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Is age of children strongly related to ability to learn various mathematical topics (e.g., percentages, common fractions)? I ask because many students in the elementary grades struggle with math concepts and have repeated failure experiences. If these same children were given a rest and the topics introduced when they are a year or two or three older, would they learn the concepts more easily? (This is a small facet of a larger question, not specifically asked, is the idea of filling young heads with as much knowledge as possible a good idea for the children who struggle with acquiring such knowledge.
New research sheds light on how children’s brains memorize facts
As children shift from counting on their fingers to remembering math facts, the hippocampus and its functional circuits support the brain’s construction of adultlike ways of using memory.
As children learn basic arithmetic, they gradually switch from solving problems by counting on their fingers to pulling facts from memory. The shift comes more easily for some kids than for others, but no one knows why.
Now, new brain-imaging research gives the first evidence drawn from a longitudinal study to explain how the brain reorganizes itself as children learn math facts. A precisely orchestrated group of brain changes, many involving the memory center known as the hippocampus, are essential to the transformation, according to a study from the Stanford University School of Medicine.
The results, published online Aug. 17 in Nature Neuroscience, explain brain reorganization during normal development of cognitive skills and will serve as a point of comparison for future studies of what goes awry in the brains of children with learning disabilities.
“We wanted to understand how children acquire new knowledge, and determine why some children learn to retrieve facts from memory better than others,” said Vinod Menon, PhD, the Rachael L. and Walter F. Nichols, MD, Professor and professor of psychiatry and behavioral sciences, and the senior author of the study. “This work provides insight into the dynamic changes that occur over the course of cognitive development in each child.”
The study also adds to prior research into the differences between how children’s and adults’ brains solve math problems. Children use certain brain regions, including the hippocampus and the prefrontal cortex, very differently from adults when the two groups are solving the same types of math problems, the study showed.
“It was surprising to us that the hippocampal and prefrontal contributions to memory-based problem-solving during childhood don’t look anything like what we would have expected for the adult brain,” said postdoctoral scholar Shaozheng Qin, PhD, who is the paper’s lead author.
Charting the shifting strategy
In the study, 28 children solved simple math problems while receiving two functional magnetic resonance imaging brain scans the scans were done about 1.2 years apart. The researchers also scanned 20 adolescents and 20 adults at a single time point. At the start of the study, the children were ages 7-9. The adolescents were 14-17 and the adults were 19-22. The participants had normal IQs. Because the study examined normal math learning, potential participants with math-related learning disabilities and attention deficit hyperactivity disorder were excluded. The children and adolescents were studying math in school the researchers did not provide any math instruction.
During the study, as the children aged from an average of 8.2 to 9.4 years, they became faster and more accurate at solving math problems, and relied more on retrieving math facts from memory and less on counting. As these shifts in strategy took place, the researchers saw several changes in the children’s brains. The hippocampus, a region with many roles in shaping new memories, was activated more in children’s brains after one year. Regions involved in counting, including parts of the prefrontal and parietal cortex, were activated less.
The scientists also saw changes in the degree to which the hippocampus was connected to other parts of children’s brains, with several parts of the prefrontal, anterior temporal cortex and parietal cortex more strongly connected to the hippocampus after one year. Crucially, the stronger these connections, the greater was each individual child’s ability to retrieve math facts from memory, a finding that suggests a starting point for future studies of math-learning disabilities.
Although children were using their hippocampus more after a year, adolescents and adults made minimal use of their hippocampus while solving math problems. Instead, they pulled math facts from well-developed information stores in the neocortex.
“What this means is that the hippocampus is providing a scaffold for learning and consolidating facts into long-term memory in children,” said Menon, who is also the Rachel L. and Walter F. Nichols, MD, Professor at the medical school. Children’s brains are building a schema for mathematical knowledge. The hippocampus helps support other parts of the brain as adultlike neural connections for solving math problems are being constructed. “In adults this scaffold is not needed because memory for math facts has most likely been consolidated into the neocortex,” he said. Interestingly, the research also showed that, although the adult hippocampus is not as strongly engaged as in children, it seems to keep a backup copy of the math information that adults usually draw from the neocortex.
The researchers compared the level of variation in patterns of brain activity as children, adolescents and adults correctly solved math problems. The brain’s activity patterns were more stable in adolescents and adults than in children, suggesting that as the brain gets better at solving math problems its activity becomes more consistent.
The next step, Menon said, is to compare the new findings about normal math learning to what happens in children with math-learning disabilities.
“In children with math-learning disabilities, we know that the ability to retrieve facts fluently is a basic problem, and remains a bottleneck for them in high school and college,” he said. “Is it that the hippocampus can’t provide a reliable scaffold to build good representations of math facts in other parts of the brain during the early stages of learning, and so the child continues to use inefficient strategies to solve math problems? We want to test this.”
Other Stanford co-authors of the study are former postdoctoral scholar Soohyun Cho, PhD postdoctoral scholar Tianwen Chen, PhD and Miriam Rosenberg-Lee, PhD, instructor in psychiatry and behavioral sciences.
The research was supported by the National Institutes of Health (grants HD047520, HD059205 and MH101394), Stanford’s Child Health Research Institute, the Lucile Packard Foundation for Children’s Health, Stanford’s Clinical and Translational Science Award (grant UL1RR025744) and the Netherlands Organization for Scientific Research.
The role of early language abilities on math skills among Chinese children
The present study investigated the role of early language abilities in the development of math skills among Chinese K-3 students. About 2000 children in China, who were on average aged 6 years, were assessed for both informal math (e.g., basic number concepts such as counting objects) and formal math (calculations including addition and subtraction) skills, language abilities and nonverbal intelligence.
Correlation analysis showed that language abilities were more strongly associated with informal than formal math skills, and regression analyses revealed that children’s language abilities could uniquely predict both informal and formal math skills with age, gender, and nonverbal intelligence controlled. Mediation analyses demonstrated that the relationship between children’s language abilities and formal math skills was partially mediated by informal math skills.
The current findings indicate 1) Children’s language abilities are of strong predictive values for both informal and formal math skills 2) Language abilities impacts formal math skills partially through the mediation of informal math skills.
Citation: Zhang J, Fan X, Cheung SK, Meng Y, Cai Z, Hu BY (2017) The role of early language abilities on math skills among Chinese children. PLoS ONE 12(7): e0181074. https://doi.org/10.1371/journal.pone.0181074
Editor: Mitchell Rabinowitz, Fordham University, UNITED STATES
Received: March 15, 2017 Accepted: June 26, 2017 Published: July 27, 2017
Copyright: © 2017 Zhang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the paper and its Supporting Information files.
Funding: This study was supported by research grants MYRG2017-00217-FED, MYRG2016-00193-FED, and MYRG2015-00221-FEDfrom the University of Macau.
Competing interests: The authors have declared that no competing interests exist.
Key Math Skills for School
More advanced mathematical skills are based on an early math “foundation”—just like a house is built on a strong foundation. In the toddler years, you can help your child begin to develop early math skills by introducing ideas like: (From Diezmann & Yelland, 2000, and Fromboluti & Rinck, 1999.)
This is the ability to count accurately—first forward. Then, later in school, children will learn to count backwards. A more complex skill related to number sense is the ability to see relationships between numbers—like adding and subtracting. Ben (age 2) saw the cupcakes on the plate. He counted with his dad: “One, two, three, four, five, six…”
Making mathematical ideas “real” by using words, pictures, symbols, and objects (like blocks). Casey (aged 3) was setting out a pretend picnic. He carefully laid out four plastic plates and four plastic cups: “So our whole family can come to the picnic!” There were four members in his family he was able to apply this information to the number of plates and cups he chose.
Later in school, children will call this “geometry.” But for toddlers it is introducing the ideas of shape, size, space, position, direction and movement. Aziz (28 months) was giggling at the bottom of the slide. “What’s so funny?” his Auntie wondered. “I comed up,” said Aziz, “Then I comed down!”
Technically, this is finding the length, height, and weight of an object using units like inches, feet or pounds. Measurement of time (in minutes, for example) also falls under this skill area. Gabriella (36 months) asked her Abuela again and again: “Make cookies? Me do it!” Her Abuela showed her how to fill the measuring cup with sugar. “We need two cups, Gabi. Fill it up once and put it in the bowl, then fill it up again.”
This is the ability to make a good guess about the amount or size of something. This is very difficult for young children to do. You can help them by showing them the meaning of words like more, less, bigger, smaller, more than, less than. Nolan (30 months) looked at the two bagels: one was a regular bagel, one was a mini-bagel. His dad asked: “Which one would you like?” Nolan pointed to the regular bagel. His dad said, “You must be hungry! That bagel is bigger. That bagel is smaller. Okay, I’ll give you the bigger one. Breakfast is coming up!”
Patterns are things—numbers, shapes, images—that repeat in a logical way. Patterns help children learn to make predictions, to understand what comes next, to make logical connections, and to use reasoning skills. Ava (27 months) pointed to the moon: “Moon. Sun go night-night.” Her grandfather picked her up, “Yes, little Ava. In the morning, the sun comes out and the moon goes away. At night, the sun goes to sleep and the moon comes out to play. But it’s time for Ava to go to sleep now, just like the sun.”
The ability to think through a problem, to recognize there is more than one path to the answer. It means using past knowledge and logical thinking skills to find an answer. Carl (15 months old) looked at the shape-sorter—a plastic drum with 3 holes in the top. The holes were in the shape of a triangle, a circle and a square. Carl looked at the chunky shapes on the floor. He picked up a triangle. He put it in his month, then banged it on the floor. He touched the edges with his fingers. Then he tried to stuff it in each of the holes of the new toy. Surprise! It fell inside the triangle hole! Carl reached for another block, a circular one this time…
40 Children’s Books That Foster a Love of Math
Storybooks provide a rich opportunity to build not only literacy skills, but also math understanding. Books with math concepts woven into the pictures and storylines can promote children's mathematical thinking and introduce foundational math concepts such as numbers, shapes, patterns, and measurement. Asking questions and making observations about the math found in picture books can support children’s curiosity and enjoyment of math.
Like many engaging pieces of children’s literature, the math picture books recommended below contain fun and interesting storylines. Many are rooted in topics kids love (like animals, dinosaurs, magic, oceans, and more!).
For example, Quack and Countby Keith Baker is about seven ducklings quacking, sliding, and flying in marshland. Throughout the beautifully illustrated story, the seven ducklings form different groups that can be added and always make seven. While reading, children can explore counting and addition as they practice counting a group of ducks that are not always neatly in a row and in fact may be hard to see—a challenging but enjoyable task.
The most important rule to keep in mind when selecting and reading a math picture book is to enjoy the stories and enjoy the children enjoying the stories! Read often, smile, and laugh. Learn more tips for reading math picture books with young children in this guide. If you’re a teacher or teacher educator, find tips for using math picture books in the classroom.
First and second graders
Predict what comes next in a pattern and create own patterns
Know the difference between two- and three-dimensional shapes and name the basic ones (cubes, cones, cylinders)
Count to 100 by ones, twos, fives, and tens
Write and recognize the numerals 0 to 100, and the words for numbers from one to twenty
Do basic addition and subtraction up to 20
Read and create a simple bar graph
Recognize and know the value of coins
Tips for Parents on Using Spatial Talk
How can you help children learn from hearing spatial words? Here are some tips for parents to engage in spatial talk. These tips can help promote strong spatial thinking in your child, and most children find spatial talk and spatial play fun and interesting!
When talking about shapes, go beyond labeling the shape. Talk about the defining features.
- “These are both triangles, because all triangles have three sides and three angles.”
- “While all rectangles have four sides,squares are a special kind of rectangle that have four sides that are all the same length.”
Make the most of spatial activities such as block building and puzzle play by using spatial talk during the activities.
- “Let’s put the big, wide blocks on the bottom, and put the small, narrow blocks on the top.”
- “I know this puzzle piece is a corner piece because it has two flat (or straight) edges.”
Use spatial talk during activities your child loves.
- When your child is on the playground, describe her spatial location as she is on the go. “You went over the bridge, and now you are running under the monkey bars!”
- Talk about space in the illustrations when you are reading books. “That giraffe is really tall and is standing behind a high fence.”
Use gestures such as pointing or tracing objects to help your child understand what the spatial words you are using mean.
- When you say “straight edge” move your finger along the edge to show your child what straight means.
- Encourage your child to use gestures when she is using spatial words.
Ask questions and play games to help your child talk about space and shapes.
- Ask your child to find shapes in the world and identify them. To help her learn to describe shapes, follow up by asking questions such as, “How do you know it’s a triangle?”
- Tell your child that you are thinking of an object in the room and have him ask you questions to guess what it is. Encourage your child to use spatial words to figure out what object you have in mind. “Is it near the chair? Is it wider than the table?”
Sarah H. Eason is a postdoctoral researcher in the Department of Psychology at the University of Chicago. Susan C. Levine is the Rebecca Anne Boylan Professor of Education and Society in the Department of Psychology at the University of Chicago. The authors are members of the Family Math and the Math+ projects of the DREME Network.
 Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101, 817–835.
 Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48, 1229–1241.
 Cheng, Y. L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15, 2–11.
 Casey, M. B., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26, 269–309.
 Levine, S. C., Ratliff, K. R., Huttenlocher, J., & Cannon, D. (2012). Early puzzle play: A predictor of preschoolers’ spatial transformation skill. Developmental Psychology, 48, 530–542.
 Pruden, S. M., Levine, S. C., & Huttenlocher, J. (2011). Children’s spatial thinking: Does talk about the spatial world matter? Developmental Science, 14, 1417–1430.
 Kersh, J., Casey, B. M., & Young, J. M. (2008). Research on spatial skills and block building in girls and boys. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 233–251). Charlotte, NC: Information Age.
 Pruden, S. M., & Levine, S. C. (2017). Parents’ spatial language mediates a sex difference in preschoolers’ spatial-language use. Psychological Science, 28, 1583-1596.
 Dearing, E., Casey, B. M., Ganley, C. M., Tillinger, M., Laski, E., & Montecillo, C. (2012). Young girls’ arithmetic and spatial skills: The distal and proximal roles of family socioeconomics and home learning experiences. Early Childhood Research Quarterly, 27, 458–470.
Teach them at a young age
When my daughter was five and already insisting on "iPad time" with unrelenting protests, my wife and I knew we had to act.
After we all calmed down, we did our best to respect her needs in the way Richard Ryan, one of the most cited researchers in the world on the drivers of human behavior, recommends: We explained, as simply as we could, that too much screen time comes at the expense of other things.
As a kindergartner, she was learning to tell time, so we could explain that there was only so much of it for things she enjoyed. Spending too much time with apps and videos meant less time to play with friends at the park, swim at the community pool, or be with Mom and Dad.
Hope for learning disabilities: The brain can change
Science has made great strides in understanding the inner workings of the brain, and one important discovery that brings new hope for learning disabilities and disorders is called neuroplasticity. Neuroplasticity refers to the brain’s natural, lifelong ability to change.
Throughout life, the brain is able to form new connections and generate new brain cells in response to experience and learning. This knowledge has led to groundbreaking new treatments for learning disabilities that take advantage of the brain’s ability to change. Innovative programs, such as the Arrowsmith program, use strategic brain exercises to identify and strengthen weak cognitive areas. For example, for children who have difficulty distinguishing between different sounds in a word, there are new computer-based learning programs that slow down the sounds so that children can understand them and gradually increase their speed of comprehension.
These discoveries about neuroplasticity provide hope to all students with learning disorders, and further research may lead to additional new treatments that target the actual causes of learning disabilities, rather than simply offering coping strategies to compensate for weaknesses.
How does understanding the brain help a learning disorder?
Using a telephone analogy, faulty wiring in the brain disrupts normal lines of communication and makes it difficult to process information easily. If service was down in a certain area of the city, the phone company might fix the problem by re-wiring the connections. Similarly, under the right learning conditions, the brain has the ability to reorganize itself by forming new neural connections. These new connections facilitate skills like reading and writing that were difficult using the old connections.
Acquire an accurate description of Piaget's theory of preoperational development for children from approximately age 2 through first grade. In general, children in this stage are beginning to understand how symbols (such as words or numbers) can represent objects, use make-believe or fantasy thought, are fairly egocentric in thinking, and do not have a firm grasp on the concept of time.
Choose specific aspects of Piaget's preoperational theory that match mathematics teaching for your age group/grade. Include concepts that easily translate into teaching strategies. For example, use the idea that the child now might understand the connection between an object and the symbol that it represents. Set up a hands-on number lesson in which groups of toys or other objects represent numbers such as five toy cars, three apples, or seven pieces of chalk.
Write your lesson plan detailing each step and its relation to Piaget's theory. Note the specific stage (i.e., preoperational) and theory idea (e.g., make-believe/fantasy, representation). Design a specific learning goal or object, such as students learning to count to 10 by themselves, or child recognizing written numerals. Make a bulleted list of materials and a numbered list of steps.