According to both international and national assessments, American students are not doing well in math [1, 2]. Apart from test scores, there are other concerns such as how much students really learn or whether we do a good job of teaching school math [3,4]. There are many reasons that lead to this unfavorable situation, but a major one is that math is a difficult subject to learn and to teach.
In fact, by doing a little research you will find that school math has always been a lively subject of debate among education experts, mathematicians, teachers and parents alike. This is by no means unique to America, although it is true that different countries have different attitudes toward and varying levels of appreciation of math. To resolve this multi- faceted problem is a difficult task that goes beyond most parents’ control of the situation. In this article, I will focus instead on steps that parents can take to help their children make the most out of their time studying math.
1. Debunk the myth of a math person
In the article The Myth of “I’m Bad at Math”[5], the authors argue that the idea of a “math person” is the most self-destructive idea in America today. Kids in school tend to believe that either they have an inborn talent for math or not. The ones who believe that they don’t fall further behind, a situation that can be explained by the concept “learned helplessness” [6]. That put them at a huge disadvantage in this technological age, especially when competition is global.
From their extensive teaching experience and from a wealth of research, the authors of the above article conclude that basic ability in math isn’t a product of good genes but of hard work. “ For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence.”
The same observation and conclusion can be found in “Grit: The Power of Passion andPerseverance” [7] by psychology professor Angela Duckworth. From her experience teaching school math early in her career to her later research work, Duckwood laid out a formula for achievements:
talent x effort=skill
skill x effort= achievements.
In her own words, no matter what we do in life, “effort counts twice”. Inborn talent has a place of its own but we are not talking about training genius mathematicians here, nor everyone needs to become a mathematician. Our modest goal is to teach our kids basic math skills, to help them overcome math phobia, to enjoy math rather than suffer from it. This goal is attainable by cultivating kids’ confidence in their learning capability and by making sure that they put in enough effort.
So the first point is not to let kids fall for the myth of a math person. That brings us to the next point.
2. Start math early
We often take it for granted that language is hard-wired in our brain, that between one and two years old most children will start talking and naturally develop their language skills. Indeed, there is enough evidence that the human species is gifted with a language instinct [8]. But what about math?
Research also shows that our species has an instinct for numbers. And this is not unique to human beings but to many other animals as well because it offers benefit for survival. More details can be found in this fascinating article from the MIT Press [9]. The number instinct is quite easy to test: just give a toddler her favorite food in two different amounts, for example the choice of 3 cherries and 5 cherries; she will show you that she knows which number is bigger even before you teach her to count one, two, three.
Children also do an incredible job of recognizing patterns. A 3-year old can easily recognize a cat in any shapes and positions: whether it is straight or curled up, sleeping, running, or partially hiding, etc. By comparison, it takes a very complex algorithm and an enormous amount of data to train a computer to accomplish the same task (see the Ted Talk “How we’re teaching computers to understand pictures” [10]).
I am convinced that the ability to compare numbers or recognize patterns shows that young children are capable of learning math. When exactly should we start teaching them math then? There is no clear cut answer to this question but from my experience, there is almost always a benefit in starting early, as early as preschool age and definitely kids should be exposed to the real beauty of mathematics in the elementary school years. Children’s perception of and attitude towards mathematics were formed very early on. By the time a kid enters middle school, it might be too late to offer a remedy for the fear of mathematics. From an early age, tell them math stories. Give them a variety of problems and see where their interests lie: some love numbers; some are drawn to shapes; some like logic puzzles. Start early but gradually and follow their cue. They will grow up having a positive attitude towards the subject.
Positive attitude is known to reduce anxiety, enhance memory and boost learning. This research [11] that examined children ages 7 to 10 shows that positive attitude, even after IQ and other confounding factors have been accounted for, predicts stronger math performance.
3. Show kids that math is everywhere
To create a positive attitude toward math, it is also very helpful to show kids that math is such a natural part of human life. The history of mathematics is closely tied to the history of human kind, from the prehistoric ages to the Ancient Egypt, Ancient Greece, the Maya civilization, China, and India. When reading history books with your kids, show them how much human beings advanced through history thanks to their ever expanding knowledge of math.
In everyday life, whether you are trying to cut a round shape or making measurements for a window, involve the kids. Ask them to help with simple calculations so they know that their knowledge is being put to good use.
Make math come alive. Don’t limit ourselves to what we think is important for the kids because that may not strike a cord with them, especially in the beginning. There is enough math in virtually any topics; we just need to look for them. In short, when picking math problems for young children, try to see the world from the point of view of the child.
4. Provide the right environment for kids to study
It starts from the most basic: good health that includes healthy food, enough exercises, and enough of quality sleep. A sufficient amount of deep, quality sleep is needed to translate what we learn during the day into long term memory as explained in this article that summarizes the original study [12]. Without enough quality sleep, the brain is foggy, preventing the absorption of new knowledge and inhibiting clear thinking.
Next, give kids space and pick the best time for them to focus on their study. If they are tired after school, an extra math class might not be the best idea; instead, let them do activities that don’t require a lot of brain power. Use the weekends for math, when they have enough sleep, when their mind is clear, when there is no rush to go anywhere.
Finally, to raise the kids’ interest in math as well as to boost their performance, it is very beneficial for them to have a small study group with other kids. This group can be formed from their school classmates, classmates in after-school classes, or in your family’s circle of friends. Kids learn so much from their peers’ different approaches to the same problem, something that even a great math instructor cannot make up for. In addition, in their study group, make sure there is teamwork as well as some level of healthy competition as that would motivate them to study.
5. Help them become independent learners
Being independent is desirable in learning any subjects, but especially so in math because math is heavy on problem solving. It is quite hard to expect a young kid to sit down at the table and start working on their homework without a reminder from the parents but actually if you look at every kid, there is always something that they do all by themselves: a 3 year old sitting still cutting large pieces of paper into smaller and smaller pieces until they cannot be cut any more; a 6 year old rejoicing in her discovery that by pulling on the rope of a newfound sled she could actually ski downhill; a 8 year old jumping to his lego construction the first moment he gets out of bed in the morning as if he had been thinking about it throughout the night.
The question is how to translate their energy and passion from other areas into academic learning and make them independent learners? Not a question with an easy answer but similar to point number 2, I find it much easier to start early. Below are two suggestions to help achieve this goal.
Regularity
Similar to doing sports of playing music, studying math requires a lot of practice and dedication. There should be a regular, agreed-upon time with the child that is reserved for math, whether it’s a 20-minutes lesson with a preschooler or a 1.5-hour math enrichment session for a third grader. Ideally the child looks forward to it, and not being forced by parents.
Active learning
Being independent doesn’t mean that the kids are left all by themselves, but rather they should be actively involved in their learning process. In the beginning, ask them to put their homework time into their calendar and encourage them to get started by themselves. They will get used to this idea that they, not the parents, are the ones who are in charge.
Teach them to be active learners: actively recalling a concept, actively looking for connections with perhaps a problems that they have seen before, and actively asking questions. The parents and teachers are there to help them but they should be the ones who initiate the learning process. It may take up to several years to build up this learning habit but once it’s established, learning will be much easier and more enjoyable.
6. Be selective on the type of math enrichment
There are many choices of math enrichment: after-school math classes, math camps, private tutoring, online apps, parent-led sessions, small studying groups between a few children, children studying by themselves, etc. Depending on the child and the family, one choice may work better than others. Whatever choice you make, be sure to evaluate it regularly and see if any adjustments are needed.
How to evaluate what learning choice is best for your child? We often talk about having fun in learning and indeed fun facilitates learning, but it should not be the sole metric. Other criteria that you may want to consider are: the breadth and depth of the subject matter, the child’s reasoning ability, not being afraid of new problems, ability to think on his feet or insisting on finding the solutions himself. Advanced kids and the ones who really like the subject will attempt to find different solutions to the same problems or make up new problems themselves.
Learning materials also play a very important role. Studying math today is not very different from studying math a hundred years ago. It doesn’t require a fancy electronic device but rather some good books, paper, a pencil, a ruler, and a compass go a long way. Just like a game, math has its own rules, strict but universal. Once the kids get a hang of it, they will have at their disposal a low-cost intellectual game with infinitely many games for them to play and expand their mind.
References
[1] Summary of PISA test score 2019
[2] Result of test score NEPC 2019
[3] “Why so many US students aren’t learning math” – an article from UCLA Newsroom
https://newsroom.ucla.edu/stories/why-so-many-u-s-students-arent-learning-math
[4] “A Mathematician’s Lament” – Lockhart’s essay available from Mathematical Association of America
https://old.maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf
[5] “ The Myth of ‘I’m Bad at Math’ ” – an article from The Atlantic
https://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/
[6] The concept of “Learned helplessness”
https://en.wikipedia.org/wiki/Learned_helplessness
[7] “ Grit. The Power of Passion and Perseverance” by Angela Duckworth
[8] “The Language Instinct” by Steven Pinker
https://stevenpinker.com/publications/language-instinct
[9] “In the Animal Kingdom, the Astonishing Power of the Number Instinct”- an article from MIT Press
https://thereader.mitpress.mit.edu/animal-kingdom-power-of-the-number-instinct/
[10] “How we are teaching computers to understand pictures”- Ted Talk
11] Summary of the study titled “Positive Attitude Toward Math Supports Early Academic Success: Behavioral Evidence and Neurocognitive Mechanisms”https://med.stanford.edu/news/all-news/2018/01/positive-attitude-toward-math-predicts-math-achievement-in-kids.html
Link to the original study and other related studies: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5854512/
[12] “Sleep Promote Branch-Specific Formation of Dendritic Spines after Learning”- an article from NYU School of Medicine that quotes the original study https://med.nyu.edu/departments-institutes/neuroscience/research/journal-club/journal-club-2014-articles/sleep-promotes-branch-specific-formation-dendritic-spines-learning