Observing a Colleague's Classroom Instruction

Friday marked the last live videoconferences of the year to the Schultz Center, leaving us at a grand total of 175 live streamed lessons in the past five years. The lessons have all greatly benefited the teacher audiences at the professional development site, because they can observe live unedited instruction, debrief with the classroom teacher, and then have conversation with an audience of their peers at the Schultz Center about the instructional practices in the classroom. However, not only has the conferencing benefited others, it has also brought great growth to the CCE teachers. CCE teachers have planned instruction, considered the purpose of why they have particular practices in place, and have articulated the reasons for their decisions in debriefing. To say it has put them on their toes is an understatement. In addition, the live conferencing has provided time for the Chets' coaches to get inside classrooms and watch instruction across the school. Furthermore, our instructional technology coach, has captured some of the lessons on videotape, and they are on our Setting the Standard ning for viewing by a global audience.

On Friday, the last two lessons were videoconferenced to the Academy of Mathematics. One of the lessons, a Grade 3 Math Workshop, focused on the benefit of games inside the MI curriculum to promote fluency in learning multiplication facts. Rather than the students simply using traditional math flashcards to memorize their facts, Cynthia's students used array cards and played a game to practice their facts. They weren't just memorizing their facts; They were learning number sense in relation to their facts. I overhead conversations like, "I know that 8x6=48, because 4x6=24 so I doubled that." "I know 8x12= 96, because 8x10=80 and 8x2=16 and 80+16=96." The students didn't just shut down when they got to an unknown fact, because they had decomposing strategies, and could figure out how to solve based on facts they already knew. They also didn't have to pick up a pencil and paper for facts like 12x9, because they had mental math strategies they could use to solve the problem.

The Math Workshop was broken into three components; opening session (15 minutes), work period (30 minutes), and closing session (10-15 minutes).

Opening Session

Ms. Rice began Math Workshop with a 5x5 array card (a card that shows the array based on the area of the problem, in this case 5 rows and 5 columns), and asked students, "What do you know about this array." After students shared the attributes and characteristics of the array, they also used strategies for solving. Skip count by 5's five times (5,10,15,20,25), or consider 5x10=50 and half of 50 is 25, or 2x5=10 and 3x5=15 so 10+15=25. Then, she modeled the playing of the game Count and Compare (much like War--directions attached to the end of this post) with a student, and explicitly explained the recording sheet she had created for them to record their work. She did a think aloud with one of the array cards she selected to model for students how she thought about the product.

Work Period

Next, students set off around the room to play the game with their partner. The teacher had strategically placed partners and gave them a bag of array cards based on their readiness to practice certain facts. This differentiation left students at their instructional level rather than at a frustrational level. During the work period, she facilitated learning by circulating to each group and asking students questions about their learning. She strategically selected students who would share in closing session to promote the learning of all classmates. If a student was selected to share, she asked them to hang on to the array card they would be sharing as a visual in closing session.

Closing Session

The class came back together for whole group debriefing. By design, the teacher had students share their thinking to show the range of strategies used in solving the problems. As the students explained their thinking, their array card was under the doc camera as a visual for other students. The classmates listened attentively, sometimes asked questions, and sometimes shared other strategies for solving the same array card. The teacher then summarized the day's learning and the workshop concluded.

Debrief

The students headed to art, and the teacher debriefed with the audience across town at the Schultz Center while sitting in the comfort of her own room. The audience thanked Cynthia for letting them observe (just 8 1/2 days before school is out for the summer), applauded her on the delivery of the lesson, and extended their thoughts about the flexibility of thinking on the part of her students. The audience asked how she formed her pairs, how she differentiate instruction with the placement of the array cards by student groups, and if she had corrected any misconceptions as she circulated. They also asked her about the recording sheet, and let her know that they would be stealing her idea and implementing it in their own classrooms the next year. The debrief concluded as they applauded her for her first ever live videoconferenced lesson, for which she appeared calm as a cucumber!

From the Instructional Coach

Ideally, teachers would be able to file into a colleagues classroom, observe, and then debrief a lesson. In this case, time and distance present the obstacle, so to overcome the barrier we videoconference the lesson. However, it accomplishes the same objective. Teachers are visiting classrooms, talking about instruction, asking about student performance, sharing ideas, and gathering new implementation strategies for their own classrooms. We started this journey within our school as colleagues visited each other's classrooms for demo lessons and had debriefs, now we share this practice district-wide with the videoconferencing, and nationally with thousands of visitors. We only hope that this practice continues to grow in many schools as teachers invite others into their classrooms to discuss instructional practices and share ideas to promote student performance.

How to Play Count and Compare

Materials:

A Set of Array Cards

1) Deal out the cards equally.

2) Place your cards in front of you with the array face up. (The product on the back is face down and used for checking purposes.)

3) Players place their cards in a stack in front of them.

4) Players draw the top card and compare it to their opponents cards.

5) The players figure out whose card is more, say the product of their card and explain their thinking, and then check the back of the card to make sure their product is correct.

6) Players record their multiplication facts on their recording sheet.

7) The player with the largest array card keeps the cards and places them at the bottom of their stack.

8) The game continues until all the cards are used in one players stack. Then, the cards are shuffled and redealt.

A Look Inside a Grade 4 Math Workshop

One look inside Room 217 and you can certainly tell that young mathematicians are at work. Lead by co-teach duo, Angela Phillips & Rick Pinchot, the young mathematicians are attentively listening to Opening Session as the teachers explain the directions to the game they will play during Work Period, Close to 1000.

Students will be paired with a partner, each partner will be dealt eight Numeral Cards, and the students will be able to use any six cards to make two three- digit numbers. The object is to try and make numbers that, when added, will give you a total close to 1000. The students will then write the numbers with their total on a Close to 1000 Score Sheet. The score is the difference between the total and 1000. They will put their used cards in a discard pile and draw six new cards for the next round. After five rounds, students will total their scores, and the lowest score wins!

The objective of the game, from the Grade 4 Landmarks in the Thousands Math Investigation book, is to have students develop addition and subtraction strategies. Though the directions do not call for it, as the teachers model from the document camera, they suggest to students that as they play, they write down the digits from each of the eight cards they draw, and indicate which cards they do not use. The teachers are interested in the numbers that go unused, the placement of the digits that the students do use, and the total score per round, because this will give them a glimpse into the student's mathematical understanding. Toward the end of this 15 minute Opening Session, the teachers strategically pair students and set them off to work. The pairing, done by design, is possible because these two teachers have analyzed and sorted student diagnostic data on number sense to create their differentiated pairs.

The students of Room 217 are well prepared to play Close to 1000, however if additional scaffolding had been needed, the teachers could have differentiated even further by having some students play Close to 100 instead. In addition, as they revisit this game, the students who have mastered the strategies may be enriched by playing the negative and positive integer variation. Scoring using this variation changes game strategy significantly. Differentiating for remediation and enrichment is a natural part of Angela and Rick's classroom instruction.

As the pairs set off for Work Period, the teachers strategically, based on their data, begin to confer with groups of students. The teachers are observing to see which students are developing efficient strategies to add and subtract numbers in the hundreds, to see who is using mental math, to see who is strategically playing the game, and to see who is struggling with misconceptions. They facilitate by offer suggestions, pointing out more efficient strategies, or talking with students on the most strategic way to use their wild cards. In their dialogue with students, they always expect students to explain their thinking articulately. Each teacher, clip board in hand, takes notes on observations and student mastery. As the teachers facilitate they are also looking for student's work that will be most appropriate to share in Closing Session to move student thinking forward. After 30 minutes, the class comes back together as a whole group to summarize and extend their learning.

In the focused and purposeful 15 minute Closing Session, Angela and Rick discuss what they saw as they facilitated instruction in the Work Period. They share three student's score cards and have the students discuss their thinking. They help lead the discussion on the placement of the digits and whether a student's score could have come closer to 1000 if the digits would have been placed differently. Students, as they revisit this game, will become more strategic in their placement of digits and will continue to use mental math strategies--all while having fun! In Room 217, young mathematicians are at work!

Overview of Math Workshop

Math Workshop at CCE consists of a 60 minute Math Investigations block and a 15-20 minute Every Day Math Counts block. These two resources work nicely together to cover all of our state's mathematics standards.

The 60 minute Math Workshop has an Opening Session, Work Period, and Closing Session.

The Opening Session consists of a 15-20 minute math lesson; the lesson can be an introduction of a new problem, a mini-lesson on a skill related to the concept students are learning, an analysis of a problem situation or a problem solving strategy, or an explanation of the assignment.

Work Period is a 20-30 minute work session where students work independently, with a partner, or in small groups. The teacher facilitates instruction by meeting with small groups to guide or advise them or assess their progress. She may make anecdotal notes about a student's progress or difficulties or use a checklist to record observations. The teacher may also individually confer with students posing questions to redirect student thinking or deepen student understanding. During Work Period, the teacher is observing the strategies students are using and noting misconceptions that need to be a focus during Closing Session. The teacher will typically select student work to share in Closing Session.

The Closing is a 15-20 minute whole group session. Selected students share strategies or solutions as the teacher leads discussion on how these strategies are alike or different and which are most efficient. The teacher may also summarize the concepts that are the day's focus or connect it to concepts studied earlier, or may lay the groundwork for concepts that will be studied next. To address and correct misconceptions, the teacher may have a student share a strategy that did not work and the class may analyze why it did not work. This closing is critical to a lesson, and the part of Math Workshop that has traditionally been overlooked.

In CCE math classrooms, you will find this workshop structure in place. You will also see artifacts that support this workshop including

• The Standards (the central artifact--all lessons are directly aligned with the standards)
• Math Journals (a place to record student strategies or reflect on learning)
• Teaching Charts (teacher-made, showcases student developed strategies or solutions, displayed for future reference)
• General Math References (hundreds chart, number lines showing positive and negative numbers, problem solving methods, multiplication charts if applicable)
• Class Diagnostic Notebook (individual standardized test reports, individual student diagnostic assessment profiles)
• Display of Student Work (changed regularly to show current work)
• Word Walls (math vocabulary relevant to current work)
• Manipulatives (in central location and labeled for easy access)
• Student Portfolios (in binders or hanging folders--showcases student work and strategies used to solve problems, may also include some graded/corrected assessments)
• Math-related Literature (each Investigation book offers a list of recommended literature to read aloud to students)

The structure of the workshop and the artifacts that support focused meanigful instruction creates the environment condusive to developing young mathematicians. :)