Community Photos: East Lansing

Community: East Lansing

Photo: Quality Dairy

Grade Level: 4

Task 1

The owners of Quality Dairy are remodeling the interior of the store. They just ordered several new shelving units and need to figure out how to set up the aisles. They want to have at least three ideas to try out and see which one they like the most.

The store is shaped like a rectangle and measures 54 feet by 38 feet. The shelves come in units that are 6 feet long and have shelf space on both sides. The owners ordered a total of 48 feet of shelving. Your job is to come up with at least three different ways the shelves could be arranged that would be the most beneficial for customers.

Task 2

In addition to ordering the shelves, the owners of QD have additional money that needs to be spent on updates to the store. They have $1200 left over to use but can’t decide what to spend it on. Since dairy products are one of their main concerns, they want to spend at least 2/3 of the money on items that will keep products cold. Below is a list of possible updates they could make:

Cash register - $75

New countertops - $350

Refrigeration Units - $160 each

New Quality Dairy sign - $240

Posters/Decorations - $40 each

Ice Cream Freezer - $200

Video Rental Machine - $500

Freezer Units - $320 each

New wall paint - $400

Pretend you are the owner of Quality Dairy and have to spend as much of the $1200 as you can. Which products would you buy to update your store? Why would you choose these products?

Additional Photos:

Possible tasks: different weight amounts, organizing the layout, buying equipment, etc.

Possible tasks: mapping effective routes, determining bus schedules, calculating bus capacity, etc.

My community: Howell, MI

In Howell, there is a festival that occurs in June called "Balloonfest".  During this 3 day festivals hundreds of hot air balloons take flight and race throughout the day.

Task 1: There is an average of 150 balloons that take part in Balloonfest every year. If 1/4 of these balloons had complications and could not race about how many balloons would take flight?
Task 2: A ride on a hot air balloon costs about $200 per person for 1 hour. If a family of 4 wanted to take a ride for 1 and a half hours how much would it cost for the whole family?

During the month of December there is a parade called the "Fantasy of Lights Parade". Thousands of people from various parts of Michigan come to see the parade that travels down Grand River right in Downtown Howell. A task about the number of lights this parade has or the amount of money it costs to put on a parade this huge would be a good way to incorporate math.

This is where I work, right on the cornor of Michigan Ave and Grand River.  It's a local coffeeshop that has been serving the Howell area for over 10 years.  A task about the number of coffee drinks it serves per day or how many coffee beans get ground each day would be a good way to incorporate math.

Higher Level Tasks based on Community

In Hartland there are several lakes, thus most students either live on a lake or have a friend that live on a lake, spending much of their summer months engaging in various "lake activities." Additionally, most Hartland residents view fireworks on 4th of July from Long Lake.

Task 1: The home owners on Long Lake have decided to put on their annual firework display.  Every 10 minutes of fireworks cost $1,000 toward the total firework display. There are 30 houses on the lake to help fund the display. How much should each house contribute to the fund?

Task 2: While there are no homes on the island of Long Lake, the land is being surveyed in order to allow docks to be built around the perimeter of the island. So far, they have determined the area of the island is 2 square miles.  Based on what you know about the relationship between perimeter and area,  how many docks can be built around the perimeter of the island? 

Other pictures:

Tasks could be created related to measurement (distance, speed) etc related to the "Whirly Ball" game

Majestic Golf Course. Tasks could be created related to the distance the ball is hit, between holes, etc. 

Documenting

While reading the NCTM assessment PDF I thought the documentation of observations was interesting.  Most of the time I think of recording and documenting observations with other subjects like literacy and social studies.  However, I think it can be very helpful in math as well.  It gives teachers the opportunity to take quick notes while interacting with students and then allows them to look back at their observations later and make interpretations.  This goes along with our project 3 lesson study which allows us to see just how important observations are.  While it is unrealistic to think as teachers we would be able to do extensive observations like this, it is still possible to conduct small and informal observations while walking around and helping students during a task or activty.

Another thing that I found interesting in this article were the vaious types of rubrics.  While I mostly use or refer to a holistic rubric, I think the other types will be helpful depending on the type of task or even subject. For example, I think the general analytic rubric would be very useful in math tasks for both the teacher and the student.  It breaks the problem down to categories like understanding, planning and getting the correct answer so it allows the teacher and the student to see where the problem lies, if there is one.

As for my thoughts on performance assessments, I have not had much opportunity to see any in math.  My teacher focuses on literacy so I see a ton of pencil/paper tests and assessments and very few performance based.  However, I have seen and conducted a few running record assessments and I think those are very benefical but time consuming as well.  They have to be done individually so it takes up a lot of time.  So I guess what I would like to know from you two is if you see any of these types of assessment with math and how that works?

Questioning & Debriefing

            At first, the main goal of the video seemed to be getting students to distinguish between perimeter and area. However, after the initial task was asked and the teacher began to walk around the room and question student thinking, the focus shifted to getting students to explain how they knew the area of the square was 9 and to help them understand the concept of square units. The teacher in charge of the lesson sequenced student responses in a way that ended with her showing a picture on the board of the 3x3 square divided into 9 smaller squares. She used this to guide students in the direction of figuring out that we use individual square units to measure area.

            The Making Mathematical Arguments article that we read this week showed several examples of effective questioning by a teacher during a lesson. The article stresses the importance of getting students to go in-depth into their thinking and back up the claims they are making. As the authors explain, having a student explain their ideas is “an essential part of developing mathematical arguments” (Whitenack & Yackel, 2002). The example dialogues in the article are good models of questions that prompt student thinking and require children to be explicit about their thought processes and agree/disagree with ideas from peers. These are things that the group member who is actually teaching during the lesson study will need to keep in mind during the lesson. Those of us who are observing will take note of how these types of questions affect student thinking.

            I noticed both similarities and differences between the debriefing protocol document we were provided with and the youtube video we watched. Like the document suggested, the debriefing video started off by reminding everyone in the group what the overall goals of the lesson were and what they were supposed to focus on during the group discussion. Also, each person who talked was sharing specific, concrete evidence of what they witnessed during the lesson. One difference I found was that the first observer shared several things that he noticed during the lesson rather than mentioning one positive idea and then letting the other observers talk. Additionally, the teacher who taught the lesson was not the first one to speak and share her ideas on how it went.

            Overall, I think the most challenging part about the lesson study will be remaining uninvolved as an observer. After having numerous classroom placements in which we have been expected to assist the teacher as needed and offer help to students who are confused, being completely removed from actually participating in the lesson will be a change. Even though it will be a different type of activity for us to get used to, I think it will be really beneficial in the end. It is good practice for working collaboratively as a team to come up with research goals and instruction and activities that can assist us in reaching these goals. It is also helpful in reminding us to place more of an emphasis on student thinking and processes rather than just what the teacher does in the situation.

Week 12

 After reading the Effective Questioning reading, I felt like I had gained a valuable resource in becoming a prepared future math teacher. Overall, the piece explicitly lays out various types of questions that can be used to help teachers act as facilitators in many different aspects of mathematical processes. I feel as if this is an aspect of teaching many pre-service teachers are uncomfortable with, yet this reading practically provides a “how to guide” for developing the exact type of language and question types that are necessary in the classroom. The questions fell within six topics, including: Promoting Classroom Discourse and Student Efficacy, Problem Solving, Reasoning and Proof, Connections, Communication, and Representation. (Nurnberger-Haag)

In the Wilkins article, a focus is placed on differentiating curriculum for gifted students. I found some common lines between this article and the effective questioning article in many aspects, as the article also provided guidelines for teachers, in the form of different activities for students. One of the activity types included integrating across the curriculum, (for example: asking students to write a letter to the President discussing which measurement system is best and why (Wilkins, Wilkins, & Oliver, 2006)) which may be tied to the connections aspect of the questioning reading, specifically in the form of asking the sample question, “Explain a situation in social studies/science/language arts, etc when this math topic could help you understand that situation.” Many of the activity types can be directly related to the various question types- demonstrating a link between the ways structuring a classroom can work to benefit in forms of differentiation as well.

 As brought up in the Problem Solving and At Risk Students article, the structure of a classroom is crucially dependant to the students who make up the classroom. Ideal classroom structures as represented in the other two articles are almost equally brought to the forefront in a form of criticism, as the author states, “I agreed philosophically that this method was an ideal method to teach mathematics, yet I also knew that the same task given to my group would bring tears and anger.” (Robert, 2002). And so, the teacher had to learn how to adapt to her classroom in a way that still challenged the students in the way the previous articles suggested, but in a more “custom-tailored” format in order to build students’ confidence to continue to reach toward more advanced tasks. Overall, the articles I read all dealt with effectively structuring one’s classroom, but also considering ways in which one must consider the individual aspects of a classroom to determine the most effective structure rather than a “fit-all” mentality. 

Measurement

I found the readings from last week and this week to be very helpful because I do not see measurement in my field placement.  One of the readings that I thought was the most helpful was "Navigating Through Measurement".  While it states that students really focus and gain understanding of measurement in upper elementary and middle school grades, students in lower elementary still begin to learn the basics.  I really thought the idea of teaching young students both standard and non standard units of measurement was a great idea.  I think students need to first understand what measurement is and what it entails and they can do this by using blocks and paperclips to show that things can be measured using a wide variety of UNITS, units being the key word here.  But I also think it is important to teach them that there are standard units of measure like pounds and inches so that they can see how it will benefit them to learn this in the real world. 

With this, I think the article "Big Ideas" does a good job of explaining why measurement is important and what students may think is the importance of measurement.  The dialogue between Carl, Juanita, Joan, and Lee explains this well and definitely gave me some good ideas about how to incorporate measurement into my own classroom in the future (comparing things).  I think it would really get students engaged if I started a measurement lesson by having them comparing their height or even sometime simple like shoe size and then opening that up into a more formal lesson.  This would get them thinking about the idea behind measurement and may help them understand more complex ideas when they arise.