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
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
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.