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Also see the free Virtual Algebra Pieces app developed by Dr. Laurie Burton of Western Oregon University. Product pages for each unit include more detailed correlation information. As a result, some PDF functionalities, such as editing, copying, and text search, are not available. Google Tag Manager. Grade level: 4—6. As an introduction to visual thinking, students use manipulatives, mental images, diagrams, and sketches to solve mathematical problems.

Includes masters for transparencies.

Download PDF. Grade level: 5—6. Students explore number concepts from basic operations to greatest common divisors and least common multiples using tile and grid paper. Transparency masters included. Grade level: 1—4. Students use base five and base ten number pieces to model whole number concepts, including place value, grouping linear measure, addition, subtraction, multiplication, and division.

Benjamin Green

Egg cartons, fraction bars, and base ten pieces help students form understandings about fractions and decimals. Grade level: 5—8.


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Geoboards, cubes, and grids are used to explore basic concepts in geometry such as geometric figures, area, perimeter, and volume. Grade level: 6—7.

The Mind's Eye (episode) | Memory Alpha | FANDOM powered by Wikia

And ironically, studying people like me is helping to reveal a lot about how our brains process the things we see around us. To begin, stare at this shape until you can remember it. Then scroll down and find three similar objects. Which ones are rotated versions of this shape, and which are not? In , Francis Galton conducted an experiment in which people had to imagine themselves sitting at their breakfast table, and to rate the illumination, definition and colouring of the table and the objects on it. But a few individuals drew a total blank. It asks people to imagine various scenes and rate the clarity of the mental picture.

Surveys show that most people have fairly vivid mental imagery; only 2 to 3 per cent report a completely image-free mind.

in your mind’s eye

For a long time, no one gave much thought to what caused this. We have a good idea how creating a mental image usually works. When you see a real object, the information captured by your eyes and fed to the brain activates a pattern of neurons unique to that object: a chair has one distinct pattern, a table another. MRI brain scans show that when you imagine a picture of that object, the same neural pattern lights up, just slightly less strongly than when you are actually seeing it.

The visual areas towards the back of his brain lit up in distinctive patterns as expected. But then came an unexpected finding.

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He also aced other tests, such as imagining standing in his own home and counting its windows. Soon after Zeman published his results, he heard from another 21 people who said they had this condition, which he called aphantasia. However, unlike MX, they claimed to have had it from birth. Take the window-counting test. Venter says it is the same for him. He says visual imagery is not constructed in just one way in the brain. There are separate circuits for things like shape, colour and spatial relationships, among much else.

It seems as if not all my circuits are disabled. It almost felt as if I was drawing the letter, I said. Kosslyn thinks the drawing sensation gives us a clue as to how aphantasics deal with apparently pictorial information.


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He suggests that to complete these tasks I am piggybacking on neurons involved in controlling physical movements rather than using the visual brain circuitry. Kosslyn once had a patient who had a stroke that damaged the visual areas of her brain and left her blind. She too could still complete what might be considered visual tasks.

When Kosslyn asked her to imagine the letters of the alphabet one at a time and tell him whether they had any curved lines, she could do it perfectly. Zeman agrees this might be how some aphantasics do it.

Math and the Mind's Eye

Zeman has evidence that points to this. Then there is Venter, who sees a connection between his aphantasia and his scientific achievements. MX provided more concrete evidence of the unique skills of people who have aphantasia. When Zeman first tested him, he gave him a classic test of proficiency with mental pictures. The challenge was to work out which images are the same as a guide image, only rotated, and which are not see diagram. The greater the rotation , the longer it takes most people to perform the mental gymnastics and work out if there is a match.

The theory goes that people rotate a mental image in their heads, and the more they have to manipulate it, the longer it takes to solve the task. Zeman reckons we all use different circuits to some extent.