A Day in the Life....of 4th Grade Math

This morning I had the pleasure of observing a fourth grade math class. Though we have two mixed 4th/5th classrooms, every morning the students regroup by grade for math, and this year Jeff and Kellyne are teaching 4th grade math.

The class began with the teachers taking the students to the basketball court, and organizing them into two groups to play a 10-minute long math version of Giants, Elves and Wizards. One group was Even and the other was Odd; the teachers would shout a computation problem (such as 4x3), and the group with the appropriate characteristic to the answer (in this case Even) would then chase the other group to a safety line, attempting to tag as many people as they could (tagged students then had to switch sides and become part of the other group). This 10 minute warm up combined mental calculations of addition, subtraction, and multiplication, and knowledge of odd and even, with a kinesthetic action (chasing or fleeing) that motivated students to attempt to speed up their computational speed.

Everyone then moved inside to the rug, where they found their notebooks and pencils, and worked on a series of warm-up problems displayed on the interactive whiteboard. The students had 10 minutes to work on their own, and then 10 minutes of whole-group sharing and discussion about the problem set, which included logic problems (Two men play five games of chess, and each wins an equal amount as the other. How is this possible?), greater/less than symbol application (155 > 99), and connected pairs of algebraic problems involving addition or subtraction with one variable (If 27 - X = 20, what is X? Next, what is X + 14?)

The class then continued a stations-based work period begun earlier in the week, for about 30 minutes. One station drew on Marcy Cook curriculum for creating dynamic triple-digit addition equations involving regrouping. Two stations drew on JUMP! Math curriculum for investigations into linear measurement and time telling. One station drew on Everyday Math curriculum for work with pan balancing (solving equations using various weights on either side of a balance scale); and the last station contained cuisenaire rods for students to use in working with the Show Me 1/2 fractions curriculum. In the last five minutes of class, students returned to the rug to preview the homework assignment, ask clarifying questions, and organize their materials.

There were many aspects of this period that artfully embodied the elementary division's approach to instruction. The introductory activity (on the basketball court) combined the use of prior knowledge with current skill development, while providing movement-based reinforcement using a high-motivation game format. The second phase of the class (on the rug) provided guided practice on current concepts and whole-group sharing of strategies for arriving at answers, balancing individual students' desires to work alone (some students wore noise-canceling headphones to help them concentrate) or in groups (some students engaged in spirited conversation while attempting to solve the problems). The third phase of class (five table workstations) allowed for student-directed choice about which concept and activity to practice, and also gathered students together to support their understanding of how the homework connected with the work they had been doing. Taken as a whole, the tripartite structure of the lesson provided adequate time in each phase for students to dive into the knowledge and skills presented, while factoring in student motivation and the constraints of their ability to maintain attention.

Friday Morning Fun

I love Friday mornings at The Berkeley School. Each K-5 grade level has a unique tradition that engages students in their intellectual learning linked to important social learning as well. In the K/1 classrooms,  parents and family members are invited in for Free Friday, a chance to explore materials, collaborate on reading, writing, and math activities, play games and puzzles, and put the child in the role of expert and guide to demonstrate (and thereby consolidate) his/her learning.  

In the 2/3 classrooms, parents and family members join students during a Reader's Workshop period. Children without family members present often spontaneously gather together in groups and simultaneously read and share a variety of (often non-fiction) texts.

Friday mornings at the 4/5 level usually begin with a "Cerritoberry" period, in which all students and teachers from both classrooms come together to do an activity (or play a game) that promotes communication and collaboration. For today's activity, students were broken up into groups of 5 or 6 and given the following survival situation (drawn from secondary Scouting curriculum, which uses it for the purposes of teaching content, whereas for TBS it was used for teaching critical thinking, communication, and collaboration):

You and your companions have just survived the crash of a small plane.  Both the pilot and co-pilot were killed in the crash.  It is mid-January , and you are in Northern Canada.  The daily temperature is 25 below zero, and the night time temperature is 40 below zero.  There is snow on the ground, and the countryside is wooded with several creeks criss-crossing the area. The nearest town is 20 miles away. You are all dressed in city clothes appropriate for a business meeting. Given a group of items you’ve recovered from the wreck (a small ax, a can of Crisco, newspapers, a lighter, etc), create a list of the items in order of importance for your survival, followed by the uses of each item and the reason why you have it in the order you’ve chosen.

Do games make effective instructional tools?

I love playing games. Rhythm and drama games, games of chance and luck, team and individual sports,  board games and card games, strategy games and logic problems, even jigsaw puzzles: I haven't met a game I didn't enjoy. One of my earliest memories -- and a favorite family story about my childhood -- is beating my father and brother in two consecutive games of Uno at the tender age of three while on a houseboat in Florida (both times I ended with two wilds in my hand).

Games are one of several powerful forms of play (along with imaginative play, rough-and-tumble play, object play, etc), and as Dr. Stuart Brown taught us, play is an essential life skill that has a direct impact on brain development, physiological and emotional health, social skills, professional success, and learning and memory. Which is why I enjoyed reading a recent CNN article about the Quest to Learn school in New York, which uses games as the primary instructional technique in the classroom.

At TBS, we also believe in the effectiveness of play as a basis for educative experience, and though it isn't the central pedagogical tool used in our classroom, it is deeply integrated into our practices. I wrote about the use of games in a K/1 Reading Workshop class this spring in Mission Moments #5, while the Investigations in Numbers, Data and Space math curriculum contains an extraordinarily rich variety of games including student favorites Roll and Record, Close to 100, Factor Bingo, and many more. Games are also a part of the Montessori approach, including the Stamp Game, which is used for teaching addition, subtraction, multiplication and division, and the Imaginary Island Project, which teaches a variety of concepts about physical and cultural geography.

Going beyond playing games for the educative experience of knowledge construction and skill building that can result, I also see great value in teaching children to think critically about how games work, as it teaches them to identify context, frames, and principles.  As a middle school teacher, I offered a course in game theory and design, in which we analyze the construction, rules, and guiding principles of games beginning with Tic Tac Toe and Rock Paper Scissors, moving on to Connect Four, checkers, and chess, and finishing with board games such as Monopoly and Risk. For a final project, students designed and built prototypes of their own games (which we then played in order to assess the design and underlying principles).

Connecting game-playing to the TBS mission to engage a changing world, check out Jane McGonigal's TED talk about games, and the possibility that games can actually be agents of social and societal change. She points to a real-life example of gamers finding a solution for how to fold certain proteins in certain ways that scientists had been unable solve as the potential for games to lead to a better world.

Problem solving is a type of game, so here's a problem that I'm also forwarding to our 4th-8th grade math teachers. It's the classic "Monty Hall" problem, and it's great for teaching concepts in probability, and for the ability to replicate and simulate variations to test answers within the classroom:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

You can check your solution here (warning, it's a link to Wikipedia).

9/7/12 Update: Here's another school using game-based pedagogy.