Final Exam
Elvira Dimas
1. Learning from Performance Assessments in Math discussed the importance and
outcome of open-ended performance in a math classroom. For a task to be a strong,
performance task, it must be able to measure students’ mathematical problem solving,
reasoning, and communication skills. It is able to measure so many component because
these tasks involve students sharing their though process towards the answer they
achieved with other for an understanding of different perspectives and approaches and
language development. From the problem-solving and reasoning, teachers can assess
students with deeper demonstrations of their thought process. In the article, performance
tasks were used to assess students’ knowledge of certain skills, like decimal place value,
and these performance tasks revealed misconceptions students have about decimals.
These misconceptions were not always revealed by the students’ final answer, but
through the explanation of the answer they choose.
One of the most shocking bit of this article was the statement from a teacher in
which this task and assessment being implemented. She reasoned, "The answer is the
most important part; if they've got it right, there's no need to look at the explanation."
Because this strategy of assessment has been discussed in class and demonstrated in
videos, there are so many ways one can refute that teacher’s idea. Performance tasks are
so useful in the classroom, especially when students are struggling with concepts but the
teacher is not sure what part of the concept, if any in specific. If performance tasks, and
several other assessment strategies we have discussed in class has taught me one thing
it’s that the students’ final answer is the most irrelevant part of math concept. It is
important to remember to shift teaching students math to teaching students to do math
because there is a crucial difference. It is crucial for student to understand how they got to
their answer for them to have a strong math foundations to keep building on.
Because the emphasis in performance tasks is the doing, in the classroom students
need to be doing math so they have the hand-on experience they can better communicate
about. Communication is key in the assessment of performance task. They perform the
skill and are expected to reason how and why they did it in that manner. Every math
concept should consider performance tasks for understand, but most especially those in
which students are inclined to rely on procedures rather than on the substance and
concepts. A math concept that is sometimes difficult for student to grasp are fractions. A
performance task could be a problem where you have number line that is labeled at 0 and
1. They have to label 1/2 on the number line. Then they must 7/10 on the same line. Have
them find and label 5 fractions between 1/2 and 7/10 on the number. It is important you
ask how they placed 7/10 where they labeled it and what strategies they used to find the
fraction in between 1/2 and 7/10. This task is open-ended so it will have numerous
answers, but student will be able to hear each other strategies and approaches they may
feel comfortable using. They are working with a math concept that can be easy to know
just to look at numerators and denominators, but adding the high level cognitive demands
encourages students to use any approaches to reach an answer, but be more focused on
how they got to their answer by having them explain their strategies. As an assessment,
the students’ explanation will be rich with their thinking process and understanding or
misconceptions about fractions based on where they placed 7/10 and which strategies
they used to place the fractions in between. Then, instruction would be directed from
what is learned through assessing their answers about fractions.
http://www.ascd.org/publications/educational-leadership/dec96/vol54/num04/Learning-fromPerformance-Assessments-in-Math.aspx
2.
a. Sunshine Cabs vs Bluebird Cabs
-average of early arrival
Arrival
Sunshine Cabs
-early arrival 5 times, out of 20 times
5/20 = .25 = 25%
-On average, Sunshine Cabs’ arrival
is early 25% of the time.
25
75
Early
Late
Arrival
5
Bluebird Cabs
-early arrival 1 time, out of 20 times
1/20 = .05 = 5%
-On average, Bluebird Cabs’ arrival is early 5% of
the time.
95
Early
Late
According to which cab service arrives earlier, on average Sunshine Cabs arrive earlier
more often. Out of the 20 times, Sarah was frequently late with both cabs, but looking through
the data, one can determine that Sunshine Cabs was earlier more often than Bluebird Cabs.
Though both cabs were late often, the better cab service would be the one that was less late than
the other. Sunshine Cabs is the better cab service because they were late fewer times than
Bluebird Cabs.
Sunshine Cabs vs Bluebird Cabs
-comparing each cabs’ earliest arrival and latest arrival
Sunshine Cabs
Earliest: 30s
Latest: 9m 15s
Bluebird Cabs
Earliest: 30s
Latest: 9m 15s
Earliest vs Latest Arrival Time
10
9
Time (in minutes)
8
7
6
5
4
3
2
1
0
Sunshine Cabs
Bluebird Cabs
Earliest Arrival
Latest Arrival
According to the comparison of the earliest and arrival time for each cab, Bluebird Cabs
is the better cab service. Both Bluebird and Sunshine’s earliest arrival time is 30s, so we can’t
base our argument off of that. You can compare the latest arrival time and choose the better cab
service. Sunshine Cabs’ latest arrival time was 9m 15s, while Bluebird Cabs’ latest arrival was
6m. Both of the are late, but Sunshine Cabs is 3m and 15s later than Bluebird Cabs would have
been, so Bluebird Cabs is the better cab service.
I think the most convincing argument is that Sunshine Cabs is the better cab service
because they arrived early 25% of the time, compared to Bluebird Cabs that arrived early only
5% of the time. The other argument I presented compared the latest arrival time each cab service
had. Bluebird Cabs was the better cab service in that argument because its latest arrival time was
not as late as Sunshine Cabs’ latest arrival time, by 3m 15s. That argument is convincing enough
because cabs shouldn’t be based on who arrives late before the other. It makes more sense to
compare how many times they are not late and come early for you to get to your destination on
time. Out of the two argument, it is more important to arrive early more often than not rather
than arrive late but not as late as another cab service and for that reason Sunshine Cabs is the
better cab service.
b. Objectives:
 Present the information given on the chart to make calculations and create charts or
diagrams.
o Appropriate calculations must be made and appropriate charts/diagrams must be
used to present the information best
 Based on the visual representations of the data and the data itself, decide who is the better
cab service.
o Argument for each cab service being better than the other
o Make valid arguments for each cab
 Determine which argument is more convincing
o Explain why
c. I would rate this as a high level task because many components defining high levels tasks was
found in the assignment. The task had students determine which cab service was better according
to the arguments they made for each. Having them make their own argument was an open-ended
part of the task. As long as they could present appropriate calculations and charts to represent
their argument, their argument was valid, meaning there were numerous arguments students
could propose. The second part of the student’s argument that makes it all a high level task and
reasoning. They are expected to explain their argument and justify it with their calculations and
visual representations. Also, the open-endness of the use of different calculations and charts
allows students with a range of skills and abilities to use whatever they feel comfortable and
confident in using to support their arguments. Because the task is about a real-life situation, there
is a connection to the procedures they may know and they are doing math by determining which
cab service is better, all based on the arguments and reasoning.
d. Rubric
4
3
2
1
Student make appropriate calculations of the data and they is presents data collected
into an appropriate chart or diagram. Using their calculations and visual
representations, students present two clear arguments defending each cab service. They
demonstrate justification with their use of calculations and visual aid, along with
written reasoning and explanations for their arguments and its credibility. The
demonstrate a great understanding of justification and reasoning by explaining which
argument is more convincing using their data presentation and reasoning.
Student make appropriate calculations and present them in appropriate charts or
diagrams. With their calculations and visual representations, they are able to present
two arguments. The arguments are considerably justified with their data presentations
and their written explanations. They demonstrate a considerable understanding of
justification and reasoning by determining which argument is more convincing and
provide a supportive explanation.
Student makes somewhat appropriate calculations and present them in a form of chart
or diagram. Using their calculations and visual presentations, they present two
arguments that are somewhat supported by the data. They use reasoning to defend each
argument, but not with enough reference to the data collected. They somewhat
demonstrate the concept of reasoning by their explanation as to which argument is
more convincing.
Student makes some calculations and present them in visual representation such as
charts or diagrams. Visual presentations do not correspond to the data given. Both cab
are not defended using the data. If two arguments are present, the explanations and
reasoning are not supported by the data or justified with their reasoning. Because two
arguments are not presented or poorly defended, they are not able to demonstrate why
one is more convincing than the other.
e.
Jamie: 5
Jamie demonstrated a great understanding of using data and visual representations to support
arguments. She demonstrate both arguments with a bar graph and calculations. The data
displayed on the graphs are accurate and they are further explained in the argument for each cab
service. Each argument was easy to understand and clear to see through the visual
representations. She was able to determine which argument was more convincing according to
her reasoning and the data given.
Hannah: 4
Hannah presented several different calculations using the data collected. She also includes a pie
chart, appropriately showing the argument of the percentage of the cabs being late and early. She
presents more than two arguments, but compares the one that defends Sunshine Cabs and another
that defends Bluebird Cabs. Each argument is supported by the data collected, the calculations
made, and the visual representations used. All that evidence she used to explain which argument
was more convincing demonstrate her great understanding of reasoning and the importance when
justifying arguments.
Ike: 3
Ike had many calculations and had them organized in different types of visual representation,
like a chart and a bar graph. The data collected was accurate and matched it on the chart and
graph. Though he displayed the data and his calculations visually, he did not use it to create two
arguments, one for Sunshine Cabs and one for Bluebird Cabs. The argument he presented was
supported by the data and his chart. He added his own reasoning to make the argument more
valid. He showed a significant amount of understanding of needing to have supporting ideas to
justify arguments.
George: 1
Though there are no calculations, George presents a chart, but he does not label it, making it hard
to understand which point is he is graphing. He presents one argument and explanation, but
because his chart is not consistent with the data his argument cannot fully be justified. Without
two presented arguments he cannot choose which one is more convincing and why. George does
not understand the importance of using data and visual representations to justify arguments.
f. (see packet)
g. To present this task, I will discuss how kids rely on the bus to get to school each morning.
This relation will eliminate any equity issues because most kids should have experience riding
the bus to school, rather than a cab around town. I will pose ‘would you rather questions’ about
riding the bus to school and be here on time, most days or any other types of transportation that
are not as reliable. This will get them thinking about why we would choose one over the other
using valid reasoning.
h. George: How does your line graph tell you that Sunshine Cabs come earlier than Bluebird
Cabs? To let him see that he cannot see the comparison from the graph alone.
Hannah: What is more important to you, for the cab to be early more often or for the cab to be
late but not as late as others could be? Why? To let her reflect on what is more important in
dependability.
Ike: What is your argument for Bluebird Cabs being the better cab service? To point out that he
does not have an argument defending Bluebird Cabs.
Jamie: What do you mean when you said that Sunshine Cabs gets to school at an average a lot
sooner than Bluebird Cabs? To clarify on which average she is talking about.
i. George: I like how you decided to create a line graph plotting the early arrival times of
Sunshine Cabs. I think that is a great start, but think through other graphs that could show that
data best.
Hannah: You put a lot of effort in making calculations and visual representations for each, and
they are very accurate too!
Ike: You made several calculation to compare and contrast both cab services. You kept it very
organized and easy to understand.
Jamie: You displayed the given data in very appropriate charts and graph, I’m sure it made the
data easier to understand for you!
4. In my first grade math class, I plan to use 4 important assessment strategies: manipulatives,
entrance/exit slips, self-assessments, and student interviews. Manipulatives is one of the most
important strategy for me because as first graders, my student will be able to think better
concretely than abstractly. I plan to use have manipulatives accessible for use whenever needed,
most especially when we are first learning a new concept. Let’s say that we are learning addition
facts, ten frames will be my go to manipulative. I will connect the concept of adding to the
strategies you can do using ten frames, like making tens then adding the rest. Entrance and exit
slips will be used in the beginning of a new topic we are about to learn so I can plan my lesson
plan accordingly. The exit slips will be used at the end of each new concept we have learned, to
also make necessary changes on concepts or parts of the concepts students may need more time
on. Between entrance and exit slips, I will find it useful to use self-assessment charts for my first
graders to fill out. This will help them become independent learners. It will also help them reflect
on what they know and what hey need more time on. This will be great for the days they are not
filling out exit slips because we are not completely done with one concept. I would not want
them to be lost until they filled out exit slips. Self –assessment can be a great way for student to
see their progress. Another way for monitoring progress or misconceptions are student
interviews. Though student interviews may not occur as often as the slips and self-assessments, I
will try to do them at least every six weeks, especially with students struggling with what we are
learning. Student interviews will reveal the misconceptions so I can change lesson plans and
provide sufficient instruction for them to master the concept. Because it is important that student
interviews be set in quiet areas, I will either have someone stay with my class while I interview
or I will hold interviews while students are working on other materials quietly. Those four
strategies are the most important to me that I want to implement in my classroom. The
manipulatives can be useful for anytime. Slips and self-assessment are strategies to monitor daily
understanding and misconception, while the student interview can help me understand students’
thinking processes.
5. Most of the required assignments were a great add-on to the materials we learned last summer
session. It was important for us to not only learn how to teach math with different approaches,
but is even more important to for us to know how to assess students and why. The research
presentation engaged us in learning why different strategies were useful when assessing
students’s work. I found it useful that were able to add assessment to our lessons plan from last
session, especially since we had to include many different strategies. Also, the focus on
assessment rather than the lesson itself for lit presentation was extra practice in using different
assessment strategies. Journals were a good activity to reflect on what the different assessment
strategies we learned in class.
6. All the activities we completed in class demonstrated the benefits of the different assessment
strategies teachers can utilize. The most memorable activity and discussion we had was about
talk moves. We used jigsaw to present our ideas to the rest of the class. We were also able to do
a gallery walk to see other groups’ work. We closed that activity by watching videos with talk
moves in use and we found similarities and differences between out article and the videos. So
many different strategies in just one activities! It was insightful to learn different ways to
promote student discussion, reasoning, and cooperative learning all in one lesson!