Week 2 Math 2 2023

Week 2

Lesson 1

Today we will:

Learn about the human spatial skills of Navigation, Tool making and Visualization

Review some research results regarding the development of spatial skills.

Let's Build it !

Spatial Thinking is the type of thinking we use to compare these two shapes. Are they identical? Are they different or simply oriented differently

What do you think?

This is a classic mental rotation test – one measure of visuospatial ability. Another spatial intelligence test presents a figure made of blocks, and asks the test taker to create an exact copy.

Why studying Spatial Thinking?

keep this question in mind so that we can answer it later

What skills are involved in spatial thinking?

Skill 1: Spatial Visualization

Visualization is a well-defined component skill within general intelligence that has an important role in spatial thinking.

Spatial visualization is a specific type of thinking skill that involves using our imagination to “generate, retain, retrieve, and transform well-structured visual images” (Lohman, 1996, p. 98), sometimes referred to as thinking with the “mind’s eye.” The discovery of the structure of DNA

The invention of the motor

The theory of relativity

are all creations borned thanks to spatial visualization.

Visualizing means creating mental images

Activity: Work in Pairs

Your friend can't see it!!

Use 5 pieces of a Tangram to create a shape. Show it to your friend only for 3 seconds, then cover it. Your friend needs to copy the same shape with her Tangram. Swop.

Can you represent these shapes?

Creating and Using Mental Representations

We can create mental images from visual experiences.

For example, think of an apple....

The image of the apple, comes easily from the visual experience of it.

We can create mental images from non visual experiences too.

People are versatile in their ability to generate and use images. They can call to mind the physical appearance of static objects or dynamic events they have directly experienced through vision, audition, and touch (Kosslyn and Koenig, 1992). They can generate spatial images from nonspatial forms of input such as reading text (Franklin and Tversky, 1990), listening to conversation, or ideas they have imagined on their own (Finke, 1989). Although imagery often results from visual input and is often described in visual terms, spatial images are not necessarily visual; they are accessible to persons who lack life experience seeing (de-Beni and Cornoldi, 1988; Cornoldi and Vecchi, 2003; Farah, 1989).

National Research Council. 2006. Learning to Think Spatially. Washington, DC: The National Academies Press.

Skill 2 : Navigation

How can we move successfully around the world?

Being able to move around the world allow animals to search for food, water and mates. But animals that move need to keep track of where they are, and must be able to return to a home base. They have different special capacities to do that (fine vision or hearing, sense the Earth's magnertic field)

(Souman, Frissen , Sreenivasa & Ernst, 2009)

Humans do not fly, lack keen chemical senses, and are not able to sense the earth’s magnetic field. Indeed, in unfamiliar environments they tend to walk in circles.

(Souman, Frissen , Sreenivasa & Ernst, 2009)

But not every thing is lost; we have the ability to represent the spatial environment and to navigate in it using our excellent symbolic ability that animals don't have.

Describe Space with language

Or invent systems of navigation

We can draw maps

"A short distance from the bustle of the city centre, you'll find grass-scented serenity within the North Wessex Downs Area of Outstanding Natural Beauty. Alternatively, to the west of Oxford is the Cotswolds, home to some of the quaintest traditional villages in Britain. This picturesque region packed with honey-coloured stone houses and market towns covers more than 800 square miles."

Reasoning Procecess Related to Navigation

Examples

Considering moving elements

Analyzing :

• direction of movement,
• manner of motion,
• speed or acceleration,
• intersection or collision.

Considering Static Attributes

• distinguishing figures from ground;
• recognizing patterns;
• evaluating and comparing size;

• determining orientation
• assessing distance
• determining and comparing location, direction and other atrtributes

Considering changes:

• changing perspective (reference frame),
• changing orientation (mental rotation),
• transforming shapes,
• changing size,

• zooming in or out,

We can say Navigation has to do with:

Location

Position

Trajectory

Orientation

Skill 3 : Tool Making

How can we manipulate objects in our world to make and use the tools which are a vital part of our adaptation , specialization and survival?

Tool making involves:a) Representation of the shape and internal structure of objects (considered independently of their position with respect to other objects or a frame of reference) b) The ability to transform that representation by imagining the object’s structure being rotated, sliced through, or changed by folding, melting, or by the application of a force (e.g., hammering). This skill is the basis of tool making.

Trasform

Shape

Colour

Size

Tool Making is still relevant in daily life

Or puzzle out how best to pack things into defined spaces..

We still need to put together furniture (“some assembly required")

Reasoning Procecess Related to Tool Making

Examples

Considering Static Attributes

• distinguishing figures from ground;
• recognizing patterns;
• evaluating and comparing size;
• discerning and comparing texture;
• recognizing and comparing color
• comparing shape
• determining orientation
• assessing distance

Considering changes:

• changing perspective (reference frame),
• changing orientation (mental rotation),
• transforming shapes,
• changing size,
• moving wholes,
• zooming in or out,

Processing Spatial Information

GMST

Kosslyn (1978) distinguished four stages in the cognitive processing of spatial information:

1. Generating a representation, either by recalling an object or event from long-term memory or by creating an image from words or ideas; 2. Maintaining a representation in working memory in order to use it for reasoning or problem solving; 3. Scanning a representation that is maintained in working memory, in order to focus attention on some of its parts; 4. Transforming a representation, for example, by rotating it to a new viewing perspective, shrinking it, or imagining its shape if it were transformed by being folded or compressed.

What affects the effectiveness of processing spatial information?

Practice

Familiarity

Practice does make it easier to create and to transform spatial representations. People can carry out these cognitive processess much faster with practice

People find it more difficult to generate spatial representations and to mentally rotate representations of novel and complex objects than of familiar and simple objects.

ok. Spatial thinking is important, but.... Can we teach it?

Yes!

Drag the triangle

Spatial Thinking in Small Children

Children younger than about 7 years of age do not tend to use imagery strategically to help them learn new information, but even pre-school age children can generate and process images based on perceptual input. Kosslyn et al. (1990) showed that children in kindergarten can look at a visual stimulus and then generate an image of it later in order to make decisions about what they saw. Ray and Rieser (2003) showed that children 3–4 years of age can listen to short stories and generate spatial representations of the story in order to judge the relative locations of objects described in the story.

Some Facts

1. Gender: The Biological Difference?

• Numerous studies report that males possess superior mental rotation skills.
• There is also evidence that spatial ability is linked with the amount of testosterone a fetus encounters in the womb (Puts et al 2007; Pintzka et al 2015).

• In an experiment on 42 women, researchers found they could temporarily boost mental rotation skills by giving volunteers a single, small dose of testosterone (Pintzka et al 2015).

2. The Training Effect

Study by Rebecca Wright and her colleagues (2008). The sample: 38 young adults at Harvard – 50% of whom were female

The test: two tasks: mental rotation, and a mental paper-folding task, participants had to mentally “fold up” a paper template and predict its appearance.

At baseline: there were sex differences. Women made more errors on the spatial rotation task. Men made more errors on the mental paper-folding task.

After 21 days of daily training (practicing each type of task), Everybody got better. And the error rates converged. Men and women were now equally good at both spatial tasks.

Results

Similar results have been reported in other experiments where adults were randomly assigned to practice spatial skills by playing certain action video games. . Overall, women made the biggest gains, and they maintained them 5 months later (Feng et al 2008).

Conclusions

We have good evidence that practice boosts spatial skills, which may explain why construction play is linked with childhood spatial ability.

We also have evidence spatial thinking affects the achievements in mathematics, science and technology

Finally, we have evidence that spatial thinking is part of many of our daily activities.

Week 2

Lesson 2

Today we will:

Answer worksheet "Learning to think spatially"

Discuss the role of language in the development of spatial skills in children

Evaluate the role of spatial representations in the process of learning.

How to teach spatial thinking in schools

Which of the boxes comes next in the sequence?

Task:

Read Chapter 4

National Research Council. 2006. Learning to Think Spatially. Washington, DC: The National Academies Press.

Answer questions from Worksheet Learning to Think Spatially

The Role of Spatial Language

It appears that children also benefit from conversation.

People often find it easier to think about a concept when they have a word for it. Can you think without words? And of course kids often pay closer attention to something if we engage them in a discussion about it. So can we help kids by engaging them in meaningful conversations about spatial relationships? Studies suggest we can.

The Role of Spatial Language

It appears that children also benefit from conversation.

People often find it easier to think about a concept when they have a word for it. Can you think without words? And of course kids often pay closer attention to something if we engage them in a discussion about it. So can we help kids by engaging them in meaningful conversations about spatial relationships? Studies suggest we can.

First, there are clear links between spatial intelligence and spatial vocabulary. In one study, preschoolers who knew more spatial words (like between, above, below, and near) were better at reproducing spatial designs with blocks (Verdine et al 2014). Spatial terms help kids think in 3-D.

How spatial language relates to the development of spatial skills

Let's watch these two videos

What Spatial Languange should we use with children?

Researchers have found several categories of spacial language:

Shape Terms

Names of 2D and 3D shapes

Spatial Location and Directions

Words that describe the relative position of objects, people and points in space. Between, into, forward, over, behind, near, far...

Spatial Features

Words describing features and properties of 2D and 3D objects, spaces, and people. Curvy, edge, side, line, corner, straight, flat...

Dimensional Adjectives

Big, little, short, tall, tiny, huge....

The role of Spatial Representations in learning, problem solving and transfer

Generating schematic-spatial representations of information requires learners to generate their own ideas about general principles and about relationships that cut across different specific problems.

Spatial representations are powerful cognitive tools that can enhance learning and thinking. Three supporting evidence of this are:

Second, generating images of “old” information that has already been learned and of the situations in which it was learned can power- fully aid in recalling the information at later times.

Third, some problems are more readily solved using spatial representations, in other cases, trying to use spatial representations can interfere with problem solving.

. First, creating spatial representations is a powerful way to encode new information that one wishes to recall at a later time.

Generating schematic-spatial representations of information requires learners to generate their own ideas about general principles and about relationships that cut across different specific problems, instruction emphasizing the role of spatial representations should foster transfer to new problems.

Research has proven to be links between instruction and transfer: the role of a) learning general principles b) learning multiple examples.

facilitate learning, transfer and problem solving

A) Learning General Principles

Wertheimer (1959) compared two methods of instructing students to find the area of a parallelogram, one that emphasized structural relationships in parallelograms and one that involved a fixed solution routine (dropping a perpendicular line and applying a formula). On problems that involved finding the area of standard parallelograms that varied in base, height, and the degree to which the corner angles differed from 90 degrees, both groups performed well. On new problems, where the shapes were atypical but applicable to the same solution logic, the method that emphasized understanding structural relationships produced far better transfer

B) Multiple Examples (variation)

The second generalization is that using multiple examples during initial learning and/or varying the conditions of practice also facilitates far transfer. This applies to the benefits of: -Varying the conditions of practice when learning motor skills -the benefits of using multiple examples when teaching students how to solve complex problems -the benefits of varying the outlines of an advanced-organizer text

Activities to develop Spatial Thinking in Children

Developing spatial language

Developing experience with objects to develop spatial skills.

In addition, a growing body of research suggests kids can improve their spatial abilities by engaging in structured block play — the sort of play where children recreate physical structures by following a model or blueprint.

Spatial Orientation Test

Activity: Make a plan of the University Campus. As you go along, use metacognition to be consious of your thinking process

Activity

• Design 2 activities to be used with children, to develop spatial thinking .
• You must upload the report with both activities in Tareas.

thanks