Joe’s Jotter: Core Skills for Revising Junior Cycle Maths

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In light of the how the last few years have panned out, students (and indeed their Parents) need to examine closely their daily routine to ensure effective learning is now happening. Maths is a subject that tends to take up more time than others and hence 3rd and 6th years should firstly consolidate what they know and then make a list of topics that they need to learn and revise going forward. Spending time on past exam questions and learning the terminology that appears on them is wise use of any student’s time now.

From this point of view, I would recommend that all exam students start a ‘Maths hardback’. Fill this hardback with new words, formulae’s not present in the log tables and keynotes. Divide the hardback into sections, one for each topic on the course. Secondly, when revising at home, students should test themselves against the clock on full or partial past exam questions. Set these as your two main targets for the next two months.

Algebra is the Language of Maths

In Junior and Leaving Cert Maths, you need a good solid Algebra foundation to build on in order to excel in topics like Geometry, Trigonometry, Functions and Graphs and Probability. I estimate that Algebra is linked to at least thirty percent of Maths exam papers at all levels now. Take time to understand the rules of Algebra especially those linked to expressions, functions, and graphs. With all its linkages, I, one hundred percent think that Algebra is the most important topic in Maths. Words and phrases that appear in your book and in the past exam papers are a close second. The State Exams Commission (SEC) now place more emphasis on students knowing and understanding what things mean in Maths. It has moved away from the traditional numerical calculations.

The Importance of English

There is also more ‘English’ than ever on Maths exam papers, and it is crucial that you start familiarising yourself with these words. If you are not familiar with the words and phrases that can appear on the paper, you may not even be able to get a question started. This would be an awful shame given the amount of time you have spent learning mathematical concepts on your course. If you have dyslexia, I understand that dealing with words in Maths is doubly difficult. You need to be aware that different words have a different meaning depending on the subject you are studying. For example, the word ‘Evaluate’ in Maths is very different to its meaning in the subject English.

In my book ‘How to ACE the Leaving Certificate’ for all subjects, there is a full chapter advising on how you can improve your Maths. In this book, I present and explain one hundred sample key words and phrases to kick start your understanding of the language of Maths. This list is suitable for both Junior and Senior Cycle students, remembering that some of the more difficult words would not appear on a Junior Cycle paper. I would strongly encourage students to create their own list and add to this one, investigating the exact meaning of words you come across daily. You will learn loads through your own active investigations.

In summary, I recommend that every time you encounter a new Maths word or formula, write down what it means to you in an A5/A6 hardback. This hack can be applied to all subjects and these hardbacks can be carried with you (literally) all the way up to sixth year. Using simple explanations that you understand in your hardbacks will help you recall what the words mean later. Being familiar with the words that appear on a Maths exam paper has now become a key component of success in the subject.

Test yourself at home in Maths

The more ‘exam smart’ you are, the better you will perform on exam day. I have seen the best students do homework to perfection all year, really knowing their stuff, but ultimately not reach their potential In Maths come June. Every year loads of super students misjudge the timing on the paper. It is imperative that you stick exactly to the allocated time for each question. In Leaving Cert Maths, the timing is different this year due to increased choice on the paper. Junior Cycle timing in Maths will be written on the paper. Please familiarise yourself with the timing of Leaving Cert Maths questions for 2023.

You should now start timing yourself on past exam questions at home. At Leaving Cert level, part a’s and b’s of Section A are a good place to start. Attempt questions that look familiar first, maybe even consulting your book/notes from time to time. It’s all learning. Once completed, check your workings out against a good exam paper solutions book. If you have struggled to make reasonable inroads into answering, I suggest you re-write the steps of the full solution on a page, really thinking about why each step is important as you write it. Every few weeks, tackle some longer questions and write out the steps (in English) how you would solve it. This better solidifies the method you used in your head.

There are many advantages to creating your own ‘home test environment’. You should constantly test yourself on material revised. During these mini home tests, use a stopwatch to ensure you are ‘sticking to the time’ for each individual question part. This is vital across all subjects, but especially in Maths. In creating this little bit of time pressure, you are replicating the exam hall environment. Train as you propose to play.

Please do get in touch with me if you have any Maths queries. I would be delighted to guide or help you in some way. Thanks for reading. Joe

‘During the next few months, do one thing each day that you really enjoy.’

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

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Joe’s Jotter: How to become a Specialist at Maths Exams (Act 1)

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Surprisingly, thousands of top students over the years have struggled when it comes to performing to their ability in Maths exams. In my experience, there is now a disconnect between how teachers teach a Maths class, and the skills students use during a Maths test.

For some students, a fear almost overcomes them with the thought of a Maths test upcoming.  Similarly, a fair percentage of students that breeze through other subject exams freeze during Maths ones. A significant aspect of Teaching Maths now is helping students overcome their anxieties, while teaching them the key techniques to retain that calmness and confidence.

Sitting a Maths exam is a skill, but it is something that if you practice and apply a defined strategy to, you can get quite good at it. Every day, I work closely with students to teach them these vital skills to excel in all kinds of Maths assessments.  Below are my insights into how to ACE any Maths exam – from the five minute class test to the ‘full on’ final state examination.

Make Changes to How You Revise and Prepare for Maths Exams

Below are some clipits of advice to help you get set for a Maths exam. Applying these practical guidelines in your revision plan and during exams will 100% improve your grades.

  1. Apply the skills you have learned from practicing past exam questions under time pressure at home. A time budget plan is a key part to success in any Maths exam.
  2. Keep a hardback of Maths notes. Being familiar with words that appear on Maths papers are vital to aid understanding of the questions you are being quizzed on.
  3. Find multiple-choice questions online or ask your teacher if they have some. These are like ‘speed-studying’ and require less time to work through and test yourself on.
  4. Attempt past exam questions. After completing each past exam question, be sure to view its exact and fully developed solution to see how your work stacks up against it.
  5. Stay alert for key words and phrases to guide you through a question. For example, the volume of an object should allow you to find measurements on it by working backwards.
  6. Use familiar mathematics to guide you. Think back to relate the test question to a concept, topic, or technique your teacher did with you in class.
  7. Formulas are key in Maths. Reflect on what formula you know that may help you solve the problem. This formula may in fact be printed on the test paper or in your log tables.
  8. Can the diagram in the question help? Writing relevant information on a given diagram may prompt relevant thoughts and connections to help you start a maths question.
  9. Show all workings. Always show how to get from one step to the next. Provide all your workings out to support your answer. At the end of each question, always ask yourself ‘Is this a realistic answer or solution to the question being asked?’ Example: Ten metres would never be an acceptable answer for the height of a pencil. You get the Idea.
  10. Read the entire question… twice. Check what the question is asking and in what form you need to present the answer. For example, you might need to round the final answer (decimal places, significant figures, scientific notation) or convert to an annual amount.
  11. Note the key Information given in the question onto your answer book. Subsequently, note the Information that isn’t present. Link these two to help complete the full jigsaw.
  12. Don’t be afraid to utilise diagrams or tables in your solution. This will clarify your understanding of the information in the question and support your workings out.
  13. Show all relevant substitution (subbing in). This shows the examiner that correct maths processes are being used (e.g. showing the substitution of an x-value into a function).

‘Act 2’ of this two part drama will follow in a few weeks… Joe

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

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Joe’s Jotter: The Importance of Getting that Extra Support in Maths.

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As a Maths teacher of the last 20 years, I understand the struggles students have with Maths on a day to day basis.  They are frustrated with not being able to understand methods in class, their friends progressing quicker than them, not being able to get maths questions started and either spending too much time or not being able to attempt homework at all.

The key to having more success in Maths is being open to new methods and using each night to practice questions that the teacher has shown that day. Maths requires a higher level of dedication and persistence than most other subjects. When I was in school in the 1990’s, only those with a strong aptitude for the subject were successful in it. I feel that today it is more important to stick the course, ride out the storms, work hard and not give up; as opposed to being a natural Maths talent.

The reality is that many students will need extra support outside the mainstream classroom, and it is important to find a teacher or tutor they can relate to and has the ability to explain concepts in simple terms. Looking for extra support in Maths is not a sign of weakness, the opposite in fact. It is often no fault of the student when they seek this extra help to try, and both boost their confidence and grades in the subject.

How an External Maths Tutor Could Benefit Your Child

That extra bit of support in Maths can make all the difference.  From a short term point of view, students need someone who can be there for them should they get stuck a question. They also need someone who can see the bigger picture, allowing them to work towards their longer term goal. Here are some of the benefits and subtle advantages of having a tutor in Maths:

  1. Parents can contact your tutor directly and keep up to date with specific progress.
  2. It is a more relaxed atmosphere where your child is more likely to ask questions.
  3. Tutors tend to focus on helping your child be an expert on ‘tackling’ exam paper questions.
  4. The tutor will hopefully give your child a more positive outlook towards the subject.
  5. The tutor will give your child insights on how to revise Maths (compared to other subjects).
  6. Most tutors will set the foundations with core work in Algebra, Functions and Equations.
  7. Your child’s confidence will grow as they rebuild core aspects of Maths they missed out on.
  8. Your child will be less anxious about keeping up in class and with their friends.
  9. It will give your child the organisational skills to plan for upcoming exams.
  10. Your child’s weaknesses in Maths will be identified and fixed quicker.
  11. Those who struggle in school usually try to hide in Maths. Tutors can tease this out.
  12. Most tutors will be contactable when students run into ‘Maths trouble’ at home.
  13. The advent of Online Maths tuition saves wasted time in the car each week.
  14. Maths tuition often shows a student’s real ability, which may not be apparent in school.
  15. Better engagement with the subject gives students that ‘can do’ attitude to work alone.
  16. Tutors can focus more on revision of key topics and ensuring core skills are enhanced.
  17. Increased help in Maths allows students to relax more and focus on other subjects.
  18. Students often move up two or three grades with that extra bit of reassurance & guidance.
  19. Students can request extra notes for topics they may be finding difficult in school.
  20. With many 3rd level courses having a Maths module, this support ‘invests in their future’.

‘It is never too late to step into your own greatness.’

 More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

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Joe’s Jotter: How to Choose Your 5th Year Subjects

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Choosing subjects for 5th Year can be daunting enough, and soon many 3rd and all Transition (4th) year students will be faced with that task in school. A 4th year student will have had more time to contemplate options, and so sometimes make more considered choices than those coming straight from the Junior Cycle (3rd year), and this is something Parents need to be aware of. It is important to put some thought into how subject choices may influence career options later. Students should now consult with all their teachers and ask them about the level of work that’s required for success in a given subject at a specific level.

Third Level Considerations

Students, if you have a third level course or career in mind, it is important now to do a little research into its content and investigate if there are any ‘minimum entry requirement’ to gain access to it. All courses now have detailed descriptions of each module online, listing out exactly what you will be required to study on a year by year basis. It is important to note that no matter what points you achieve; you will not be allowed onto a course unless you achieve its minimum entry requirement (if it has one). This may guide you to choose particular subjects. In the case of compulsory exam subjects (which you will be studying anyway), obviously there is no choice to make there. However, if there is a requirement on your desired course to score a certain grade in a foreign language or other subject, you will need to opt for this subject if your heart is set on that course. However, to this tune, I would strongly recommend you have a plan B and C in place when choosing courses and will discuss the importance of this in articles later in the year.

In relation to specific college requirements, it is useful to know that the NUI colleges (UCD, UCG, UCC, Maynooth etc) require a pass in a third language [excluding English and Gaeilge] for many of their courses. However there are now exceptions to this: UCD has dropped this requirement for Engineering and Agricultural Science, and Maynooth has removed it for Business, Accounting, Finance and Law. Trinity, UL, DCU and the Institutes of Technology don’t have this third language requirement, except for language courses. Again, the advice here is to double check the requirements online for each individual course and college.

There are also ‘Subject requirements’ on courses. Examples include: to study Primary teaching, you need a H4 in Irish, Engineering courses may require honours Maths and sometimes a science subject, Medicine may require two science subjects (one being chemistry) and Nursing may also require a science subject. The savvy student will do some research on websites like Qualifax and Careers portal to get a handle on the exact requirements of courses they are Interested in. Be fully informed prior to CAO time.

The Eight ACE ‘Do’s’ for choosing Subjects

All in all, when it comes to subject choice, students should think a little about their futures, talk to teachers, look at courses they may have an Interest in and discuss with their peers gone ahead how they found studying the subject. Take your time and choose well. It may be wiser to choose subjects you have an interest in, as opposed to ones you feel you must choose in order to get into a certain career later. It is definitely a balancing act. Here are my eight ACE do’s for subject choice for 3rd and 4th year students:

  • Do…Choose subjects you enjoy learning about
  • Do…Discuss it with as many people as you can including teachers and peers etc
  • Do…Try and keep your options open as much as possible
  • Do…Choose subjects you have some kind of a flair for or Interest In
  • Do…Research each subject’s content on www.curriculumonline.ie
  • Do…Choose subjects linked to a possible future career you are considering
  • Do…Write down the Pro’s/Con’s when trying to decide between two subjects
  • Do…Make the final decision yourself (not your friends, teachers, or parents)

Final Choice Advice

The best advice I can give about subjects is to select ones that keep your options open.

You can best do this by choosing one foreign language and ensuring that at least two of the other three subjects picked are ones you have an interest in or flair for. Remember that you will be spending a lot of time studying your chosen subjects over the next two years and the nightmare scenario would be dreading going into that class each day. I myself selected a subject I regretted taking in 5th year, but luckily was allowed switch later. You may not be as fortunate in your school, so try and get it right the first time to save any unnecessary anxiety. I also have a degree in a subject that I didn’t study for my Leaving Cert. Life can be funny, so my advice is ‘rule nothing out’ and keep as many doors open as possible.

In choosing subjects, always play to your strengths. For example, if business is something you are really interested in, you could choose Business and Accounting (assuming they don’t clash on the school timetable). Similarly, if Science is your area of passion, you could opt for two of the Science subjects i.e. Biology, Chemistry or Physics. Applied Maths or Agricultural Science may also be other options here.

Enthusiasm for any subject will foster a desire to learn more about it and studying these subjects in Senior Cycle won’t even feel like learning. If you are struggling with this decision, put all the information and swaying factors out on the kitchen table. Usually, your heart will guide you one way or the other at that stage. I wish you every success with your decision. Joe

‘Compare yourself against yourself, not how much work your friend is doing.’

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

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Joe’s Jotter: Grade Inflation 2023 – Remarkable Subject Stats

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With Leaving Certificate grades ‘apparently’ rising recently, I decided to do my own comparison analysis of Leaving Certificate results from the years 2018 and 2022 as per Table 1 below. There had already been a steady rise in performance and points over the last twenty years anyway, but a recent sizable increase was now apparent. So, are our students working harder or is there something going on in the system?

Upon inspection, the percentage of students scoring a H4 or above in 2022 (A H4 is between 60% and 70% at higher level) has produced very surprising results. What amazed me from looking at the statistics was how grades in many subjects have jumped. In the eleven subjects I sampled, the average increase (H4 grades or above) when comparing LC 2018 to 2022 was almost 10%. As a Maths teacher, it is particularly concerning for me to see a cosmic jump in my own subject. I feel that Leaving Cert higher level Maths is now consequentially devalued, as there is no way students are performing that much better in four short years.

 

Table 1: The percentage of students that scored a H4 or above in LC 2022 and 2018

Sample Subject Percentage of Students achieving a H4 or above (2022) Percentage of Students achieving a H4 or above (2018) % Increase for students between 2018 and 2022
Music 97%  89% +8%
Technology 83%  72% +11%
Engineering 81%  70% +11%
Irish 79%  70% +9%
Design & Comm Graphics (DCG) 79%  70% +9%
Home Economics (S&S) 79%  68% +11%
Accounting 69%  63% +6%
Biology 68%  61% +7%
Chemistry 67%  61% +6%
Maths 81%  60% +21%
Physics 68%  59% +9%

*Source: Data from www.examinations.ie

From this data, my feeling is that you cannot compare Leaving Cert students who completed exams before 2018 to the 2021 or 2022 cohort; and of course we are doing so. This throws up a lot of questions about where our education system is going. It seems a new benchmark has been set for future student results, and we aren’t going back.

Is it a ‘medal for everyone’ mentality now? How can we compare Leaving Certificate results before, during and after the pandemic? Even the recent 2022 results (with Covid 19 a much less significant nuisance) are very high. I view this Grade Inflation as ‘optics’, and how Ireland’s PISA scores ‘need’ to compare globally. I welcome the Leaving Certificate review now, with a view to more continuous assessment; but there must be proper teacher input.

With increasing marking scheme flexibility and grades rising, the original bell curve is being rewritten. Students are evidently being ‘marked up’ on their efforts and are possibly heading to college with unrealistic expectations. Can the class of 2023 actually revise and prepare their own high quality notes? With many struggling in first year in college, it seems no. Students are scoring higher than ever, but are they more knowledgeable than their predecessors? Radical percentage increases over short periods of time does not sit well with me. Will these changes serve our students well for third level study and future life? To be honest, I am doubtful. Not everything in life will be handed to you. Joe

More details about Joe’s Maths Tuition Classes 2023 for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the below links:

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition
ACE Maths Solution Books: acesolutionbooks.com/ace-solution-books-package/

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Joe’s Jotter: Preparing for a Mock Paper in Maths (3rd & 6th Yrs)

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As third and sixth years prepare for their Mock Paper in Maths, here are some quick pointers to help them be ready. Some students get quite anxious about the Mock examinations, but I always feel the focus should be on preparing and being ready for the final June exams. Here are my ACE tips for the Mocks 2023:

  1. Focus on getting the timing right for each question on the day. This is one of the main ‘learnings’ to take from the Mocks. You should come away with better timing skills.
  2. Practice easier past exam question that you feel confident on beforehand. I wouldn’t take on ‘rock hard’ or new content that may actually sway your existing confidence.
  3. Write down all the formula’s that you need to know for the exam (those that are not in your Log Tables). Be very familiar with what formulas are in your Log Tables.
  4. I would give the textbook a break for a short period. Know the core skills and use your notes from class to help you tackle more straightforward questions in preparation.
  5. Do Maths revision in short bursts. Maths can be quite intense, especially if you take on longer past exam questions. Forty mins max and then take a break. Stay fresh!
  6. Rotate your Maths revision between topics over the next few weeks. This will keep your brain more tuned and aid motivation. Note all the key points into a hard back.
  7. Target three main topics on both Paper 1 and Paper 2 (Leaving Certs) as opposed to trying to cover the whole course. It isn’t possible in two weeks. Sensibility rules!
  8. Get advice from a Maths teacher. Ask your teacher ‘how should you best prepare for the Maths mock?’ Each teacher will have their own take on best to prep for this exam.
  9. Invest in a good Maths Solutions book. This will allow you to check your solutions to questions in a step-by-step manner at home. ACE Maths Solution Books will help here.
  10. Be realistic with your Maths Mock exam. You have still so much more to cover in class and haven’t actually sat down to do a full exam paper yet. Time is still on your side. 

To find out more about how to approach the Mock examinations for all subjects (among other topics), there is a full chapter with advice and guidance on it in my ACE Study Guidebook entitled ‘How to ACE the Leaving Certificate’ for all subjects. This textbook is suitable for all students from second year to sixth.

Wishing you all the luck,

Joe.
ACE Maths Tuition
W: acesolutionbooks.com