I’m sure many of you have seen the 1988 movie “Rain Man”. Ray (Dustin Hoffman), the main character in the movie, is an autistic man that was a “genius” in his own way. His brain was just like a calculator that could solve complex straight math questions like 4343 x 1234 or the square root of 2130 in a matter of seconds. But when it came to math application questions, even a very simple one like how much money would have left if he had $1 and spent 50 c, he had no clue. At all.
Here is the link to the scene; you can skip the beginning part of the video and start at minute 7:00.
We have seen many cases like this; of course they’re not as extreme as Rain Man. Kids who are really good in addition, subtraction, multiplication and division but struggling in math application problems, or real problems that they encounter in daily life. If there are 14 lockers, half of them are empty, and the other half have 7 books each, how many books are there? To get to the number operation of (½ x 14) x 7 is a challenge to them, but if you ask them what is (½ x 14) x 7 they can answer right away.
These students are playing Pico Fermi Nada to figure out a three or four digit mystery number. Pico Fermi Nada is just like the number version of Wordle with a little twist :) and it's a great exercise to strengthen their problem-solving mind.
What are the causes of students struggling with problem solving?
According to this paper by Jemmy Louange and Jack Bana, a study on Grade 7 students in Perth, Australia found that there are three main factors causing poor problem-solving performance (from biggest to smallest)
Lack of number sense
Lack of number sense is the biggest cause. Number sense is the ability to quickly understand, estimate and manipulate numerical quantities. Children with strong number sense think flexibly and fluently about numbers, and can visualize and talk comfortably about numbers. Number sense is very much like problem solving in the sense that you have to read the problem, try to understand it, plan a way to solve it and come up with a reasonably accurate answer. Number sense is to make sense of a number, and problem solving skill is used to make sense of a problem.
Roy the Rain Man thought that a candy bar costs $100 and a brand-new compact car costs the same. It’s an extreme case, but we have seen cases similar to this. Kids lacking number sense see numbers as meaningless and not interconnected – such as relying on algorithm to deduct 177 from 179. They cannot recognize the magnitude of numbers. They rely on pen and paper to count simple math like 45x2 or half of 70.
According to studies in this paper by M Maghfirah and A Mahmudi, written calculation skills are not always accompanied by good number sense. Rules-based math learning and standard algorithms can reduce students’ math thinking and prevent conceptual learning.
Read Success in math = Success in life?, Why your child should know Doubles Facts – while they’re young, Numerical Fluency: Where The Magic Happens for more information about number sense.
Lack of language proficiency
This paper by Vicente Bermejo, Pilar Ester and Isabel Morales concluded that the language of instruction has a direct influence on the development of mathematical thinking. Solving algorithms in a second language is pretty much not as a big deal as problem solving. But for problem solving, where language has a fundamental role for concept understanding as well as working memory, performance is always better when the dominant language is the mother tongue.
This looks like a common problem with many of our students who attend French Immersion schools. They admit that often they don’t understand their math teacher’s explanation. And we all know that math concepts build upon themselves; so when a student misses grasping a math concept, it will create problems in the next level. Often when these students bring their homework, they don’t know the meaning of some words. Les problémes de mots are already challenging in your first language as you have to visualize the case and think in multiple steps to solve it, and they are even more challenging when presented in your second language.
Perhaps deeper studies need to be done on the impact of French as a second language on students’ problem-solving ability in French Immersion schools in Canada, but nevertheless this is the feedback that we are getting in our centre.
Mathematics anxiety
Math anxiety is an emotional condition related to feelings of displeased, afraid, anxious, depressed, worried, bored and refused when discussing numbers, solving mathematical problems in daily life, or studying math in the classroom (The Role of Mathematics Anxiety and Mathematical Problem-Solving Skill).
Math anxiety has a negative impact on math learning in general. Teachers need to motivate students to learn math by creating comfortable and enjoyable learning environment, reduce student math anxiety with interesting learning methods, and choosing the right learning approach.
We have a student who was forced to come to our centre in his first sessions, but after three weeks, he said to his mom cheerfully “I want to come here every day!” And his mom was so grateful when she heard his son said “I know now that I’m not stupid”. Caring teachers armed with the right instructions and right methods can make a difference in a child’s life.
Read Math anxiety – the unnecessary fear that can prevent your child achieving their full potential to learn more about how to overcome math anxiety.
What’s next?
When you see your child struggles with problem-solving, find out how severe it is. If it is really an issue, investigate what the cause of the problem is. Is it because of their lack of number sense, lack of language proficiency or math anxiety? Often these three are interconnected. Then take action before it’s getting to be too much for your child, and before it’s becoming too hard to correct. Perhaps it’s time to find a teacher or tutor that can understand and accommodate your child’s learning style, or perhaps taking option to learn math in your child’s first language would be more beneficial, etc.
Read Teaching Problem-Solving skills through math and Mathnasium Program: Why it works! to learn more.
We want our children to be ready to face the real challenges in life, and not to become a Rain Man.
Mathnasium of Red Deer is your neighbourhood’s math-only learning centre, and we are here to unlock your child’s potential and set them on a path to lifetime success. Our centre director, Riwan, and the whole team, would be happy to meet you! We are conveniently located in the shopping destination area in Red Deer: 5250 22nd St, Unit 30 B – at the Gaetz Avenue Crossing shopping centre, in the same area as Chapters Indigo/Starbucks, Michael Arts, Petland and Ashley, and the phone number is 403-872 MATH (6284).
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