Math Education Utopia - My Field Trip

In April of 2010 - I went on a field trip to visit my sister's math classroom at the ABC Stewart School located in Columbus, IN.  This is an independent private school with a strong Montessori influence.
My sister, Nancy, and I regularly discuss education and both enjoy the creative process that goes hand in hand with effective teaching.  Below are my observational notes and photos from my first visit to see her in action.

4/6/2010
ABC Stewart School, Columbus, IN
Nancy Hiquet – Math teacher
Autumn Heilman - Assistant math teacher


This is a multi age classroom. This room is very organized and every wall is full of shelves with an enormous variety of math manipulatives. The room has nice carpeting and it’s walls are a comforting shade of yellow. A small recent newspaper article is on the bulletin board with the news that Purdue University will now require all incoming freshman to have at least four years of high school math.

The math curriculum was primarily developed by the school's founder, Merry Carmichael.  It is a hybrid of Mortensen math and more traditional work from a 1987 math textbook program that provided 3 levels/styles of instruction for each skill. The more traditional work has been added to support the standardized testing that parents have requested and Nancy can group students according to the support they need. Math facts proficiencies are also emphasized at every grade level with the timed tests but students progress individually.





The two teachers work full time for about the salary of one teacher in a public school. But as a result they have a division of labor that gets everything done at school. They do not have to take work home. It is a trade off they have willingly accepted. Students are relaxed and comfortable. They comply readily with all directions and instructions. Nancy will be the math teacher these students have every year from 1st through 6th grade. She gets to know each student very well and the students become expertly trained in her instructional methods. Also once her classroom procedures and expectations are established the students do not need to be retrained every year. This is a huge time saver at the start of any new school year.

At 10 am the 6th graders arrive for a 90 minute block.  Normally there are 11 children in this class – a very small size. These are the oldest kids at the school. Students enter and begin by pulling personal previous work from their individual files and making any necessary corrections. For the first half of the class student work is individualized as the teachers loosely monitor student’s work and give individual encouragement or support if asked.  The teachers also intervene if they notice work has stalled,  is not at the level it could be, or that a student is just off task. One student asks an algebra question and this query results in an immediate small group (2 students and 1 teacher) instruction at the whiteboard.


Nancy comments that this group is the chattiest of all her classes but also the highest achieving as far as understanding complex algebraic concepts. Based upon my relative classroom observations the students mostly display positive energy and an appropriate conversational tone with each other.

Nancy ends individual corrections work and students are instructed that it is time for timed tests. Each student’s progress for completed timed tests is displayed on a chart in the corner. Nancy stands at the corner and instructs each student (who have lined up) as to which test they should take out of the file cabinet. Nancy has the timer and calls pencils ready …then go. Students work quietly and quickly on their separate tests. (This also eliminates cheating since everyone has a different test). She notes the time when the student stands up to bring her their paper and writes it on the top of the paper. Because of the small class size this is a feasible system. There is no argument from the students. They are used to the routine. Tests must be completely free of errors in the allotted time to count as completed.



Now the boys in the front row are instructed to dismantle the front row tables to create enough floor space for the class to sit on the carpet around Nancy. This transition takes 2 minutes to complete and is very smooth and quiet. Students carry out “stations” which appear to be thin boards of plywood about 2 ft square and place them on the floor for a personal work space. Two of the students work on a different skill book work with Autumn quietly at one of the back tables.

Students on the floor receive a Mortensen math booklet. Nancy has a plastic organizer full of manipulatives on the floor. She also uses the white board. Nancy “builds” a complex polynomial expression with the counting manipulatives on the floor. These students use the vocabulary words “exponents” and “variables” correctly and easily. Using the arrangement of manipulatives, Nancy, with student input, writes the corresponding polynomial expression on the white board and then performs the algebraic operations to multiply and combine terms. Students each work on their booklet to show the picture of the manipulative build on the floor and then must label it to show where the terms originate. As students work, Nancy asks to see and approve the work before each student moves on to the next page. This is manageable with 8 -11 students. She makes comments about neatness, use of space on the page in addition to the actual math work.
The class period lasts 90 minutes but things are never boring or rushed.

At 1:15 a combined 4/5th grade class enters- 18 students - 9 boys and 9 girls. Every seat is filled.

Students begin by doing some seat changes directed by Nancy. Then students line up by the filing cabinet to get their timed tests based upon Nancy’s directions as she consults their individual progress charts. Nancy gives several strong suggestions for mental preparations to begin timed tests. For example, as they wait for the test to start several students work the problems mentally to practice the addition skills. Once the timer begins every student works quickly with great concentration.



Following the timed tests – each student picks up a new Mortensen problem solving booklet that they will begin as a large group today for in class work. Nancy does the first example on the whiteboard:

8x + 9 = 7x + 12 step by step she solves for x Then they draw the pictures of the counting manipulatives that correspond to the steps of the problem.  Students follow along and write down the steps in their booklet. Nancy reiterates that they must label their drawings with the appropriate numbers.  It is a slightly different style than I learned but makes just as much sense. I probably didn’t learn this level of math until 8th grade or freshman year of high school.



Nancy holds high expectations for her students in academic rigor, achievement and behavior.  Disruptive, disrespectful or other undesirable behaviors are immediately nipped in the bud in a calm and respectful way. Students are made clearly aware that they have crossed a boundary and are expected to correct it.

There are multiple formative assessments throughout the lesson, verbal and written. She keeps the ball rolling and students do not have time to be off task during her presentation at the white board. A student may look confused or have questions from time to time but the absence of student frustration is notable compared to the public school classrooms I visit. A majority of public school students in the urban classrooms I visit go immediately to the emotion of frustration and give up too easily when presented with a problem or any type of critical thinking. These students trust Nancy when she reassures them that it will all work out and to keep working.
 
Students do their own work. I do not observe any copying or asking partners for answers. While students then work at their seats they have two adult teachers to check work and provide support. A few students help each other to figure it out in a constructive and positive way. Nancy’s focus is on the student’s and their work product (learning outcomes).

Just another day living in math education utopia.

My Day with Dr.Carl

Dr. Carl Wieman is a rock star in the world of physics.  In 2001 he shared the Nobel prize in physics for producing a Bose-Einstein condensate. 
Since that time he has used his prize and notoriety to directly facillitate research and advancements in science education.  As a result of that continued work he has been awarded the National Science Foundation Director's Award for Distinguished Teaching Scholars. 
 
It is extremely rare for one person to be honored by two such distinguished groups in a career.  And it is even less probable that I would have the opportunity to meet such a person. Thanks to a chance email from my former Arsenal Technical High School teaching partner Dr. Mark Blachly - I spent the better part of a day in March 2010 in the presence of this science visionary. 
 

Dr. Wieman's visit to IUPUI had a full day of scheduled events.  I was able to register for the morning session entitled "Science Education in the 21st Century: Using the Methods of Science to Teach Science" and the afternoon physics department colloquium "When The Virtual World is Better Than Reality; Teaching Physics with Interactive Simulations".  Two days before the event I heard of a small group meeting with Dr. Wieman in between presentations and inquired if I could please join.  Within minutes I received official permission via email, and could hardly contain my delight.

A full version of the morning presentation can be viewed on youtube via a recording at Cornell University in 2009.  In my extremely brief summary, Dr. Wieman's research and recommendations for science education confirm my own observations and experiences spanning the last ten years. This is exciting and humbling all at the same time.


Following that presentation, I listened to several questions posed by university faculty concerning the state of teaching and learning in science at the university level.  Much of the discussion focused on convincing and supporting faculty to have better rapport with undergraduate students and to take an interest in improving their instructional methods through interactive authentic learning activities for the students.  We were now in the small group meeting and I had to speak up.

 I argued that unless the scientific community makes a fundamental change to be inclusive rather than exclusive, the goal of realizing the full potential of science education will not be realized.   People (students, parents, and teachers) can become intimidated by the scientific establishment.  Most elementary teachers are afraid to even try science in the classroom especially physical science.  Science in high school and college is used as a gatekeeping system for academic and career tracking.  Science is considered the domain of "smart people" (whatever that means).

Because I was so cheeky, I was invited to attend the luncheon that followed with Dr. Carl and the select IUPUI higher ups.  To my delight I was able to sit at the same table as Dr. Carl and was able to relate to him that just that week I successfully used two of the online science simulators with a fourth grade class. He was genuinely interested as these simulators are primarily written for middle school through college level curriculum.  We had a pleasant conversation about the thoughtful elements that are included in each simulator and their flexibility for student exploration.

The 4th grade students and I had been working on energy and static electricity.  Play around with the simulations we used below.

Click to Run

Click to Run

For more of these high quality online simulators (and did I mention that they are completely free?) check out the website:

http://phet.colorado.edu/

It was a great day and I feel so fortunate for the experience!

Most Excellent Holiday Physics Activity

Before you throw away that silver Christmas tree tinsel, check this out!





Just when you thought you were out of ideas for winter break!

Woodrow Wilson Fellows

The six pre-service teachers I have been quoting in the Middle School Observation excerpts are part of the group pictured below with Indiana Govenor Mitch Daniels.  They are participants in the Woodrow Wilson National Teaching Fellowship Program.

For more information about the program:
click here for the official IUPUI School of Education news blurb

Observe and Reflect in Middle School - Week 3

Alright - delayed as it is --- here is a summary of my Woodrow Wilson Fellows reflections in week three of their middle school classroom placements.

Indianapolis schools start their school year in mid-august. These excerpts are from the school week dated August 24-29th, 2009.

 “I will stick by my second week’s statement: the students are indeed smart.  However, let me add that I had no idea how short an attention span these sixth graders could have.”

 “I got to see a student’s light bulb turn on for the first time. She went from, 'I don’t get it,' to, 'Oh, ok!'  It was great. I think she understood the whole time. She just needed that experience to convince herself that she understood.”

 “I am a little surprised at the diverse array of graphing abilities. Some did excellent graphs and some had no idea what they were doing.”

 “We are starting to see the ones who don’t want to work.”

 


 “They (certain students) are definitely an example of those that seem bored but are really not absorbing the material you are teaching them.”




 “Some of the students that did not do so well (on a pop quiz) seem lacking in their motivation for learning. I hope this will improve over time and those students find some source of intrinsic and/or extrinsic motivation.”

 

“There are some kids who face really monumental struggles, and it gives me a perspective on their attitude and behavior. On the other hand, there are some things I'd just rather not know about a kid.”

 

 “One student has a diagnosed ulcer due to a stressful home situation. Both of his parents have a high probability of going to jail this semester due to drug dealing. He is an only child so his grandmother with most likely take guardianship. His resource teacher says that he has lots of potential. He is definitely street smart. It was good to know this information. She says he will be at school most days because that is where he gets his meals and school is a better place to be than home.”

 “I thought that I might initially have a problem giving zeros out for missing homework, but there are so many students that you really just do the job and don’t worry about it too much. I guess this is another balance issue.”

 

 “Now I am extremely curious to see how the out-of-school suspension will affect his behavior when he returns to school.”
 

“One student was very mad at the other and was pacing around the room with lots of energy trying to control himself. I complimented him on his self control and sat him at a different table looking away from the other kid who had made him angry. Usually they sit across from each other at the same table. This method worked well. Both kids were fine for the rest of the class. Later I complimented the angry student in the hall way again for his self control. It was neat.”

 “Question: What is the best way to approach a girl about dress code? She is one of the bigger girls in her grade and today is wearing a jean/underwear combo that allows her butt to hang out while she is seated. I don’t really think that’s something we want to or should see!”

 

 

“Luckily classroom management was not a major issue. I’m finding that giving clear guidelines and expectations at the beginning of each activity helps classroom management a lot.  I’ll need to learn to consistently do that.” 

 

 “I hope I’m not falling into 'mean teacher' mode."

 

 “(Another teacher I observed) ‘played dumb’ a lot with the honors class and let them come up with much of the answers to their questions.”

 

 “We were busy doing a lab activity, so there was a lot happening in the room. A student decided to leave the classroom without permission. I was glad that I saw him leave because he did it quietly. He was not disruptive. It’s crazy to think how long we would have continued class without knowing he was gone!”

 

 

 

 “I think that I’m starting to grow and come out of my shell more and more. I enjoy the challenge it poses to get out of my comfort zone.”

 

 

 “It seemed like this week things finally started to be somewhat routine. The students are showing their true colors, and most people (students, teachers, administrators) have stopped talking about the fact that it's the beginning of the year. In fact, I seem to be the only one who is still trying to find my groove!”

 

 

the plot thickens.....

Ideas for the Science Fair - recent science news stories

After a long blogging hiatus this semester, I am greeting you with some recent science news stories to inspire all those upcoming science fair projects.

Science News

#1 - High School CSI in action!
New York High Schoolers May Have Discovered New Cockroach Species    By Scott Hensley
(click on the title to read about it)





#2  In honor of my two children.......and reducing male spillage at toilets everywhere,

There's A Fly In My Urinal  by Robert Krulwich
(click on the title to hear the broadcast story, watch a short video clip, or read more)

 



 
 
 
 
 
 
I especially love the idea of error analysis and the discussion of spillage quantification.
 
 
#3 - Continuing the insect theme (and because my youngest son got an ant farm for Christmas:)
 
Ants that Count   also by Robert Krulwich 
(click on the title to link to hear the broadcast story or read more)

 
 

Happy holidays to all and safe travels!

Observe and Reflect in Middle School - Week Two

More excerpts from my Woodrow Wilson Teaching Fellows weekly reflections as they continue their first weeks of full immersion field experience in an urban Indianapolis middle school.

“This is getting interesting.”

“Last week everyone was happy and smiling when it was all fun and games, but now that there is work to be done a few cracks appear in those once smiling faces, and we can see personalities popping out.”

"I look forward to seeing the kids every day. They are a mystery. I never know what they are going to bring each day. That makes it exciting. It forces me and the teachers to stay on our toes and be prepared for the unexpected.”

“I went around (to the students) and did a lot of one-on-one help. I felt like I was struggling with word assistance in ways that should have been easy to understand. Maybe this is something that just takes practice. Maybe you just learn ways of saying things that work???”

"We had our first opportunity to grade papers. What an experience! … We had some papers where the children were supposed to write in complete sentences. Do you give credit for sentences that start with a capital letter but have no punctuation at the end? How much credit do you give for sentences where nine sentences end in periods, but one sentence doesn’t? Since it is the beginning of the school year, are you more lenient because they are getting back into the groove of school or do you play hardball?”

“Is anyone else tired when they go home?”

“I’m hoping to get some practice with classroom management and discipline. I feel like that is one particular area where I will need a lot of practice. …Maybe I’ll get lucky and the kids will be bad this week so I can get a lot of practice.”

“It was sad to think that after four days of school a student had five documented offenses that prompted a call home.”

“Our teacher uses seating charts to place students in the most appropriate seat to make them successful. (Our teacher) continues to change the seating charts as some of the seat assignments have not worked as well as anticipated.”

“We collected their (first assignment) from the previous day. Several students did not seem to have theirs with them. It seemed odd to me that so many would ‘forget’ on the first one.”

"Throughout the week I started to feel more and more satisfied with my decision to teach.”

Indianapolis schools start their school year in mid-august. These excerpts are from the school week dated August 17-21st.