Forgetting Curve

This is a curve that I have seen quite a few times now, and I know it looks complicated, but bear with me. This curve shows the benefits of spaced repetition, and in this article I would like to explain it to you. 

So what can you do to prevent this? You memorize it before you forget everything. In the diagram, the threshold is set as 90%, but I would hope to remember at least 70% of what I memorized when I recheck and restudy. Still, after I have first learnt something, I try to recheck my notes within the first 12 hours. That way, my forgetting curve is less steep, like the light green curve, and it would take around 30 days to forget 60% of what I have learnt. During the weekends, I always revise what I have learnt as my 2nd repetition, reboosting my memory up to 100%. Of course, this is my personal experience, and you can adjust it to your personal schedule or follow the diagram above. No matter what, this is the advantage of spaced repetition: not only does it help you with memorization, it helps you not forget something for a longer period of time the more times you repeat the memorization.

In my personal experience, this is something that applies to nearly all subjects, and it can be annoying sometimes. Oh, why do I have to do this? I already know everything here! That is why people find studying not easy at all. It requires you to retain information, during the breaks or the holidays, and yet one missed repetition could be the difference between knowing what you are doing during a test and forgetting everything that you have learned in class. Obviously, I am not telling you to study everything that you have learned in school every day. But you should at least look through your notes every once in a while (and the period is up to you to decide), in order to ensure you actually know everything and haven’t forgotten too much of the information that you have learned. 

I hope this article helped you in your learning journey!

Memory For Mathematics

Mathematics and memory. These two things seem unrelated… or so I thought. In this article, I will be exploring why memory is important for mathematics.

Many people argue that memorizing formulas is necessary for mathematics. I don’t completely disagree. Being able to memorize formulas is a good skill to have for mathematics. Let’s take an example. Being able to memorize the quadratic formula x=-bb2-4ac2a is a very good thing, especially when you don’t have a formula booklet. It helps you to solve quadratic equations much faster. However, I also believe that in order for people to become better mathematicians, we should not just memorize things because we are told to. We should actually try and get to the formula itself using things that we have learned. Continuing my example, quadratic formula can be induced from completing the square: ax2+bx+c=0, a(x2+bax)+c=0, a(x2+bax+b24a2-b24a2)+c=0, a(x+b2a)2-b24a+c=0, a(x+b2a)2=b2-4ac4a, (x+b2a)2=b2-4ac4a2, (x+b2a) = b2-4ac2a, and therefore x=-bb2-4ac2a. Of course, I am not saying you should induce a formula every single time. It would take too much time. Besides, if you mess up the induction stage, you will get the wrong answer. What I am saying is that you should know how to get to a formula, just so that you can induce it in case you didn’t memorize it. Memorization comes naturally afterwards, once you have induced it or used it many times. That is probably the only reason why I can memorize  a formula, not because I tried to stuff it in my head with force, but because I know how I can get to the formula, and I used it a couple of times.

Memory also plays a big role in mental math. I have always used mental math myself, and it involves calculating things in your head, without calculator, pen or paper. If you were asked what is 1 + 1, in math class, with no humor intended, you would nearly immediately say 2, very likely without any “working out” on paper. If I asked you something more complicated, like 13 times 46, you might need a calculator. I would calculate in my brain, 13 times 4 is 52 (and this comes from my memory) and 13 times 6 is 78 (once again, from practice and memory), and 520 + 78 is simply 598. This process is done in a few seconds for me, but might take longer for others. Some harder questions could also take me a longer time, but most calculations involve knowing the basic stuff in your head completely. If you were to ask me to memorize the multiplication tables I would probably get nearly nothing wrong, probably 1 wrong in a 100 questions. Being able to do mental maths reduced my reliance on calculators as well, which means I don’t really use my calculator except during class and when I solve complex math problems.

Memory and math may seem unrelated at first. But when you dive deep into mathematics and its fields, memorizing and understanding the formula, as well as mental maths, can enhance your mathematical abilities. I hope you enjoyed this article!

Memories

Decisions we make as people are all based on what we know. Our memory is what allows us to keep in mind our past experiences and turn them into lessons that drive our decisions, and in turn that shape the person we become. Everything that shapes your personality is based on memory, for example, education . When a child gets grounded for doing something, his memory will automatically link the action they did to being grounded, preventing it from happening again. It is also what allows us to remember school lessons and use them when needed. But what factors affect our memories and how we remember things ? Memories are not fully reliable, creating a bias in our decision making. Factors like sleep, emotions, attention, interference and reconsolidation impact our memories, in both positive or negative ways.

Getting enough sleep is a critical factor of memory. It is when our brain strengthens the information, ensuring an efficient storage. During sleep, the brain processes and solidifies the memories of the day, turning them into a more robust and long term storage. The brain also links new memories to old ones. Establishing a connection makes it easier to remember and to retrieve later. A lack of sleep weakens these connections, making it harder to learn and remember, because we struggle to focus and to be efficient. Lastly, sleep allows the brain to remove the useless memories and to only keep what is important, allowing it to centralise and to make space for the useful memories. 

Another factor is emotions. Emotional experiences activate the amygdala, a part of the brain that processes emotions. This part of the brain communicates with another part of the brain called the hippocampus, the part that forms our memories, in order to strengthen them. Moreover, emotions trigger the release of stress hormones, like cortisol or adrenaline, which positively impact the responsiveness of the neurons in the amygdala and the hippocampus. This leads to stronger memory consolidation, making emotional events more likely to be remembered over time than neutral ones. Emotional experiences also tend to catch more of our attention, leading us to focus more in order to remember the most significant details. However, prolonged or extreme emotional states, such as traumas, tend to act like a bias and can lead to faulty memory processing. 

The next factor is attention. The attention decides which information is important enough to be stored and remembered. When attention is divided, such as when multitasking, the brain struggles to process the competing information, leading to a weaker remembering. Attention is also required to search for memories and to remember things, and it also helps to make them more solid, in order for them to be more permanent. However, the relationship between memories and attention is not one sided, as memories also dictate when to pay attention or not, based on past experiences.

Interferences also affect our memories. This refers to old or new memories being similar to other memories, creating confusion and an overall weakening of the two memories. Retroactive interference refers to new information making it harder to remember old information, while proactive interference refers to old information hindering the ability to learn new information. The more similar the pieces of information are, the more likely it is to create interference.

Lastly, reconsolidation affects our memories by making them temporarily unstable and susceptible to modification after they are recalled. If it can help to update memories and strengthen them, which keeps memories relevant, it can also weaken them before they are stabilized. New memories can be used to update older ones, in order to consolidate them by integrating new pieces of information. For example, a highly traumatising experience can be updated with new, calming information, lessening its emotional impact. Therefore, it is often used therapeutically, by intentionally recreating a traumatic experience, but modifying it so that it is less emotionally impacting, in order to reduce the trauma. Reconsolidation can also weaken memories if new information is contradictory to older pieces of information.

To conclude, memories are not full and accurate representations of what we experience as they are constantly impacted and modified by our brain. A lack of sleep, a lack of attention and interference weaken memories, whereas strong attention and emotions help to make them more solid. Moreover, reconsolidation modifies our memories based on other memories, keeping them updated, or weakening them due to contradictory information. Therefore, our memories are in constant upheaval and time can make them less reliable.