumference: 25 feet, 35 feet, and 40
feet.
Your Mom asks “what is
circumference?” You answer by explaining
______________________________________________________________________________________________________________.
Your Mom likes your
thinking but wants the circumference to
be bigger. You both agree on 50 feet. Your Mom then asks, “How much planting soil
will we need for this area?” Do you know
how to figure that out too?” No problem
you say. You tell her that the amount of planting soil needed will be
the area of the circular garden. You
explain that the area of the circular
garden is _____________________________________________________________.
DIRECTIONS TO COMPLETE THE
GARDEN
Complete the story by:
1. Describing
the next steps to finish planning the garden.
2. Creating
a diagram to show the backyard’s dimensions and where the circular garden will
be placed. Identify the circumference,
diameter, radius, and Area of the garden.
Remember to answer the question of how much planting soil is needed.
3. Label
all your work and remember to include your name and class number.
Performance Assessment 1 -
Checklist
Learning Target:
Use reasoning with
proportions and ratios to determine measurements, justify formulas and solve
real-world and mathematical problems involving circles and related geometric
figures.
Specific Learning Outcome:
Interpret data,
organize information, and describe key vocabulary by demonstrating an
understanding of the proportional relationship between the diameter and circumference of a circle and that the unit
rate (constant of proportionality) is Pi.
Student
|
Interpretation
Understands
what’s being asked
|
Organization
Organized
required information and labeled properly
|
Writing
Uses
complete sentences, proper punctuation, etc.
|
Understands
key vocabulary (meaning)
Circumference,
Diameter, Radius, Area
|
________________________________________________
Performance Assessment Type 2
Finding Pi
Introduction:
Pi is a number. In fact, it is a
ratio. Let's find Pi.
Instructions:
1 1. Take the piece of string you have at your table and
measure it with your ruler. Measure the
length using centimeters (cm). Record your measurement.
2. Now, make a circle
with your string. Try to make it as
round as possible so that no part of the string is jutting out or it looks
more like an oval than a circle. We want
a circle.
3. Once your circle is made, carefully measure its diameter using your ruler. Again, use centimeters (cm) for
your measure. Record your measurement.
4. Record the measure of your circle’s radius.
5. Record the measure of your circle’s circumference.
6. Use the circumference
and diameter measures to perform the
following division: Divide
your circle’s circumference by its diameter. Record your result to the nearest thousandth. Do this twice to check that your result is
the same each time.
7. Raise your hand when you are finished. Compare your result with other groups in
class. What did you find?
8. Find the Area
of your circle and record your result.
Result
|
Length
of String
|
Diameter
of Circle
|
Radius
|
Circumference
Diameter
|
Area
of Circle
|
1st Time
|
|||||
2nd Time
|
Learning Target:
Use reasoning with
proportions and ratios to determine measurements, justify formulas and solve
real-world and mathematical problems involving circles and related geometric
figures.
Specific Learning Outcome:
Interpret data,
organize information, and describe key vocabulary by demonstrating an
understanding of the proportional relationship between the diameter and circumference of a circle and that the unit
rate (constant of proportionality) is Pi.
Student
|
Interpretation
Understands
what’s being asked
|
Organization
Organized
required information and labeled properly
|
Understands
key vocabulary (meaning) and mathematical concepts
Circumference,
Diameter, Radius, Area
|
________________________________________________
Reflection
In creating my Performance Assessments, I wanted to observe students using their reasoning and critical thinking skills while working with the data. As I learned, performance assessments focus on the process of solving problems or completing tasks. My primary emphasis with these assessments is to see what students can do and how they reach their solutions.
I would set students up in groups of two for each assignment, although both can be done individually as well. Performance Assessment 1 asks students to integrate writing into their solution. The expectation here is that students will be explaining their solution and drawing conclusions from the data while thinking through the process.
Performance Assessment 2 requires students to sequence their thinking to affect their final answer. It also provides a compare / contrast discussion when speaking with other student groups. This is a critical component because students see and hear what their peers came up with, reinforcing the learning target.
Both assessments can be given either at the start of a unit or within a few days of starting. Obviously, students need some background knowledge in dealing with geometry and understanding the vocabulary terms like diameter, radius, and Pi, so these assessments are not to be initiated without some prior knowledge or instruction.
Going forward, I will definitely use these two assessments in my classroom. My goal will be to help students understand the "why" in their learning and give me a good perspective of my instruction techniques. I believe performance assessments are a good tool in providing a road map to help students meet their learning targets.
________________________________________________
3 – S Process Assignments Matter Chapter 1
S
|
What statements can you make about the reading? What did you learn that others need to
know?
The statements I can make about the reading are that the type of assignments
matter for student success. As the
reading points out, “well crafted assignments hold the potential to make
learning and teaching more focused and relevant …”
I learned a couple of things. First, as Robert Marzano points out,
students should be held to “…high expectations …” that lead to “… establishing
challenging goals …” (2003, p.35).
This means the rigor of your class assignments must be present to
align with your high expectations.
Second, “task predicts performance,” (City, Elmore, Fieman &
Teitel, 2009, p. 30). There is a
strong correlation to the type of assignments as excellent vehicles to
prepare students for the routines and demands of college work.
|
S
|
What strategies will you try?
How will you apply your learning?
One strategy I will try include is
showing students the “why” behind the learning. It’s obvious we can get to the ‘what’ and ‘how’
but teaching to the ‘why’ is critical to evidence outcome. The example used in the reading is Ms. H’s
English class. She used explicit /
intentional teaching after assigning her class to write a critical review of
a novel. But before she let them
begin, she taught the students the step-by-step skills needed to produce a
critical review.
I will also remember to hold my students
to high expectations and ensure the rigor of their learning is at a high
level. I will apply this in the
classroom by making sure my instruction is clear, explicit, and intentional,
so as to benefit the students learning outcomes. As the reading points out, “… because
assignments are evidence of outcomes as well as the production of the
outcomes.”
|
S
|
What is the source? Where did
you get the information?
The source for this 3 – S
Process is Chapter 1 of our text: Assignments
Matter: Making the Connections That Help Students Meet Standards by Eleanor
Dougherty.
|
3 – S
Process Assignments Matter Chapter 5
S
|
What statements can you make about the reading? What did you learn that others need to
know?
The statements I can make about the
reading are that there is a method for building on student learning by
sequencing assignments. Assignments
are “… the stuff of units and courses; they deliver on the big ideas, themes,
concepts, topics, or issues that constitute a course.”
I learned that a well sequenced course
connects content and skills from assignment to assignment and unit to
unit. I learned that the best student
learning experiences occur along a progression of complexity in assignments,
which allows coursework to prepare students for the next grade level.
I also learned about the 5 principles
that help guide unit & course design: 1) Thoughtful engagement, 2) Literacy as
common practice, 3) Value, 4) Manageability, and 5)
Pressure gently applied.
|
S
|
What strategies will you try?
How will you apply your learning?
I like the strategy of thinking about
ways to sequence assignments and putting that sequencing in the design of a
unit. I will use the 5 Principles to
guide my unit design, instruction, and student assignments so that I build a
learning progression.
The trick
will be to sequence / scaffold my assignments in accordance with the right
learning progression in math.
Since math content is generally taught in a progression anyway, this
may be easier than it appears. I
believe the key will be defining the students’ products and activities that
best suit the increased learning they will need to continue on.
|
S
|
What is the source? Where did
you get the information?
The source for this 3 – S
Process is Chapter 5 of our text: Assignments Matter: Making the Connections
That Help Students Meet Standards by Eleanor Dougherty.
|
3 – S Process Assignments Matter Chapter 8
S
|
What
statements can you make about the reading?
What did you learn that others need to know?
The statements I can make about the
reading are 1) that data analysis
is integrated into education, 2)
assignments should be collected, stored, reviewed, and assessed and, 3) the
data culled from this process helps inform teachers about their instruction
and aids in curriculum design.
I
learned that in any school there should be a “file drawer” of all student
work (i.e., assignments) across grade levels.
Teachers and other school staff should collectively assess their work
and discuss the students’ learning outcomes.
This process only seeks to help better target instruction, target
standards, and guide future curriculum approaches.
|
S
|
What
strategies will you try? How will you
apply your learning?
I like two specific strategies outlined
in the reading. The first is “calibrating alignment to standards.” This requires selecting one or two
standards in an area to calibrate, and then create your collection of
assignments for these standards. After
you have the collection, either in a PD session or, asking a peer group of
teachers separately, to match each assignment to the corresponding
standard. This presents a somewhat
unbiased point of view.
The second strategy I will try is to
employ a strong reteaching practice for students when I see a lack of
understanding, either through instruction or after analyzing
assignments. I learned that reteaching
should simultaneously repair and ratchet up demands, gently but firmly moving
students along a learning progression toward achievement.
|
S
|
What
is the source? Where did you get the
information?
The source for this 3 – S Process is
Chapter 8 of our text: Assignments Matter: Making the Connections
That Help Students Meet Standards by Eleanor Dougherty.
|
