Mt. Baker Student Observation Project


By
Kim Franklin
Neal Schlegel
Rick Romito
Jack Feil
Pat Brauer


Table of Contents:
Overview
Pat
    • Lesson Plan
    • GLE Lesson Alignment
    • Observation Team & Pre-Observation Form
    • Lesson Observations
    • Lesson Reflection
Jack
    • Lesson Plan
    • GLE Lesson Alignment
    • Observation Team & Pre-Observation Form
    • Lesson Observations
    • Lesson Reflection
Rick
    • Lesson Plan
    • GLE Lesson Alignment
    • Observation Team & Pre-Observation Form
    • Lesson Observations
    • Lesson Reflection
Kim
    • Lesson Plan
    • GLE Lesson Alignment
    • Observation Team & Pre-Observation Form
    • Lesson Observations
    • Lesson Reflection
Neal
    • Lesson Plan
    • GLE Lesson Alignment
    • Observation Team & Pre-Observation Form
    • Lesson Observations
    • Lesson Reflection
Resources
    • Pre Obervation Information
    • Junior and Senior High Bell Schedules
    • Observation Tools


Overview:
This project focuses on how well students are engaged in math lessons. Teachers observed lessons to see if the lesson that was being taught was engaging students and really meeting the objectives of the lesson.

By clicking on each teacher’s name to the left you will be able to look at the four steps in the process:


Pat:

Lesson Plan

Lesson Plan

Topic:  Introduction of Vectors

Objective:  Students will discover the x and y components of a vector to determine the resultant motion from two different forces.  In addition, the student will be able to use the polar form of vectors to determine the resultant motion/trajectory.

  1. Introduce the situation outlined in the attached worksheet.  Emphasize the idea that the wind in pushing the plane in a direction that is different than the direction the plane is heading.
  2. Student will work on the worksheet.
  3. Have students share their diagrams and calculation for situation 1 and 2.
  4. Summarize the addition of vectors.
  5. Work through the following example with the class.
    1. A boat is heading northwest at 18 knots.  The ocean currents and wind are pushing the boat in a northeasterly direction at 2 knots.

                                                               i.      Write a vector is polar from for the boat

                                                             ii.      Write a vector in polar form for the current.

                                                            iii.      Convert the vectors to rectangular form.

                                                           iv.      Add them together.

                                                             v.      Convert back to polar.

  1. Vectors also work with forces.  Go through the attached problem.
  2. Homework is out of the book..p. 450 #9-17,19,20

 

The (click this to download---->) worksheet to view.

 

 




GLE Lesson Alignment

The GLE’s (Washington State standards) below are aligned with the lesson. 

In addition, the student use their knowledge of polar/rectangular coordinates and/or the law of sines and cosines to solve the given problems.  At the end of the lesson the students will be able to identify the horizontal and vertical components of a vector that is given in polar form (magnitude, direction).



MA-9/10.2.1.1.a. Use strategies to become informed about the situation (e.g., listing information; examine the table for patterns; create a scatter plot to look for patterns; asking questions).
Component 2.2 Apply strategies to construct solutions.
MA-9/10.2.2.2 Apply mathematical tools to solve the problem. [W]
MA-9/10.2.2.2.b. Use mathematics to solve the problem (e.g., use algebra to write equations for the two linear models, solve the system of equations using either symbols or technology).
EALR 4 The student communicates knowledge and understanding in both everyday and mathematical language.
Component 4.2 Organize, represent, and share information.
MA-9/10.4.2.2 Understand how to express ideas and situations using mathematical language and notation. [W]
MA-9/10.4.2.2.a. Explain how division of measurements produces a derived unit of measurement (e.g., miles traveled divided by hours traveled yields the derived unit [miles per hour]). (1.2.2)
MA-9/10.4.2.2.b. Describe the location of points that satisfy given conditions (e.g., the set of points equidistant from a given point; a point equidistant from a given set of points). (1.3.3)
EALR 5 The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.
Component 5.1 Relate concepts and procedures within mathematics.
MA-9/10.5.1.1 Apply multiple mathematical concepts and procedures in a given problem or situation. [W]
MA-9/10.5.1.1.a. Estimate derived units of measure (e.g., miles per hour, people/year, grams/cubic centimeters). (1.2.6)
MA-9/10.5.1.1.b. Determine the final coordinates of a point after a series of transformations. (1.3.4)


Observation Team & Pre-Observation Form

Observers:  Jack Feil, Kim Franklin

The purpose of this is to provide the observer with a context for the lesson and a focus on what the teacher being observed would like feedback on. 

Pre-Observation Information for Mr. Brauer’s Lesson

Please fill out the following questionnaire prior to meeting with your observation team.  The purpose of this is to provide the observer with a context for the lesson and a focus on what the teacher being observed would like feedback on. 

  1. What is the primary mathematical idea that you will be developing with this lesson?
    1. I will be trying to introduce the idea of a vector. 
  1. Are there other mathematical ideas that are included in this lesson?
    1. We have been working on trigonometry and polar coordinates and the students will be expected to make use of it in this lesson. 
  1. What are the mathematical ideas that you were working on prior to this lesson?
    1. Trig and polar coordinates, law of sines and cosines. 
  1. How do you anticipate your students will do with this mathematical idea?  Where do you anticipate they will struggle?  What is it about the material that will cause the students to struggle?
    1. They will struggle with breaking the components of motion into horizontal and vertical components.
    2. In addition, we the vectors are not perpendicular, they will struggle with how to apply the trig to the horizontal and vertical components. 
  1. What evidence can the observer look for to demonstrate that the students are successfully working towards understanding of the concept being taught?
    1. Applying trig to the resulting forces.
    2. Using language like the law of sines, cosines, vectors, and polar coordinates. 
  1. What areas of the lesson would you like the observer to focus in on?
    1. The use of the contructivist approach to teach vectors.  Primarily, is the time spent constructing the vector idea worth it as opposed to a direct instruction approach. 
  1. Are there particular students that you would like the observer to focus in on?  What is it about this group of students that you want feedback on?
    1. All the groups.

  2. Attach an up-to-date seating chart with pictures if possible so that the observer can identify students by name. Provided



Lesson Observations

Kim’s observation notes of Pat’s Integrated Math 300 class 5th period, March 30.

Good warm up problems applicable to the upcoming lesson.Most students applied themselves early.  Working in pairs seems to work well.  Being a woman, I was disappointed that more girls either lost interest or needed help.  For me, it gives relevance to the distance=rate x time problems (current and wind) we do at level 100, also the introduction to polar graphing.



Ken’s observation notes of Pat’s Integrated Math 300 class 5th period, March 30.

Since I haven’t figured out how to create a link, I’ll just write mine here:

Rick’s Observations

First, thank you for letting us come in and observe.  I know it can be uncomfortable having so many peers watching even though we are paying attention to the students. I appreciate your rapport with this class.  It’s not the easiest group to navigate.

Warm up-most of the students on my side of the room were engaged in the warm up.  They used terms like Pythagorean Theorem and sine and cosine.  Students who had difficulty got good explanations from those who understood the process.

Going over the warm up:  again, most students were attentive and involved in all three explanations.

Exploration-There was a lot of discussion about using trig functions and the Pythagorean Theorem to solve the problems, but most of the groups made no connection to the Law of Sines or Cosines, and so they floundered.  As Pat went around the room explaining the process, at least one member of the pair understood and were able to solve the first problem.  Most of the pairs were engaged in trying to solve the problem. 

On the second problem most of the groups still didn’t make a connection to what they had been doing previously, and about half of them stopped working and started to talk.  Only after the second process was explained did they renew their efforts.  Good use of trip terms once they had the process.

Class explanation:  When Pat was in front, many of the students were paying attention, probably 90%.  This dropped off to about 50% by the end of the 3rd explanation, partially because it was difficult to hear in the back of the class.  Ryan’s solution was missed by about half of the groups.

Group explanation of vectors-most of the groups had their attention on the board during the explanation, but ...

Continuation of the exploration:  only about 25% of the students were engaged after the explanation.  The rest of the students had pretty well checked out.

I left at this point, but I would have liked to see whether or not they re-engaged.

Jack’s Observations:

Thanks, Pat for allowing the opportunity to observe your class. It is always encouraging to watch and be engaged in the learning process. You did a excellent job of class management. You were continually monitoring class engagement.
Most (95%) of the student groups worked on the task provided. There were those few students who waited for the others in their group to solve the problem for them, and were not engaged directly in the group task. This, too, happens in my class and I wish there was an answer to having 100% involvement.
The lesson on Vectors was well done. The student questions were well designed to direct the learning to the desired outcome.  There was good student interaction within the groups that I observed.

WELL DONE !






Lesson Reflection

The lesson went well until the introduction of vectors in question number 5 on the worksheet.  The jump from the idea of direction and distance to an x and y component was too much of a leap for my students.  This was especially true for students who did the calculations using the Law of Cosines idea.  I would build in some work with simply vectors previous to this lesson or break the work up at question 4 and use the previous work to introduce and answer the questions 5-8 as a class. 

What I liked?  The students were engaged with the problem and successfully calculated ground speed and were able to distinguish it from air speed. 



Jack:

Lesson Plan

Observation lesson for March 23 during 7th period.

Eight grade: MathThematics, McDougal Littell

Module 4 section 5  Working with triangles, Right On!

The Stage has been set previously by using paper squares to make sides of triangles of different shapes. Today we will look at the group of triangles that form one right angle.

The class is broken into two parts : 30 minutes before lunch and 60 minutes after lunch.

Before lunch we will look at all the special triangles that form right angles among all the triangles that were formed from squares made the previous day.

Beginning of the class I will demonstrate using a plastic teaching tool. It  demonstrates the property that the square sides can be joined uniquely in right triangles. That the square of the two Legs add together to form a square of the Hypotenuse. We will discuss when to add and when to subtract squares to find the missing length of a side.

The students will be given a work sheet to practice completing the square. This will further reinforce the mathematics of squaring sides and adding, then finding the square root to find the length of the missing side.

Students work in small groups to compete the worksheet #1.

We break for lunch.

After lunch we worked on a second worksheet #2 with additional examples of right triangles where students needed to find lengths of a missing side. On the back side of the worksheet were four word problems for students to solve. They were encouraged to draw a picture to better understand the problem situation.

The final portion of the class will be used to give a short quiz to check on student understanding of the Pythagorean method of finding sides of triangles.

Lesson Handouts (Click the links below to download.)

Worksheet 1 page 1
Worksheet 1 page 2
Worksheet 2 page 1
Worksheet 2 page 2
Quiz







GLE Lesson Alignment

The GLE’s (Washington State standards) below are aligned with the lesson.  The two GLE’s are from the Geometric Sense (1.3) which are the foundation for the content of this lesson.

MA-8-1.3.3.b. Apply the Pythagorean Theorem to find the length of a side of a right triangle or distance between two points.
MA-8-1.3.3.c. Explain a method for finding the missing side of a triangle in a real-world setting (e.g., the height of a totem pole or building).


Observation Team & Pre-Observation Form

Observation team Neal and Rick and Ken

Pre-Observation Information for Jack’s Lesson

Please fill out the following questionnaire prior to meeting with your observation team.  The purpose of this is to provide the observer with a context for the lesson and a focus on what the teacher being observed would like feedback on. 

  1. What is the primary mathematical idea that you will be developing with this lesson?

    To explore the use of the Pythagorean theorem with right triangles. How to find the missing side of a right triangle. To understand the relationship of the two legs to the hypotenuse in a right triangle.
     
  2. Are there other mathematical ideas that are included in this lesson?

    Similar triangles, proportions, and basic geometry.

  1. What are the mathematical ideas that you were working on prior to this lesson?  

    We have been working on basic triangle relationships using the similar, proportional, and congruent figures. 
     

    We were working with square and square root numbers.

  1. How do you anticipate your students will do with this mathematical idea?  Where do you anticipate they will struggle?  What is it about the material that will cause the students to struggle?

    Students will work together to solve the length of the missing side. Most will follow the lesson and understand.

    Students will struggle with the idea of which side to subtract or add another.

    They just want to follow a procedure and not think about relationships of sides.
     
  2. What evidence can the observer look for to demonstrate that the students are successfully working towards understanding of the concept being taught? 

    Most obvious is the ability to find accurately the missing length of side by looking at student work. Through student conversation it should be evident which individuals need clarification or help in understanding. The types of questions that are asked, too, reveal student understanding.
     
  3. What areas of the lesson would you like the observer to focus in on? 

    Please observe student conversation. Are students talking in Procedures & Facts (PF) , are they making Justifications (J), or have the move on to Generalizations (G) . Compile # of student comments that fit in each category.

  4. Are there particular students that you would like the observer to focus in on?  What is it about this group of students that you want feedback on?

    No particular group is identified.


  5. Attach an up-to-date seating chart with pictures if possible. "Provided"



Lesson Observations

Ken’s student observation notes for the March 23rd observation 7th period.

Rick’s observation notes:

First of all, thank you, Jack, for letting me sit in on your class on Friday.  I know it can be uncomfortable for the teacher to have others in your classroom.  I always learn something when I visit another class.  I really appreciated your manipulative of the Pythagorean Theorem.  It gives a clear visual image of the geometry behind the equation.

           I wasn’t sure how I was supposed to use the document you gave me so I basically did a running record of student involvement during the lesson.  I tried to break it up into roughly equal 5 minute time frames, but there are no guarantees. 

           My observation is broken into what you were doing at the time, what kind of discourse was taking place, and what the students were doing at the time.  I hope this is what you expected.

1.  Explanation of the relationship between the squares on the sides and squares on the hypotenuse.  PF-90% of the students watching the demonstration, 2-3 answering questions.

2.  Reverse the procedure and explaining how to find the size of the sides from the squares on the sides.  PF-80% of the students watching.  Same 2-3 answering the questions.

3.  Students were asked to look at the worksheet and find the size of the side on the first problem.  PF-80% of the students were looking at the sheet.  4 pairs were talking about solutions, many were asking how do you find it.

4.  Explanation of the how you find the size of the hypotenuse.  J-25% were listening to the explanation and response by the other students.  Most of the others were either trying to figure out the first problem or had started talking amongst themselves.

5.  Discussion of what kind of triangles this works with. G-10% were listening to the answer.  Most were either still trying to work on the worksheet or had given up and were talking.

6.  Helping students work on the worksheet.  PF/J-50% of the students were working on the worksheet with some success.  25% were asking for help from other students or were deriving incorrect answers.  25% were lost and just talking to each other.

7.  Continuing to help student pairs.  PF/J 25% have good understanding of the process and are completing the worksheet.  25% have some understanding of the worksheet, but have several answers wrong.  25% are still looking at the worksheet but don’t really understand.  25% are clueless.

The session ended with the lunch bell.  I didn’t come back after lunch, so I missed the rest of the lesson. 

Rick



Lesson Reflection

Lesson went well. The majority of students were engaged in the entire lesson.

In reviewing observers comments - most student interaction was at the procedure and fact level. There was some generalization done by students with limited Justification of tasks. This is not an unexpected outcome but I am trying to move toward having deeper conversations.

The goal is to have students gain greater understanding through their ability to explain themselves not just give procedures and facts to each other.

The results of the 5 question class ending quiz. 100% answered the first three questions correctly. The final two application questions were difficult for many (25% success rate).



Rick:

Lesson Plan

The goal of the lesson is for students to rewrite inequalities in 2 variables in slope-intercept form and then to graph those inequalities.  This is the second in a series of lessons on inequalities. 

1. Warm up.  Reintroduces some of the ideas of inequalities from Monday’s lesson, also is a teaching moment for working with quadratics, the next topic we will discuss.

2.  Check and stamp last night’s homework assignment, pg. 457.  Questions and answers.

3.  Group discussion of rewriting inequalities in slope intercept form.  Start with rewriting equalities, a skill they have already practiced.  Discuss the differences in rearranging inequalities.  Give some samples of rewriting inequalities.  Have students practice the task themselves. 

4.  Discussion of why rewriting the inequalities is important.  How do we graph equations in slope intercept form?  What is different about graphing inequalities in slope intercept form?  Examples.  Students practice.

5.  Hand out the worksheet and have students work on it together.  If there are any major problems, bring class together to discuss.



GLE Lesson Alignment

The GLE’s (Washington State standards) below are aligned with the lesson.   

MA-9/10.1.5.1.c. Translate among equivalent numerical, graphical, and algebraic forms of a linear function. RL, MC]
MA-9/10.1.5.2 Analyze a pattern, table, graph, or model involving repeated addition (linear) or repeated multiplication (exponential) model to write an equation or rule. [W]
MA-9/10.1.5.2.f. Represent systems of equations and inequalities graphically. [RL, MC]


Observation Team & Pre-Observation Form

Pre-Observation Information for Rick’s Lesson

Please fill out the following questionnaire prior to meeting with your observation team.  The purpose of this is to provide the observer with a context for the lesson and a focus on what the teacher being observed would like feedback on. 

  1. What is the primary mathematical idea that you will be developing with this lesson? 

    Rewriting inequalities in slope-intercept form and graphing them.                   

  1. Are there other mathematical ideas that are included in this lesson?  

    Properties of inequalities, graphing
                                                      


  1. What are the mathematical ideas that you were working on prior to this lesson? 

    Properties of inequalitiesSolving inequalities in one variable.                            


  1. How do you anticipate your students will do with this mathematical idea?  Where do you anticipate they will struggle?  What is it about the material that will cause the students to struggle?

    I think they will do fine since this is very similar to graphing equalities.  They might struggle with graphing in slope intercept form.                           

  1. What evidence can the observer look for to demonstrate that the students are successfully working towards understanding of the concept being taught?   

    Successfully rewriting the inequalities and successfully graphing them.                                                                         


  1. What areas of the lesson would you like the observer to focus in on?   
    Student involvement in the process.
                                                                         


  1. Are there particular students that you would like the observer to focus in on?  What is it about this group of students that you want feedback on? 

    I’d like to know what students who are not understanding the process were doing prior to being given the worksheet.                 




Lesson Observations

Ken’s student observation notes for the March 23th observation 5th period.


Lesson Reflection

I thought this lesson went very well.  I kept the progression orderly and the students seemed able to follow along quite well, using their previous experience.  Everyone was engaged and I had the feeling that they felt successful even when the problems grew tougher.  

Kim:

Lesson Plan

Fractals, Patterns, and Sequences

Warm up: typed Geometry notes with some short fill-in-the-blanks, we read as a class, discuss and make diagrams.

Objective: see GLE alignment

Materials: Lab sheet 1A (MathThematics 3 Module 4), colored pencils & rulers

Students extend a geometric fractal pattern, a tree with 3 branches at the end of each previous branch half as long, making each new set of branches a different color.

Students fill in a table of: number of new branches, length of one branch, total length of new branches, and height of tree.  As a class, we discuss the patterns found in the table, what each sequence is approaching, extend the sequences, and write a rule for the nth term. In previous work they have seen sequences approaching infinity or zero, but in this instance the height of the tree is approaching 4 inches, 2+1+.5+.25+.125 ...,hence this is their first look at a limit.

Homework: bookwork that reinforces extending sequences and stating a rule for the pattern.

 




GLE Lesson Alignment

The GLE’s (Washington State standards) below are aligned with the lesson. 



MA-8-1.5.2.D. Use words or algebraic symbols to describe a rule for a linear relationship between two sets of numbers (e.g., given a table, describe a rule). [CU]


Observation Team & Pre-Observation Form

Pre-Observation Information for Franklin’s Lesson

Please fill out the following questionnaire prior to meeting with your observation team.  The purpose of this is to provide the observer with a context for the lesson and a focus on what the teacher being observed would like feedback on. 

  1. What is the primary mathematical idea that you will be developing with this lesson?

A fractal produces several numerical sequences that can be extended once the pattern has been deduced.

  1. Are there other mathematical ideas that are included in this lesson?

a) sequences are approaching 0, infinity, or some number in between those two extremes

b) fractals produce interesting geometric shapes in which perimeter and area take on new meanings

  1. What are the mathematical ideas that you were working on prior to this lesson?

geometric shapes and their definitions

  1. How do you anticipate your students will do with this mathematical idea?  Where do you anticipate they will struggle?  What is it about the material that will cause the students to struggle?

Fractals, limits, infinity within an infinite space are a cognitive leap for middle schoolers; some will begin to understand and some won’t be ready for it.

  1. What evidence can the observer look for to demonstrate that the students are successfully working towards understanding of the concept being taught?

Whether or not the student can successfully complete the table of sequences that goes with the drawn fractal.

  1. What areas of the lesson would you like the observer to focus in on?

see #5

  1. Are there particular students that you would like the observer to focus in on?  What is it about this group of students that you want feedback on?

This class has several special ed students as well as students who score low due to poor attendance.

  1. Attach an up-to-date seating chart with pictures if possible so that the observer can identify students by name. Provided



Lesson Observations

Ken’s student observation notes that I took on March 7, 2007. These are the two sites that Kim recommended to her students: A Fractal Gallery and a fractal generator site.


Lesson Reflection

The warm up was an of an introduction to geometry which lead to some interesting student statements and observations. Especially interesting was the concept that all geometric figures are infinite sets of points but some have finite measurements (segments, angles, polygons.)

Even with me demonstrating on the document camera, drawing a fractal with branches that are fractions of an inch proved difficult for about one-third of the class. (mostly special-ed students)  In the future I would go back over the markings on a ruler between 0 and 1 inch with students. It was very helpful to have other adult helpers in the room to assist those students having trouble. 

All of the students stayed on task while drawing the fractal, and most took pride in making it look nice. Some wanted to simply copy the table rather than think for themselves on the more difficult columns such as total length of new branches and tree height.

Most students were on task for the discussion about what each sequence was approaching: zero, infinity, or a limit such as 4 inches.



Neal:

Lesson Plan

Lesson Plan:  Period 1, March 22nd, 2007

Observed by Scott Smith and Pat Brauer

Objectives:  Geometric/Measurement (of Area) Reasoning, Problem Solving, and Communication.  Group Cooperation.

Materials Needed:  Document Camera, LCD Projector, one 2 foot by 2 foot white board per group, white board markers for groups, and copies of (click  to download---->) Copper Bracelets  for each student.

Background Information:  Groups have done similar work in the past, so the process is not new to them.  They should be getting better at working in groups, following a problem solving process, and effectively describing the steps they went through to solve the problem.

8:00 - 8:05  Announcements, Attendance, Agendas

8:05 - 8:20  Mathercise.  Begin lesson with warm-up/review problems on volume, mean, and percents.  Then discuss answers as a class.  Students show answers and work to classmates with the document camera.

8:20 - 9:24  Copper Bracelets Problem.  Students get 2’ x 2’ white boards and white board markers.  As a group, they work on developing a solution (there are several alternative strategies) to a problem that is projected with the Document Camera and LCD Projector.  As groups get the correct solution (with all work shown), they are then given individual copies of the problem and they each follow a writing strategy process (modified from Bryan Harpel) to explain exactly how they solved the problem.  Teacher circulates and provides assistance, guidance, and clarification as needed.  Homework is to finish the description of how they solved the problem.




GLE Lesson Alignment

The GLE’s (Washington State standards) below are aligned with the lesson.   

MA-7-1.2.5.e. Use given dimensions to determine surface area and volume.
EALR 2 The student uses mathematics to define and solve problems.
Component 2.1 Understand problems.
MA-7-2.1.1 Analyze a situation to define a problem.
MA-7-2.1.1.a. Use strategies to become informed about the situation (e.g., listing information, asking questions).
MA-7-2.1.1.e. Define the problem (e.g., find the smallest number of free throws Bonita needs to make out of 25 attempts in order to top Juan?fs percentage).
Component 2.2 Apply strategies to construct solutions
MA-7-2.2.1 Apply strategies, concepts, and procedures to devise a plan to solve the problem.
MA-7-2.2.1.b. Select and apply appropriate mathematical tools for a situation (e.g., guess and check, calculate Juan?s percentage and create a table of values [with or without technology] for Bonita?s percentage).
MA-7-2.2.2 Apply mathematical tools to solve the problem. [W]
MA-7-2.2.2.a. Implement the plan devised to solve the problem or answer the question posed (e.g., in a table of values of percentages for Bonita?s possible results and percentages, find the range of values that yield a percentage larger than Juan?s; find the smallest of those and use that number).
MA-7-2.2.2.b. Identify when an approach is unproductive and modify or try a new approach (e.g., if a result is larger than 25, return to see if the percentage computation is accurate and if it is computed correctly).
MA-7-2.2.2.c. Check the solution to see if it works (e.g., if the solution is larger than 25, it makes no sense in the given problem).
EALR 4 The student communicates knowledge and understanding in both everyday and mathematical language.
Component 4.2 Organize, represent, and share information.
MA-7-4.2.2 Apply communication skills to clearly and effectively express or present ideas and situations using mathematical language or notation.
MA-7-4.2.2.c. Clearly explain, describe, or represent mathematical information in a pictorial, tabular, graphical, two- or three-dimensional drawing, or other form as appropriate for the mathematical information (e.g., time, distance, categories), audience, and/or purpose such as to perform or persuade with notation and labels as needed.


Observation Team & Pre-Observation Form

Observers:  Scott Smith, Pat Brauer, Ken Bakken

The purpose of this is to provide the observer with a context for the lesson and a focus on what the teacher being observed would like feedback on. 

Pre-Observation Information for Mr. Schlegel’s Lesson

Please fill out the following questionnaire prior to meeting with your observation team.  The purpose of this is to provide the observer with a context for the lesson and a focus on what the teacher being observed would like feedback on. 

  1. What is the primary mathematical idea that you will be developing with this lesson?
    1. Students will be working on communication skills, problem solving skills, and the writing process.
  1. Are there other mathematical ideas that are included in this lesson?
    1. Students will be using logic, geometry, probability, and the mean in statistics.
  1. What are the mathematical ideas that you were working on prior to this lesson?
    1. Students have been working on the same skills listed in the previous question especially, 3-D geometry, GSP, and probability.
  1. How do you anticipate your students will do with this mathematical idea?  Where do you anticipate they will struggle?  What is it about the material that will cause the students to struggle?

    • Students should do well with this because they have done similar activities  before.   Students may struggle with the volume problem.  They may try to calculate rather than estimate.
  1. What evidence can the observer look for to demonstrate that the students are successfully working toward understanding of the concept being taught?

    • My observations of the students will determine the pace of the lesson and whether they move on and progress through the lesson.
  1. What areas of the lesson would you like the observer to focus in on?
    1. Do the groups stay on task?
    2. Is everyone participating within the groups?
    3. Who leads the group?
  1. Are there particular students that you would like the observer to focus in on?  What is it about this group of students that you want feedback on?
    1. Any of the groups will be fine.

  2. Attach an up-to-date seating chart with pictures if possible so that the observer can identify students by name. Provided



Lesson Observations

Ken’s student observation notes for the March 22nd observation 1st period.

Scott’s notes:

Group Numbers
  1. Confident- students drew rectangles with supporting work. (erased) The drawing was out of proportion, but right ratio.
  2. Great process from the beginning: math to picture all good.
  3. Process excellent due to Candace.
  4. Another great process. They thought about two areas. Then they drew 2 areas with supporting math, labeled numbers. Colton was going for the ride, but was learning.
  5. 21/5=4 21/7-----> 25/5=5---->5+3=8 Bracelets Then they drew the picture; they struggled (Kayla mute)
  6. Areas of each: 5x7=35
                          21x35=525 ----->525/35=15
    Rudy was out of it.
  7. 35/5=7-----> Now changed ideas.
    (made 3x5 strip)         (Schlegel saved the day!)

    Pat’s observations
    1. Jonathan 7 divided by 21, 5 divided by 25 Correct idea- wrong use of language

    -working by division; I led them into drawing a picture.

    2. Brianna’s group- slow to get started 7, 14, 21
        5, 10, 15, 20, 25

    3. Kiara’s group Dream solution-Excellent idea-Done!

    4. Tiffanny’s group-Made a diagram, but some of the group members were not sure if it was correct.

    5. Jonathan struggles with the transition from math 25/5=5 --->21/7=3 to the diagram. First answer was 8 (5+3); tried to draw a diagram, but got confused.

    6. Jessica’s group- took total area and then divided by the area of the bracelet.

    7. Jonathan’s group-Students found the ’hardest’ part was writing out the answers at end and not figuring out the original problem.

    8. Sarah’s group- they wrote out their answer and explanation on the white board. The rest of the group copied the solution. Is this what you were looking for?

    9. Kiara does not like writing out the solution.

    10. Katelyn finds the explanation is the easiest part. (English is her favorite subject.)

    11. Good review of problem by showing students’ work on the document camera.






Lesson Reflection

I was glad to participate in this lesson study process, but I would have liked more in-depth conversations (pre- and post-) with my oberservers.  However, after reflecting back on the lesson and reading their observations, I felt like this lesson went very well.

I think the use of white boards was especially effective with my class.  White boards are nice to use because they’re not intimidating to groups; if a group makes a mistake, it’s easy to erase and fix it.  Also, I’ve noticed that because the white boards are big, the whole group gets more involved than if an individual is recording ideas on a single piece of a paper.  They provide a way for the group to get together and discuss their ideas.

Besides using white boards, the way I structured the lesson helped make sure all groups felt responsible for solving the problem and showing their work.  Despite the craziness of the day (spirit day and emergency drills), all groups came up with a solution to the problem.  Once groups had correctly solved the problem and shown their work, I then had each student explaining their problem solving using a writing process.  I like this strategy, because I feel like every student has an opportunity to see the correct answer and see it worked out so they don’t get stuck from the beginning.  However, by having students write about how they solved the problem, I can see how well they understand the problem and students have individual accountability.  It’s interesting to see how individuals from the same group can have such different descriptions of their solution.

I was impressed by how well my students worked together in this lesson.  The work we have done on collaborating has paid off.  I was surprised by who some of the leaders in the discussions were, how many different strategies students had to solve the problem, and some of the difficulties and communication problems students had (what do you do about the student who says I divided 5 by 25 when he did the opposite?),

I especially felt like this lesson was effective when I heard some of the observers saying we should use white boards and this problem-solving and writing process throughout the junior high and high school campus.


Resources:

Pre Obervation Information

The team developed the Pre Observation Information sheet. Its purpose is to help the observer with the context for the lesson and a focus on what the teacher would like feedback on. The main focus is observing student engagement.

This is the
Obsevation Schedule that the team created on February 26th.

This is the
No Limit Grant Teachers Schedules for the team members.




Junior and Senior High Bell Schedules

Mt. Baker High School BellSchedule


Mt. Baker Junior High Bell Schedule


Observation Tools

These two tools were adapted from ideas and samples from the Teacher Development Group (TDG)

Student Observation Tool Form 1

Student Observation Tool Form 2