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.
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