Thursday, October 11, 2012

Goals for Children's Development

Goals for Children's Development & Learning - Infants, Toddlers & Twos
     The overall goal of the Early Head Start program is to support all areas of child development - social/emotional, physical, cognitive, and language development.
     Education Goals and Objectives follow:
  • Social-Emotional Development: To learn about self and others - trusts known, caring adults, regulates own behavior, plays with other children, learns to be a member of a group, and uses personal care skills.
  • Physical Development: To learn about moving - demonstrates basic gross motor skills, demonstrates basic fine motor skills.
  • Cognitive Development: To learn about the world - sustains attention, understands how objects can be used, shows a beginning understanding of cause and effect, shows a beginning understanding that things can be grouped, uses problem solving strategies, engages in pretend play.
  • Language Development: To learn about communicating - develops receptive language, develops expressive language, participates in conversations, understands and uses words, enjoys books and being read to, shows an awareness of pictures and print, experiments with drawing and writing.
Curriculum
     Curriculum plays a vital role in achieving the goal of enhancing the social competence and school readiness of children. Early Head Start programs must implement a curriculum that supports each child's individual pattern of development and learning style.
     Goals and objectives are what children need to learn. Curriculum is the roadmap for getting there. For young children, it is provided through routines and experiences. The Early Head Start program utilizes the following curriculum resources: Creative Curriculum for Infants and Toddlers, Program for Infant-Toddler Caregivers, First Steps, Conscious Discipline, and Language is the Key, Baby Signs, Games Babies Play, I Love You Rituals, and others.
Individualization
     The Early Head Start program recognizes the uniqueness of each child as an individual. Therefore, children's progress and abilities are measured based on their own skills. Using information gathered from screenings, observations, assessment, and evaluations, staff are assisted in developing individualized planning for children.
Parent Involvement & Education
     Parents and families are key players in Early Head Start programs. Since parents are recognized as their child’s first teacher, staff seek to inform and support parents so they can guide the early learning of their young children.
  • Home visitors and teachers use the Parents as Teachers Born to Learn curriculum to provide families with information about parenting young children.
  • Parents learn to be observers of their children during socializations (early learning playgroups) at the Early Head Start center. Through an approach called Parents Interacting with Infants (PIWI), staff strive to support the parent-child relationship and to involve parents in their child’s learning experiences.
  • Parenting information distributed throughout the year include materials from United Way Born Learning campaign, Zero to Three booklets, Noodle Soup parenting tips, and others.
Inclusion of Children with Disabilities
     A formal evaluation is conducted, if needed, to diagnose a developmental delay. The evaluation process provides an in-depth view into the child’s skills and needs. EHS staff and parents collaborate with the early intervention agency such as Early On or Project find to conduct evaluations and to plan strategies for intervention. Families receive an Individualized Family Service Plan (IFSP) that details expected outcomes.

 Info source from: http://www.nemcsa.org/headstart/ecdhs_b.aspx

Mathematics teaching Resources

Great Websites

Formative Assessment Strategies for Every Classroom: An ASCD Action Tool, 2nd Edition by Susan M. Brookhart

Website:http://www.ascd.org/publications/books/111005.aspx

West Virginia Department of Education: teaching 21 century students
Website: http://wvde.state.wv.us/teach21/ExamplesofFormativeAssessment.html

801 Mathematics Unit 3 Everyday Math


TE 801 Unit Planning Project
“Visual Patterns, Number Patterns, and Counting”

Section 1: Big Ideas and Standards

Big Ideas:  Guided teaching unit will focus on:

·      Understanding numeric, place value and telling time patterns while creating concrete patterns
·       

Common Core State Standards (CCSS):

·      CCSS.1.MD.3 Tell and write time in hours and half-hours using analog and digital clock

·      CCSS.1NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases

·      CCSS.1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another

The mathematics standards above are connected to the big idea because students will learn how to use patterns to understand telling time, counting and place value.

Standards for Mathematical Practice:

Model with Mathematics
Analyze relationships mathematically to draw conclusions. Students routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.


Section 2A: Pre-Assessment

1st Grade Classroom
Math Unit 3 Pre Assessment

Nombre:_________________________________

Fecha: _________________________________



1.    Dibuja el próximo patrón de figuras. Draw the next shape pattern.


_____________________________


    
 2.  Cuenta de 2s en 2s hasta el 12. Count up by 2s.

2, 4, ____, _____, _____, _____,


   3. Cuenta las monedas. Count the coins.
Macintosh HD:Users:elenarosas:Desktop:Lincoln_Penny_Obverse.jpgMacintosh HD:Users:elenarosas:Desktop:Lincoln_Penny_Obverse.jpgMacintosh HD:Users:elenarosas:Desktop:Lincoln_Penny_Obverse.jpgMacintosh HD:Users:elenarosas:Desktop:Lincoln_Penny_Obverse.jpgMacintosh HD:Users:elenarosas:Desktop:220px-1945-P-Jefferson-War-Nickel-Reverse.JPGMacintosh HD:Users:elenarosas:Desktop:220px-1945-P-Jefferson-War-Nickel-Reverse.JPG

   4. Que Hora es? What time is it?
Macintosh HD:Users:elenarosas:Desktop:images-1.jpg

Antes (before)
Numero (number)
Después (After)
5
6
7

8


10

5. Completa la tabla. Complete the table.








Pre-Assessment: Results
·      This Friday Oct 12, 2012 I will be assessing my students, currently I have 28 students normally everyone no one is absent. Based on what I have observed during math lessons my students know how to count by 2s until 24 and by 5s until 50. They know how a quarter and penny looks like, they know what a square, triangle trapezoid, circle, hexagon looks like, they have an understanding of how to use a number line, number grid and they understand simple pattern concepts.

·      Based on what I know from my students mathematically for my unit I plan to include activities that require some form of manipulative to maintain my students interested and to help those visual learners. For most of my lessons I plan to have 15 minutes mathematics learning centers. I will place my students into 4 different groups in order for me to target those students that will need more support.


Section 2B: Formative and Summative Assessments

Formative Assessment:
·      Thumbs up/down: If you agree or understand.
·      Choose three or four different formative assessment strategies to use repeatedly throughout your unit.
·      Design a system (tied into the Standards and Big Ideas for your unit) for keeping track of individual student growth based on your on-going use of formative assessment.

Sunday, April 29, 2012

Measurement Lesson Study

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

 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.



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