Learning as Puzzle Solving

"A thinker is very much like a draughtsman whose aim it is to represent all the interrelations between things." (Wittgenstein, Culture & Value)

Learning is often completed collaboratively with others, and features a sense of mutual accomplishment as the learners embark on a journey of discovery, consolidation and confidence. The seven principles of "learning as puzzle solving" are taken from the following reference:

  • Geekie, P., Cambourne, B., & Fitzsimmons, P. (2004). Learning as puzzle solving. In Grainger, T (ed) The RoutledgeFalmer reader in language and literacy (pp 107 – 118). London: RoutledgeFalmer

Please continue to read to explore the seven principles and how they apply to effective teaching.

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Elements of the Reading Process: A Schematic Diagram

The following image presents the elements of the reading process as a flow chart that roughly identifies levels of reading processing. I ask you to imagine a reader holding a text within the hands. Whether or not any comprehension occurs begins at the fundamental first steps: is adequate attention being paid to the text? Does the reader have the language and the knowledge to adequately draw meaning from the text? It is a process of both top down and bottom up processing, in which the top down process brings background knowledge and prior experience to bear on the reading and the bottom up process involves decoding, defining new terminology, and making sense of sentences through a knowledge of a syntax. 

Elements of the reading process

The following diagram further represents how both top down and bottom up processes interplay in an interactive approach to reading instruction. 

Courtesy of Dr Neil Anderson, Brigham Young University

A Letter from An Anxious Teacher

17 November 2013

 

To whom it may concern,

 

I am a teacher. I stand in front of awaiting eyes, ears, mouths and minds. I don't always stand in front. Sometimes I sit side by side or sit gathered in circles. I have plans for my students. I have expectations. I would like to consolidate skills through practice. And I want to consolidate these practices by providing opportunities for my students to learn and to practice and to grow. I have a picture of what a successful learner looks like. I think I have this vision. I think it is a fair vision. I feel that every child can achieve. I am deeply curious about my students. Most importantly, I see education as transformative. I need to remind myself of this. I shouldn't need to, but I do.

I can point to those in the classroom who share my expectations. They know what success looks like and they have the means to work toward the goal. They are more or less motivated. I don't want to let them down. I want to support and challenge them.

I am still nervous, though. I have set up the environment. I have laid out my expectations. I have planned out my lessons, and I have planned regular opportunities to scaffold the learning for the apprentices that are before me. I feel that my teaching will be engaging. Not just fun ... The learning will be engaging and the discussions will be engaging. I tell myself this, but there is no guarantee. I need to be honest in my reflections and determined in the way I navigate this ship.

Despite being nervous, I am enthusiastic. I am passionate about what I teach, and I know the students can share this passion and find pathways to apply this learning. I care and believe that I can inspire (or, at least persuade) my students of the importance of what they are about to learn. 

I am still nervous, though. Some will need more support than others. Some may even get lost at times. I think I can tap into their knowledge and interests. I think we will both be learning together.  I will make myself available. And I am dedicated to monitoring their learning, reflecting on their growth and intervening when extra support is required. That’s my professional duty. And I really believe that through practice and opportunities, the students take this learning on.

I know there will be those who it will be difficult to reach. There will be some students who are not at school everyday. There will be others who face considerable learning challenging. And there will be others who may need some time to trust or to engage. I do not accept that I will not reach these students. I do accept that I will need to reach beyond the school walls to build partnerships and seek advice.

I will teach with kindness and urgency. I will demonstrate expertise and empathy. I will do my utmost to be of service to the students and the community.

 

Yours sincerely,

 

Anxious Teacher

Wittgenstein and the Elements of Reading

It is not particularly novel to say that reading is a process that involves decoding, meaning making and interpretation (or assessment). It is also quite straightforward to say that this sequence occurs within a context in which factors such as the immediate purpose, expectations and other participants affect how and why one reads. The sequence is represented in the following diagram (with further commentary to follow).

In Wittgensteinian terms, the reader progresses from aspect seeing (decoding) to meaning making (picture theory) to assessing (language games). The reader sees the text, gathers some sense from the text and extracts some meaning from the text as part of overarching conversations and conventions.


Let us imagine that I have a newspaper article in front of me. In order for me to have any hope of understanding the text, I need to take the following into account:

  • I need to be able to decode the language if I am going to have any hope of extracting any meaning from this text;
  • Even if I can decode the text, I will need to be able to extract some sense from the sentences in text, which would involve construing the states of affairs being represented (or referred to) in the text;
  • I will need to be struck by the content of the article, which means I will need to know the significance of what I am reading, of what particular details mean, of why the article was written in the first place, and of the tradition of long  information reporting; and 
  • I will need to be part of the greater conversation ( of the language-game ) of which the text is part.

What if it was not a newspaper article but an economic text? I would be at a loss even though I may have sophisticated decoding skills and robust general comprehension practices. My exclusion from general conversations of economics demonstrates that the above process works just was well in the reverse. That is, if I am aware of the "conversation" to which the text belongs and I understand the intention of the reader-writing exchange, then I am in a better position to know what may and may not be significant in the text, even I may need some help. I may be able to read more strategically and I am also in a better position to clarify ambiguities in the text because I have prior experience and knowledge to call upon when I am stuck by particularly dense or awkward phrasings.

In a teaching sense, certain texts may be more or less within a learning zone of proximal development . We want to be able to facilitate contexts in which students have the time to practice development in each of the four areas:

  • decoding --> moving toward fluency
  • meaning making --> process information to interpret, visualise, draw connections, compare, represent, clarify, etc
  • assessing --> extract significance, apply ideas, understand intentions, respond and react, summarise and synthesise, etc. 
  • participating --> being part of knowledge communities and practices in which it may be necessary to consult a text in order to take part. 

Last but not least ... whenever I see the following quote, I think of the satisfaction when someone has thoroughly comprehended a text:

"Often, when I have had a picture well framed or have hung it in the right surroundings, I have caught myself feeling as proud as if I had painted the picture myself. That is not quite right: not “as proud as if I painted it, but as proud as if I had helped to paint it, as if I had, so to speak, painted a little bit of it. It is as though an exceptionally gifted arranger of grasses should eventually come to think that he had produced at least a tiny blade of grass himself." (Wittgenstein, Culture & Value)

Vision and Determination: Ideal Qualities for Every Teacher and Learner

"Each morning you have to break through the dead rubble afresh so as to reach the living warm seed." (Wittgenstein, Culture & Value)

Talk of best practices, teaching programs, cycles, and progressions can lull the casual observer into believing that programs on their own bring about result. A program's success is only as powerful as the vision and determination of the teacher delivering it and the learning engaging in it. We should not forget that learning is work, that skills and knowledge can and will be forgotten (if not reinforced), and that teachers and learners need to wake up each morning to ponder yesterday and reach for the "living warm seed" of today's and tomorrow's and the next day's learning. Schools (and other forums of learning) may be full of a great many activities (the 'rubble'), but teachers and learners must regularly return to the significance of all the activities (the 'warm living seed') that all the hard work is seeking to attain. 

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Managing a Balanced Approach to Literacy: Part Five

The teacher’s role is to arrange tasks and activities in such a way that students are developing (Verhoeven and Snow, 2001). The teacher - therefore - must be "aware of the learning intentions, [know] when a student is successful in attaining those intentions, [have] sufficient understanding of the students’ prior understanding as he or she comes to the task, and [know] enough about the content to provide meaningful and challenging experiences so that there is ... progressive development”  (Hattie, 2012, pp. 19). The classroom and the whole school should promote "a coherent curriculum [that] helps students ... acquire basic skills as well as the strategies needed to tackle challenging tasks (Newmann, Smith, Allensworth & Bryk, 2001) ... Success builds on success, because as students gain confidence, they are willing to work harder and can more readily learn.” (Au, 2005, pp 175). To work toward this aim "what ... [is] needed is ... a theory of social learning which would indicate what in the environment is available for learning, the conditions of learning, the constraints on subsequent learning, and the major reinforcing processes.” (Bernstein, 1964, pg. 55) 

To contribute toward this aim, Gambrell, Malloy & Mazzoni (2011) identified ten features that comprehensive literacy instruction should include. Seven of the features are summarised in this journal entry. Click Read More below for the full discussion.

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Managing a Balanced Approach to Literacy: Part Four

As raised in the previous journal entries, a balanced literacy pedagogy must

  • focus on building skills;
  • scaffold rich and diverse comprehension;
  • model and support composition as a cognitive and social practice;
  • anchor reading and writing in authentic, real world learning practices; and
  • motivate and inspire learners to become (embody) the role of readers and writers.

The goal is to foster learners with robust language systems who are equipped with the habits of mind for comprehension and composition with an awareness of how literacy serves as a mediating tool in real-world practices. Even though we have identified that literacy development requires explicit instruction on linguistic elements, progressive practice in comprehension and composition, and rich opportunities in authentic reading and writing practices, this does not mean that the instructional dilemma has been resolved.

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Book Tip: Showing and Doing: Wittgenstein as a Pedagogical Philosopher

By Nicholas C. Burbles, Paul Smeyers, and Michael A. Peters.

Burbles, Smeyers and Peters have collected an excellent series of essays which are directly applicable to an educational perspective of Wittgenstein's philosophy. The premise of the book "Showing and Doing" reflects the ways in which individuals are brought into knowledge and practices, including technical as well as ethical domains. The book's chapters probe cognitive aspects of learning (e.g. imagination and concept-constructing) as well as social factors (e.g. communities of practice and apprenticeships).

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Managing a Balanced Approach to Literacy: Part Three

At one stage, I became very relaxed. I felt that I had come to a resolution. If someone walked up to me and asked, ‘what are the core components of literacy?’, I would be able to declare

  • — control
  • — comprehension
  • — practices

 

First, literacy is a notation which requires a significant amount of control over the linguistic system.

 "Just as in writing we learn a particular basic form of letters and then vary it later, so we learn first the stability of things as the norm, which is then subject to alteration." (Wittgenstein, On Certainty #473)

One main tenant of this is as follows, ‘overlearning the basics of decoding reduces the amount of mental effort to read.’ 

"This shape that I see - I want to say - is not simply a shape; it is one of the shapes I know; it is marked out in advance. It is one of those shapes of which I already had a pattern in me." (Wittgenstein, Zettel, #209)

 

Courtesy of Reading Hozisons

As Maryanne Wolf (2008) would say, the more fluent one becomes, the more cognitive space is made for higher order processes in reading (e.g. comprehension). The learner takes time to be able to develop the confidence to extract meaning from the written word.

"A script you can read fluently works on you differently from one that you can write; but not decipher easily. You lock up your thought up in this as though in a casket." (Wittgenstein, Culture & Value)
 

 

Wolf (2008) is quick to remind us that fluency provides the cognitive space for comprehension but this does not guarantee that the learner will make the leap to making meaning independently. Learning to read requires one to develop the habits of the mind that enables the learner to concentrate, visualise, process and get the gist of the text.

A thinker is very much like a draughtsman whose aim it is to represent all the interrelations between things. (Wittgenstein, Culture & Value)

Reading is serious exercise for the brain, and the act of reading is the subject of the imagination and of the will. We must acknowledges that learners need considerable help to paint the pictures that are encoded in the squiggles that appear on the page.

Ask: What result am I aiming at when I tell someone: "Read attentively"? That, e.g. this and that should strike him, and he should be able to give an account of it. (Wittgenstein, Zettel, #91)

 

If we refer to the diagram to the left, we will see the significant range of cognitive activities that a reader must be encouraged to engage in to draw connections, pursues conclusions, and seek clarity.

 

And - indeed - James Paul Gee reminds us that, “After all, we never just read "in general", rather, we always read or write something in some way. We don't read or write newspapers, legal tracts, essays in literary criticism, poetry, or rap songs, and so on and so forth through a nearly endless list, in the same way. Each of these domains has its own rules and requirements.” (Gee, 2003, pg 28). Therefore,  “Even when we want to think about a child learning to read initially, we want to think about what sorts of texts we want the child eventually to be able to read in what sorts of ways. No learner grows up able to read all sorts of texts in all ways.” (Gee, 2003, pg 28)

In these cases, learning to read is embedded in certain practices - the things we do in the great hurly burly of life. "The pupil must want to go on alone in taking language to the world, and that what is said must be worth saying, have a point (warning, informing, amusing, promising, questioning, chastising, counting, insisting, beseeching, and so on) ... If it is part of teaching to undertake to validate these measures of interest, then it would be quite as if teaching must, as it were, undertake to show a reason for speaking at all.” (Cavell, 2005, pg 115) I think of terms like "intention", "expectation", and "purpose".

 “I shall in the future again and again draw your attention to what I shall call language games. There are ways of using signs simpler than those in which we use the signs of our highly complicated everyday language." (quoting Wittgenstein in Monk, 2005, p 69)

 

“Following a rule, making a report, giving an order, and so on, are customs, uses, practices or institutions. They presuppose a human society, and our form of life.” (Phillips, 1977, p 36) .

 “When the boy or grown-up learns what one might call specific technical languages, e.g. the use of charts and diagrams, descriptive geometry, chemical symbolism, etc. he learns more language games ... Here the term ‘language game’ is meant to bring into prominence the fact the speaking of language is part of an activity, or a form of life ...” (Wittgenstein quoted in Phillips, 1977, pp 29 - 31)

It is this concept of language games that brings the final piece of the puzzle: acquiring the literacies (and numeracies) requires an understanding of literacy as part of authentic, real world practices. A balanced pedagogy requires the following: (a) regular, explicit instruction in linguistic features, (b) time spent on strengthening comprehension, and (c) embedding this development in authentic practices so that the learners are developing a repertoire of linguistics practices. 

 

More yet to come ... Zones of Proximal Development and Activity Systems .... 

 

References 

  • Cavell, S. (2005). Philosophy the day after tomorrow. In S. Cavell, Philosophy the day after tomorrow. (pp. 111 - 131). Cambridge, MA: Belknap Press.
  • Gee, J. P. (2003). Opportunity to learn: a language-based perspective on assessment. In Assessment in Education: Principles, Policy and Practice, Vol 10, No. 1, pp 27 - 46
  • Monk, R. (2005). How to read Wittgenstein. London: Granta Books.
  • Phillips, D. (1977). Wittgenstein and scientific knowledge. London: MacMillan Press.
  • Wittgenstein, L. (1967) Zettel. Edited by G.E.M. Anscombe and G.H. von Wright. Berkeley: University of California Press.
  • _____________ (1980). Culture and value. Translated by Peter Winch. Chicago: The University of Chicago Press.
  • _____________ (1969). On Certainty. Edited by G.E.M. Anscombe and G.H. von Wright. Translated by D. Paul and G.E.M. Anscombe. New York: Harper Torchbooks.
  • Wolf, M. (2008). Proust and the squid: the story and science of the reading brain. Cambridge: Icon Books.

Managing a Balanced Approach to Literacy: Part Two

In the previous entry, I suggested that different pedagogical approaches distinguished a skills-based perspective from a usage-based one. Both are required for teaching and learning. In the earlier entry, I alluded to the difference, but I didn't elaborate on this observation.

To recap, a skill-based approach emphasises the ongoing development of language skills, such as phonemic awareness, spelling, sentence construction, reading fluency, vocabulary development and basic comprehension. As a schema, this approach imagines a learner as progressing in a linear development of increasing sophistication. In such a perspective, a teacher is vigilant in monitoring the increasing competency of the learner and the teacher hopes to see his or her student acquire and demonstrate a robust knowledge of language.

On the other hand, a usage-based approach emphasises use, for want of better term. The teacher seeks to present the learner with regular, rich opportunities to read and write in a range of ways, each of which helps the learner to read and write meaningfully.  In such an approach, language knowledge is only one piece of the puzzle. The learner must also assess the situation or text, be guided in reading/writing to suit the situation or text, and develop certain intentions and expectations to guide purpose and comprehension. As a schema, this approach imagines a learner developing a repertoire of writing experiences and a library of his or her reading history. This approach is governed by the age-old saying, "we are what we read?" 

Why do I suggest that there is something of a paradigm shift? Dr Neil Anderson describes one (skill-based) as intensive instruction and the other (usage-based) as extensive instruction. A skill-based approach requires a teacher to be diligent, focused on detail, encouraging, exact and skilled at monitoring and assessing. A usage-based approach requires a teacher who understands the importance of authentic, meaningful literacy; knows how to model and monitor the processes of reading and writing; knows how to establish opportunities so that activities are transformed to memorable events; and can reflect on what students should be able to read and write and why.

usage-based approach would declare, "my students have learned to Tweet. They not only write Tweets, but they are aware of what can be achieved through the use of social media." Meanwhile, a skills-based approach might be skeptical and wonder whether the Twitter skills are contributing to the students language knowledge, which - then - can be tapped into for further development. The usage-based approach may place too great an emphasis on particular forms of communication (but not as aware of the needs for the students to develop general linguistic abilities). At the same time, the skills-based approach needs to be aware of the ways to foster linguistic development through authentic practices.

Similarly, I recently observed a series of writing workshops with fifteen enthusiastic Year 5/6 students. The facilitators of the workshops were definitely deploying a usage-based approach as they conjured a group environment in which students were announcing lines of poetry across the room for the creation of individual and group compositions. Amongst the energy, a student called for my attention and asked. "How do you spell 'splendid'?" I quickly assisted, but I was left to wonder,  'what if I was not called upon? Would that splendid line of poetry exist?' The above example reminds me of the reading experience. How many times have I witnessed exciting reading possibilities stopped in their tracks as the learner struggles to decode the text. 

"A script you can read fluently works on you differently from one that you can write; but not decipher easily. You lock up your thought up in this as though in a casket." (Wittgenstein, Culture & Value)

Learners need both skills and opportunities. There is more yet to explore, but that must wait until another day.

 

More to come ... 

 

Managing a Balanced Approach to Literacy: Part One

There is a concept in physics known as the Heisenberg's Uncertainty Principle. It holds that one can know the velocity of a particle and the position of a particle, but one cannot know both at the same time. In other words, one can know the exact velocity of a particle at a given time but not its exact position at that time. Similarly, one can know the exact position of a particle at a given time but not its exact velocity at that particular moment. 

I am proposing that there is a similar phenomenon - at least, metaphorically - that occurs in the circles of literacy pedagogy, which I will refer to as (drum roll, please) the Parallel Dimensions of Literacy. It holds that a teacher can foster a 'skills-based' literacy pedagogy and a teacher can establish a 'usage-based' literacy pedagogy, however, the teacher cannot use the same theoretical position to describe the two approaches to teaching. One must shift the paradigm as one moves between a focus on form to a focus on meaning. 

I am not suggesting that teachers must be one or the other. In truth, both approaches are required, and the best teachers at all levels are those who are equally equipped to develop and monitor core skills whilst providing rich opportunities for students to read, write, speak and learn in authentic, meaningful contexts. 

One can advocate for a skills approach which adheres to a deep knowledge of linguistic structures and focuses on structure development but which suffers from a decontextualised explanation of meaning that does not adequately address how conventional and cultural forms of meaning affect development. On the other hand, one can establish a rich environment in which learners explore (in reading) and express (in writing) knowledge and social activity, but the pedagogy can be seen to gloss over specific developments in phonology, orthography, morphology, syntax and grammar.

The diagram below (presented by Dr Neil Anderson) labels this contrast as Intensive versus Extensive Literacy Instruction.

 

A Model for Balanced Reading Instruction (Dr. Neil Anderson)