Calculus is one of the most challenging subjects students may take. Some students may find that learning calculus in a classroom may be overwhelming or impossible to understand. Due to its difficulty level, finding a private calculus tutor can be crucial for ensuring academic success.
Here are a few of the reasons why students struggle with calculus:
Students attempt calculus before they have grasped previous concepts
More than any other subject we learn at school, maths requires us to build off of existing knowledge and skills. We ought to be fluent in basic maths before we can progress. Unfortunately, this frequently doesn’t happen. Due to large class sizes and the need to move quickly through a packed syllabus, teachers move ahead before all of their students are fully comfortable with a topic. In maths, this is disaster. It is why so many students feel they do not “get” maths. They are working on difficult problems before they have got to grips with the tools needed to tackle them.
It is abstract
Basic arithmetic, geometry and algebra are all easily explainable with references to the real world. As a calculus tutor helping students who struggle with maths, I can draw upon examples of apples and oranges, of how much things cost, or of real life shapes on a page. This helps students contextualise concepts. However, there is no such analogy to help with ideas of “derivative”, “rate of change”, or “limit” when teaching calculus. It seems like a lot of rules with no relation to anything real.
It is non-intuitive
Before we learn calculus, concepts we cover in maths are mostly intuitive. Once you get your head around the idea that xis just a number, it follows that 2xis double that number, or x+1 is one more than it. With calculus, this is not the case. Why should it be that when you differentiate x2 you should get 2x? Why does integrating give us the area between the curve and the x-axis? It doesn’t seem to make sense.
Students have been taught rules but not reasons
A quick fix for students struggling with maths is to learn rules to solve specific problems. But this is akin to papering over cracks in order to sell a house. As time goes on, those cracks are going to cause big issues. Students need to understand what they’re actually doing. With particular regard to calculus, many students don’t know what a function really is. They think of it as just another equation instead of an “input-output machine”. This means when we introduce calculus as a way of describing how functions behave, the student has no idea how to interpret that. A function can behave?!
The good news is that this can all be fixed. If you are struggling with calculus there are simple steps you can take:
Fill in previous gaps
Make sure you fully understand all the calculus concepts you have covered in previous years. Even if you passed your exam that year, take the time to go back and make sure you really understand what’s going on and why. A calculus tutor can help you with this.
Speed up your basics
Calculus draws on many different areas of maths and the problems can take time. They can be overwhelming. If you can speed through the easier aspects of solving a problem, the brain power required to solve calculus problems is reduced dramatically. Go back and practice easier questions and methods until you can do them in your sleep.
Practice calculus problems
Calculus can be hard. It’s not that intuitive at first and there’s a lot to get your head around. But maths is like a musical instrument or a language – you get better with practice. If your basics are solid, but you still can’t do calculus problems, just keep practicing them. Every day if you can! With time they will start to flow and become natural to you.
Share now :
Anxiety: the real reason you fail exams
July 9, 2018
What is the definition of anxiety?
There are a number of definitions of anxiety. The primary one is…
It’s the anticipation of a future (or sometimes a past) threat. Fear is incorporated in that definition, but this is usually regarded as a real threat to survival, rather than a perceived threat.
High stress levels can result in muscle tension, poor sleep patterns, cautious behaviours and/or avoidant behaviours. These maladaptive behaviours include failing to attend events, usually cancelling last minute and avoiding specific social situations, like giving speeches. But, it also incorporates other mental disorders, including OCD, social phobias and panic disorders.
Due to poor definitions and sometimes even diagnosis. It’s pretty clear that a huge amount of people, at some time in their life, will suffer from anxiety. It can be born out of a daily hassle or an upsetting issue, like workplace stress, family arguments or daily commutes. Anxiety affects, more or less, everyone. But how people cope with it differs immensely.
Are there specific examples of exam–related-anxiety?
A key example is exams stress. There is a clear correlation between state anxiety (mental worry) and exams. Usually, as exams draw nearer, anxiety levels can rise to detrimental levels. Lotz and Sparfeldt found that “State Test Anxiety showed an overall increase and peaked shortly before exams.” They also found that “Trait worry and emotional stress correlated substantially with State Test Anxiety.” (Lotz and Sparfeldt 2017)
So, in the lead up to exams, students’ State Anxiety (unpleasant emotional arousal and stress, cognitive based (thought processes)) and Trait Anxiety (individual difference and biological predispositions) rise. Individuals with naturally high levels of trait anxiety, and those who are ‘worriers’ are already more prone to high levels of State anxiety. Hormones can also play a part. It’s suggested that females experience higher levels of trait anxiety than males. This corresponds to girls reporting higher levels of stress in exams.
Does school life fuel anxiety in children?
Not wanting to go to school is a common morning ritual, but there’s a difference between not enjoying school and fearing going to school. Communication with children is the only real way to know and to help. With culture and society expecting more from children and even nursery kids, there is a rise in anxiety-related issues. At this age, it’s extremely hard to help, as sometimes, communication skills are still growing and changing. Intervention at this age is not really advisable or wanted by parents – they just want their kids to be happy.
But with new exams, the 4+ for example, and the issue with stretched staffing in schools, identifying and helping children with this is really hard. On the other end of the scale, it’s well documented that university students struggle with pressure, stress and anxiety. The rise in these cases, you’d assume, is isolation (universities have a very much ‘get on with it’ approach in their support) coupled with exam stress. This is leading to an increased state of numerous anxieties, and it’s becoming commonplace at university.
Another issue, which is giving rise to anxiety, is the school environment.
A school is a fantastic breeding ground for stress. Exam stress, pressure from teachers, social conformity, bullying and ridiculously high expectations on students all lead to one thing. The issue is that no one is doing anything to help. Children are on their own, and when they are on their own, they are on their phones. As discussed by Simon Sinek, we know that phones and specific apps are addictive. This addiction is not even being treated. If kids do have the skills to help alleviate their stress and recognise their anxieties, they don’t use them. Their addiction– the smart phone, the cause of a lot of anxieties– is easy to access and to be influenced by. If you can’t leave your phone alone for 2 minutes, that’s an addiction. Addictions lead to dependence, and dependency leads to worry and stress.
Schools don’t focus on individuals, they focus on cohorts– “90% of our students gain A-B at A-level.” Schools are exam factories, focusing on the masses, not the individual. As far as social support and stress interventions are concerned, schools are failing. It’s important to note that I’m not, as one myself, blaming teachers. Their jobs are full-on, and they won’t have time to help individuals. Schools should implement tutoring sessions, to help specific children, to help them deal with their anxieties, rather than assuming that either the stress will dissipate, or ‘everyone is in the same boat during exams’.
So, does small group and one-on-one tutoring work?
One-on-one mentoring is proven to work. It’s proven to alleviate stress and reduce arousal and also boost motivation and confidence. In 2015, Cliff Boutelle found that focusing on personality factors and traits between mentor-mentee relationships helps to reduce anxiety and stress. We’re back to traits again. To reduce anxiety, stress and depression we need to look at people’s traits– how they operate, how they think and how they work. Yes, it takes time and effort. But it’s worth it long term, as you have students who aren’t stressed and perform well.
What does other research show us about anxiety?
Research and studies into anxiety in early life have been associated with long-term adverse outcomes and negative effects in adult life. These adverse outcomes include substance abuse, depression, abnormalities in brain function and personality disorders and dysfunctions. And more often than not, poor intra and inter personal relationships.
‘Dependency was also a big factor; high anxiety leads to nicotine, drugs and alcohol abuse’ Alexander McFarlane et al. Other studies have shown that gastrointestinal problems and sleep disturbances were significantly related to stressors, Ashley E. Nixon et al. Nixon also found that ‘it’s important to examine physical symptoms, as they are related to a wide range of job stressors.’
Psychological stress and anxiety can lead to physiological illness, both acute and chronic. Kiecolt-Glazer found that in a number of medical students, natural killer cells (white blood cells) were significantly reduced. What was interesting, is that these NK cells were reduced more severely just before their finals, compared to two weeks before and a week after their exams. This shows that while stress causes high anxiety in the short term, it’s also a long-term health worry, and can result in immune-suppression.
What about people’s own experiences?
More recently, Megan Nolan discussed the rise in her worries and fears from her own experiences, and subsequent application to students taking exams this year. She recalled the time when ‘my chest simply stopped letting me push it out so that air could flow in.’ This is scary. It’s now estimated that there has been a 70% increase in anxiety and depression in teenagers over the past 25 years. That is alarming – and as far as I’m concerned, it’s not something that anyone really talks about. Obesity and diet are covered by the press every day, very few mention arousal, stress or depression. Specifically compared to the volume of new cases and diagnosis.
A student I taught discussed more with me, his teacher, than his parents, peers or friends. I think he saw it as a form of weakness. He thought it was just him who it affected. Nonsense, it affects everyone – in its own way. Anxiety is bad, it’s inhibiting, it’s painful, but it’s not lonely, you’re not on your own! Some people habitually bite their nails, twitch, or look from the corner of their eyes during conversation. Some people get a dry mouth and others can only look at the future pessimistically. But that’s ok, we’re all different. What we need are coping strategies.
How can I reduce my anxiety levels?
There are a few ways to reduce it. First, you need to look at somatic and cognitive anxiety management techniques. Somatic techniques include deep breathing and progressive muscle relaxation. These are usually non-specific techniques and can be used in a number of anxiety-provoking situations. Whereas, cognitive techniques are more specific, like anxiety in a social situation. You need to recognise your anxiety– the feeling of dread and sickness when preparing for a social situation, or an interview, or an exam.
You can use specific techniques for coping and these are anxiety controlling skills. These skills include positive self-talk, rational thinking and imagery. They do require time, effort and often a mentor to support you. However, they are lifelong skills that will help reduce anxiety, stress and fear.
Are there any other techniques?
Two other non-invasive techniques are meditation and mindfulness. Meditation has been adopted in many countries, although these are usually countries which are less focused on exams. A school in San Francisco, however, ran a meditation programme and found an improvement in pupil’s behaviours, work ethic and happiness. Years later, the school now has some of the best attendance rates in the city. Reduced anxiety and stress leads to improved mental health and cognitive function. Mindfulness has also been used, but it’s been criticised as it can result in some children becoming more anxious as they’re focusing on their specific stress.
Tutor House is looking for people – students, parents and teachers to share their experience of anxiety. How it affected/affects their everyday life? And how you beat or are coping with anxiety?
How does the International Baccalaureate (I.B) work?
September 12, 2012
,,An increasing number of private and grammar schools are now offering the IB programme.
Students undertaking the IB need to have strong subject knowledge in humanities and sciences.
Private tutoring can help identify and boost students weaknesses. At tutor house we can help with Essay writing, Languages, Social and Natural Sciences and Mathematics.
Contact tutor house for assistance.
The IB Curriculum:
Students choose from one subject from each of the six compulsory groups. In addition, the IB programme includes Extended essay writing (in-depth essay of one of the subjects the student has chosen) Theory of knowledge (students reflect on the nature of knowledge by examining areas including perception, emotion and artistic and historical aspects) and Creativity, action and service (completing tasks outside of the classroom.)
The six groups are:
1: Studies in Lauguage and Literature
2: Lauguage acquisition
3: Indiviuals and societies
4: Experimaental science
5: Mathematics and computer science
6: The arts
N.B- The sixth subject chosen by students may be a arts subject (group 6) or another subject from group 1-5.
The Cambridge Pre-U course helps prepare students for university. The course has become popular in recent times as an alternative to A-Levels. The Pre-U course follows on from IGCSE and Cambridge Secondary 2 qualifications.
The Pre-U course is available in 27 subjects, students choose from three.
Tutors at tutor house have experience in teaching Pre-U and can help all students via private tuition and support.
At tutor house we provide short and long-term home schooling. We listen to the student’s requirement and devise a programme most suited to them. This can include private tuition, one-on-one support, special educational support and residential tuition, both in the U.K and abroad.
Why UK children are academically falling behind other nations
December 20, 2013
Why UK children are academically falling behind other nations
Tutor House was recently asked to do an interview live on the BBC. Alex was asked a number of questions relating to the latest PISA results and how they’re relevant to our educational standards.
Why is the UK lagging behind other countries around the world? And why is Asia paving the way to academic success?
Is short, Asian countries, including China, Singapore, Hong Kong and Japan place huge importance on education, learning and tuition. Students spend hours of additional time, outside of school, being privately tutored. Passing exams and going to university is the most important thing. Teachers and tutors are well respected in Asia, they’re idolised and looked up to. That’s not really the case in the UK. Yes parents require tutors for they’re children, and 1 in 4 children are tutored at some stage in their lives in the UK. However, it’s the time and effort that non-western students spend on their education and studies. In some Asian countries children spend up to 5 hours a day studying, most 16 year olds in the UK, that would be per week.