Dad: Im not angry, Im disappointed.
Sam: Do you want to hear my side of it?
Dad: Sam, how can there be two sides?
Sam: Look, I got every question right on the final and the only reason why Mr. Spangler failed me was cause I didnt write out the solutions.
Dad: Why not?
Sam: I do them in my head.
Dad: Did you tell him that?
Sam: I did. He didnt believe me. He said that if he cant do them in his head, then I must be cheating.
Dad: Well, thats ridiculous! How can he fail you for being smarter than he is?
Sam: Thats what I said.
Dad: You did? Howd he take it?
Sam: He flunked me, remember?

The Day After Tomorrow, Twentieth Century Fox.

Does your child answer math problems accurately and with seeming ease, but seldom, if ever, show the steps taken? Can your child accurately answer complex long division or algebraic equations, but not be able to tell you how the answer was found?

Many students are visual-spatial thinkers. They think in images, not in words. They have powerful right hemispheres, the source of considerable creativity, imagination, multi-dimensional thinking and visualization. Visual-spatial learners are the kids who crave for time with such joys as building, painting, drawing, daydreaming, dancing, music making, and letting their creative imaginations soar. They struggle to find the time or inclination to put their clothes away, maintain some degree of organization, and you can forget altogether about punctuality. They have the most incredible, A-Ha! moments of discovery, invention and problem solving, but the skills of managing a time schedule or showing their work may absolutely elude them. (Please see the quiz at the end of this articleIs Your Child a Visual-Spatial Learner, for more information on how to identify your childs preferred learning style.)

For visual-spatial learners there are few classroom requests more frustrating than, Show your work. Because this type of learner intuitively grasps the big picture rather than taking what would be a painfully slow series of steps to reach a conclusion, the demand to show your work, is nearly an impossible task. Visual-spatial learners (VSLs) very often just see the correct answerand theyre usually right. They cannot tell you how they know, they just know. They cannot show you how they got their answer, they just got it.

In no subject is this a greater problem than in math. Because many teachers are left-hemispheric sequential thinkers, they teach in a step-by-step manner and expect their students to solve math problems in a step-by-step fashion. They also tend to anticipate that their students will be able to demonstrate their work by detailing the steps they took to arrive at their answers. The same is true for textbook developers and those who construct state achievement tests. But, for someone who thinks in pictures and sees the correct solution without ever taking a step, this could result in a devastating outcome. Every day, students are admonished, even accused of cheating, because they are intuitively able to reach accurate solutions to complex math problems but absolutely unable to explain how they got there. Most of the time, just like the character Sam quoted earlier, they lose partial or full credit for their answer because they did not show their work. A mom from Australia recently shared with me that her sons teacher gave only one point for a correct answer, but four points per problem for showing his work, something he was unable to do. He was failing math, yet he had all the correct answers!

At a time when thinking outside the box is a revered ability in the business world, when to be able to find solutions to complex problems is highly regarded (and dont we desperately need answers to todays complex problems?), isnt it time we stop penalizing these students for their innate gifts and begin honoring what comes naturally to them?

Until that day, however

It is quite likely that this new school year will include gifted visual-spatial students sitting in math classes at various levels, being docked credit for accurate answers they cannot support with detailed steps. Nearly every standardized achievement test in the United States deducts credit when the steps are not shown to solve a particular problem. Classrooms have penalized gifted children with weak sequential skills for too long. So, I propose its time we teach visual-spatial learners to fight back! Show your work, doesnt have to mean complete the problem exactly as I, a left-hemispheric, auditory-sequential thinker would. It means, teach me, the left-hemispheric, auditory-sequential thinker, how you did this so I can do it myself. Show me, in the way I learn best (step-by-step) how to do this. When students know the material well enough to teach it, they really know it. If we help our visual-spatial students learn how to explain their answer to someone who does not think in images, then weve succeeded in teaching them to show their work, how to offer the smaller details, and, hopefully, to cease the unfair practice of losing credit on their tests and assignments. In the bargain, weve also taught them to honor that individuals do not all think alike.

While I was homeschooling my children, I found that one of the best tests of whether or not they had truly learned the material we had covered was whether they were able to teach it to someone else. This was true for math, history, geography and a wide range of subjects. Often, my sons were asked to teach their dad whatever new social studies material had been covered that day (which made for great dinner conversation!); or they taught their math-phobic grandmother a new concept they had learned in Algebra. You just cant fake knowing it if you are asked to teach it. The caveat was, and should be for all visual-spatial students, that the demonstration of their knowledge did not have to mirror the way a teacher or textbook presented it. As long as they reached a correct solution, they were given the freedom to use their own methods. There is almost always more than one way to skin a cat!

Until weve created an understanding of different learning styles in the classroom, well have to help our gifted visual-spatial students cope in what traditionally is a predominantly left-hemispheric environment. With the knowledge of how they think and learn best (in images), coupled with the understanding of what their teacher expects from them in order to receive the highest amount of credit possible (demonstrated work), we can help our students succeed. Teaching them to work backwards may help accomplish this.

First, visual-spatial students should be allowed to perfect whatever strategy works for them in solving their math problems. Then, have them test their methods with a calculator to be certain their answers are correct. Once the students have polished their own unique systems, gradually increase the difficulty of the problems so that they can continue to test their methods. When they have consistently answered the problems correctly, using their own strategies, show them how to work in reverse. In other words, they can continue to use their methods (so long as they produce accurate results) to arrive at an answer and then work backwards through the problem to show the details to someone who needs to be shown the steps, or work.

For example, in the long division problem below, lets suppose that the student, using whatever mental or written method this student has created, arrives at a solution and has proven it is correct by double-checking the answer with a calculator.

26 15 ) 390

Now that the answer is known, the student simply works through the solution to show the steps. So the first work to show is 15 x 2. This answer is then written directly under the 39:

26

15 ) 390

30

Next, show the student that auditory-sequential learners cant just hold numbers (or other images, for that matter) in their head as easily as visual-spatials do, so the next work to show is to subtract the 30 from 39 and bring down the next digit:

26

15 ) 390

30

90

The student doesnt need to figure out how many times 15 goes into 90, because he or she already knew (saw) that! It must be 6. But the auditory-sequential thinker will need to be shown, so just write out the last bit of work:

26

15 ) 390

30

90

90

0

While it may seem obvious to the student, the last number showing in any problem such as this must be 0 or the work has not been shown in a manner in which the teacher, or another auditory-sequential learner, can follow.

By working backwards through their math problems, visual-spatial learners can demonstrate the steps of their work so that the auditory-sequential learners they must communicate with (primarily teachers) can give credit for showing work. The teacher may never truly understand how a visual-spatial student arrives at an answer, but the work they are seeking is there. By demonstrating their work in a manner that can be interpreted by sequential thinkers, gifted visual-spatial students can finally begin receiving grades commensurate with their abilities.

Working backwards in other academic areas This logic, of working backwards to provide the steps a teacher is looking for, works in other academic areas, too. Well-organized written reports are often a challenge for visual-spatial students to create. The research involved is not typically a problem as most every gifted student enjoys learning a subject in depth, but the orchestration of ideas into a coherent report can be difficult. Teaching the student to organize mental images will help. The concept of webbing or using specialized software (such as Inspiration or Kidspiration) to get help students get their mental pictures down on paper is a great first step. Webbing is a way of getting all the ideas for a subject on paper, in a visual manner, rather than a sequential way, and then building from those ideas. For example, suppose the assignment is to write a report about a favorite animal. The student is to research the animal and write a detailed two-page report. Because VSLs naturally think about big picture ideas first, a web is often easier to create than a standard outline which starts with small details and builds to a big picture. The first step in creating a web is to have the student brainstorm all the possible related ideas one can think of. No idea is silly or should be thrown out at this stage. The web might look something like this:

In the web above, an outline would be created with the largest circle, Horses, as our main subject. The sub-headings would include breeds, care of and, feeding of with sub-sub-headings as hay, carrots, mustang, palomino, etc. The finished outline might look like this:

I. Horses
A. Feeding of
1. apples
2. hay
3. carrots
B. Breeds
1. mustang
2. palomino
C. Care of
1. riding
2. grooming
D. Racing

Next, have your student watch videos, look up related sites on the Internet, talk to a specialist (perhaps a veterinarian in this case) and read books to gather information on each of the areas necessary for the final report. The student should take notes on everything learned. Such notes might be more useful if written on color-coded index cards. For instance, in our example of a report on horses, green index cards might be used for any information learned about feeding horses, yellow cards for the information learned about various breeds of horse, etc. Keep in mind that notes dont have to be written words. If your child prefers to think in pictures, it may be more meaningful to take notes in pictures. These could be actual drawings of what is learned. For example, the child could draw pictures of what horses eat, rather than writing the words, hay, carrots, and apples.

Finally, have the student gather all of the note cards with the information researched. If the cards are placed in order by color so that all the information about how to care for horses is together and all the information about breeds of horses is together, and so on, then the report can be written directly from these colored note cards. Or, have your child lay the note cards out on a table, or even on the floor, then, starting with the cards that have information about the largest circles of the web, place the cards of information about the smaller circled ideas after each of those. If the student has written all the notes of a similar idea on the same colored note cards, then the cards are easily grouped together with the main idea on top of the pile and all the matching cards underneath. The same is done for each set of colored note cards. Or, the student might actually lay the note cards out and lay a piece of string on top of the cards, going from one idea to the next. (I got this idea from Steve Haas, a visual-spatial teacher himself!) When the cards are collected following the order of the string, the flow of the outline will be complete. The report should come together in an organized manner because the notes were strung together in an organized mannerliterally!

On a first draft, dont ask the student to worry about grammar, spelling or punctuation. The focus at this stage is just to get the mental pictures into words and the words onto paper. Once the rough draft has been created, then the student should go through it looking only for spelling errors. Once any spelling mistakes have been corrected, have the student go through the draft again looking only for punctuation errors. Finally, the report should be reviewed again, looking only for grammatical corrections. Dont insist that your child try to catch everything the first time the rough draft is read throughthere is too much to look for and potentially revise.

The whole process of organizing ones research or thoughts, then creating a polished piece suitable for a grade that is truly commensurate with ones abilities, can be daunting not only for the visual-spatial student, but for the parent as well! At what point should you jump in to offer assistance? Is letting the child dictate the work okay? After just how much head banging is it alright to take over the proofreading function? My recommendation to parents is this: learning should be fun, it should be a passionate exploration into previously unknown realms. When ones learning style gets in the way of that, it can have damaging effects on the end product and the students self-esteem. If the child is in complete distress about the assignment, its time to help out. But a gentle weaning may be in order at some point. After all, you cant be there through the highest levels of your childs educational career. In adult life, the visual-spatial learner will have learned compensation skills, will know that his or her best work may be as part of a team that relies on the individuals right-hemispheric skills over spelling ability or ability to recall math facts, and will likely have another method (calculator, spell-checker, assistant) to attend to those areas in which this learner is weak (organization or time management, for example). The skills of the visual-spatial learner lie elsewhere and will be wisely used and valued much more in adult life than while the learner is in school.

So, while it very much needs to be your childs own work, I see nothing wrong with taking dictation, so long as the typist only types what has been dictated. This would include punctuation, grammar, and challenging spelling words. Then, with a printed draft in hand, a parent might say, On this page there are three spelling errors, two problems with grammar and five missing punctuation items. Can you find them? Make it a sort of scavenger hunt. Often, just reading a passage will help the child to see (by hearing) where the problem is.

Know that this will get easier for your child. Like most things, it just takes practice. Most of what is asked from them in school is left hemispheric in nature: writing, spelling, math facts, reciting dates and names, etc. I liken this to a broken hand. If you are strongly right-handed and you break your right arm, you can learn to write with your left hand. Eventually, you will be able to produce legible writing, and with even more practice, you will be mostly proficient at writing left-handed. But it will never be your best work. It will never be the most efficient way for you to write. This is what we ask of children with strong right hemispheres. Yes, they will be able to compensate and get by, but you will never see their best work and it wont be the most efficient nor effective way for them to learn. Employing techniques that activate and engage the right hemisphere, however, by incorporating color, humor, music, metaphor, patterns, hands-on activities and passing on an understanding of the overall big picture, will always be the most effective way to reach a visual-spatial student. (For more information on teaching and parenting strategies for visual-spatial learners, please visit www.visualspatial.org.)

Auditory-sequential vs. visual-spatial

Just in case youre not sure if you have one of these kids, heres a quiz that includes many of the characteristics of visual-spatial children. If you arent certain about a question, ask your children to answer it! (Or you can have them take the VSL Quiz for Kids from the website, www.visualspatial.org.) Most people who think in words cant possibly imagine that others are capable of thinking in pictures and vice versa. Unless you are also a visual-spatial learner, you may be very surprised to hear about how your kids think, learn and understand the world around them.

The Day After Tomorrow. Directed by Roland Emmerich. Beverly Hills, CA: Twentieth Century Fox, 2004.

Please complete this quiz to find out more about your childs learning style.

Yes No
1. Does your child think mainly in pictures instead of in words?
2. Is your child good at solving puzzles or mazes?
3. Does your child like to build with LEGOsTM, KNexTM, blocks, and other construction materials?
4. Does your child often lose track of time?
5. Does your child know things without being able to explain how or why?
6. Does your child remember how to get to places visited only once?
7. Can your child feel what others are feeling?
8. Does your child remember what is seen and forget what is heard?
9. Does your child solve problems in unusual ways?
10. Does your child have a vivid imagination?
11. Is your child talented in music, dance, art or drama?
12. Can your child visualize objects from different perspectives?
13. Is your child organizationally challenged?
14. Does your child love playing on the computer?
15. Is your child terrible at spelling?
16. Does your child like taking things apart to see how they work?
17. Does your child have at least one visual-spatial parent?

If you answered yes to at least 9 of the above questions, your child is most likely a visual-spatial learner. Copyright held by Alexandra Shires Golon. From Golon, A. S. (2004). Raising Topsy-Turvy Kids: Successfully Parenting Your Visual-Spatial Child. Denver: DeLeon Publishing.