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Concrete to Abstract

Hands-on & concrete activities

Play is the basis of all learning.

Introduction

This page takes a deep dive into the terms: hands-on, concrete, iconic, semi-concrete, symbolic, formal operational, abstract, minds-on, and how they relate to learning and teaching and Jerome Bruner's instructional modes and learning modes.

Resources

 

Pretest for hands-on learning activity

Check the following, that you consider a hands-on concrete learning activity?

▢ Making an analog clock from a paper plate, brass fastener, and two strips of oak tag cut as a minute hand and hour hand.

▢ Using money to count change.

▢ Rolling spheres of different masses down hot wheels ramps.

▢ Using base ten blocks to add double digit numbers.

▢ Cutting out fraction strips.

▢ Pour vinegar onto baking soda

▢ Sorting rocks into categories

▢ Taking apart a flower and drawing the different parts

▢ Looking at one celled organisms in a magnified viewer.

Before we consider how hands-on these are, let's review the concrete or abstract nature of objects, then review definitions of hands-on.

Concrete - abstract model for media

Concrete to abstract model

 

The model shows a continuim of concreteeness and abstractness between real objects as concrete and text as abstract. The placement of the objects between these two extreems will vary depending on how they are constructed. The placement of examples on the model is one example.

The example below suggests how different representations might vary from concrete to abstract for representations of the concept of face.

Face picture to text

Source - Understanding Comics. Scott McCloud. 1993. p48.

The real life person would be the most concrete representation of a face, then a photograph of one, then a drawing, sketch, icon, text, description (what has two eyes a nose and a mouth), and poetic description (Shakespeare) would be the most abstract of these examples. All representations have value depending on the situtation in which they are or will be used.

Therefore, one should consider how different kinds of repesentations, from concrete to abstract, should be selected for a particular situtation so as to select the best to comunicate or present information for the particular learning situation.

Let's consider another way to look at concrete and abstractness.

A real person, photograph, painting, drawing, sketch, and icon.

Concrete to abstract face

Source Understanding Comics. Scott McCloud. 1993. p45.

A real person is a unique representation specific to that person, a photograph might be one person, but could include other look alike people, a drawing might represent a few, thousands, a rough sketch millions,and an icon could represent everyone.

The object or situtation to communicate will guide the selection of media tht can be used to more accurately represent it along with the developmental ability of the person who will try to understand what is being communicated with the type of media and the representation.

Some possible situations are modeled with Bruner's six instructional modes

  1. Experience,
  2. Simulation,
  3. Multimedia,
  4. Single media,
  5. Reading, and
  6. Lecture.

and three learning modes,

  1. Concrete,
  2. Iconic or semi-concrete, and
  3. Symbolic, abstract, or formal operational.

Bruner and many others believe the most effective learning takes place with concrete enactive experiences. Known as hands-on experiences or hands-on learning!

I would add that effective learning starts with concrete enactive experiences and continues with semi-concrete and to formal operational as learners mature and gain experience with different concepts. See Examples of how learners (K-12) represent algebraic proofs that are concrete, semi-concrete, and formal operational for addition of any two odd numbers (ODD + ODD = EVEN) always resulting in an even sum.

Six instructional modes & three learning modes

Instructional modes

 

These models show how ideas can be represented on a continuim from concrete to abstract, and instruction can range from concrete to abstract with examples such as experience, simulation, multimedia, single media, reading, and lecture. Instruction that should begin at a concrete experience level and transition to formal and abstract levels as learners develop and better understand concepts and skills being learned.

What is hands-on?

Hands-on experiences or hands-on learning are experiences that happen with concrete enactive experiences. But what does that mean?

Most everyone agrees an important part of hands-on has to include manipulation of concrete objects that accurately represents the concept to be learned.

That means a hands-on activity should include an experience with a concrete representation of the concept so the learner can conceptualize the concept with the experience. A more meaningful concrete experience helps the learners construct a concept with the concrete representation that has the essense of the concept embedded in the objects being manipulated.

With this in mind hands-on becomes more than an activity., and more than a process, it can be a way of teaching and learning with meaningful representations.

Some conditions that are necessary for an experience to be hands-on:

When we observe learners using a manipulative in a hands-on activity we can literally see how their external representations mirror their internal representation. A great way to assess and infer their conceptualizations more accurately.

Concrete activities have enormous emotional benefits:

I certainly encourage the use of concrete manipulatives, but drawings, or notes that might include symbols are just as important for learners who are concrete as the iconic symbols connect to physical objects and the interactions on them help learners to transition their learning from concret, to iconic, to symbolic and formal operational.

Okay! If your still hanging with us, let's explore the nine activties in th pretest!

Pretest explored

Let's review some considerations for each activity and you can decide the strength of each as being concrete.

Making an analog clock from a paper plate, brass fastener, and two strips of oak tag cut as a minute hand and hour hand.

Considerations:

  • A clock does concretely represent the passage of time, it takes an hour for the hour hand to make one complete circle and it takes 12 hours for the hour hand to make a complete circle.
  • The rotation of the Earth, that time is based on, isn't represented concretely. For example 12 hours, in the spring and fall would represent one-half rotation of Earth or two circles of the hour hand is one Earth rotation for any day.
  • The activity includes construction with manipulation, which many people associate with hands-on and can be semi-concrete operational if learners are considering time is represented by hours and the hours repeat as represented on the clock by the hour hand. Similarly with minutes.
  • A problem for young learners is that the same area or distance each hand on the clock travels, represents different values 1-12 for hours and 0-60 for minutes.

Using money to count change.

Considerations:

  • Coins are concrete representations for their values.
  • Coins are not proportional concret representations of their value. Children have a difficulty because their size is not proportional to their value. Often think dimes are less than pennies and nickels.

Rolling spheres of different masses down hot wheels ramps.

Considerations:

  • Experiencing real objects in real time is concrete.
  • Properties (mass, materials from it is made, ...) can be experienced in real time and their interactions with the ramp.
  • Height and slope of ramp can be experienced in real time and their interactions with the spheres.
  • Interactions can be observed and concretely related to the properties of the ramp and spheres.

Using base ten blocks to add double digit numbers.

Considerations:

  • Experiencing real objects in real time is concrete.
  • Each block proportionally represent a value.
  • The physical movement of the blocks together (join) concretely represents addition.
  • The concept of base ten is represented concretely.

Grid paper, hundred charts if not concrete are deffinelty semi-concrete and most often used in middle grades. They can be drawn on paper with notes, fill4d in grids, photo copies of different shapes and objects, and are best used after learners have many experiences with three dimensional concrete manipulatives. Such as Cuisenaire rods, multi-colored disks, and geometric manipulatives.

Cutting out fraction strips.

Considerations:

  • Experiencing real objects in real time is concrete.
  • Each strip is cut to proportionally represent the fractional value of the designated whole.
  • The concept of fractions is represented concretely.

Pour vinegar onto baking soda

Considerations:

  • Experiencing real objects in real time is concrete.
  • The properties of vinegar is represented concretely.
  • The properties of baking soda is represented concretely.
  • The interation is represented concretely.
  • The new substances are represented concretely.

Sorting rocks into categories

Considerations:

  • Experiencing real objects in real time is concrete.
  • The properties of each rock is represented concretely.

Taking apart a flower and drawing the different parts

Considerations:

  • Experiencing real objects in real time is concrete.
  • The parts of the flower are represented concretely.
  • The properties of each part of the flower is represented concretely.

Looking at one celled organisms in a magnified viewer.

Considerations:

  • Experiencing real objects in real time is concrete.
  • A magnification of the organism is an enlarged view or representation.
  • A magnified view is proprotional.

Summary

Activities and representation that are not concrete are not bad. They are fine for learners that are experienced enough to be able to attend to them and understand what is being communicated. When you are not sure of the background the people you will be communicating with have, it is a good idea to start concretely and continue as appropriate from their as you learn about their abillities.

Obviously formal abstactions can be powerful and are often the goal for many educational outcomes when learners are capable to achieve them.

 

Extension

Is touch math?

Maybe. Is counting hands-on? If it is, then touch math is hands-on. If counting isn't, then touch math isn't.

The worst thing about touch math is once learners begin to use counting as a strategy for solving problems, they will continue to use it. It becomes very difficult to change to something more efficient and they won't until an alternative is found more useful, easier, and comfortable.

However, the problem is, that they become such good counters, that they don't look for something else, or aren't willing to give it a try, without considerable urging!

Touch math is usually used when teachers don't understand better ways to facilitate learner's mathematical understanding and problem solving. See many more efficient ways - in the development of number sense, place value, and operations.

 

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