Let's try a little experiment from reddit...
Imagine a ball on a table. Now, someone walks up to the table, and gives the ball a push. What happens to the ball?
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Next, answer these questions:
What color was the ball?
What gender was the person that pushed the ball?
What did they look like?
What size is the ball? Like a marble, or a baseball, or a basketball, or something else?
What about the table, what shape was it? What is it made of?
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Were you able to quickly answer those questions based on what you previously imagined or did you have to go back and re-imagine the scenario visually? Did you struggle with this?
Many of us use one of two strategies for "imagining" what's going on. We either visualize or conceptualize. If you are a visualizer, you were probably able to easily answer the questions about the ball. Your table may have been a familiar table in your house, or the ball may be been a favorite ball you have. We often use familiar or preferred items for these visualizations. Many of us fall into the "conceptualizer" category though. If you conceptualize, instead of visualize, you understand what is would possibly look like for someone to knock a ball off a table and what would happen. Your mind's eye doesn't picture each detail, but rather gives a vague idea, or possible even uses words and sentences, to formulate what would happen.
As a neurotypical adult, conceptualization may work perfectly fine for you. It may keep your head clear to focus on other things and prevent you from getting lost in details. However, we need to acknowledge how strong mental imagery helps our children comprehend, understand and problem solve through their daily activities; especially as they are learning concepts. Once a concept is learned and understood, conceptualization is easy and potentially time saving. It can be much harder trying to conceptualize without a visualization first.
Math is a big area for visualization skills prior to conceptualization. Often times we assume that because our child can state numerals proudly and in order "1, 2, 3, 4, 5!", she also understands what one of something looks like versus three. Math moves fast and once the numeral order is established, we are expected to add, subtract then multiply and divide. So for that little girl who can count in an orderly fashion but lacks the visualization of "one" versus "three", working with these numbers will become memorized at best. With memorized understanding of basic math functions, word problems will be an even greater challenge as the demands and steps increase.
Using small items as counting objects, such as coins, blocks, trinkets and other tangibles, will aid your child in visualizing numeral and math concepts. While learning to count, it's important to use these counters to help create the mental imagery necessary to understand what counting by 1's, versus 5's, versus 10's truly looks and feels like.
Another motivating way to improve visualization of math concepts is to use food. Pizza, oranges and apples can all easily be cut into fractions. Bananas can be sliced into coins for counting. Following recipes provide functional application of fractions and other quantity concepts.
You can use these ideas to teach simple counting or even harder concepts such as currency and taxes. A great way to teach this concept is to use a cookie or pizza, cut into slices. Pretend a puppet or sibling wants to take the whole cookie; how many slices would your child "pay", or give to you, to stop that puppet from stealing? How many slices would your child give for you to clean his room? Not only are you teaching bartering using a desirable item, but you're also discussing negotiation and placing a varying value on intangible items.
Continuing to use visualization techniques for math, go outside! Use a tire swing or the slides to understand angles. If you're able to build a slide, that's an excellent way to apply geometry! Concepts of higher/lower also relate to math and quantity and are easily visualized and experienced on playground equipment.
Using a multisensory approach will increase your child's ability to create vivid visualizations in order to understand and express concepts. The more vivid and dynamic the mental image is, the more manipulable it is and the better your child can even extrapolate, predict and negotiate from this image. Be aware of how you're discussing and teaching concepts. Are you a conceptualizer or a visualizer? How can you ensure your child is building strong mental images and concepts?