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:
Materials & supplies needed: (per team)
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Launch (20 minutes)
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. 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. |
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
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Length of Path
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Notes
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Feet
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Inches
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Centimeters
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Hands
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String
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Straws
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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.
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
