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.

Sunday Reading

Federal attention to the need for early childhood education waxes and wanes. The Washington Post's recent article illustrates the complexities of addressing the topic; I find it problematic that someone would define a good ECE program as one that develops "skills and knowledge in language and literacy, math, science, social studies and the arts, while also addressing social, emotional and physical development." That sounds like a good approach to elementary school, but not to early childhood, where students are 3 and 4 years old. How about nurturing a love of learning, developing a sense of inquiry, providing opportunities for creative self-expression, and giving children the chance to play?

Public education in this country is under attack from all sides, and there's no easy answers to how to fund all the necessary programs. The Governor taketh and the Governor taketh again; he's cut $3 billion in funding (on top of about $18 billion cut by Arnold in the previous three years), and he lets schools charge fees for after-school sports - fees that function as an equity barrier for many students who find not only community connection and self-esteem, but also a reason to continue to pursue their academic studies, in the context of those sports teams. For an in-depth look at the value of non-academic programs on student learning, check out this article by June Kronholz on EducationNext.

Singapore Math has many similarities to the TERC: Investigations in Number, Data and Space curriculum that we use at TBS. As The Columbus Dispatch points out, at the core is a focus on understanding why an answer is what it is, not just what that answer is. It's a focus on process, not product, and it allows for the multitude of strategies that allow children to develop the necessary number sense to understand why the efficient, standard algorithm works.

I shared this blog post on digital citizenship by Mary Beth Hertz with the K-8 faculty, because it has a good perspective on what can and should be teachable, and resources to support that view.

Stateimpact from NPR offers a critique of flipped classrooms. I heard Salman Kahn of Kahn Academy speak last year at the NAIS Annual Conference, and I blogged about it then. Using videos of instruction that students can watch repeatedly is wonderful; for those who struggle to absorb all the necessary information the first time through a lesson, this is an enormous help. Likewise, having a benchmark standard to determine mastery of a concept, and an infinite number of problems to with which to practice that concept, is useful. And, the data analysis tools that Kahn Academy provides to teachers allow a detailed level of insight into the child's approach to tackling problems and returning to the instructional video for review. In fact, I was so excited when I returned home that one of our 4th grade teachers began experimenting with integrating Kahn Academy into the classroom for teaching math, and I watched several videos with my 8-year-old daughter. But there are deep issues with the flipped classroom as well, starting with the fact that all lessons are delivered as didactic lectures. There's no room for inquiry and discovery in this model.

Here's an inspiring post from Dave Saltman about the deeper legacy of Steve Jobs (hint: it's not the computer).

Today's learning walk: division reigns supreme

While out buying ham and cheese croissants at Cafe Fanny for a special Mother's Day breakfast yesterday, my 7 year old daughter asked me how to divide 120 into three equal parts. She quickly understood that 60 was half of 120, so 120/2 = 60, and with a little bit of prompting she understood that 30 was half of 60, so 120/4 = 30, but 120/3 remained a puzzle to her. This morning riding our bikes in to school, I tried to break it down a different way; first, we determined that 120 is made of up 12 groups of 10. Then, we agreed that 12/2 = 6, and 12/4 = 3, after which she was able to reach the conclusion that 12/3 = 4. At which point we counted by 10s (aka multiplied) to reach the conclusion that 120/3 = 40.

While doing a 45 minute walk around the 2nd-5th classes today, I saw numerous ways in which students were engaged in mathematical thinking building their division skills.

One group of second grade students was working on static subtraction, using either a bead frame or working mentally with just a paper and pencil. Subtraction is an important concept on its own, but it is also foundational to division, which can be conceived of as repeated subtraction (the inverse of how multiplication can be seen as skip counting, which is repeated addition). The other group of second grade students was working with the division board, a Montessori material that literally makes division visual (in this image, 12 beans have been divided into 4 equal groups of 3 per group).

Third grade students were also working in two groups. One was doing

"pencil & paper" work on a group of problems that included addition, subtraction, multiplication and division of numbers with four digits. The other was learning to write the remainder of division problems such as 32/10 in more sophisticated mathematical expressions, from "3 r 2" (where "r" = "remainder) to 3 & 2/10, to 3.2, using materials including the Stamp Game, Fraction Tiles, and Test Tube Division. BTW, the Stamp Game is an incredible material that can be used to teach all four operations (in this image, 2432 x 4 = 9724), and some important extensions of those ideas - you can check it out here.

In 5th grade, students were working on graphing. In the story problem, one child had grown at a steady rate from age 2-10, while the other had grown more rapidly from age 2-4, and then less rapidly from age 4-10. They had been given the choice of either completing a table showing the two rates of growth and then plotting those lines, or drawing lines to represent the growth and then determining the amount of growth in interval to fill in the table. In a fascinating bit of insight into 5th grade mentality, every single one of the 21 students had chosen to draw the lines of change first - which left them to work out some complicated division problems involving decimals.

Today's learning walk

My absolute favorite aspect of being in administration is the ability to go into every classroom in the school and observe students and adults teaching and learning together. Today I did a "learning walk", in which I managed to see nine classes in about 80 minutes. As Tony Wagner says in The Global Achievement Gap, "The learning walk is one way to essentially audit what's taking place in a group of classes in a given period of time.... you have a snapshot of the teaching and learning that take place in that school. It's obviously not a way to evaluate individual teachers or an entire course, but this kind of sampling detects patterns within and across schools."

My walk began in the middle school, where I observed a 7th grade science class discuss a recent experiment on photosynthesis, and the relative effect of heat compared to light on the process. I then moved into a 6th grade math class, where students were putting the finishing touches on their Plan-A-Park Projects, and consulting this rubric to improve their work. In a 7th grade math class I watched as students wrestled with multiplication using negative numbers, predicting patterns and utilizing thinking routines to explain their thinking. In 8th grade English, students were engaged in a Reader's Theater read-through of the final scene from Romeo and Juliet.

I headed to the elementary level, where a work period was underway in Temescal Creek. Half the students were working with various pattern works from the TERC: Investigations curriculum, and the other half were using math-based Montessori materials such as the Stamp Game and Bead Frame to extend their understanding of multiplication and division. In Blackberry, students played class-favorite Roll and Record, or created number sentences based on the culinary exploits of the titular character in The Very Hungry Caterpillar by Eric Carle. In Laurel, students chose from a variety of activities during Reader's Workshop, including card work with consonant blends, sound/symbol association, investigation of short "a", spelling work using the Wilson Fundations program, and games that involved matching initial blends to word families.

In Strawberry, students were engaged in a poetry writing workshop. They worked at a range of places along the writing process continuum, from brainstorming to draft to editing to publishing, on pieces including concrete poems in the shape of rivers and boats, acrostics, and prose poems. One student was working on his mastery of syllables:

Geckos can blow our minds asunder.

They can climb and it makes us wonder,

Is destroying their habitat a blunder?

Students in Cerrito were working on poetry as well; they read a poem titled Melodic As Machine Guns, and analyzed it for "unbeautiful imagery." They then moved on to brainstorming ideas for their own unbeautiful poems, developing one of those ideas into a full-fledged concept, and writing a first draft. My learning walk ended in Sweet Briar, where students ended their mornings in a read-aloud, before discussing appropriate transition to hot lunch, and the cleaning procedures to use with the non-disposal plates and silverware that were introduced this week.

Several consistencies and patterns jumped out during my learning walk. One was the degree of individualization that was structured into the program, as seen in the Blackberry, Laurel, Temescal, Cerrito, Strawberry, and Wildcat (6th grade) classrooms; in each case, children were engaged in activities that were related by theme, and provided with an opportunity to choose from within the structure provided by the faculty. In contrast, the 7th and 8th grade students were working on the same work at the same time, as a collective group - a technique that happens throughout the school as well. Another similarity was the emphasis on creativity; from Blackberry's literature-based number sentences to the poetry of the 4/5 classrooms and the math projects in 6th grade, students were given opportunities to express their creative thinking in the service of problem solving. Equally present was the emphasis on critical thinking; first grade students were asked explain why certain numbers showed up more often than others in their game of Roll and Record, 4th grade students were asked to analyze poetic imagery, and 7th grade students were asked to reason about the impact of different conditions on the result of their science experiments. The importance of understanding the role of patterns in mathematical thinking showed up from Kindergarten, where a child pasted pictures from The Very Hungry Caterpillar in a "sweet, not sweet" pattern, to the third grade TERC: Investigations work, to the 7th grade attempts to predict and extend patterns abstractly. And finally, in six of the eight classrooms I visited without consulting a schedule prior to the start of my walk, students were engaged in mathematical and language arts, which has me wondering if it was coincidence, or a manifestation of how our teachers plan their days.

2nd grade math observation

Last week I watched a 2nd grade math class that effectively provided entry points to the content through multiple modalities, and that combined teacher creativity with the TERC: Investigations curriculum that forms the core of our K-5 math program. The students began by standing in a circle. In response to teacher instruction, they then used body rhythm - drumming on their own bodies - to make up patterns, starting with a clap of the hands and then a pat of each hand against their shoulder blades. After repeating this several times, they moved on to a second rhythm - a clap of the hands, a pat of each hand against their shoulder blades, and slap of each hand against their waist. They continued in this vein, developing more and more complicated patterns. The students then all sat, and came up with semantic descriptions of the patterns they had made - "clap pat pat," "clap pat pat slap slap", "clap pat pat slap slap snap snap," and so on. The third step was to translate these word patterns into alphabetic patterns - ABB, ABBCC, ABBCCDD, etc. Finally, still working in the group, they turned these alphabetic patterns into snap-cube patterns, by building chains of different colored cubes in repeating patterns.

In the second half of the class the students moved to the tables for individual work, coloring in unique patterns on handouts. Some students used the alphabetic strategy to create the patterns which they then colored, others built snap-cube chains which they then copied, and others jumped straight to mentally creating patterns and coloring the squares on the page. Pattern making and skip-counting are key ideas that underlie the development of number sense about the operations of multiplication, and each child used a strategy that was effective for him-or-herself, that fit into the child's developmental schema, and that s/he knew would allow him/her to be successful - the very design of the TERC: Investigations curriculum. It was really fun to watch, and to see the students then using those patterns to answer predictive questions ("what will be the color of the 30th block of this pattern?").