August 24, 2014 – Indeed! Unless you are keen on how neurons change connections in the brain as children move from having to count on their fingers to just recalling memorized facts, there is nothing surprising about the fact that children who practice their times tables get faster and better at doing calculations!
The National Institutes of Health in the United States recently funded a research project that focuses on how the brain organizes itself when children learn math. Subjects were tested twice, about 1.2 years apart. While the brain was scanned by a Magnetic Resonance Imaging (MRI) machine, the subjects were shown arithmetic calculations, such as 7 X 8 = 54 and they had to indicate if the answer was ‘true’ or ‘false’ with the push of a button. The speed and correctness of the responses were used as measures of how well the children knew their arithmetic calculations and the MRI scans showed the scientists what parts of the brain were used while the processing occurred ( 7 X 8 = 54 is false, by the way J).
“As the kids got older, their answers relied more on memory and became faster and more accurate, and it showed in the brain. There was less activity in the prefrontal and parietal regions associated with counting and more in the brain's memory centre, the hippocampus, the researchers reported Sunday in Nature Neuroscience”. This excerpt taken from Lauran Neergaard’s article in The Associated Press, dated August 18, 2014
Helen Shen, reporting on the same research for the scientific journal ‘Nature’ stated, “Consistent with previous psychology studies, the children relied heavily on counting out the sums, whereas adolescents and adults tended to draw on memorized information to calculate the answers.”
"This paper is really a very novel contribution," says Daniel Ansari, a developmental cognitive neuroscientist at Western University in London, Ontario. "We've known for a long time that there's this developmental shift in strategy, but we've known very little about the fundamental underlying mechanism."
When I was a youngster, well over 50 years ago, we were told that we should use the “3 R’s” to ensure that we learn something well. No – this is not the 3 R’s of “reading, ‘riting, and ‘rithmatic”. I’m talking about “Repetition, Review, and Recency”. It worked for me back then, and it still works today. I’ll address these items later when talking about study skills.
Things are not the same today as they were back in the ‘50s. In those days, students were given a failing grade when they couldn’t demonstrate an understanding of what they had been taught. I’m not just talking about secondary school students - students were held back in elementary school too. Today, nobody fails. Everybody advances to the next grade regardless of what they know or don’t know. Failure is still a reality in colleges and universities, however.
I don’t expect elementary school students to do a lot of homework. After all, childhood only comes once and there is so much to be explored and learned outside of the classroom. However, parents who want to ensure their child has a good foundation for secondary school mathematics will spend a reasonable amount of time at home every weekend going over the week’s work. Drilling arithmetic facts with flash cards, for example, will ultimately get those facts memorized by the brain and help in future mathematics classes. Unfortunately, today’s children don’t put a lot of effort into memorization. Instead, they rely on the internet for instant Wikipedia information and calculators for computations. Parents should still push their children to memorize facts. Future academic success, especially in mathematics, is dependant upon effective brain development.
Today’s secondary school students do little homework and they know they won’t receive a failing grade if it is not completed. They twitter and tweet, Facebook, and chat for endless hours with friends on their cell phones. Unfortunately, they are doing themselves the greatest disservice at a time when they are just a few short years away from college or university.
“At some universities, an estimated 4 out of 10 students will fail to finish the course they started after either dropping out, switching to another institution or graduating with a lesser qualification.”
“In England, the University of Bolton had the worst drop-out rate with 21.4% of students quitting higher education after just a year. An estimated 45% of undergraduates will fail to complete their full degree course, it emerged.”
“Drop-out rates were as high as a third at the University of the Highlands and Islands in Scotland and hit almost a quarter at the University of West Scotland.”
“Across Britain, the number of students dropping out increased from 28,210 to 31,755 last year – a rise of almost 13%.”
“In all, 8.6% of students quit higher education after 12 months last year compared with 7.9% a year earlier. Some 21.6% are expected to fail to complete their degree.” ~Excerpts fromThe Telegraph, August 22, 2014
It’s no different in Canada.
"It's a lot harder than I thought it would be," said the 17-year-old English student (Natalie Czerwinski) at the University of Toronto. "High schools don't prepare you very well for lectures 'cause they really spoon feed you'."
"They speak very slowly and put everything on the board, and you copy it down and you know exactly what they want you to know, whereas here it's a lecture, and for an hour a guy's talking and you're like, 'Oh My God I don't know what to write'."
“Students and professors argue high schools don't adequately prepare teens for one of the most stressful transition periods they will face – their first year of university. And about one in six students never complete their studies.”
“About 14% of first-year students drop out, according to the Persistence in Post-Secondary Education in Canada report, which analyzed data from Statistics Canada's Youth in Transition Survey.”
“The overall post-secondary drop out rate was about 16%, suggesting that those who are going to drop out, do so early on.” ~ Excerpts fromThe Star, August 22, 2014
As a former high school teacher, I used to argue that elementary schools didn’t adequately prepare students for the rigors of high school mathematics. Sadly, I now have to admit that high schools don’t adequately prepare students for university. When I graduated from an Ontario high school in 1966 there were only two graduates in my school who attained the rank of “Ontario Scholar” – students who achieved an overall average of 80% or more. Today, there’s likely to be only two students out of a group of 100 who don’t graduate with an average of 80% or more! Are today’s students smarter than we were? No. The unfortunate reality is that they are “spoon-fed”, as Natalie said in the Star article. The reality of their situation strikes home once they enter university.
When universities look deeper into the question of WHY students fail or have so much trouble, the answer usually comes down to “poor study skills”. ‘Studying’ doesn’t just refer to the act of ‘preparations the night before an exam’! It also includes doing homework, going over lecture notes, doing research, and finishing assignments. Unfortunately, some colleges and universities are also lowering their standards in order to ‘rectify’ the problem of student failures – but this just postpones the inevitable shock to the realities of the working world.
What can parents and students do to prepare adequately for the rigors of post-secondary school education? What can students in high school and university do to actually learn the material being taught? How can their ‘study skills’ be improved? Part of the answer lies in those “3 R’s” that I mentioned earlier.
Repetition: practice what you’ve been taught
In a classroom, the math teacher introduces a new topic. Students get to try one or two example problems at their desks before the lesson ends. That’s not enough to reinforce the learning. In mathematics, EVERY concept and skill builds upon previous ones and forms the foundation for future topics. Miss out on a few fundamentals early on, and everything becomes increasingly difficult in years to come. In order to reinforce concepts, students must practice. If homework is assigned, do it! The teacher picks out appropriate examples in the homework assignments to illustrate different aspects of the lesson. No two cases are exactly the same – so trying as many different situations as possible exposes the student to a variety of problems - laying a better base for courses yet to come. If a student is hoping to enter into Maths, Sciences or Engineering in university, then ensure problems from the most difficult section of the exercises (i.e. Part C) are attempted – even if they were not assigned.
The homework problems tackled in the evening provide good practice – and “practice makes perfect”, as the old saying goes. Practice is required for proficiency – even if perfection isn’t quite attained.
Review: go over the material again as soon as possible
When I was at the University of Toronto studying MPC (that’s Math, Physics and Chemistry), the courses and labs were intense. Even though most of my work was in maths and sciences, I still took minors or electives in English, philosophy, and psychology. I agree with 17-yr old Natalie -- listening to a lecture for 50 minutes and taking notes isn’t easy. My days were long, compared to those of a student in General Arts, yet I always made a point of sitting down at my desk after dinner and socializing in order to go over my lecture notes. I would open the textbook to find the relevant section related to the day’s lecture – and I’d read it. Then I’d read my notes, jotting down – in the margins - clarifications and extra points from the text. Once that was done, I’d then take fresh sheets of paper and I’d rewrite the entire lecture notes in good form, including my additions and examples. I’d do this for a math course or a science course or an English course or a philosophy course. It was important to review my notes while they were still fresh in my mind so that my jottings would still make sense. Putting this off until the weekend, or until studying for an exam, doesn’t work. It’s not surprising that hand-scrawled notes, taken in haste during a lecture, make no sense one or two months later. My rewritten notes were always clear, and included both the professors’ key points and further clarifications from the course textbook.
It is also a proven fact that the mere act of writing – even if it is just the rewriting of previous notes – makes more connections in the brain than the act of reading. Even when studying for tests or exams, I would go over my notes and write again! This time I would jot down key points and reorganize them into summaries. The ‘review’ – and the ‘writing’ – reinforces the learning more than ‘reading’ could ever accomplish. And put those test summaries in your notes, at the end of chapters or sections, to be used for studying for final exams. The key point to note, though, is that I’m talking about writing by hand – not typing on a keyboard, thumbing, or twittering.
Brain imaging studies show that cursive writing activates areas of the brain that do not participate in keyboarding. Check out the Psychology Today article in the “References” section of this article, where you’ll find very interesting statements such as this one:
“The benefits to brain development are similar to what you get with learning to play a musical instrument. Not everybody can afford music lessons, but everybody has access to pencil and paper. Not everybody can afford a computer for their kids—but maybe such kids are not as deprived as we would think.”
In any course or class, it is important to review tests or assignments when they are returned to the student. I’ve seen many students retrieve their test paper, glimpse at a bad mark, and then chuck it into the garbage can. Returned tests and assignments are excellent vehicles for learning. A low mark on a question indicates you do not understand a segment of the studies. Time should be spent going over the test, opening textbooks to find the proper material or to review the technique for generating the correct answer. Redo the solution or rewrite the answer. Then - most importantly – file the test in with your notes, after the relevant section, followed by your “corrections” page. Later, when studying for your final exam, you will review your notes and go over the returned tests. You will be reminded of your areas of weakness but know how to answer the questions properly.
Recency: ensure that you go over everything before tests
If you’ve been doing a great job of “review” and “repetition,” then this last ‘R’ is easy. It is common sense that one will remember something better the more recently it has been studied. I’m not talking about trying to relate to a police officer the description of a purse-snatcher who suddenly ran out, yanked the purse off a woman’s shoulder, and then dashed off into a crowd. Such incidents happen quickly, suddenly, and have a shock element to them – and many witnesses will give different descriptions of the same incident, even minutes afterwards. I’m talking about focusing, concentrating, and studying. I’m also not recommending leaving studying to the last possible minute! You should still be studying well in advance of a test – writing notes and summaries – but as near as possible to that test, you should go over your notes and summaries one last time. That “last spike” may finally drive the idea home, especially for those more difficult concepts. At least it will be fresher in your mind as the test paper is handed to you.
I started this article on the subject of how the brain reorganizes itself as math facts are learned. I spent a great deal of time talking about study skills and my “3 R’s”. The “References” section that follows, ends with more brain research studies and brain development – including those that discuss the benefits of writing by hand, of reviewing, and of repetition. The references I provided below include strategies for teachers to help students consolidate learned material into long-term memory. Everyone has a role in helping students learn better: teachers, parents, and the student.
The greatest responsibility falls upon the shoulders of the student. Get into good work habits. Follow a routine every time you get home from school to ensure you understand your notes, that you practice by doing more problems, and that you do your research and assignments. Practice. Memorize. Write. Write. Write – don’t just read. Summarize. It all starts with flash cards in grade one. 1 + 1 = 2. It could end with an undergraduate degree in Math and Science. It worked for me.
References & Resources
Brain Reorganization as Children Learn Math Facts
Brain scans reveal how children’s minds learn math – Associated Press
Developing brains switch math strategies – Nature: International journal of Science
How children’s brains memorize math facts – Science Daily
Brain Scans: Technologies That Peer Inside Your Head – if you want to learn more about MRIs
University Failure Rates
Has Ontario taught its high school students not to think? University Affairs (Sept. 10, 2007)
Help your child develop good study skills – for secondary school students
22 Science-Backed Study Tips to Ace a Test – for secondary & university students
Best Study Skills – Five Strategies – Memory-improvement-tips.com
Work your brain – for university students (University of British Columbia)
Articles for Educators
Brain-based learning strategies – Florida Education Association (FEA)
Memory, Learning, and Test-Taking Success – ASCD (Association for Supervision and Curriculum Development)
Brain Development & Learning Techniques
Why writing by hand could make you smarter – Psychology Today
How handwriting trains the brain – The Wall Street Journal
Memory and the importance of review – Bucks County Community College -This article discusses reviewing & keys to remembering:
1. Choose to remember
2. Visualize or picturing information
3. Relate the ideas & information to others
4. Repeat what you wish to learn
How to retain information – CollegeAtlas.org
This article discusses memory improvement techniques such as:
1. Attention (Concentration)
4. Starting Right
7. Building Background
9. Whole and Parts
13. Spaced Practice or Distributed Practice
15. Sleeping Over It