Leverage Four Dimensions of Knowledge

How deeply would you like your students to understand the world around them. Just knowing something is not enough.

Gaining knowledge is extremely complex and in this article, I divide it into four dimensions that build on each other.

Clearly when we have learnt something, we know it. But how do we know it? Do we know it as an isolated single fact? Do we know it as connected to other related information? Can we use and apply what we know? And, can we communicate what we know to others?

These questions indicate to me that there are four dimensions to learning:

-Know

-Connect

-Mobilise

-Communicate

Let's have a look at these in detail.

Know

Children come to know something through several steps. Even before they have language, they learn through their senses. They notice patterns in what they are sensing and apply meaning to their experience. An example is infants 'knowing' they will be fed when they hear a parent enter the room shaking their feeding bottle. A combination of a sensation with meaning is called perception and it is an early form of knowing.

As the child grows, they are able to visualise and then label the persons, objects and occurrences around them. Mental images are the immediate way children begin to represent the real world in their minds. It moves them from reliance on the concrete 'here and now' to contemplate the world in the abstract. Children learn to picture things in their minds and they learn to name them. This development of language is very powerful. But we want children to do more than know what something is. We want them to connect their knowledge to everything else.

Having the facts, knowing what something is, is important knowledge. But it is static. Very often, in early years, and indeed, other educational settings, all an educator is asking for is recognition.

?‘What shape is this?’

‘A square.’

‘Great answer.’

This ‘great answer’ is only the beginning!

I love the way da Vinci frames this idea in his statement that ‘everything connects to everything else’.

Encourage students to make connections

Thinking is habitual. We get used to doing it in a particular way. If we want children to spontaneously connect the dots between different pieces of information, to put it in a broader context, we must encourage them to do it regularly so they lay down a neural pathway to do it. We want connecting to become habitual. We want them to have a neural superhighway for connecting stuff.

Connect

There are many ways to connect knowledge. And in this section, we'll focus on internal and external connections using two of the most crucial thinking skills - comparison and categorisation.

Perhaps the most logical place to start is to connect something to itself – internal connections.

Whole and parts

Beyond recognition, knowledge becomes more complex; and we don’t have to go too far to explore this complexity. We can start by simply unpacking the whole and parts of a single entity. An entity is something with an individual and specific existence. It has boundaries. In this case, let’s again use the square mentioned earlier. If we extend thinking past recognition, we can unpack the features of a square. Four equal straight sides, four 90° corners and two sets of parallel lines. (And there are MANY more features of a square.)

As you can see, the minute we start to unpack the whole and parts of a single thing, we are already connecting. We understand one thing in light of another.

Comparison

From doing a whole and parts analysis of an individual entity, we move on to comparing one thing to other things. Students benefit when they learn to do a structured comparison. It makes sense, at first, to compare what is the same or similar about the things we are focusing on. Then later explore what is different.

Initially, the square may be compared to a rectangle. They have several similarities.

When we connect ideas, we understand the features of each individual thing; then we focus on the similarities and differences in those features in something else. With regards to the rectangle and the square, they are similar in all except one feature. The square has four sides of the same length. The rectangle has two sets of two equal sides and each pair can differ in length.

Comparison is not so much a single thinking skill as it is a compact battery of individual skills. In general, we have a focus entity A and a target entity B. We observe the focus and target entities in detail, have a goal for the comparison, determine the criteria for comparison, discard what is irrelevant, and come to a conclusion about the comparison process (Feuerstein et al. 1980).

Comparison makes thinking more efficient.

So, what can comparison relate to? Comparison denotes how things are equivalent, similar or different, by size, distance, volume, height, form, position, weight, orientation, function, age, effort, complexity, beauty, value, temperature … capacity to annoy you?

When comparing two of their friends, children select specific criteria rather than doing a hazy comparison. They compare height, hair colour, loyalty, personality and many other features. We call this ability comparing apples with apples. This kind of targeted thinking and comparing is a very transferable skill.

A further fundamental aspect of comparison is to keep track of what remains the same and what has changed or transformed. For example, if six oranges have been cut in quarters, there are 24 pieces, but the fact remains that all the parts originate from six oranges. This is the conservation of constancy – tracking what is the same.

When we match things that are similar, we begin to sort them into groups.

Categorisation/classification

The square and the rectangle belong to the superordinate category: two-dimensional linear shapes because they are composed of straight lines and they enclose an area. Categorisation and classification do the job of being umbrella words for elements that belong together. Dedre Gentner, a foremost language researcher, has demonstrated that comparison processes are central in children’s learning of relational knowledge in categories (Gentner 2005).

You will no doubt see how this brings order and organisation to our knowledge. It has been doing so since time immemorial. For instance, in the discipline of biology, animals and plants have long been classified into different species.

It is important to remember that depending on the feature that is the focus, a single entity can belong to more than one category. A red circle can belong to a colour category and shape category. This is the basis of Venn diagrams. A person may be a sibling and a spouse.

Categorisation has two parts: the superordinate category and the elements. Let us say that a child is out in the rain. Someone says, ‘It’s wet weather today,’ which gives us some information.

We could just park that.

But, if the person says, do you remember the other day when it hailed? That was really stormy weather! What do you think hail is made of?

The child might respond: ‘It was made of ice and I know ice is made of water! It made my hands freezing!’

The companion asks: ‘And what is rain made of?’

‘Water.’

‘Yep, and is there any other weather where water is important?’

The child is building up a repertoire of knowledge about weather. The superordinate concept starts to inform the elements, and the elements make the superordinate category clearer too. This is a two-way mechanism for consolidating meaning and information. When they encounter snow, sleet, drizzle, mizzle, mist or fog, they might have a better understanding about weather; and each of these unique kinds of weather. Categories are a way of generalising knowledge. Going from the specific and particular to the universal. The universal is good for transfer.

Knowing and connecting as static knowledge

So far in this discussion we see the connection of information, but we are still in an area of static knowledge. We have information about single entities and how they are the same or different from others. We can see the relationships between them. The knowledge is not yet mobilised.

But don’t underestimate the immense value of this knowledge. If we don’t know exactly what criteria, attributes or features things have, and how they are the same or different from one another, the concepts won’t be consolidated enough to mobilise them!

Mobilise

As we have seen, connected knowledge, even if it is static, is extremely important. But knowing and connecting knowledge are different from mobilising knowledge.

When we mobilise knowledge, we apply it to achieve a goal. For example, making a decision is mobilising knowledge, because we are evaluating something and projecting the consequences of a course of action.

How do children mobilise knowledge?

A young child usually knows the colours, blue, red and yellow. He or she connects that shades of blue are similar in colour to the primary colour blue; that blue is different from yellow; and that all three are colours. The child mobilises the knowledge when something is done with it.

Children might sort the colours into groups. For instance, this often happens when children are playing with blocks and other loose parts. They use all the blue wishing stones in one area, all the green in another and all the yellow somewhere else. They might have the blue stones to represent water, and the green ones, grass.

Once they learn that you can create secondary colours by mixing the primary colours, they activate the knowledge at the painting easel as they try to get the exact colour orange to paint marigolds. They might even add white to lighten their colours.

At the primary level, students know the addition and subtraction symbols in maths, and apply their knowledge when they use the symbols to solve equations.

They understand what a magnet is, and they use one to move a puppet they have designed across a board with the magnet underneath and out of view.

Mobilisation is the active use of knowledge

I will unpack this further to explain the two main kinds of mobilisation. The first kind, closed-ended mobilisation, has a predictable outcome, while the second is open-ended. For knowledge to be mobilised, several elements need to be activated and work together to achieve a goal

?Predictable or closed-ended mobilisation

Predictable mobilisation is when we use information towards a known goal. This is usually when specific information needs to be mastered and used during application tasks. Once a child has learned a new idea or unit of work, you might provide exercises, or arrange materials to achieve a task. Children learn about balance, and they learn how to make things balance. Solving maths problems, using heat to melt ice, using a plan to write an essay. In all these scenarios, knowledge is mobilised, but we know what we are trying to achieve. If we are doing a jigsaw puzzle, or solving a crossword, we need to activate several kinds of knowledge, but we know where we are going with it.

Problem-solving with a predictable outcome is not necessarily easy. It can be anything from simple to extraordinarily complex.

Like comparison, problem-solving is also a compact battery of sub-skills. First and foremost, we have to define the problem, then we harness or develop a procedure for solving it. We gather all the pieces of information; we plan and then we manipulate the parts or steps to achieve the end result. We need to prioritise the steps into a sequential order. We go through the procedure and reach a solution or conclusion.

This is more than connecting knowledge, it is using it as a vehicle to get to a new product or destination.

In some tasks, the sequence of the steps is more important than in others. You can’t put a cake into an oven until the batter is mixed. But you might assemble a model aeroplane in several non-sequential steps towards the concluding step. Sometimes the steps are reversible; I can undo a jigsaw puzzle but I can’t un-bake a cake. (Actually, I struggle to even bake a cake!)

An example here might help as we move from predictable to open-ended mobilisation. As a primary school teacher, you will have been teaching addition, subtraction and possibly the beginnings of multiplication and division.

Predictable mobilisation has you develop 12 problems for your students using the operations that have just been covered.

Next, to ramp up the challenge, and use an open-ended mobilisation, you set a challenge to find 17 ways that 17 is the answer. This problem is so widely opened, that you wouldn’t possibly be able to predict everything your students come up with. Some might stick to addition and just add up different numbers. Others might use a combination of all the operations. If you are lucky, some of them will bring in knowledge that you haven’t taught yet, and surprise everyone. Open-ended mobilisation is the bridge to creativity.

Open-ended mobilisation

There are many times in life when we act with no precise or known outcome, harnessing our current state of knowledge and using our best assessment to project or imagine what might eventuate. This kind of mobilisation can go in more than one direction, with different possible outcomes. But we still need a process to activate our intention.

Like problem-solving, in open-ended mobilisation, we will have some goal in mind. Usually, we visualise or imagine what we are trying to solve or achieve. Even if we are just feeling our way, like selecting a fabric, we monitor what we are feeling to make a decision. We use our experience to formulate a process. We use thinking skills like hypothesising, imagining, modelling, evaluating and creating. Hypothesising is if…then thinking. As an educator, you would like children to hypothesise. When they don’t know the exact answer – it is something to be verified or discovered. Most scientific investigation is based on hypothetical thinking.

It is not an accident that this kind of thinking is seen as high order thinking and is usually at the top of any knowledge taxonomy. This includes the well-known and enduring Benjamin Bloom’s taxonomy (Guskey 2001), the revised Bloom’s taxonomy (Eds. Anderson et al. 2001) and the work of John Biggs and Kevin Collis on Solo Taxonomy (Biggs 2016). In Biggs and Collis’ work, this high order inventiveness is called the extended abstract.

The Nobel nominee, and cognitive psychologist, Reuven Feuerstein also created a comprehensive taxonomy of 28 cognitive functions categorised under input, elaboration and output (Feuerstein et al. 1980).

We know automatically, I think, that primary school children will use high order mobilised thinking. But you might ask, ‘Do preschool children do this?’

When I was teaching we organised a drama incursion about a fairy who needed her wings mended. The incursion was based on a playground conversation I had with a child during outdoor play, which later developed into a research project with the group.

I was sitting on a bench and a child came and stood directly in front of me, eye to eye. (This is an object lesson in itself. I don’t think she would have done it if I was standing at that time.) She said, ‘Mrs Wriggler (translation: Kriegler, and, yes, we did use the formal surnames!), I was thinking about making some wings. I was imagining my sewing machine … and my wings will have some web patterns on them’. Then she was quiet for a minute, looking at my upper body and shoulders, and continued: ‘I can’t lend you them.’ Quiet contemplation …, ‘But, I can make you some. I will need a much bigger sewing machine’. Then she turned and skipped off on her tiptoes, fluttering her arms and humming to herself.

Astounding. Not only had she combined and mobilised several sources of information about how to make wings, but she had calibrated what she would have to do to adjust her project to accommodate my dimensions! She had mentally compared the size, shape and functionality of sewing machines, to compare focus A and target B entities; she and me. She had perceived a problem, used all the pieces of information at her disposal, applied logical reasoning and hypothesised that a bigger sewing machine was just the ticket!

Later that day my co-teacher and I asked her to explain her ideas to her peers in a group meeting. We asked whether she would like to try and make some wings the following day. She thought that was a grand idea. Other children got excited – and it launched a project about wings of so many different kinds. Birds, butterflies, fairies, dragons; and the mechanical wings for planes and rockets. Her wings stretched into zoology, fantasy, engineering and science.

Mobilised, high order thinking is definitely at home in the kindergarten.

Linking back to agency

After the discussion in these first three sections of the article, a predictable conclusion might be that you see the mobilisation of knowledge as much more important than static knowledge. In the last decade or so, there has been much written and discussed about content knowledge not being that important, and that the emphasis should be on the process. You will also hear people say that the process is more important than the product. I am a great believer in process. But I’m also a great believer in content and in product.

At the 12th International Conference of Thinking (ICOT) in Melbourne in 2005 (Curriculum & Leadership Journal Website 2005), I was excited to attend an address by the global expert on creativity, Edward de Bono. He raised the point about how educators value content versus process. He said that content was highly necessary in creativity. When you are creating, you consciously – or in a wonderful unconscious aha moment – put together two disparate elements in a new relationship. A new idea, solution, humorous comment, or illumination occurs. He gave to indicate that the more children know, the more likely they are to be able to generate creative ideas. De Bono calls traditional knowledge ‘vertical knowledge’, which he sees as ‘effective but incomplete’ and which needs to be supplemented with the ‘generative qualities of creative thinking’. He states, ‘there is no antagonism between the two sorts of thinking. Both are necessary. Vertical thinking is immensely useful but one needs to enhance its usefulness by adding creativity and tempering its rigidity’ (De Bono 1998).

From De Bono’s statements and the discussion above, we can see that there is a close relationship between static and mobilised knowledge: they fuel each other. When we know and use information, we gain experience and skills. We reach a new platform. From that new launching point we can take on a more complex challenge. But we can’t go from zero to full throttle without fuel. When we say that we need to offer children open-ended activities in order not to impinge on their creativity, we should also say, don’t put them in that situation without the knowledge or process required for them to embrace and enjoy the challenge. Sir Ken Robinson considered the two in this way: ‘Imagination allows us to think of things that aren’t real or around us at any given time, creativity allows us to do something meaningful with our imaginations’ (Robinson & Aronica 2010).

In honour of the now late, Sir Ken’s comments, how do you use your imagination and creativity?

Communicate

Communication is multimodal

To some it might seem strange to list communication as one of four separate headings about knowledge. But it is a unique kind of knowledge. It is the means to encode and decode information. It is the package, not the substance. The goal of all our efforts in education is that students will be able to express what they have learned and what they know, think, feel and imagine.

Communication can be broadly categorised into two domains: verbal and non-verbal. Verbal communication includes oral language, reading and writing. Non-verbal communication includes all body language and gesture, and the expression of ideas through media, movement and materials.

Each type of communication has its own structure, alphabet and vocabulary. Simply put, for music it is the composition, the melody and the notes. For dance it is the form, the choreography and the steps. Whether it is spoken language, painting, movement, sculpture, music or dance, there are central conventions and elements we learn to recognise and respond to in order to understand what is being communicated. The systems for communicating knowledge are separate from knowledge. They are the means to encode and decode knowledge to share it.

If you are conversant with the internationally renowned educational philosophy from Reggio Emilia in northern Italy, you will know that Loris Malaguzzi (the progenitor of the philosophy), saw children as having a hundred languages for expressing themselves.

The child

is made of one hundred.

The child has a hundred languages

a hundred hands

a hundred thoughts

a hundred ways of thinking …

The poem emphasises the multi-modal nature of communication. Communication is internal, in the mind and the emotions; and external, expressed with the voice and the body. The educators in Reggio Emilia talk about ‘the expressive, the communicative and the cognitive languages’.

I believe this is the perfect way to talk about communication. It emphasises the infinite ability of the human mind and body to create forms of expression that enable us to formulate and share our experience and our understanding of the world.

Children express their knowledge using ‘words, movement, drawing, painting, building, sculpture, shadow play, collage, dramatic play, or music to name a few’ (Edwards, Gandini, & Foreman 1998).

In the early years, the expressive languages should not be thought of as belonging to the curriculum area of art. Rather, this expression, using media, tools and materials, is the child’s vehicle for engaging with the world to develop understanding of what it is and how it works.

As educators we talk about developing students’ literacy which usually refers to verbal communication (speaking, reading and writing). But children can become literate in all modes of communication.

There is great diversity in the modes we use to communicate information and meaning: concrete manipulative, photographic, pictorial, graphic, tabular, schematic, symbolic, verbal written, verbal spoken, gestural, postural, locomotor and digital. You are likely to add even more. Students thrive when they learn to decode and encode the structure and elements of each.

For example, the tabular format is highly underestimated. Knowledge of what a column is and what a row is, how the flow of the communication goes from left to right and from the top to the bottom, is assumed, not often overtly explained and understood. It is pivotal for understanding x and y axes later in maths. (Of course, these directions for tables are not the same in all languages.) There are also conventions when interpreting pictures in books, for instance what is above a character is usually interpreted as being spatially behind it. Speech bubbles and thinking bubbles are different.

Decoding and encoding modes of communication

In general, decoding of information is arrived at first. Young children’s language learning is exponential. Most often, their receptive language is much stronger than their expressive language. It is important to scaffold and strengthen the progress from receptive to expressive language. There are multiple ways we can achieve this, and they will be explored in detail soon.

If you are yawning as a primary teacher at this point, (I see you!), let me say that this is also true of older children when they are learning new things. It takes a child about 40 repetitions of a word in context before they have genuinely consolidated it. So, even with older students, we need to be aware of developing solid vocabulary, that ensures children not only understand it but can activate and articulate it with the appropriate meaning in the correct context. There is a big divide between receptive understanding and auto-expression of that understanding. Expressive language does not only operate in conversation with others, but is also a stepping stone to children’s self-talk, or what we call interior dialogue. Self-talk is a vital component in thinking and learning. Where do you do most of your thinking, planning and problem-solving? (And I’m not talking about in the car or in the shower!)

When children articulate their knowledge, they are encoding. This is a higher level of skill than decoding. They have to come up with and activate the words themselves. This activation of recall is a recognised way that memory is enhanced (Buzan 2010).

A similar gap in skills occurs when children are learning to write. In the same way that receptive language is more advanced than expressive in young children, so too there is a huge gap between what an early primary student can tell you and what they can communicate in their writing. If we insist that students write down their ideas, and we don’t also give them the opportunity to communicate their knowledge orally, or in non-verbal modalities, we could miss out on about 80% of what they really know or think. So, as we are introducing children to a new mode of communication, it is good practice to allow them to continue using the one they already have a sophisticated grasp of so that their expression is maximised.

Once students learn the structure, vocabulary and alphabet of different modes, they are in a position to use the rules, or break the rules, to generate unique and creative products. Later we will explore the excellent information on the top-level structures of language as elaborated by Benjamin Bartlett (Bartlett 2003).

We want our student to know, connect, mobilise and communicate.

Being aware of all four dimensions of knowledge will help us to take students through them so they go way beyond just knowing something but having a full understanding they can communicate to others.

This article is based an excerpt from my book Edu-Chameleon - Leverage 7 Dynamic Learning Zones to Enhance Young Children's Concept-Based Understanding.

If you find value in this article, please share it with your colleagues!

?Lili-Ann Kriegler (B. A Hons, H. Dip. Ed, M.Ed.) is a Melbourne-based education consultant and award-winning author. Lili-Ann’s primary specialisations are in early childhood education (birth-9 years), leadership and optimising human thinking and cognition.?Lili-Ann is a child, parent and family advocate who believes education is a transformative force for humanity.?Her current part-time role is as an education consultant at Independent Schools Victoria and she runs her own consultancy, Kriegler-Education. Find out more at?https://kriegler-education.com . Lili-Ann’s book, Edu-Chameleon explains in detail seven dynamic ways to present content in the classroom and is easily purchased via her website.