TE 402 - Math
Daily Lesson Plan
Date: April 19th, 2012
Grade: Fourth
Teacher: Emily Baker (Elena, Katie & Nicole)
Mentor Teacher: Michael Ann Foltz
Lesson Time: 9:00am
Lesson Duration: 1 hour
Lesson topic and purpose:
Measuring a crooked path with standard and nonstandard units and compare the effectiveness of both styles of measurement.
Rationale:
Students have yet to begin a unit on geometry and measurement, this
lesson will provide students with an introduction to measurement with
standard and nonstandard units and let them compare their effectiveness.
This will help students to know how to measure in their daily life and
what type of unit will be the best for the type of measurement they are
doing.
M.UN.04.01 Measure using common tools and select appropriate units of measure.
Goals/Objectives for today’s lesson:
- Use
a high level task with measurement in which students have six means of
measurement (3 standard, and 3 nonstandard). Students will need to pick
the three types of measurement that best work for the object.
- Students will be able to use non-standard and standard measurement and then compare their effectiveness
Materials & supplies needed: (per team)
- Six copies of worksheet with data table
- Six rulers that have inches and centimeters
- Six evenly cut strings
- Six packs of straws (5 straws in each pack)
- Masking Tape-->Create six crooked paths that are identical with the masking tape
- 24 Note cards explaining group roles
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Launch (20 minutes)
- Students
will need the prior knowledge of how to measure things. To scaffold
those who do not have this prior knowledge we will model using a ruler
to measure a line drawn on the board.
- The
teacher will motivate the students in the lesson by getting them
excited about the crazy path. We will talk about how this is a special
math path that is unlike any other path they have walked on.
- We
will help them make connections to prior lessons by asking them about
any prior knowledge they have about measurement to see what and how they
have learned it.
- Today
we’re going to get to do some measuring around the classroom. Now this
is no ordinary day of measuring. We’re going to get to use a lot of
different kinds of tools and decide on which works best.
- First I want to ask you all if you know what it means to measure the length of an object.
- Call on students to relay answers looking for finding the distance between one spot and another.
- What kind of things do we measure? Have you ever measured anything? Why might we measure these things?
- Open
up a discussion to talk about the meaningfulness of measurement to help
make real-life connections. Listen for answers about times when
students themselves have been measured or have measured something else.
Probe students to explain how they measured things or why they were
measured. Possibly look for examples of measuring their height at the
doctors or at home. Why do they measure things. What is one reason that
it could be important to measure the length of a path?
- What kind of tools do we use to measure things?
- Listen
for rulers, tape measures, etc. A list will generated on the
smartboard. It is expected that students will say ruler, foot, yard,
inch, tape measurer.
- Have you ever thought of using other things to measure? What things might you use?
- Listen for feet, string, etc.
- We
are going to get to travel on a special math path. Now this path is
unlike any other path you have ever been on. It is a crazy crooked path.
You are all going to be in groups that I have picked to measure the
length of the path. Have you ever measured the length of a path before?
- Listen for any answers that may actually be connected experiences of measuring distances.
Explore (20 minutes)
During
the activity, the students will be arranged in six groups of four
students. The students in each group will be assigned roles and
responsibilities. The roles will include data collector, manager,
material, and reporter. The small groups will be spread out throughout
the classroom, working with their own set of materials and crooked path.
The
task that the students are going to work on at this point of the lesson
is similar to Activity 19.3 “Crooked Paths” in the “Developing
Measurement Concepts” article. Each of the six groups will be given a
crooked path (made of tape on the classroom carpet) to measure. The task
is for the students to measure the crooked path with different
nonstandard and standard units. The students will have six different
options of nonstandard and standard units to choose from, including
string, straws, hand, and ruler(inches, feet, centimeters). The students
will choose three of these to measure their path with. All the students
will pitch in to help out with the measuring. They will record the
length of the path on a basic data chart for each unit that they measure
with.
The
task can be solved in many different ways, depending on the units of
measurement chosen. They have the choice to decide which they want to
attempt to use. The students could use the nonstandard units to measure
if they feel more comfortable with those, or they could choose to use a
standard unit. Some of the nonstandard units will vary in their
measurement from group to group (such as hands). This will generate
interesting discussion about the distinction between nonstandard and
standard units later in the lesson. The students could measure the path
with some standard and some nonstandard units.
The
students could lay the units of measure next to the path, mark the end,
move the unit of measure up, and repeat the process to measure (using a
unit that is shorter than the path). The students could find another
object in the room that is the same length as the unit of measure and
use that in addition to the unit given to aide them in measuring the
path. The students could also measure segments of the path and then add
them up separately.
We
think that the students are most likely going to measure the path with a
mix of standard and nonstandard units. They will use the first method,
which is where they line the unit up next to the path and move it up as
they measure.
The
students may not understand how to appropriately use a ruler, and they
will not measure accurately using this unit. They may not know how to
measure something that is longer than its length. The students may not
stretch a flexible non-standard unit all the way to its full length to
measure. They may not realize that measuring with hands does not come
out the same for every group, and they may not see the problem with
measuring with nonstandard units. In addition, the students may have a
difficult time measuring the path because it is crooked and not
straight. They may not know how to go about measuring it by following
the crooks.
While
they are doing the task, we will ask, “Why did you chose that unit?”,
“How are you going to use that unit to measure?”, “Since the path is
longer than the unit, how are you using the unit to measure the whole
path?”, “Is it easier to measure with the nonstandard and standard
units? Why?”, “Which units work better for measuring the path? Why?”,
“Which ones are the most precise?”, “Have you discovered any problems
with using any of the units? What did you discover?”, and “How do the
units compare to each other?”
Specifically … (monitoring and supporting students’ thinking)
While students are working, we will see the students using the units to
measure the path. We should hear the students discussing which units to
use and how they should use each unit. The students should be gathered
around their path and be focused on precisely measuring the path. We
should also see students writing down their measurements on the given
data chart.
To
assess the students’ understandings, we will ask, “Why did you choose
to measure the path with that unit?”, “Which units are easier/harder to
measure with? Why do you think this is?”, and “How did you use that unit
to measure the path?”
In
order to advance students’ understanding of the mathematical ideas, we
will ask, “Are you getting the same number for each measurement? Why are
you getting different numbers? Which measurement do you think is the
best one/most accurate one? Why? If you were trying to make a path in
your yard, which unit would you use? Why? What if you had to buy bricks
for your path? What measure would you use to find out how many bricks
you needed?”
The
questions that I would ask to encourage students to share their
thinking with others or assess their understanding of their peers’ ideas
would be “What did you think the path should be measured with [student
name]? Why did you think this? What do the rest of you think? Do you
agree/disagree? Why? How did it feel to measure the path with that you
[unit]? How does that compare/contrast with the unit you used [another
student]?”
To
ensure that the students remain engaged in the task, we will give each
student a role and remind them of their responsibilities to the rest of
the group. The manager of the group will make sure their group members
are staying on task. If a group does not know where to begin, we will
suggest that they talk to each other to get ideas. Then we will
encourage them to try measuring with the unit they feel most comfortable
with. If they have trouble with that unit, we will tell them to try
using another unit instead and come back to that one. If a group
finishes the task almost immediately and becomes disruptive or bored, we
will tell them to measure the path with the other units given. After
they measure the path with all of the given units, they can go ahead and
measure other objects around the classroom. If other groups are really
struggling, they can also help those groups.
If
a student gets caught up in the non-mathematical aspects of the
activity, we will re-focus their attention to the goal of the activity. I
will encourage them to be an active member of their group. If they like
playing with the units, I will encourage them to be an integral part of
physically measuring the path. They may be caught up in the
non-mathematical aspects because they do not understand why it is
worthwhile to do the task. I will give them an authentic and relatable
example for when they would use this skill of measuring a crooked path.
If they like, they can even pretend that they are completing an activity
like that (such as measuring the spine of a fossilized dinosaur for a
science museum so that they can put it on display). If they are really
interested in the writing part of the activity, they can do more of that
for their group and record their observations in writing on the data
sheet. I will encourage them to play an important part in getting the
path measured.
Summarize (_10-15_ minutes)
For
the last part of the lesson, students will gather as a whole class to
discuss the solutions, strategies, and ideas they have learned about
nonstandard and standard units of measurement.
To
get students attention, teacher will clap her hands twice to call for
their concentration on the next activity. (Teacher will follow the
everyday normal whole class routine discussion process in order for
students to know what to expect.) The teacher will instruct students to
return to their assigned desks and sit near each member of their group
in order for them to continue working as a team.
The
teacher will prepare the students to have a discussion by structuring
the whole group discussion into a mathematical learning environment
where every student will feel secure of sharing thinking and ideas.
Before starting the classroom discussion the teacher will remind
students of the discussion rules. Such as listening carefully while
someone is speaking, respect each other comments, raise hand, etc.
The
class discussion will be organized first by having students sit in a
position where they face directly to where the teacher will be leading
the discussion. In order to accomplish the mathematical goals for the
lesson, the teacher will initiate the interaction. For instance, by
asking a set of questions that the group reporters respond and the
teacher evaluates the responses in a manner that generates an active
engagement discussion.
To
distribute the chances of participation evenly during this activity
students will be encouraged to participate even though it may not be
their group role. Teacher will provide enough time for students to think
and write their answers if they wish.
To
maintain students interest in the discussion teacher will challenge
students to think by incorporating manipulatives and physical activities
if necessary. When students respond to questions teacher will provide
constructive feedback. Teacher may affirm briefly, provide more
deliberate information or make simple corrections.
Specifically:
The
solution paths in which students will share their responses during the
class discussion will start with saying the three chosen tools,
mentioning any unexpected outcomes of choosing those tool, and solutions
that groups agree to apply in order to obtain reasonable results. The
group solutions will be presented in a chronological order where
everyone will have the opportunity to share obtained results and
observations been made.
The
order in which solutions are presented will help develop students’
understanding of the mathematical ideas that are the focus of the
measurement lesson by carefully scaffolding their thinking while they
were reasoning before, during and after the crooked path activity.
The Following are specific questions that the teacher will ask:
*To
make sense of the mathematical ideas that the teacher wants them to
learn: Ask students to explain why one of three given non standard units
may be a better choice for measuring the length of the crooked path.
Why do you think is it important to compare lengths that are not straight lines?
Now
that you have your results in your groups, can you predict if maybe the
paths you were given is shorter or longer than your peers?
(Students may think that some paths may “look longer” based on it being more spread out than another more compact path.
*To expand on, debate, and question the solutions being shared:
Ask
students to think back as they were completing the exercise, comparing
responses and reaching on an agreement as a group what difficulties they
found in relation to utilizing non standard v.s. standard units.
Does any group have an argument as of why certain paths may look longer than others?
What groups choose to use strings to measure the crooked path? Was this unit helpful to understand?
*To make connections between the different presented strategies:
Which of the three non standard and standard chosen units of measurement worked better to measure the path? Why?
*To look for patterns:
Ask
group reporters to share their results and any compare with the rest of
the groups. Encourage them to analyze the whole class results and find
any patterns.
If you were given the option to choose a different unit of measurement what would you have chosen?
*Begin to form generalizations:
What
units of measurement units should be used to obtain precise results?
What units of measurement should only be used to demonstrate estimations
and approximations?
The
teacher will summarize the main ideas of the lesson according to the
lesson content rationale and content objectives. As a class the teacher
will help students agree on which units of measurement will work better
to utilize in future activities in order to obtain more precise results.
The
teacher will bring closure to the lesson and help children reflect on
their experiences by clarifying any uncertainties and explaining the
importance of learning how to utilize different types of nonstandard and
standard units.
At this point of the lesson the kind of feedback that the teacher will
want from the students is to hear what worked while during the crooked
activity. If they had any trouble identifying measuring tools, filling
out the data chart or gathering information while performing their group
roles.
• Transition to next learning activity Before the next learning activity teacher will review
how to use nonstandard and standard measurement tools. For example the
teacher may show a picture and explain how non-standard measuring tools
can help people when shopping for many household items, moving
furniture, etc.
A
transitional activity will be “Changing Units: where the teacher will
have students measure a length of a classroom object with a specific
unit. Then with a different unit that could be either smaller or twice
as long the original unit. To better debrief/explain this activity the
teacher may say “ If the desk is 40 inches long, how many feet is that? | Academic, Social and Linguistic Support during each event:
The
same language/choice of words will be used throughout the lesson to aid
in students understanding and reduce student confusion.
Asking
students about prior knowledge will not only excite them about the
activity but put them all on the same playing field, allowing them to
all have some background knowledge about measurement.
During
the launch section of the lesson students will remain in their normal
seating arrangement to help them maintain their composure while
instructions and beginning instruction and discussion is going on.
Students
will be working in groups to aid one another in the task and overall
comprehension. Students will be warned that if are not working well in
their group that they will be removed and have to complete the task on
their own.
Student
groups have been predetermined by the teacher. Groups are arranged to
aid in students learning, linguistic and social interactions.
Each
group was first was given a student that is high achieving within math
and is a member of Insights (excelled learning program). Every member of
Insights also is known for their good attitude within the classroom.
Next
each group was given a low achieving math student.This ensures that
struggling students are fairly evenly distributed throughout the groups
and will be able to find support.
Finally
the remaining students were distributed throughout the groups. Their
group placement was determined by the existing group members to ensure
they are not with friends (to reduce students being off task) and are
with people that they work well with.
Within
the groups each students will be given a specific role, which will
randomly assigned. This will give each student purpose within the group
and hopefully ensure that all parts of the task will be completed within
the allowed time and that students are able to stay on task.
The
teacher will float around the room throughout the task to help with any
issues that might arise. The teacher will be able to explain and give
need further directions if a group or groups are struggling.
Assigned roles should help students remain on task throughout the activity,
Students/Groups that finish the task early may use other measurement tools to collect extra data.
Students
will remain in their groups but return to the desks. Each group will
sit together/near each other in the desks in order to communicate with
one another and support ideas they have discovered.
The same language will be used as the previous parts of the lesson to support understanding.
The spokesperson role will define who speaks and who is in charge of speaking in a group.
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Assessment:
Teacher
will informally assess students learning through their responses during
group activity, whole class discussion and individual data recording on
measurement worksheet.
During
the mathematical activity and discussion the teacher will assess
students learning by asking probing questions that will make students to
think, make conjectures and allow the teacher to make anecdotal records
of students responses which will reveal their thinking and reasoning.
For
example: While students are measuring the crooked path in groups, the
teacher will engage students in conversations asking such questions as
“Why did you decide to use that specific non standard unit? What other
measurement unit that perhaps is not available will you have used? Can
you use any units of measurements to obtain the same result?
The
teacher will use the informal assessment gathered information from the
fourth grade class to verify if students have successfully learned the
content lesson objectives. The information will also serve to identify
mathematical concepts in which students may still struggle to inform
future lessons.
| Academic, Social, and Linguistic Support during assessment
The teacher will observe the student interaction and responses in the learning environment .
If
time allows the student will be assessed on a conference one to one
between the teacher and student where student will share ideas, reason
and/or explain a measurement concept. |
Basic worksheet for collecting data while measuring. Nicole will
print out copies one for each group for the students to use.
Units of Measure
|
Length of Path
|
Notes
|
Feet
| | |
Inches
| | |
Centimeters
| | |
Hands
| | |
String
| | |
Straws
| | |
Elena’s Notes: 4/19
Introduction/Launch
During
this part of the lesson students were curious and worried about what
they would have to do during the math lesson. I think that this part of
the lesson was successful in generating student’s interest to work on
the prepared lesson. Once groups were organized and roles were given,
students seemed to be very excited to work together as a group.
The
teacher started the lesson by stating what students were going to learn
about and they were going to work during the math task.
Ms.
Baker asked why do we use standard units? Five students raised their
hands, one student said: Measure to see how long stuff is, how tall it
is. Another student said: is it to measure width, length and high? Once
all students shared their ideas Ms. Baker brief summarized what standard
units are.
Ms. Baker asked: What kinds of things do we measure?
Students
immediately raised they hands, some of the items that were mentioned by
students were; desk, computer, screen, TV monitor, yourself, book,
window, smart board, Friday folders, projector, door, keyboard, CD disk,
pretty much everything. One student answered the question with a
wondering tone: you can measure your shoes? Then Ms. Baker replied, how
many inches do you think is your foot long? Then she briefly explained
how some people shoes measure different inches depending on the size of
the person’s foot.
Ms. Baker asked: Who has measured something before?
Students
answered: Water, yourself, desk, and dog. One student in particular
mentioned that he measured himself at Michigan Adventures to see if he
could ride a game by himself.
Ms. Baker asked: Why do you measure? What is the purpose?
Students answered: Because curiosity to see how much things are and to ride game at parks.
Ms. Baker asked: What are some tools that you can use to measure?
Students answered: Leveler, measuring tape, ruler, tablespoons, cups, shoes and you can use mostly anything.
Ms. Baker asked: What are other things you can use to measure?
Students answered: Kilometers, millimeters, centimeters, and strings.
Once
students had a concrete understanding of measurement Ms. Baked asked
what were some of the items mentioned standard and nonstandard units.
Students said that measuring tape and ruler are standard units. As
opposite strings, shoes, pieces of paper, or any other thing that does
not have specific measures are nonstandard units.
The
teacher explained how students were going to work in groups; she
divided the class into 5 groups of four students. Ms. Baker explained
the worksheet and how it included two columns length of path and notes
for students to add data about the crocked path measurement.
Before
the material managers gathered materials for their groups Ms. Baker
explained that the measurement of a ruler equals to 1 foot. She
demonstrated by showing that each ruler has a total of 12 inches and
that it equal to 1 foot. However she reminder that 1 foot means 12
inches not human foot.
Ms. Baker asked: Which side of ruler are inches?
Students
answered: larger numbers, centimeters are smaller numbers. Then Ms.
Baker explained how students were going to choose three of the units of
measurement available to measure the crooked path. Ms. Baker assigned
group roles while students were silently reading their assigned job
descriptions.
Exploring
Group 1: Students
could not complete task they spend too much time figuring out how to
measure with straw because they could not bend it. They had 50 inches
and 3.5 straws, they were measuring with 1 string the whole path it
seemed that they could not agree on whether to use all six strings or
only one.
Group 2: Students
started the task by measuring the crooked path first with inches then
figuring out how many feet by dividing the number of inches into 12. So
they divided 64 inches by 12 equal to about 5.4 feet.
Group 3:
Students started with the strings, they predicted how many strings
would take to cover the whole crooked path. When I observed this group
the students stated that they have completed the task. The data that
they had on their worksheet was: 10 feet (smelly), 12 hands (hard), 6
strings (kind of hard) and 6 straws (really hard). Student’s thought of
using their fingers to measure the path as well. I noticed that their
feet data wasn’t correct because they measured with human feet instead
of using the ruler or using the units.
Group 4:
When I arrived to observe this group I notice that they were measuring
the crooked path with their own feet. Most of the students from this
group were distracted on their worksheet they had data but no comments
on the note section. They had 11 feet, 47 inches, 10 centimeters, 6
strings and no straws.
Group 5:
Students from this group seemed confused could not agree on how to
measure the crooked path. I noticed that in the Straw Section of the
worksheet students had different fractions written: 7/8, 2/8, 4/8, 1
1/3, 7/8, 1 1/8 etc. While I was observing students were figuring out
how to measure with strings, the Mentor teacher was sitting in her chair
also observing how students were thinking. She explained that they can
bend string to measure she also said “Make sure ends of strings are
touching each other” Students finally decided that to cover the whole
crooked path it takes about 6 9/10 strings. Some of the notes that this
group had on their worksheet were strings non-competitive and not whole
straw fit too long. Ms. Baker suggested students to used the back of
the paper to do their math calculations to facilitate their work. Asked
students to stay focus and do measure the crooked path in 3 ways.
Math Work:
All
student groups utilized different methods depending on their units to
calculate the crooked path. Some of the methods they used were
divisions, conversions, fractions, decimals and estimations. Most of the
group members were able to explain what they were doing and backed up
their reasons. Group 5 had trouble explaining why they had too many
fractions under the straw section, one student said: Is hard to
calculate when you cannot bend so we thought of estimating with adding
fractions. Something that was unanticipated for this task was that I
even though students were told the difference between feet and human
feet 2 or 3 groups still measured with human feet.
After observing all five groups I noticed that students choose
different units of measurement depending on their math abilities and
thinking. Some groups choose to only handle non-standard units because
they thought that they would have less trouble measuring while other
groups choose to use only standard units because they had more
experience and know that they would have accurate results. There were
also two groups that choose to use a mixture of both it seemed that they
wanted to experience both methods of measurement.
Group Work:
Students
did not have too much trouble negotiating because they took their group
roles seriously. Everyone knew that their responsibility and role was
as important as anyone from their group. I noticed that the director
from team 2 made sure that her group members stayed on task at most of
the times. Two students from group 3 changed their roles once because
the material manager appeared to be ashamed of walking to grab the
materials.
From
observing all five groups at different times during the lesson I was
able to observe that everyone played their role well. If someone did not
know how to measure or spell other members of the group helped. It
seemed that students knew well that their jobs was to work as a team and
agree on certain decisions.
Discussion
Once
time for the task passed the teacher asked students to return to their
seats and make sure to be next to their group members. Teacher asked
students how the task went? Students answered: had, awesome and decent.
Teacher asked: who measured in feet, inches, centimeters? Students raised their hand.
Teacher
asked students to share their data with the class, first she asked for
feet results. Groups had different results: 5.4 feet, 10, 11 and 5 feet.
Then, the eacher asked why answers might be different? Some students
responded: because some groups may have more tape on their crooked path
than others and because foot size may be different. Ms. Baker explained
once again that every path was equal and that they were supposed to
measure in feet, which is a standard unit not an actual foot.
Then students shared the reset of the data: Inches 64 in, 47in, 87 in, and 50 in. Centimeters 266 cm, 10 cm, and 8 cm. Hands 11 and 12: Strings 4, 6, 6, and 6 9/10; straws 6.5, 35 and 7.
Student’s
mathematical thinking during this activity was made public and visible
to the entire class. Students were encouraged to share their results and
to comment based on what they experienced. The teacher stated that
during this activity everyone could share his or her thinking, ideas and
observations. Student’s data was written on the smart board for the
whole class to observe and compare.
Some
of the questions that promoted higher thinking during this activity
were: What happen why numbers are so much different? Why measuring with
feet’s was difficult? Which of these units are standard units? What is a
standard unit? What is a non standard unit? How big is a centimeter?
How many think 266 cm, 10 cm, 8 cm is correct raise your hand?
Why
hand results may be different? (Student answered: because we all have
different size hands) Why hands could be a standard unit? Are hands
same size? How about straws? Why the strings were helpful for this
activity? (all strings were evenly cut and easy to bend.)
Why
are hands difficult to measure with? “You cannot really measure a lot
it might be too small” “we only have two hands, cannot use both at the
same time while measuring with them”
What
strings have in common? (Student responded “same length”) What is the
best way to measure? What do you think which is the most effective way
to measure? (for this question students voted 3 different times by
raising their hands) (More students agree that standard units and
strings were the most effective methods of measuring for the given task)
Would strings be the most effective item to measure all things? Then students immediately responded no)
Is
everything in this world exactly the same size? Were straws easy to
measure with? (Students responded, “No, it was hard to bend them).
In
regards to the straws data teacher asked why there are 35 straws? Team
spokesperson responded; because I did it, then teacher asked student to
demonstrate how he obtained his answer in a crooked path that was
located on front of the classroom. She asked students how many inches
does a straw measure? Then carefully the student measured until he
realized his mistake and that he had forgotten a step to find the
closest solution.
• Summary/Closing
The
activity was closed with a brief review of what standard and
nonstandard units are and how can they be used to simplify life. The
closing part of the lesson provided coherence to the activity because
students made sense of why units of measurement are important.
Elena’s Reflection TE 402 Lesson Study Project:
I. Lesson Observation Notes:
A. Introduction/Launch: The
teacher started the measurement lesson with letting students know what
they were going to learn about and briefly explaining the task. To
students build background knowledge Emily asked the following questions:
Why do we use standard units? What kinds of things do we measure? Who
has measured something before? Why do you measure? What is the purpose?
What are some tools that you can use to measure? What are other things
you can use to measure? What are other things you can use to measure?
And which side of ruler are inches? Five students raised their hands,
one student said: Measure to see how long stuff is, how tall it is. Once
all students had an opportunity to share their mathematical thinking
and answer the teacher brief summarized standard and non-standards
unit’s definitions. Students clearly demonstrated that they had an
understanding of what things can be measure. The following is a list of
things that students mentioned: desk, computer screen, TV monitor,
yourself, book, window, smart board, Friday folders, projector, door,
keyboard, CD disk and “pretty much everything”.
From
the lesson observation something that stood in my memory is noticing
how students questioned and wondered so much about measurement concepts
and related it to real life situations. For example, one student
wondering “can you measure your shoes? Then Emily replied, how many
inches do you think is your foot long? She briefly explained how some
people shoes measure different inches depending on the size of the
person’s foot. However, I believe that this short conversation could
have been the cause of why some groups measured the task path with their
human feet instead of using the standard unit. Another real life
situation that one student in particular connected with the lesson topic
was how he measured himself at Michigan Adventures to see if he could
ride a game without an adult. Students mentioned other instruments that
can be used to take measurements such as leveler, measuring tape,
thermometer, ruler, tablespoons, cups, shoes and “you can use mostly
anything again”. Once students had a concrete understanding of
measurement the teacher asked students to separate those mentioned items
into standard and nonstandard units. Students said that measuring tape
and ruler are standard units. As opposite strings, shoes, pieces of
paper, or any other objects that don’t have specific measures are
nonstandard units.
When
the teacher had an idea of how well students understood the
mathematical concepts she proceeded to explain grouping roles and task
instructions. Students were divided into 5 groups of four students.
While students gathered into their groups the teacher explained the data
worksheet and the crocked path. Before
the material managers gathered materials for their groups the standard
“feet” unit concept was defined and explained briefly. Emily
demonstrated that 12 inches equal to 1 standard foot and explicitly
mentioned that the task asked to measure in feet standard units not real
human foot. However from my observations it was noted that students
weren’t fully paying attention during this activity because they were so
engaged and intrigued for their group responsibilities. During this
part of the lesson Emily explained the crooked path task instructions
and how they were going to choose only three of the units.
B. Exploring:
For this part of the lesson I decided to briefly observe each group in
order for me to have a concrete idea of how students were thinking.
Furthermore, during the lesson planning student role titles were
carefully choose in a way that every students felt like they had an
important function in their team. While observing all five groups I
noticed that all student took their role seriously though if anyone
needed additional help each other supported themselves. Two groups
followed task instructions however the rest of the groups employed most
of the task time to complete the whole list of units on the data sheet
instead of spending that extra time on carefully measuring their path.
If groups finished earlier the teacher allowed students to explore other
units or revise their work. In summary from all five-group
observations; group 1 could not complete task because they spend too
much time figuring out how to measure with straws. Group 2 began the
task with first measuring the crooked path with inches then figuring out
how many feet by dividing the number of inches into 12. In the
contrary, Group
3 first measured the crooked path with non-standards units, it seemed
like they predicted how many strings would it take to cover the whole
path. Group two completed the task earlier however their results weren’t
relevant to the task expectations. From group two observations I also
noticed that their feet data wasn’t accurate because they measured with
human feet instead of using the ruler or calculating with their standard
units. Group four measured
the crooked path with their own human feet as well. It appeared that
the students from this group were distracted on other unrelated task
events. Students
from Group five were confused and frustrated because they could not
agree on what units to use to measure the crooked path. In the straw
section they had written down different fractions, while I was observing
students were figuring out how to measure with strings. On couple
occasions the mentor teacher intervened this group to explain that they
strings can be bendable to measure more accurately she also said “Make
sure ends of strings are touching each other”. Throughout the whole
lesson Emily made sure that students were on task, she monitored all
groups and facilitated assistance if they needed additional help. At one
point during the task she called groups attention and suggested
students to used the back of the paper to do their math calculations to
smooth their work.
E. Discussion:
For this part of the lesson students were instructed to gathered as a
whole class but clarified that groups must seat next to each other.
Students seemed to be confused they were unsure if they were allowed to
seat in different spots given that this was the first time they had
worked in groups. According to Emily field observations students
normally work individually in any school related task. Once students
were well organized, the teacher asked students how they felt about the
task. Some students said, “It was challenging” “fun” “different”
“awesome” and “desent”. To initiate discussion the teacher asked who
measured in feet, inches, centimeters? Then, teacher asked students to
share all groups’ data in order. After data was collected on the
smartboard, to persuade students thinking Emily asked why feet data was
different? Some students responded “because some groups may have more
tape on their crooked path than others”. Then the teacher once again
explained that every path was identical and that the task asked to
measure in standard feet units not an actual foot. Student’s
mathematical thinking during this portion of the lesson was made
relevant and visible to the entire class. Students were encouraged to
share their results and to comment based on what they experienced. Some
of the questions that promoted higher thinking during this part of the
lesson were: What happen why numbers are so much different? Why
measuring with feet’s was difficult? Which of these units are standard
units? What is a standard unit? What is a non standard unit? How big is
a centimeter? Why hand results may be different? Why hands could be a
standard unit? Are hands same size? How about straws? Why the strings
were helpful for this activity? Why are hands difficult to measure with?
What strings have in common? Would strings be the most effective item
to measure all things? Is everything in this world exactly the same
size? Were straws easy to measure with?
Summary/Closing: It
was understood that in one single lesson students could not easily
grasp with all measurement concepts especially if it was unknown exactly
what standard and nonstandard units content background knowledge they
had. The teacher closed the lesson with summarizing what standard and
nonstandard units are and how can they be used to simplify life. During
the closing activity Emily also reviewed briefly explained student’s
misconceptions, compared and clarified task results. The mentor teacher
felt the necessity of recalling students that they had already learned
what standard units are, she defined and explained how both standard and
non-standard units differ. Overall the lesson closure provided
coherence to the activity because students made sense of why units of
measurement are important and how these can be used.
II. Reflection on Lesson Focus and Student Thinking: The following reflection of the mathematics lesson is composed of gathered information from my colleagues and individual notes.
When
TE colleagues and I select the mathematical subject for our lesson
study it was seeing that four-grader students may have some background
knowledge on how to use tools to measure and what standard units and
non-standard units are. As we planned our lesson plan it was anticipated
what students were likely to do during the lesson and generated
questions that could be used to promote students’ thinking. However,
during the mathematics lesson observation on April 19, 2012 at Attwood
Elementary School, MI it was observed that students struggled with
visualizing standard and non-standard units. Now after reviewing my
colleague observation notes and original lesson plan I noticed that some
sections of the lesson were rephrased to better accommodate students
learning experience. It seemed that wording of the task confused
students for example the majority of the fourth graders had a
misconception between the unit feet concept and human body part “foot”.
Students did not had a clear understanding of how to use standard units
for example some students could not use their rulers to measure
accurately. While Emily promoted higher thinking and engaged students by
asking persuasive and higher level questions it seemed that some
students wondered silently. From my colleague observation notes I
believe that if visual images and practical examples were presented
during the introduction and launch activity students recalling of
previous schooling measurement instruction would have been successful.
Assigning groups was chaos through the end of the launch activity given
that this was the first time that students had experienced teamwork in
their class. There is a possibility that the grouping and short task
conversations between teacher and students could have been the reason of
why students misinterpreted task instructions.
III. Lesson Modification:
After reflecting if I was to re-teach the lesson I would
modify the lesson in a way in which students will gain valuable
knowledge and not just experience a repetitive lesson with some
reasonable improvements. Therefore, if I was to teach the same topic for
this lesson I would definitely modify the task, I state this not
because the original task was irrelevant but because I would like my
students to build constructive knowledge not just replicate the same
experience. For the modified lesson I have additional staff or
volunteers to monitor students because I will ask students to go outside
by the playground area and measure an already planned crooked path.
(Paths to measure could be from a specific tree to a playground bench,
or game, etc). I believe that for the modified lesson teaching students
will gain more realistic and valuable learning experiences. I would
introduce the lesson with first stating the content objectives of the
lesson in order for students to be aware of what they will be learning
and expected to perform during the task. Then I will build background
knowledge following with a clear definition of what standard and
non-standard units are. If necessary I will utilize a PowerPoint or
Smart Board presentation with images and written explanations for
students and ELL to visualize while recalling information. If necessary I
will create a KWL chart on the Smart Board to debrief students
measurement background knowledge. Then once students have a well
understanding of the concept I will promote students thinking by
explicitly linking standard and non standard concepts with student’
background experiences. To prevent task instruction misunderstanding I
will adjust teaching speech appropriate for student’s academic and
mathematical proficient level. Because during the original lesson
teaching students were distracted with grouping I would wait to assign
groups until task and any other necessary clarification were stated.
Throughout the original task students appeared to be confused therefore,
for the modified lesson plan I will carefully scaffold the assignment
by using an instructional framework approach where I will teach, model
and offer opportunities for students to practice the task if necessary.
Once any misinterpretations had been clarified I will assign roles and
groups then I will remind students of classroom rules and task behavior
expectations. For the discussion activity, I will have students return
to the classroom and similar to the original lesson have them sit next
to their group members. I will follow Emily’s procedures but I will
organize data on the Smart Board for students to visualize. Three
approaches that I would not change from the original lesson plan are
frequent opportunities for interaction and discussion. I think that
Emily Baker did a great job with these methods she provided sufficient
wait time for student responses and clarified concepts even though
students weren’t fully on task towards the ending of launch activity.
For the closing activity of the lesson I will review key measurement
concepts and strategies. Ask students if they have any questions or
feedback from the task. To further assess students learning and practice
I will give them a homework assignment where they will come up with a
real life path and a measuring unit that they will use to simplify their
lives (it could be their house to school, park to school, favorite
store to restaurant, etc. As I said at the beginning creating a
meaningful lesson keeping in mind the same concept would be more
functional than re teaching a modified lesson that students have already
experienced it would only convey more lesson planning issues to the
lesson study instead of scrutinizing students mathematical understanding
and thinking.
IV. Highlighting issues related to teaching this area of mathematics:
Some
of the general issues related to the teaching of measurement standard
and non-standard units that I would like to pursue during my teaching
this coming year are clear definitions of both concepts and knowledge on
how to utilize measurement tools. In order to effectively teach this
area of mathematics a set of several measurements mini lessons must be
taught throughout a week. Diverse meaningful activities, examples and
opportunities for students to learn and share ideas must be available in
order to improve student mathematical thinking and learning experience.
Students must know how to identify the appropriate tools and techniques
to determine length measurements using both standard and non-standard
units. From observation notes it was noticeable that students struggled
with collecting, organizing and representing their data it proves that
students need to gain conventional skills such as representing data
using tables, tally marks, and making decisions to make things easier.
As conclusion it must be understood that length measurement skill is not
immediately understood by younger children VandeWalle in his article
states “upper elementary children and middle school students still may
have challenges with length as they learn to investigate other
mathematical problems. Therefore “the temptation is to carefully explain
to students how to use these units to measure and then send them off to
practice measuring” (VandeWalle, 2010).
Work Cited:
Echevarría, J., Vogt, M.E., & Short, D. (2004). Making content comprehensible for English learners: The SIOP Model. 3rd Ed. Boston: Pearson/Allyn & Bacon.
Stein, M. K., Smith, M. K., (2011). Five Practices for Orchestrating Productive Mathematics Discussions. VA: National Council of Teachers of Mathematics Press.
VandeWalle,
J Karp. K, & Bay-Williams., J. (2010). Elementary and Middle school
Mathematics: Teaching Developmentally: Developing Measurement Concepts.
Chapter 19.
Varoz,
Stephanie & Gina Post (2008). Supporting Teacher
Learning:Lesson-Study Groups with Prospective and Practicing Teachers.
The national Council of Teachers of Mathematics Inc. Website: www.nctm.org
