Class 17: 10/25/11-UTeach Institute Visitors & Back of the Envelope Problems

Today there were visitors in our class from St. Petersburg College, Arkansas State University, University of Arkansas at Fayetteville, and New Mexico State University whose schools are interested in replicating the UTeach program.

We spent the first part of class going through introductions. Students talked about the UTeach program and our recent field experience at Manor New Tech. High School. Some of the positive things said about the UTeach program were that in this program, we are thrown into the classrooms our first semester so that we immediately get teaching experience. Also, many students noted the sense of community in the program and that many of us have the same classes together. Students were able give suggestions on how to improve the UTeach program. Some of the things mentioned were classroom management classes, teaching classes more specific to our content areas, changing the Research Methods course to make it more applicable to our fields, and having more chances to teach individually throughout the program.

Today’s agenda included doing “Back of the envelope problems.” As Dr. Petrosino explained, these problems are a little untraditional and don’t lend themselves to easy answers, but they get you thinking about the process. They deal with estimation and coming close, keeping us thinking on our feet. We split up into 5 groups, and each group was given a different question to explore.

1) How man kilograms of leaves fall in New England in the autumn?

2) What is the number of heartbeats in a lifetime (human, mouse, elephant)?

3) Since 1492, how many people have crossed the Atlantic?

4) How many piano tuners are there in New York City?

5) How many hairs are on your head?

My group was assigned problem number 1. We first thought about ways we could approach this problem. Some suggestions included thinking about how many trees there are in New England and how much the leaves of one tree weigh. We realized that we didn’t know the specific numbers that we needed. For example, we wanted to use the square mileage of New England, the number of trees per square mile, and the number of trash bags used to collect the leaves of one tree. After many assumptions, we came up with our answer of 1,250,000,000 pounds.

We began group presentations on how we approached our problem. Each group had to make predictions and use previous knowledge to come up with their solutions. We had to think of creative ways to go about each problem (for example, one group used a silver necklace to determine the circumference of their group member’s head). We all had to make a lot of assumptions to go about our problems which led to more assumptions.

We ended the class thinking about how we might justify using these kinds of activities in our future classrooms given the push in Texas to stick to state standards. Our discussion of this topic will continue next class.

Each day in PBI a different student takes responsibility for blogging about what goes on in class. Today’s blog is brought to you by ­­­Vanessa.

Class 16: 10/20/11-Legacy Cycle Project

Agenda:

1. Brief View of the Road Ahead
2. Legacy Cycle Groups
3. Krajcik, McNeill, and Reiser

Dr. Petrosino began class by going over the agenda for the day. The road ahead includes starting on our Legacy cycle projects within groups (which are to be discussed later in the class) and doing more extensive reading on PBI. As we finish the semester, we will also be reading critiques and counterarguments to PBI; this is important so that we can continue to improve the PBI method and compare the benefits of various teaching methods.

Dr. Petrosino then began giving us information about our Legacy cycle projects that are due in approximately a month. Individuals may choose to work alone if preferred. Otherwise, groups should have two to three members. It is not required that all members of a group be of the same discipline (e.g. a chemist and a mathematician may create an lesson together). In addition, lessons could be on any subject desired (within the secondary and middle school scope). There is a curriculum model provided in the reading which is useful for thinking about the legacy project. Feedback and revision is important in PBI but we will not have sufficient time for that. Therefore, we may redesign an older legacy cycle from the web page if desired.

Dr. Petrosino then began a lecture on the reading of Krajcik, McNeill, and Reiser. This reading is assigned for us to read by October 27^th, 2011 (one week), but Dr. Petrosino decided that he would give a previewing lecture on the reading.

There is a constant tension between the state and federal government on the debate as to who has power over education. The states feel they hold the ultimate power on their state’s education since they provide the funding for it. In terms of curriculum and instruction, the state writes the curriculum and teachers must be certified through the state.

Standards tell us what to teach but not how to teach it. With numerous standards and limited time, we tend to go back to direct instruction in order to cover anything.

How do we move from content standards to learning goals? The reading discusses this and common Design Issues with curriculum. The Atlas of Scientific Literacy is very helpful to see how content is related to better plan and explain the sequence/structure used in the classroom.

Each day in PBI a different student takes responsibility for blogging about what goes on in class. Today’s blog is brought to you by Cassandra.

Class 14: 10/13/11-"Back of the Envelope" problems

Dr. Petrosino began class today by asking, “What do you know about pi?” and “Who can give me a value?” Student responses were the usual 3.1459 with some students carrying the decimal out farther than others. A few minutes of discussion then occurred centered around those two questions and the idea of estimation. The discussion concluded with Dr. Petrosino stating estimation is closely related to guessing. The class was then challenged to consider if grading estimations is possible, and if so, how it could be done fairly for students in their classrooms. This question remained the central theme throughout the duration of the class.

The majority of class time was activity based. Dr. Petrosino introduced the students to their activity by showing them some ““back of the envelope” problems (also know as Fermi Questions). Some examples shown were those that Bill Gates would ask in his interviews for Microsoft. The class was then divided up into groups of three and had ten minutes to solve one of the three Fermi Questions presented. The three questions presented are the following.
1.  What is the total weight of all the leaves in New England (in Kg)?
2.  How many crossings of the Atlantic Ocean have occurred since 1492?
3.  How many hairs on the average 20 year olds head?

Students were required to use assumptions and estimations to perform the calculations required. Their assumptions came from their own background knowledge, and collaborating with their groups. This element of collaboration was crucial in making their answers more precise. After the ten minutes were over each group presented their findings on the board in front of the class. These presentations allowed other students to see what each group discovered and compare answers. After the students were comfortable with the process of trying to solve one of these problems Dr. Petrosino presented more challenging Fermi Questions.

The activity did a wonderful job of demonstrating some of the elements of a Legacy Cycle. It consisted of a challenge, multiple perspectives and going public (Klein & Harris, 2007). The class ended with Dr. Petrosino explaining the difficulty of putting these questions on standardized test. The students agreed that these “back of the envelope” problems would be extremely frustrating to solve on without collaboration and under the pressure of a test. In response to the challenge question, estimations problems, like the Fermi Questions, allow students to use problem solving and critical thinking skills, but should be solved through collaboration in groups instead of individual. For more information on Fermi problems and the solutions follow this link!

Each day in PBI a different student takes responsibility for blogging about what goes on in class. Today’s blog is brought to you by ­­Casey.

Class 13: 10/06/11-Petrosino/Lehrer/ and Schauble

Tomorrow, Friday, is the first day the PBI students will be in the field, teaching day one of their 3-day teach at Manor New Tech High School. Our TA Sara started class by reminding the class of expectations during our teaching experience, including: appropriate professional attire, early arrival to classes, and having confidence and enthusiasm while teaching! Prudie handed out rubric for the field trip teaching experience happening Saturday at McKinney Falls, and there was a reminder that the rubric for Friday and Tuesday’s teaching experiences were in the Course Documents on Blackboard.

Dr. Petrosino encouraged the students to not burden themselves with the burden of being perfect because the high school students are the true audience – not the observer. The average teacher makes an instructional modification every minute, so expect at least a couple during your 75 minutes with the students. There will be moments where accommodation and “just-in-time decisions” will be needed. Take time to listen. Quiet isn’t a bad thing. Flexibility is key. Give the students time to talk and think and yourself time to listen, react, and interact. Keep in mind what things are important – what the ultimate goal is. It’s not your rubric so much saying you did a great job. The goal is engagement and thoughtful learning. There is great value in the cycle of reflection, interaction, and ability to make modification.

About ten minutes was given to teaching teams to gather and address last-minute issues, such as “Who is bringing what materials,” and “Who is taking the reins during the lesson at different points?” before the class discussion turned to the paper that had been assigned as the reading homework for the class.

For class today, we read “Paper structuring error and experimental variation as distribution in fourth grade.” (Petrosino et al., 2003) PBI student groups spent five minutes discussing the reading amongst themselves in order to determine if the experiment discussed therein was “big P” or “little p” and then to find points to defend their position. Groups wrote their ideas of “big P” and “little P” reflected in the paper on large sheets of paper distributed to each table with markers.

On a previous day, after reading two complimentary papers on Project-based Instruction, the class had defined “little p” as a project as many have come to know it. In general, it refers to projects in class that are more about making sure the students are doing something with their hands than being as much purpose-driven or problem-solving. Often, in a “little p” scenario, students are not sure of their purpose or goal or the connections the activity has to anything else. In contrast, a “big P” project is informed by theory, involves scaffolding, is learner-centered, driven by a problem or question, is relevant to the students in the place they are in, and builds community and discourse.

Something to consider is that the existence of a “big P” or a “little p” does not imply that one is inherently bad while the other is perfectly good. In reference to the paper, we discussed that perhaps one “little p” aspect was that although the project was taught over an 8-week timespan, a few days each week direct instruction was the mode of instruction. It was acknowledged that this particular paper did not necessarily emphasize Project-based Instruction. There were certainly “big P” attributes, such as the cycle of the first couple of activities of measuring the flagpole and the pencil and seeing the differences in experimental error building up scaffolding for the students before they attempt the largest challenge of the rocket launch. Their culminating challenge was to determine if rockets with rounded or pointed noses will go higher. The projects helped the students reflect on comparison of attributes, manipulation of variables, models of a situation to real world implications and in current work: measure and distribution. The trajectory of the project offered scaffolding by emphasizing standard deviation and distribution in a generative way for the students, who were also allowed many opportunities to present their data in their own way.

Teachers are Vygotsky’s bridge – the learned other – the archway between the child’s world and the scientific world. This project sequence explored: “When is a difference really a difference, and when is it simply within normal variance?” How we start launching rockets and want to make educated guesses about which design makes the highest height? We are almost intellectually dishonest with kids when we give them simplified situations with big effects and the data is not problematic. This project in the paper tries to give the students tools to use to decide when can you say with confidence that differences in results are due to the design difference.

At the end of class, the question arose from math majors who study the Moore Method how does that method compares to what is being taught in PBI. Dr. Petrosino shared that while he has not observed the Moore Method in practice, based on what he knows, the Moore method does not have the pronounced scaffolding discussed in PBI. In PBI, the instructor is obliged to be thoughtful of the scaffolds and collaboration supporting the learning goals.

Each day in PBI a different student takes responsibility for blogging about what goes on in class. Today’s blog is brought to you by Laura.

Class 12: 10/04/11-Peer Feedback on Lessons

For the first ten minutes of class Prudie, our UTeach master teacher, went over the logistics for the weekend field experience, and then we were split into groups. Each group had three teaching pairs, and each teaching pair had 15 minutes to present part of their lesson and seek advice from the other two pairs.

In my group, the first group was teaching a 10th grade geometry class a lesson about similarity and congruence using the side-angle-side and angle-angle-angle postulates.

For their warm-up, they plan on reviewing the distance formula, and classifications of triangles. Their driving question is, “How can you use mathematics to design a zip line at McKinney Falls”. The hypotenuse of the triangle would be the zip cable. On the first day of teaching they plan to introduce the question and have the students begin to design their zip line using what they know about triangles. At McKinney falls, they plan to show the students the location at which the park had decided to build the zip line. Students are to scale up their models, and determine if they fit the specified location. If they did not, they were to make adjustments to their calculations to make it work at this location. They would also use the GPS to take points and use that to help with their calculations. On the final class day, students will make any personalized changes to their design using the GPS coordinates, and create a model of final design with poster board, dowels and string to present to the class.

The second group is teaching a 9th grade biology class. Their objectives are ecology, food webs, and the effects of invasive species. Their challenge is to find a new organism to introduce into the ecosystem in hopes of helping it recover from the devastating drought. The first day they planned to review the concepts of trophic levels and food webs, and introduce the challenge to the students. Out at McKinney falls, the students would observe and take notes on the life they saw, and its relationship to other forms of life. The teaching group expressed concern about what to do at McKinney Falls and how to keep the students on track, and one person suggested they limit their students to the aquatic environment. On the last day, this group planned to have their students discuss the effects of the new species interacting with the preexisting species, and create a food web.

The third group was teaching a 6th grade math class about graphing, latitude and longitude, and the Cartesian coordinate system. The first day they planned to make the students experts at the GPS probes. Out at McKinney falls the students would participate in a treasure hunt and find “buried treasure” using layered transparencies making a map that they could then scale up to the park using GPS coordinates.

Each day in PBI a different student takes responsibility for blogging about what goes on in class. Today’s blog is brought to you by Anne.

Class 11.5: 09/29/11-Planning Session with Mentor Teachers

The purpose of today’s planning session was to meet with mentor teachers and discuss lesson plans for our upcoming teach.  It was in a relatively relaxed environment, which created a great setting for students and teachers to voice their ideas and concerns regarding lesson drafts.

The actual event was set to occur from 6-8PM, but the room (SZB 312) was opened early for groups to get a head start.  It was required that every group bring some form of rough draft of their legacy cycle.  Dr. Petrosino was relaxed in how we presented our rough draft; word documents, Google docs, and notes on notebook paper were all acceptable forms of a rough draft.  We primarily needed to have written evidence of an outline for our legacy cycle, proof that we had a basic structure; simply explaining lesson ideas to your mentor teacher without any documentation was not acceptable.  There was no required structure of the lesson draft, contrary to the norm for 5E lesson plan drafts. 

At approximately 6PM, when most students and teachers had arrived, dinner was served.  The provided meal helped contribute to the relaxed atmosphere; there were several types of pizza, salad, cookies and brownies, and various sodas.  Some groups took their meals upstairs to a vacant room on the fifth floor for a quieter working environment due to the congestion of the room.  After about 20 minutes, every group had finished dining and was hard at work.

As mentioned earlier, groups needed to create an outline of their lesson prior to the evening planning session.  Groups have had several collaboration periods during class, and many made significant progress on their legacy cycles during the field trip to McKinney Falls on the 26^th.  Meeting with mentor teachers during the evening planning session served as a time to review the progress made between the field trip and our most recent class period.  A large portion of the discussion revolved around smaller lesson details, such as supplies, trouble shooting, and the order of activities.

Personally, my fellow group members discussed worst case scenarios with our mentor teacher.  We predicted a maximum and minimum number of student attendees for each class to allow us to better predict the amount of supplies we would need and how groups would be formed for the lesson challenges.  We made an extensive list of all the needed supplies; it contained approximately fifteen items.  Within those needed items we determined which would be easily accessible through the UTeach supply room and which our mentor teacher could supply (such as scissors and sidewalk chalk).  We plan to use Labquests in our challenge, so we planned how many we would potentially need and what we would do if we didn’t have access to them and/or they ran out of batteries.  The solution to this issue was to collect GPS coordinates beforehand (we are using the Labquests for GPS purposes) or use a simple GPS app on a smart phone. 

Another significant issue we discussed with our mentor teacher was how weather conditions would affect our activities.  One of our activities involves measuring the height of an object by looking at its shadow.  We visited McKinney Falls in the morning on our field trip, and we came to realize that shadows would likely be in a different location in the afternoon, when we are planning to teach.  We thought of an alternative was to present the activity so it was not reliant on shadows; after all, even if we were teaching in the morning, there is always a chance it will be a cloudy day. 

Our group ended the session by exchanging contact information with our mentor teacher; we also linked her in to our Google doc with our current lesson outline.  We left the evening with clear ideas of what we needed to change in our legacy cycle in order to make it the best possible activity for our students.