Learning by design: teacher pioneers

Caroline Williams-Pierce and Theodore F. Swartz

Abstract

Purpose – This purpose of this paper is to introduce innovative ways to design, develop and implement original learning experiences, by defining certain design elements with illustrative vignettes from the classrooms of teacher pioneers.
Design/methodology/approach – A new rubric of design elements is presented that synthesizes and illustrates theoretical and empirical research.

Findings – Teacher pioneers implement instructional design elements in a manner that supports the subordination of learning to teaching in their classrooms.
Practical implications – The rubric organizes criteria to design, implement, analyze and evaluate the extent to which instructional resources and approaches, at all levels and in all content areas, are likely to foster learners’ independence, autonomy and responsibility.

Originality/value – This paper provides a useful, concise and clearly explained rubric of design elements that, when most effectively implemented, can prepare students to meet, with enthusiasm and confidence, whatever comes their way.
Keywords Learning, Technology, Teaching, Rubric, Designing, Teacher pioneers

Paper type Case study

Teachers often must play the part of the pioneer if changes are to be made. Pioneers forge ahead in spite of difficulty, learning all they can before striking out for new territory. They study maps, anecdotal records, and talk to those on the edge of the frontier. They take old knowledge with them, but expect to develop new strategies, solve novel problems, create new language to describe what they see, and share what they learn with those who have not yet made the journey. Pioneers learn as they go. (Armstrong and Bezuk, 1995, p. 187)

The above quote inspired a book edited by the first author, Teacher Pioneers: Visions from the Edge of the Map (Williams, 2016), which is filled with chapters written by teachers ranging from elementary school to postsecondary, with a wide variety of learning goals. As the edited volume nears publication, we have sought to share the overarching principles that guided the contributing pioneers in their innovative classroom designs. The incredible diversity in content, context, age group, learning goals and instructional techniques and materials apparent in the chapters have made it difficult to synthesize precisely the criteria successful teacher pioneers use to design their learning environments. One theme echoed loudly throughout: the subordination of teaching to learning. Consequently, we present here a rubric for designing and assessing the quality of instruction based upon the work of Caleb Gattegno, and illustrated by cases from the book.

Throughout most of the second half of the twentieth century, until his death in 1988, Gattegno (1987a, 1987b) described and refined a pedagogy he called the subordination of teaching to learning. Essentially, he proposed replacing reliance on memory, as the primary human capacity for learning, with functionings. Dozens of books and many articles he authored express his insight into those functionings – which he also frequently referred to as the learning powers of children. He transformed that insight into a wide range of

instructional materials, techniques and activities that appeal to such powers, rather than to memory. They endure under the following trade names: Words in Color, for literacy; Visible and Tangible Mathematics; The Silent Way, for learning second languages.

Readers interested in Gattegno and his proposals will find the attached bibliographic references useful. Meanwhile, we offer the following example for a glimpse of how he saw functionings as the correct basis for education:

Cuisenaire rods, the use of which Gattegno expounded and promulgated in many countries, are a set of manipulatives for learning about the algebraic relationships and principles that underlie arithmetic. The rods come in 10 lengths, varying from 1 to 10 centimeters long, with each length assigned its particular color. They can be arranged, end-to-end, in “trains”, providing a visual and tangible representation of addition. When those “trains” are composed of rods that are all one color, learners recognize (a functioning or learning power) that repeated addition yields a process, commonly labeled multiplication. Students fortunate to connect with teachers skilled in using Cuisenaire rods to subordinate teaching to learning, become aware that a reciprocal transformation (another learning power), i.e. doubling/halving, yields, from one “multiplication fact”, several others [. . .] without memorization. They master the times tables, not through repetitious drill, but rather through engaging and varied practice that builds on recognizing and transforming and triggers additional functionings, including stressing and ignoring, retention, evocation and recall.

At a public elementary school in New York City – the Bronx Charter School for Better Learning (www.bronxbetterlearning.org) – teachers endeavor to practice the subordination of teaching to learning. For most, that involves shedding their trust in memory as a powerful learning capacity for most people and replacing it with faith in every one of their students’ more reliable intellectual powers, or functionings. To support the teachers’ clarity about the nature of the school’s pedagogy, one of this paper’s authors, Theodore F. Swartz, has developed a useful rubric (Figure 1). It provides a lens to assess the degree to which the time students spend in school yields learning that is energizing, permanent, joyful and leading to their awareness of themselves as both highly competent and deeply interested in academic subjects they might otherwise experience as too difficult or uninteresting.

The rubric aligns with five crucial aspects of subordinating teaching to learning, defining a successful learning context as one that:

fully recognizes and directly addresses each child’s brilliance;
by design is entirely flexible, trusting that teachers can craft accurate, precise questions, challenges and activities when provided with the right set of materials and techniques;
appreciates the power of play and relies on all learners’ natural impulse to improve themselves in a wide variety of endeavors;
views academic achievement as essential, while realizing that the teacher’s proper focus is exclusively on process, and that outcomes remain the learners’ concern; and
welcomes mistakes as inevitable, yielding information crucial to adjusting instruction – in the moment – so that learning guides teaching, rather than the opposite.

Using the rubric to reflect on a lesson or a series of lessons yields insight into how effectively a teacher implements a widely accepted set of educational design principles, seen from the perspective of Gattegno’s contribution to the improvement of education.

We visit each of the rubric’s nine design elements below, describing the most effective management of the element and then illustrating each with the story of a teacher pioneer. We then contrast each story with a more traditional perspective on what learning often looks like in classrooms. We emphasize that the effective implementation of a single design element does not guarantee a powerful learning experience, and furthermore that each illustrative chapter from Teacher Pioneers demonstrates the effective implementation of multiple principles, although we highlight just one in each case. There may also be long learning experiences in

which some of the elements are absent at certain times, due to the constraints of the classroom context or perhaps omitted intentionally by the teacher to forefront certain design goals.

We also note here that we subscribe to the perspective that teachers are made, not born, and that the teachers listed here have made themselves into pioneers. That process is personal, never ending and iterative, with experience and self-awareness continuously informing one another:

Sometimes for me the activity of teaching is shaped by my awareness of what needs to be done. At other times it is performed in ignorance of what I need to do, but in the actuality of my teaching I remain alert to learn how I need to teach. In the first case my awareness gives form to my actions. In the second case my actions educate my awareness. (Gattegno, 1975a, 1975b)

The layout of this article is inspired by Gee’s (2005, p. 15) Learning by design: Good video games as learning machines, and provoked in part by his conclusion that learners “need good designers who guide and scaffold their learning [. . .]. For schools, these designers are teachers”. Like Gattegno, Gee considers learning – not teaching – to be the primary purpose of such design. Consequently, we highlight the designs teachers are already implementing, and how such designs strongly support learning.

Instructional design elements: how their most effective implementation elevates learning above teaching

An overarching principle throughout this article is that “people must be allowed to do their own learning, which can only take place through the exercise of their will” (Swartz, 1975, p. 22). Consequently, carefully including the elements explored in this section (and summarized in Figure 1) supports learners in developing interest, agency and motivation to exercise their own will to learn in the designed contexts. In the following section, we introduce each design element, give theoretical examples of both least effective and most effective implementation of those elements and highlight a particular chapter within Teacher Pioneers that exemplifies an effective, appropriate and innovative use of that design element.

Design element: supporting understanding

Most effective implementation of the element. The learning experience provides a direct visual/auditory experience of the essential nature of how something works. One can handle this element successfully in a variety of ways and within a variety of contexts, as long as the experience supports direct access to the integral nature of the content under investigation by the learner. Supporting Understanding varies widely in implementation, but the most effective use of this principle refers not to teacher-to-student explaining, but rather to providing the opportunity for content to speak to learners directly. For example, a teacher could ask students to create a “train” of, say, six purple Cuisenaire rods (each of which is 4 cm long), arranged end-to-end. Then he/she might invite them to create another train, composed of four dark green rods (each 6 cm long), and pushed up against the first one, with the ends aligned. A potentially productive question would be: “What do you notice about the two trains?” Once number names are assigned by the students to the lengths of each single rod according to how many centimeters long each is, students easily, based on what is now visual and tangible, let the content reveal that “4 sixes equal 6 fours” and vice versa. The teacher could then suggest that the pair of trains be reassembled, by the students, into two, separate, single colored rectangles, one with the purple rods placed against one another, side-by-side, and the other, with dark green rods, similarly arranged. When either of the two rectangles is placed on top of the other and aligned in the right way, observation of the equivalence of the two rectangular areas yields direct, unwavering insight into the commutative property of multiplication, especially as further examples are similarly experienced.

Teacher pioneers. Teacher pioneers use their deep knowledge of both learning and content to design experiences that create awareness in students of the essence of whatever subject matter they study.

Example. Howell et al. (2016) developed an electricity unit in their 8th grade science classes using electronic textiles (e-textiles). E-textiles use “soft textile materials sewn and embroidered with conductive thread, integrating tiny computers (microcontrollers) and lights (LEDs) with traditional crafts” (chapter 13). In other words, students used technology in a variety of forms to design, sew and build their own electronic art, using copper tape and conductive thread with switches and various circuits.

Electricity is a difficult “concept” to interact with directly, so Howell and colleagues developed e-textile projects that encouraged students to design original artwork that required the correct wiring and logic to perform as the students desired. Hence, the correctness of student work was evaluated by the electricity itself – if the correct lights did not activate, something was wrong with the wiring. How electricity works was the content that students engaged with, through their e-textiles projects. The instructors provided support, but did not constrain their direct experiences.

Implications. Supporting understanding effectively means giving the content the opportunity to speak for itself – to provide the learner with the chance to directly engage with a challenge to understand a concept’s essential nature. To the contrary, teachers who, for example, model the standard algorithm for multi-digit multiplication and then require students to mimic the steps, using memorized multiplication tables, should expect conditioned compliance, with little or no insight into the underlying algebra that yields the procedural steps.

Most effective implementation of the element. The learning experience provides ample opportunities for free exploration and investigation of what is possible. Effective implementation of this element also can range widely in look and feel, depending upon the context, content and learning goals; however, it is crucial to note that effective use of Levels of Initiative does not imply a laissez-faire approach. It does require attentiveness and flexibility. The teacher remains vigilant, asking questions and adjusting precisely the nature of the challenge, at the same time giving ample opportunity for learners to test their hypotheses, give reign to their curiosity and contribute uniquely to their experiences with the content. Autonomy is essential. For example, prompting learners to understand life in seventeenth century England by developing and sharing their own fictional historical character provides structure to support learning goals, while affording space for individual interests, curiosity, and unique contributions to the group’s collective growth in knowledge and insight.

Teacher pioneers. Teacher pioneers use carefully designed and flexible contexts that provide parameters, while also leaving ample space for learner creativity, thoughtfulness and autonomy.

Example. Martin (2016) built a four-day camping “Mystery Trip” for a rustic, deep woods camp for boys, using mobile devices with GPS and place-based augmented reality software. The Mystery Trip provided a narrative framework, spurred occasionally by messages from camp that were triggered by GPS location. For example, during the first day of hiking, they received a notification that their camp was invaded, and that they were being tracked by the invaders. As the hiking trip continued, they received additional messages about the invasion, and found out that they had to climb mountains to intercept and decode messages from the invaders.

Martin notes that “because the storyline was fragmentary [. . .] they had plenty of space to fill in the details with their own musings, and to apply their own experiences to the narrative plot” (Chapter 10). Some groups of boys carefully avoided other hikers (potential invaders) on the trails by moving off-trail and trekking through the woods directly, which required them to develop their ability to read maps and match those maps to landmarks. Others focused on more closely hiding any indication of their passing, taking the Leave No Trace mantra to heart in a way they hadn’t before. Martin’s design provided powerful impetus and desire for his boys to develop their nature-related skills, while also leaving sufficient space for creativity, inventiveness, argumentation and initiative.

Implications. Proper handling of Levels of Initiative requires teachers to privilege the curiosity, creativity and autonomy of their students over their own content expertise. In other words, while teachers design and provide learning goals embedded within learning contexts, they also accommodate unique paths and new contributions to the content. Consequently, teachers who, for example, release learners to themselves investigate and recommend readings or videos about seventeenth century England, or even have them play a rich, open-ended educational simulation, encourage the sort of initiative and creativity that lead to independence, autonomy and responsibility. A more traditional limiting of their students’ study to a pre-determined corpus of resources instead fosters dependence and passivity.

Design element: affording practice

Most effective implementation of the element. The learning experience provides constantly varied practice to build speed and strong criteria for correctness. Learners have frequent opportunities to increase efficiency and accuracy, yielding ease and fluidity in a skill. Successfully affording practice requires variation and freshness, rather than mere repetition, so that content is met in novel contexts and changing representations. For example, a photography class can afford practice (and a practiced eye) for lighting nature scenes by having learners take photographs at various times in the day, followed by

comparing and evaluating the resulting aesthetic effects. Their facility to apply needed adjustments to the varying situations increases.

Teacher pioneers. Teacher pioneers design opportunities for practice in contexts that become more advanced, complex and challenging as the learner progresses.

Example. Isaacs (2016) teaches game design to middle school students, using a wide variety of software, like GameStar Mechanic and Portal 2. Regardless of the software, he focuses on his learners’ iterative game design skills, starting with a detailed design document and initial development of the game, then cycling through playtesting, evaluating, conferencing with others and refining, until the final version is ready for publication. The cyclical process serves as the practice field: learners discover bugs in their code, breakdowns in the way their game guides players and unexpected outcomes. Their game becomes more nuanced and sophisticated as they anticipate their players’ needs, thereby requiring them to increase their facility in writing and debugging code.

Isaacs supports his learners through a type of practice very different from a more traditional approach (e.g. memorizing multiplication tables through static repetition). He frames the notion of “practice” as “iterative design”, thereby avoiding the dulling and boring exercises typical of more common instructional methods. He notes that:

Iteration is an essential life skill. It involves the process of following an idea through from conception to completion in a systematic and meaningful way. Iterative design puts students in the role of designer as they conceptualize an idea, develop a product based on their idea, recruit feedback in order to improve upon the idea, implement changes based on feedback, and continue cycling through this process until their product is complete. (Chapter 16)

In short, Isaacs’ view of iteration creates facility in all relevant aspects of skilled game design, including complexity and nuance.

Implications. Affording Practice means providing varying challenges that, by their nature, motivate, since they avoid strict memorization, per se, yet still produce speed, accuracy and, ultimately, automaticity. Doing so deviates profoundly from traditional drill. For example, many teachers require students repetitiously to employ the standard algorithm for long division until their pupils memorize the procedure. They thereby miss a ripe opportunity for their students to become aware of, and then to practice, the process of repeated subtraction as the basis for breaking large quantities into a given number of equal subsets (with or without remainders). Since approaching division from that angle invites sundry creative solutions, students can practice a variety of tactics, including those that are most efficient (if not necessarily aesthetically pleasing) and therefore lead – through discovery, active inquiry and collaboration – to some semblance or even a re-discovery of the traditional algorithm.

Design element: testing

Most effective implementation of the element. The learning experience tests capacity to apply learning to new content or challenges. This element is one of the most crucial, as it highlights the importance of supporting learners’ applying their knowledge and know-hows to face what is not yet known. That meeting of the unknown, with confidence and equanimity, should be the primary goal of education. We therefore define mastery as the stage at which a developed skill is functioning so smoothly that it opens the door to new learning. It follows that the most effective test of students’ mastery of, say, using context clues to decipher word meanings would be to use that skill to unlock the mysteries of a complex and challenging poem, in which the author uses common words in uncommon ways.

Teacher pioneers. Teacher pioneers provide opportunities for learners to demonstrate their increased capacity by applying it to meet constantly more complex problems.

Example. Dikkers (2016) designed a turn-based board game, WarLords!, based upon the popular videogame series Civilization, so that his middle school geography class could

experience the influence of geography on human history. He chose a region of the planet to be represented by pixelated blocks on butcher paper that they then laminated for their game map, and developed an accompanying rule set. Each pixelated block was color coded to represent a different type of geographical feature, such as mountains, rivers, arid territory and so on, and created a particular impact on the developing empires of his students. For example, a green square represented flat lowland, which supported a population growth of 20 people per turn. Brown borders on such a square represented arid lands and lessened the growth rates of the empire by halving the birth rate to 10 people per turn.

As the game progressed, Dikkers revealed historical factors that would influence his students’ empires. Students would discuss which factors he might reveal over lunch, and ask him to include specific factors, such as irrigation of the arid lands. He would respond by asking them why he should include irrigation, requiring them to investigate and report on the geographical and societal benefits of the process. Dikkers added many of these features along with irrigation, such as food preservation, boats to allow fishing and city building, complicating the game even as he made it more authentic. By doing so, Dikkers built upon his students’ learning, requiring them to modify previous rules and strategies they had developed to the new combination of factors that guided the game, and assessing their learning through their ability to change and adapt.

Implications. With the most effective testing, teachers assess learners – and learners assess themselves – by observing their ability to apply their knowledge and/or know-hows to new content, demonstrating their previous learning through its use in developing additional understandings. In contrast, teachers who, for example, teach vocabulary through giving word and definition lists, and then test their pupils’ ability to reproduce those words and definitions, unnecessarily limit their insight into the extent of the students’ mastery. Verbatim reproduction of material often indicates temporary recall. Deeper, more permanent integration of new vocabulary would be revealed through an exercise that required robust understanding of previously presented words to unlock the meaning of a new set.

Design element: motivation

Most effective implementation of the element. Effective implementation of this design item taps the innate urge to know, incorporating challenges that avoid potentially distracting elements. Effective motivation could involve the careful design of provocative projects that present puzzling problems, stripping away the more esoteric aspects of the concept under investigation, such that learners can ignore them until they are more advanced, or until they happen to discover them themselves. For example, providing a digital simulation of a familiar physical object (say, a ball moving through space) that illustrates Newton’s First Law, and contrasting it with the behavior of a physical ball rolling across a table, can provoke learners to explore the whys and wherefores of the behavioral differences. Learners engage with that challenge not because they want a good grade or praise; rather, because it is inherently interesting and satisfies their innate need to know.

Teacher pioneers. Teacher pioneers design learning contexts that provoke the natural human state of curiosity.

Example. Glazer (2016) asked her students both to design and to play a game based upon Beowulf. Glazer’s inspiration, Trent Hergenrader, highlights that role-playing “sessions are lived experiences of fictional characters, each of whom have personal histories, attributes, desires, flaws, and motivations” (Hergenrader, 2016, Chapter 4), which requires students to deeply interrogate those lived experiences to enact them during gameplay. Glazer’s use of Beowulf set that world specifically as both learning content as well as the context for the students’ exploration and creativity.

During the game creation phase, her students were tasked with developing the game board, characters and rules, leading them to research the geography and history of the poem, and then argue enthusiastically about the world as it should be represented in the game. During gameplay, each small group was led by a student gamemaster, who provided the initial storyline for other students’ characters to engage with, and reacted to their activities according to the rules, characters and board. In short, Glazer provided a learning context for a complex topic that provoked students’ curiosity about Beowulf, motivating them to research deeply and understand the characters within the epic poem in a way that aligned with the natural desires of the students to understand humans in a different time and world.

Implications. The element, motivation, encourages teachers to design learning opportunities that make learners wonder “why?”, thus tapping into innate curiosity, rather than depending upon external motivators. Consequently, teachers who, for example, use Jeopardy-style games to reward learners who memorize Newton’s laws and their formal definitions, are using external structures that are irrelevant to the content and that prize speed of memorization over actual understanding and inherent interest.

Design element: gaming techniques

Most effective implementation of the element. This element, when well implemented, offers activities that are, by their nature, game-like and always directly related to the content; the better the learner does, the more opportunities for increased challenges. The label, Gaming Techniques, refers directly to the learning principles that appear in well-designed videogames, many of which can be replicated in academic learning experiences (Gee, 2005). In particular, effective implementation of this item requires that learners engage in activities that increase in difficulty and complexity, within a context that provides the required criteria and practice. For example, a computer science teacher may begin to teach programming through a series of increased challenges in a visual programming language, such as Scratch, with design challenges that are “unlocked” in such a way that learners are rewarded for their increasing expertise with tasks that push them to develop even more.

Teacher pioneers. Teacher pioneers use game design principles to support deeper content-based experiences, engagement and learning in their classrooms, using a variety of digital and non-digital tools, all related directly to the content.

Example. Darvasi (2016) designed a role-playing game in his classroom that immersed his learners in the world of One Flew Over the Cuckoo’s Nest, deciding that:

My English classes would become the psychiatric ward from Ken Kesey’s classic novel. Students would be transformed into patients, playfully subjected to the mock-tyranny of a behaviorist regime. The game would be theatrical, ironic, satirical, unpredictable, oblique, self-reflexive and, ideally, insane. It would be a video game played in the real world. (Chapter 5)

When he introduced this game to his classrooms, he dressed as Nurse Ratched, and began calling his learners “patients”. He introduced incentives, goals, mini-games, currency, and a structure that encouraged the “patients” to report on each other, developing a gentle sense of paranoia, just as in the novel, while still keeping it playful and fun.

Darvasi designed game mechanics that directly related to the book, so that playing the game meant deeply digging into the world. For example, as learners “leveled up” in the game, they became labeled “chronic”, and any points they earned while playing were automatically divided by four, making it harder for them to win the game by reaching 100 points. The label “chronic” is used in the novel to indicate incurable patients, and in the novel’s world, the longer patients stay in Nurse Ratched’s control, the worse they get – which aligns with Darvasi’s design of lessening rewards the more advanced the learners are in the game. As another example, in the novel, cigarettes are the black market currency in the ward; in Darvasi’s classroom, “cancer sticks” became the game currency. Other aspects of the game were also designed after the novel, such that the learners – instead of

simply reading and discussing the book – lived the experience they were meant to understand.

Implications. Gaming techniques is an element that teachers can infuse fully into the classroom, allowing learners to experience more complex, responsive and powerful engagement with content that increases in difficulty as they progress. Consequently, teachers who give their learners free range with software such as Scratch may see such openness as supporting internal motivation and design choices, but truthfully, careful crafting of design challenges can support such characteristics as well as further advance learning.

Design element: progression

Most effective implementation of the element. This element, properly executed, incorporates many opportunities for exhilarating expansion, with a sense of a topic’s full scope and complexity. Whereas subject matter is often atomized and overly simplified in formal education, efficacious application of this design element requires that learners see and explore the unvarnished phenomenon. In that manner, they can take advantage of opportunities for intuitive, intelligent leaps of insight. Doing so taps their capacity to synthesize, as well as analyze, as early as possible in their investigation of new areas of study. For example, learners reading Margaret Atwood’s A Handmaid’s Tale should be supported in their recognizing how sundry themes – of gender, race and power in history and society – are woven together and support one another in a complex interplay.

Teacher pioneers. Teacher pioneers support a joyful and exhilarating exploration into the complexities of topics, through deep analysis of and connections to other aspects of the topic and the world.

Example. Wilmot (2016) is a fourth grade computer science teacher. When his learners would not stop talking about Minecraft, he found a way to bring their interest into his classroom. Minecraft, while a game, is also a platform – that is, learners can build their own experiences and share them. Wilmot decided that instead of developing a curriculum, he would let the implementation be organic, driven by both him and his learners. As a result, learners built:

[. . .] collaborative research projects, biography builds, Google Earth re-creations, social studies connections, digital dioramas, and history lessons. They have mapped our solar system with glowing planets and surrounding asteroids. They have built the Orphan Train, Pompeii, the Great Wall of China, pyramids, functioning lighthouses, petting zoos, malls, hotels, theme parks, bomber planes, and pirate ships. (Chapter 8)

In short, Wilmot’s learners used design, history, architecture, astronomy and countless other topics in their computer science class, thinking about, analyzing and connecting numerous aspects of the human condition. By allowing his learners to meet head-on the full complexity of their chosen topics, Wilmot gave them the gift of maintaining a sense of and respect for the entirety – even enormity – of their topics, while allowing them to focus attention on one or more aspects at a time.

Implications. Progression is essentially the element of keeping the topic under study naturally connected to the complexity of the world, both within the topic itself (such as the multiple themes in Atwood’s book) and the surrounding contexts of the normally siloed topic. Consequently, a more traditional approach to A Handmaid’s Tale might invite learners to oversimplify, addressing the themes separately and isolated from one another, thereby distorting the true and complex nature of the phenomena.

Design element: retention and recall

Most effective implementation of the element. This element calls upon and invigorates mental powers that support full understanding (e.g. watchfulness, inventiveness, imagery, retention, recall, hypothesizing, analysis and synthesis), with strict minimizing of memorization per se. Teachers can implement this aspect well in a wide variety of ways, but variation is key: Supporting Retention is not about the repetition of decontextualized facts,

but about the development of ways of knowing and understanding the world, without and within. For example, instead of drilling the multiplication tables, learners can examine the patterns of numbers that emerge during multiplication, and develop their own hypotheses about the dependable behavior of numbers, both in the traditional multiplication table and beyond. Consequently, a teacher who challenges her learners to discover patterns of multiplying invites them to engage in many of the mental activities listed above, as they propose and discuss their discoveries. She supports them in finding out – for example – that multiplying nines produces a pattern, such that digits in the tens place increase by one, while digits in the ones place decrease by one.

Teacher pioneers. Teacher pioneers design contexts that support learners in authentic (and often messy) investigation, discussion and practice.

Example. Saunders and Holden (2016) developed and iterated two games in his elementary science classrooms, Matter Quest and Intergalactic Jury, designed to focus on planets, states of matter (e.g. solids, liquids and gases) and scientific reasoning. The games were designed to be what Saunders and Holden call gameful learning experiences, and used both traditional science materials (e.g. pipettes and graduated cylinders) and various digital media (e.g. videos, wikis, and presentation software). Students participated in authentic scientific inquiry guided and provoked by both games, and being both formally and informally assessed throughout the process.

One of Saunders’ main goals in his classroom is to support scientific inquiry, which aligns closely with the mental powers this principle embodies. He accomplished this by designing his two games to support students in pursuing their own scientific interests within the umbrella of his purpose:

I gave myself space to create on the fly, improvise reflectively, and yield to the creativity of my students as codesigners. Together, our learning produced the types of positive results that I hadn’t achieved through traditional methods. My students left our classroom demonstrating an ability to engage and explore the world (and beyond!) with a level of autonomy and mastery that they did not have only a few months earlier. Part of that growth was due to my facilitation of a space where students could explore and practice like scientists, with authentic tools, and pursuing genuine curiosities. (Chapter 15)

Saunders’ students investigated complex topics of their own choosing – such as interstellar travel, black holes and asteroid shields – conducted research, contacted prominent researchers, developed hypotheses, made predictions and concluded by sharing their research with their classroom community. The retained and readily recollected details and facts connected with their chosen subject matter was a by-product of their active, mental engagement.

Implications. Supporting retention and recall effectively means providing learners with the repeated opportunity to develop their own strategies for investigating and developing their understanding. Teachers must allow their learners the option to choose their own paths, as the memorization of the content isn’t the goal – rather, the purpose is students reaching awareness of their mental powers and how consciously applying them within the area of study yields sustained retention and easy recall. Consequently, teachers who, for example, merely point out the patterns that emerge when multiplying by nine risk having students who later forget the pattern and are far less likely to use their powers to analyze, hypothesize and recognize to rediscover it on their own.

Design element: handling mistakes

Most effective implementation of the element. The best way to manage this element is to welcome mistakes as guidance. The teacher can remain neutral regarding errors during practice activities, so long as the results directly inform the learner about the adequacy of the attempts. Providing external feedback and tracking of accuracy during or after testing are also both appropriate and important. When properly managed, Handling Mistakes is an element carefully incorporated regularly during all stages of learning – ideally, each learning

environment has established norms that welcome mistakes and the opportunities for learning they provide, and has normed structures in place that support learners’ comfort with mistakes and affords them the time and criteria to self-correct. For example, a learner that classifies lava flow as metamorphic rather than igneous provides a welcome opportunity to discuss the roots of the word igneous (from Latin for fire), and the nuances of the way that metamorphic rocks change in their form over time. A teacher who welcomes the opportunity provided by such a misclassification can facilitate a powerful learning experience, and support learners in feeling comfortable in both making mistakes and learning from them.

Teacher pioneers. Teacher pioneers afford their learners space to try, fail and try again, learning from each experience.

Example. Vann (2016) designed his classroom around a technique he called failing forward – that is, supporting failure and learning through inquiry. When he found the original Lego Mindstorm kits in his classroom closet, he began learning how to use them, and developed a project for his learners. The goal of the project was to create a pre-programmed robot that would be able to find, pick up and transport an aluminum can to the recycling bin. When he introduced the project, he said, “Don’t be discouraged when it doesn’t work the first time. In life things rarely work exactly how you want them to on the first try” (Chapter 12). He explicitly invited them to fail forward.

Some of Vann’s students didn’t fully embrace his exhortation, and instead of feeling comfortable about failing, they asked him what they should do. Vann writes, “to their disappointment, I handed them only one part, a connector piece to bridge two axles together” (Chapter 12). In doing so, he refused to weaken their learning experience by directing their next steps, and pushed them to dig into trying, failing and learning.

Implications. Handling mistakes requires that teachers allow learners to feel comfortable making mistakes and learning from them, trusting that the missteps will provide all involved with the feedback progress requires. In particular, teachers who support discussions and investigations around misconceptions and misunderstandings allow for more fruitful opportunities, where learners do not flinch from challenges. Alternatively, a teacher who merely marks the classification of lava flow as metamorphic as incorrect is, essentially, indicating to the learner that he or she is not behaving appropriately in the learning environment, thereby discouraging both willingness and comfort to make mistakes.

Conclusion

Teacher pioneers are often the first to create and implement innovative learning experiences, which new technology frequently allows or inspires. Those teachers skillfully implement instructional design elements to guide their innovations within the “forge and the crucible of the classroom” (Catir, 1975). As a result, their students benefit from rich opportunities to see and understand the world, to meet their unknown futures with eagerness and equanimity.

References

Armstrong, B.E. and Bezuk, N. (1995), “Multiplication and division of fractions: the search for meaning”, in Sowder, J.T. and Schappelle, B.P. (Eds), Providing a Foundation for Teaching Mathematics in the Middle Grades, State University of New York, Albany, pp. 85-119.

Catir, Z. (1975), Educational Solutions Newsletter: Teachers Are Made, Chapter 3.

Darvasi, P. (2016), “The ward game: how McMurphy, Mcluhan, and Macgyver might free us from McEducation”, in Williams, C. (Ed.), Teacher Pioneers: Visions From the Edge of the Map, Chapter 1, ETC Press, PA.

Dikkers, S. (2014), “WarLords!: deconstructing digital games for classroom use”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 5, ETC Press, PA.

Gattegno, C. (1975a), Of Boys and Girls, Educational Solutions Inc Worldwide, Ontario.
Gattegno, C. (1975b), Educational Solutions Newsletter: Teachers Are Made, Chapter 2, Educational

Solutions Inc Worldwide, Ontario.

Gattegno, C. (1987a), What We Owe Children: The Subordination of Teaching to Learning, Educational Solutions Inc Worldwide, Ontario.

Gattegno, C. (1987b), The Science of Education, Part I: Theoretical Considerations, Educational Solutions Inc Worldwide, Ontario.

Gee, J.P. (2005), “Learning by design: good video games as learning machines”, E-Learning, Vol. 2 No. 1, pp. 5-16, available at: http://doi.org/10.2304/elea.2005.2.1

Glazer, K. (2015), “Beyond gameplay – using role-playing game creation to teach Beowulf in a high school English class”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 3, ETC Press, Pittsburgh, PA.

Hergenrader, T. (2016), “Immersive learning – using role-playing games to teach creative writing, literature, and history”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 4, ETC Press, Pittsburgh, PA.

Howell, J., Tofel-Grehl, C., Fields, D. and Ducamp, G. (2016), “E-textiles to teach electricity: an experiential, aesthetic, handcrafted approach to science”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 13, ETC Press, Pittsburgh, PA.

Isaacs, S. (2016), “Teaching the iterative process through game design and development”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 16, ETC Press, Pittsburgh, PA.

Martin, J. (2016), “Unlocking a mystery: designing a resilient place-based game”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 10, ETC Press, Pittsburgh, PA.

Saunders, T. and Holden, J. (2016), “From improvisational puzzle to interest-driven inquiry”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 15, ETC Press, Pittsburgh, PA.

Swartz, T. (1975), Educational Solutions Newsletter: Teachers Are Made, Chapter 5, Educational Solutions Inc. Worldwide, Ontario.

Vann, W. (2016), “A first-year teacher’s experience with PBL and lego robotics”, in Williams, C. (Ed.), Teacher Pioneers: Visions from the Edge of the Map, Chapter 12, ETC Press, Pittsburgh, PA.

Williams, C. (Ed.) (2016), Teacher Pioneers: Visions from the Edge of the Map, ETC Press, Pittsburgh, PA.

Wilmot, J. (2016), “A space to create: teaching with Minecraft”, in Williams, C. (Ed.), Teacher Pioneers: Visions From the Edge of the Map, Chapter 8, ETC Press, Pittsburgh, PA.