# Blog

#### Math and Spatial Skills Work Together

By: Mia Daucourt

Sometimes when we are skilled in one area it makes it easier for us to do well in another related area. For example, even without previous yoga training, a dancer is likely to do better at yoga than a person who has never trained in dance because a dancer will have more flexibility and coordination than the average person. Similarly, a person who excels at one sport is likely to have an overall athleticism and level of hand-eye coordination that makes him or her do well in most athletic, sports-related activities in comparison to people with no experience in sports training. Well, the same reciprocal relations, in which well-developed skills in one area help you do well in another related area may also be found with academic skills.

Geer and colleagues at FSU recently investigated the possibility that being good at math early on may help kids with their spatial skills later on. Math skills include understanding what numbers represent, how to count, how numbers are related, and how to do calculations, like adding numbers together or multiplying them. Spatial skills are how we understand the space around us in terms of both direction and distance. The researchers used a sample of 312 first- through third-grade students to look at three specific spatial skills: spatial perception, spatial visualization, and mental rotation. Spatial perception is the most basic spatial skill; it’s how we perceive the direction and distance of objects and things in relation to our own bodies. Spatial visualization is how we keep track of and manipulate this spatial information in an instance that requires multiple steps of spatial information, like remembering directions to get from point A to point B. Mental rotation is our ability to visualize and mentally move and rotate a two- or three-dimensional figure in our heads, like when you are looking at the pieces of a bookcase you are building and you can rotate a part of the bookcase in your head to visualize where it would fit.

If you’re struggling to think of how math and spatial skills would be related, simply think of a number line. A number line is a way to visualize numerical information spatially. For example, when you are given a number line from 0 to 10 and told to place the number 6 in the correct spot on the number line, you know to place it somewhere that is more than halfway, but less than three-quarters of the way because 6 is more than half of 10 but not by much. Fundamentally, the number line is teaching you a lot about numbers by using spatial information. That number 6 marked on the number line shows you that any numbers below 6 are less than 6. It also shows you that the distance from 6 to 1 is greater than the distance from 6 to 7. These are basic number properties that makeup fundamental math knowledge, but the information is being visualized spatially with the help of a number line. This allows you to hold onto a lot of number properties and math information without having to memorize it. Instead, by visualizing this information instead, a lot of memory space is freed up for more advanced math knowledge, like what you need to solve a multi-step complex math problem. Thus, it may be the case that children with stronger math skills early also have stronger spatial skills.

Geer and colleagues looked at how math and spatial skills developed separately and together. They expected how children did in one school year to be related to how they did in the same skill in the following school year, essentially meaning that the same skill would build upon itself. They also expected how a child did in one of the skills in one school year to influence how they did in the other skill in the following school year, meaning that one skills would help build upon the other skills. To measure children’s math skills the researchers gave the children a math test that included concepts about fractions, algebraic equivalence, word problem solving with addition, subtraction, and multiplication, measurement, map scaling. To measure spatial visualization and mental rotation, children were given a puzzle task and to measure spatial perception, children were given a water task. For the puzzle task, children were shown puzzle pieces and a grid and asked where the pieces needed to go to create a new object, like a turtle, out of the puzzle pieces. For the water level task, children were shown images of bottles tilted to the right or left at various angles and asked to draw a line where the water level would be if the bottle were half filled with water. The right answer is always to draw a horizontal line, but many kids tend to draw a line parallel to the bottom of the bottle.

Overall, the researchers found that if kids did well in math they also did well in spatial skills and vice versa and that there was stable growth in both math and spatial ability from first to third grade, with the exception of the water level task where children stayed the same from first grade to second grade. They also found that math and spatial skills, with the exception of spatial visualization built upon themselves. In addition, when the researchers tested for differences between boys and girls in how kids started out and how much they grew in each of the separate skills, they did not find any sex differences in growth, but they did find that first grade boys started off with an advantage in their spatial ability. Finally, when looking at how spatial skills influence the development of math skills across elementary school, the researchers found evidence of a reciprocal relation between math and spatial skills, with early success in one domain leading to later success in the other domain. Specifically, they found that early spatial visualization and mental rotation skills, but not spatial perception skills, predicted later math skills, and later math skills predicted all the spatial skills measured. Thus, kids’ spatial skills supported their math skills and kids’ math skills supported their spatial skills. Just like a dancer would do well in yoga, a kid with strong spatial skills would do well in math (and vice versa).

We cannot be certain based on this study why these reciprocal relations were found, with elementary children’s math skills supporting the development of their spatial skills and their spatial skills supporting the development of their math skills. Maybe kids who do well in math are more likely to visualize mathematical information spatially in their heads, so their work with math also improves their spatial skills or maybe when children use spatial strategies to solve math problems, their spatial skills are improving. No matter what the explanation, the important takeaway from Gear and colleagues’ work is that math and spatial skills are intertwined and we need to target both domains in early elementary school to support children’s math and spatial development. The finding of a sex difference in spatial skills in first grade also means that we should work on exposing girls to more spatial information before first grade. Boys often play with Legos and other toys that incidentally teach them about spatial relationships, whereas playing with such toys is rarer for girls. It would be a good idea to expose girls to the same toys and games that boys typically use to help their early spatial development.

Citation: Geer, E. A., Quinn, J. M., & Ganley, C. M. (2019). Relations between spatial skills and math performance in elementary school children: A longitudinal investigation. Developmental Psychology, 55(3), 637-652.