Content of the material
- Maths Is Everywhere
- Mental Multiplication Using Factors
- General Multiplication Tricks
- Simplify Before You Solve It
- Diagnosis Treatment of Dyscalculia
- To square a two-digit number, round it first
- How to learn math for students
- 1. Practice makes perfect
- 2. Review your mistakes
- 3. Focus on concepts, not processes
- Using Games as Tricks For Fast Calculation
- Keep the learning fun
- How to Learn More Advanced Mathematics (FREE Resources)
- Steps to Studying Math on Your Own
- Step 1. First, determine where you want to end up
- Step 2. Determine where to start, obviously
- Step 3. Find a Syllabus to Avoid Unnecessary Depth
- Step 4. Gather your References, Solution Manuals, and “Solved Problems” Types of Books
- Step 5. Prioritize Deep, Concept-Based Learning
- Step 6. Put Links to Resources in One Place
- Step 7. Set aside time for BOTH studying and problem-solving
- Step 8. Cultivate Deep Work
- Step 9. Avoid “Practice, Practice, Practice”, Do This Instead
Maths Is Everywhere
Whether you intend to enter a profession directly related to the Maths sector or not, you will still benefit from having these skills because Maths is fundamentally everywhere. If you have a part-time job at your local shop, you will know how Maths can come into play in just about any profession; when your till lets you down or spreadsheet gets corrupted.
It’s also really useful to know how to do quick and effective mental arithmetic in our everyday lives, whether it’s for budgeting when doing the shopping, working out measurements on a DIY project, observing patterns when sewing, etc…
You can’t get away from Maths, no matter how hard you try!
And while we all have a mobile phone, we don’t always have it to hand when we need it and, when we do, we waste a lot of time just looking for the “Calculator” app, and then getting fed up with the numerous ads that pop up whilst we are trying to type in our calculation quickly.
Even if we did consult our digital calculators at every opportunity, how can we be sure that they are right? We have become so reliant on technology these days that it has led us to feel helpless when it fails us. Behind all the computers, there is always a human being checking that they are running as they should. While human error can and does happen, our conscience means that we are pretty reliable as beings.
Going back over the basics of mental arithmetic can help you get out a lot of trouble during your exams. However, it’s not just for when you’re doing your A Levels. It can also help you make the most of other situations, such as during maths tutorials with a maths tutor.
So, how do you do it? How do you get better at maths? Are there exercises, techniques, or ways to improve your maths level?
Mental Multiplication Using Factors
Like rounding up, one of the multiplication tricks is to factor the number before multiplying it. Let us look at how to do that by trying to multiply 45 x 22.
1. Factor the number
2. Multiply the number with the first factor (left to right)
4. Multiply the product with the second factor (left to right)
In the multiplication tricks we saw earlier, you will have to remember the product of the first digit to add/subtract with the product of the second digit. However, in mental multiplication using factors you just multiply the second factor with the first product, so you don’t have to remember so many numbers as you calculate.
Now you try multiplying 21 x 63 using the factor method. The procedure is the same as before and you can find it below:
General Multiplication Tricks
Let us now look at how to do mental multiplication for 2 digit numbers now. The multiplication tricks we saw earlier needs to be slightly modified. Let us see how to do that with an example. Multiply 36 x 32.
1. Break the multiplicand
2. Multiply from left to right
3. Add the individual answers together to get the final answer
You can solve the same problem by breaking the multiplier instead of the multiplicand. Your choice will depend on which gives you the simpler addition process in Step 3. Try to select the number that has the smaller one’s digit because that will usually result in you adding smaller numbers, in most cases.
Now you try multiplying 26 x 23. The procedure is the same as before and you can find it below:
Simplify Before You Solve It
The key is to simplify before you start. Victor writes:
“Revenue = 2 million buyers x 15% market share x $300 revenue per buyer
Most people gravitate to solving a math problem in exactly the form in which it is presented, but it’s often easier to simplify the problem into a series of smaller problems. For example, I notice that the first number ($2 million) and the last number ($300) are easy numbers to multiply, so I would mentally rewrite the equation as follows:
(2 million x $300) x 15%
That works out to $600 million x 15%”
Diagnosis Treatment of Dyscalculia
Treatment of dyscalculia is not administered with medication. What is used to help both adults and kids cope with dyscalculia is the use of both learning strategies that are specialized and strategic accommodations. The specialized learning strategies allow those suffering from dyscalculia to learn how to compensate for the difficulties they face when dealing with math and eventually approach math with confidence.
The treatment strategy taken for dyscalculia is a long-range goal. What this strategy aims at is teaching calculation techniques and build the reasoning skills that are necessary for one to solve math problems. If the treatment strategy is more short-term than long-term, the treatment should focus on the removal of obstacles in the way of learning, therefore, making math easier to use both quickly as well as accurately.
Cognitive training products is one place an adult can turn who’s asking “why can’t I do math in my head?”. CogniFit, for example, aims to help adults with dyscalculia “improve cognitive skills affected by this disorder.” These cognitive areas include memory, perception, attention, coordination, and reasoning. Activities that users participate in during the program “strengthen the neural networks involved in the cognitive abilities altered in dyscalculia”.
Resources: www.additubemag.com, www.webmd.com, www.halfpennydevelopment.co.uk, , www.disabilityinkidlit.com
To square a two-digit number, round it first
Say you need to square 46. First round it to the nearest multiple of 10 (by adding 4), then subtract the same amount for a new number, so you have 50 and 42. Then multiply those two numbers, and then add the square of the amount you rounded up by: (in this case 4²). So 46² = (50*42)+4² = 2,100+16 = 2,116.
By the way, when I did this mentally, 50*42 was still a little hard for me, so I turned it into 100*21. Combining mental maths tricks really increases your power.
If you didn’t follow that, here’s a longer explanation that might do the trick.
How to learn math for students
There are many ways to learn math – in school, with a tutor, using online math learning websites – but whatever way you’re learning, there are some basic principles to keep in mind. Remember: the only way to learn mathematics is to do mathematics!
1. Practice makes perfect
Nothing that’s worth having comes easy, and a solid grasp of mathematics is no exception! This is a skill that will develop only by being practiced over and over again, so use your spare time to practice equations, exercises and basic arithmetic. This is perhaps one of the most essential tips to learn maths. You’ll see – and feel – a difference in a matter of weeks.
2. Review your mistakes
A lot of mathematics is all about problem-solving, and to solve problems you need to apply different solutions until you find the right one. If you got the wrong answer, review your process and identify the mistakes.
Why is this one of the key tips for learning mathematics? That’s because understanding where you went wrong in your approach using a step-by-step process is the best way to strengthen your skills and avoid making the same errors again.
3. Focus on concepts, not processes
Math is a sequential subject: you need to understand one problem thoroughly before moving on to the next. If you only know the process of an equation, you’ll find it more difficult to understand where it fits into solutions for different problems in the future.
In fact, in a study conducted by the Cognitive Science Society, students who used a problem-solving-first approach consistently outperformed students who learned the mathematical solution before trying to solve the problem with it. By understanding the problem before knowing the solution, students could more clearly identify the logic behind the problem and what processes would be involved in solving it.
That’s why the best way to learn math is to understand the concepts and logic of each solution rather than memorizing the process.
Using Games as Tricks For Fast Calculation
Struggling maths students at school are a common issue. A lack of mental arithmetic can negatively impact students’ futures. A study carried out in 2014 highlighted that 40% of students at primary school have problems with maths.
It was also shown that these problems at primary school included multiplication and division tables, decimals, and representing large numbers.
Given these findings, new programmes tend to have a focus on mental arithmetic. After learning subtraction, addition, and multiplication tables, mental arithmetic also includes:
- Establishing reflexes,
- Refining logical thinking,
- Getting used to working with numbers,
- Learning the properties of numbers.
To help children get better at mental arithmetic, you should ensure that this practice is fun. Let them learn while they’re having fun! This is a great way to encourage them to enjoy numeracy.
Keep the learning fun
Learning has to be progressive. Games are a good way to learn to calculate without being subjected to the stricter aspects of tutorials with a maths tutor.
The best thing about this is that, now that we access to so much technology, playing games to enhance logical thinking is so easy.
Downloading apps on our mobile phones is like second nature to us, so why not use this to your advantage and download some of the amazing free games at your disposal. All you need to do is search ‘Maths games’ in your app finder to find a massive list of suitable games!
Otherwise, why not try out some of the websites and applications suggested by Tech Advisor, which has listed the best mathematical apps for children.
As a parent, you may be reluctant to let your child have a mobile phone at too young an age. But, why not tell them that they can have a phone if they use it for school work and revision? Or, introduce some quiet time at the same time each day whereby you allow your little ones to play games on a tablet for 20 minutes (and you don’t even have to tell them that this is for educational purposes – they’ll never know!).
How to Learn More Advanced Mathematics (FREE Resources)
If you want to take your Mathematics Knowledge to the next level, here are some helpful links.
I can’t teach you myself so here are better resources that discuss the topic:
- How to Learn Advanced Mathematics Without Heading to University
- Quora – How can I best learn advanced mathematics on my own?
- Here’s How to Teach Yourself Physics and Math
- Essential Math for Data Science
Steps to Studying Math on Your Own
I’m going to interrupt you for a bit to make something clear: I created this guide to help people who feel like they’re lagging with their Math skills and want to review it, or people who just want to study Math on their own for some reason.
Each example that I’ll give you is just that–a mere example to help you get the point I’m trying to make. It’s still up to you to apply these steps to your own situation.
Step 1. First, determine where you want to end up
Math builds upon itself, so if you want to learn a subject, say, Calculus, always ask:
What subjects are the prerequisites of this subject?
In my own study, I often ask myself a “skill” based question, rather than a topical one.
“What skills do I have to learn to get better at this one?”
Problem Solving is a skill, after all. You can’t get better at problem-solving if you don’t have the tools; the individual mastery of prerequisite topics.
Which brings me to my next point.
Step 2. Determine where to start, obviously
Now that you have determined your end subject, it’s now time to decide which general topic to start with.
For example, Calculus and its applications are easier if you have the knowledge of Analytic Geometry and Trigonometry.
But Analytic Geometry has some Trigonometry elements included.
So, you can decide to start with Trigonometry.
However, if you don’t have the knowledge of “which is the prerequisite of which” I highly recommend that you find an online curriculum.
Here’s one good roadmap for someone who’s learning Math for Data Science.
Step 3. Find a Syllabus to Avoid Unnecessary Depth
If you’re lost, you go to Google Maps.
So what do you do when you don’t have a roadmap or a sequence to learn Math?
Use an already-designed Syllabus. They’ll be the roadmap to your self-studying success.
As I’ve mentioned earlier, these can be easily found online.
I mean, just a single Google Search will give you what you’re looking for.
Or, you can just look at your university’s resources and check syllabi for Math subjects.
Step 4. Gather your References, Solution Manuals, and “Solved Problems” Types of Books
Conventional Math learning requires that you go to school, attend classes, do your homework, and then wait for it to be checked before you complete the feedback loop.
I say that’s highly inefficient.
When there are solution manuals or Solved Problems types of books available, it’s better to actually use them side-by-side to your own problem-solving routine.
For this one, I like the “Schaum’s Outlines” series of books.
The problems are rather hard, the discussions are concise and straight to the point, but you’ll certainly get better at problem-solving EASILY.
Just to be clear, I’m not saying that you should look at the solutions each and every time you’re solving a problem, but whenever you get stuck, you can easily get out and actually learn the solutions faster.
This tight feedback loop is what will allow us to learn math FAST and at our OWN pace.
“What if I don’t understand the material?”
It’s either you don’t have the prerequisites mastered (or not at all), or you’re using an overly complicated book.
Lastly, common sense says that this guide is not the “end-all-be-all” of self-studying Math. You can always consult others when you really get stuck even when you have a solution manual (perhaps it has a typo error or something).
Step 5. Prioritize Deep, Concept-Based Learning
This is brought out by the point raised above, which is to use solution manuals for learning Math to create a quick feedback loop.
However, it’s highly misunderstood by some students.
They feel that when they can memorize how a difficult problem is solved, then that’s good.
It’s a BIG mistake to memorize something you don’t understand.
Relevantly, it’s also a BIG mistake to just understand something but you don’t practice it.
Learn WHY the steps work, because if you do this, you learn once, and solve many.
Step 6. Put Links to Resources in One Place
Since you’re going to be mainly self-studying using Digital Resources, it’s handy to have them all in one place.
Perhaps make them your browser’s homepage.
Make a shortcut or something.
The thing is: make it SO easy for you to access your resources so that you don’t feel friction when you want to study on your own.
This makes it easier to form your study habits–which is always better in the long run.
Step 7. Set aside time for BOTH studying and problem-solving
As I’ve mentioned earlier, just understanding isn’t enough.
You have to practice what you’ve learned.
Just as a beginner can’t play a piano masterpiece instantly after someone good teaches him how to do it, learning new things in Math doesn’t happen with your “aha” moments.
Learning happens when you recall information from your head, not when you’re trying to put things in there.
So, aside from your “absorbing” time, set aside time for practice.
Step 8. Cultivate Deep Work
While practicing, it’s important that you do so without distraction.
Working without internal and external distractions and focusing deliberately on the task at hand, aka Deep Work, improves how your neurons fire together when activated.
This happens because a sheath called myelin is formed whenever you retrieve a piece of information or practice a skill.
When your attention is channeled into practicing problem-solving, you effectively tell your brain that ONLY those neurons activated during problem-solving should be sheathed with myelin.
When you’re distracted, however, this phenomenon happens poorly, and learning chunks don’t form very well.
Step 9. Avoid “Practice, Practice, Practice”, Do This Instead
This is probably the most common advice given to students who ask “how do I get better at Math?”.
We don’t need more time to practice. We just need to practice better.
Practicing is certainly vital, but there are two kinds of practice: Unproductive, and Productive Practice.
If you do everything in a long stretch of time, infrequently during the week, and just repeating the same problem for multiple times until you “get it” before moving on to the next one, then that’s Unproductive Practice.
Productive Practice is smart practice.
Here’s how to do it. Two EASY Steps.
- Spread your practice throughout the day, and throughout the week
- When you get the basic idea of a concept, don’t answer multiple problems with the same solution; answer multiple, unrelated problems. (Interleaving)
By doing these, you’re saving a TON of time and energy into learning your Math.
One easy way to do this is by using Anki, but you’ll have to be a bit creative in creating your decks and settings.
The key is to learn the fundamentals, and that’s why I created a free course.
Who says learning Math should be tedious, and time-consuming?
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