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

Joe’s Jotter – Should I Persevere with Higher Level Maths in 2023?

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More students over the last few years have taken on the task that is Leaving Cert Higher Maths. In June 2022, out of the 57,347 who sat a Leaving Certificate Mathematics Paper, 21,265 of them opted for higher level (37%). Even though the bonus points are very enticing, students need to be careful and be fully aware of what exactly they are embarking on. In my experience, there is a lingering doubt among many 5th and 6th years about being able to tackle higher Maths. Scoring low grades in class tests doesn’t really do much for confidence, but it doesn’t automatically mean you should change level. The question is: Should you remain battling higher level Maths or is it worth the time and effort at all?

This article should reassure those suitable for higher (those who fight the good fight day after day) that they can in fact achieve what they are aiming for. Each year, deciding Maths levels is a tricky issue for students and involves many considerations. It is made even more complex in this subject with the bonus points at play. For those of you who are unsure about higher Maths, it may be worth applying some logic to any inclination to switch. As well you know, us ‘Maths creatures’ are very logical beings lol.  I find that logic is more factual and definite in making decisions like this. It may be more sensible to apply a touch of it here, rather than just using pure emotion. Don’t get me wrong: your gut feeling is important too; but read on to understand what I mean…

I Can Take on this Challenge

Firstly, there is a misconception out there that if you fail Maths, you fail the full Leaving Cert. This isn’t true at all. The two worst things that can happen if you are unsuccessful in Maths is that you will have that low grade for Maths on your CV. Or, if a certain grade in Maths is a requirement for a specific third level course, you will not be offered that course no matter how many points you get; that’s as bad as it gets.

I think having a good Interest in Maths is a great starting point in taking on higher level. Enthusiasm for this subject will go a long way to achieving your desired goal in it.  Students, do you secretly enjoy the challenge of those long practical questions in double classes, or do you dread the thoughts of Maths homework each night? Do you like working with numbers or are you mis-understanding the majority of your teachers’ methods? These are some initial questions to ponder.

Personally, I feel that students know in their heart what level Maths they should be doing. If you feel in your gut that you are lost in class or if it is taking too much time away from other subjects; then reflect and talk it through now. If your anxiety about the subject is getting too high and your grades are dropping, it may be time to move. Definitely, if you have struggled to grasp much of the basic Algebra in fourth and fifth year, it may be a sign that the standard is too difficult for you. However, remember also that there are so many varied topics in Maths, and you may have a flair for some and no real interest in others. Very few of us are good at everything, even the best of the best.

Head Above Water

I always feel that students scoring above thirty percent (approximately) in Class, Christmas and Mock examinations should be able to raise their game to get over the line in the State exams. Students scoring consistently below thirty need to look into their heart and start conversations with their teachers, parents and indeed themselves about what to do. It is important not to remain in the class for the sole reason that your parents want you to do honours. Only you know the content of the Maths course you are studying and how it is going for you. Many students and even some Teachers place too much emphasis on the spring Mock result. I disagree with this premise and prefer to look at the bigger picture. From a percentage assessment point of view, I feel you need to look at a combination of exams sat (even fifth year ones) and indeed your Junior Cycle grade. Keep in mind that the upcoming mock examinations in springtime tests topics across the complete course at a time when you haven’t fully completed it yet.

Is there a Template for Staying or Going?

My intention in this article isn’t to outline a template for who should remain or drop down, as there are a lot of factors that need to be considered. I am simply encouraging you to reflect and balance the argument for yourselves. Over the years, I have taught a substantial number of students who I considered borderline higher level students. Many of them remained at higher and actually ended up outperforming those I perceived as rock solid higher level candidates. Maybe these students felt like they needed to work harder and hence prepared better consequently. There is a lesson in this. American Basketball player Kevin Durant once said, ‘Hard work always beats Talent when Talent doesn’t work hard enough’. The statistics also stack in your favour.  In June 2022, 98.4% of students who attempted higher level Maths got a H6 grade or above and therefore picked up the 25 bonus points. That is extremely high!

In general, your teacher won’t put you too far wrong when decision time arrives. By the middle of sixth year, they know your strengths, weaknesses, and the limits of your capabilities, assuming they have taught you since the start of fifth year. Timing is also an issue. If you do need to drop down to Ordinary level, I wouldn’t leave it any later than Easter. This gives you some time over the Easter holidays, and when you return for the final term, to get familiar with the Ordinary level standard and format of the exam paper. Changing levels on the day of the exam is totally unadvised and should not be considered.

Factors That Will Guide Level Choice

In summary, think about and discuss the below factors in detail with your parents and teachers before attempting to change levels in any subject. Along with mock performance, here are the other factors to consider when making decisions regarding level changes:

  • Your teacher’s opinion.
  • Your ‘potential’ points change.
  • Your Junior Cycle performance.
  • Your attendance in class thus far.
  • Your ‘working relationship’ with your teacher.
  • How much you enjoy studying the subject.
  • Results in previous Christmas and Summer tests.
  • How much of the course you have done thus far.
  • Your own gut feeling and attitude towards the subject.
  • Results in all your class tests since the beginning of fifth year.
  • The amount of effort you are putting into this subject balanced against others.
  • Minimum entry requirements for third level (e.g. a H6 in Maths maybe?).

Before making your final decision, take out a piece of paper and write down all the pros and cons of remaining at higher level or changing.  On the back of the sheet, write a few paragraphs on how you are actually feeling about it right now. Keeping the above list of factors in mind, the answer you are searching for should appear somewhere within these pages as your thoughts and feelings stream out. Use these thoughts to answer your own doubts and plough on from there. Contact me if I can advise you in any way. Joe

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

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

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

*****

*****

 

Joe’s Jotter: How to Become More Competent in Maths 2022

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Grasping a subject of difficulty is always a big challenge for even the best students. One of those subjects is too often Mathematics. Maths seems to have developed a ‘bad boy cred’ over the last twenty years, but I feel things are getting better slowly and I know students feel more positive about it since the introduction of Project Maths in 2008. In general, I think students are enjoying the more practical approach in the subject since these changes. The existing course is however still quite long, and you need to box clever in order to pin it down. Many students are still trying to come to terms with the number of words on Maths exam papers and indeed how they link to the concepts. I totally get this. However, I still believe you can learn to grasp the key concepts without being born a Maths genius.

Can Anyone Be Successful at Maths?

People regularly ask me about this, and I believe Maths is a subject everyone can do well in by being willing to try different methods. For sure, parents have a role to play here, so students should get them involved. Parents can get involved in homework from an early age and should be encouraged to send notes to the teacher if there is a particular area their child is struggling with. Above all, it is imperative that Parents pass on a positive attitude about Maths early on. A ‘can do’ attitude gives the student belief that they can face problems in the subject and come through them. Encouragement and positivity are the most constructive way any parent can help boost their child’s ‘Maths conviction’.

Maths is Learning by Doing

To me, Maths is a subject where you need to be continuously ‘learning by doing’ and the importance of attempting exam style questions cannot be underestimated. Reading through questions and text like you do in other subjects will not work in Maths. Having access to a structured solution book for exam questions is important. Inevitably with some challenging questions in the subject, you will run into difficulties getting started and this is where having the first line or two of the solution can be extremely helpful; a detailed solutions book is ideal for this. I believe that referring to the first part of a solution and then revisiting the question yourself is a very efficient way of developing key Maths skills. This technique isn’t one much practiced in other subjects, but Maths is unique in itself as we know.

Skills That will Improve Your Maths

You must adopt different approaches to improve success in Maths. A genuine attempt to start a question in Maths will allow you to gain momentum and progress to apply the concepts you have learned in class. In my experience, the biggest stumbling block to achievement in Maths is getting the question started; but a single grain of rice can tip the scales. In general, if you are finding it difficult to get started and feel lost in Maths, start by practicing the part (a) questions in your past exam papers and work your way upwards to part (b) and so on. If you are an exam student, go back on your 2nd or 5th year notes to refresh those key basics. The majority of students just fire notes from previous years in a corner. Past notes should be stored carefully for ease of access later. It’s amazing how much you will recall about what you wrote down and what advice your teacher gave you back then. This is a good starting point. As you always hear me say, Algebra is jewel in the crown at all levels. Maths is about having a go, knowing the tricks, when to use formulae, consistent practice and really believing in your ability and the work you have done. Joe

“The harder you work, the luckier you get. Every effort will open a door.”

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

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

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

*****

*****
Photo:@ZhangChaosheng

Joe’s Jotter: Wholesome Summer Foddering for Students

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Summer is a time for rest and reflection. As a student, do you ever think about your diet and the foods you eat? Do you go overboard on the junk food at times? Here are some pointers to read and have a think about as we approach mid-summer 2022. This article is not to lecture you, but rather to make you think about little adjustments you could make to ensure you are giving your body and mind the best possible chance as a new academic year approaches.

Target One or Two Improvements

Rather than aiming to overhaul your diet and what you eat, start by targeting one specific area for improvement before the new academic year kicks off. This should be something that is most relevant to you and is changeable, for example, breakfast. If you are someone who doesn’t eat a healthy breakfast, you could start by prioritising that. As you become more consistent with that meal, you can work on other mini targets, like eating more fruit and vegetables or reducing sugary drinks. It is important to be realistic about what you wish to achieve and give yourself a reasonable time period to achieve it.

Progress on any changes made should be judged over several weeks (rather than days), as new habits take time to form. Get a shopping list together and ask your parents to stock the fridge and freezer with specific whole foods. The more whole and natural a food is, the better. For example, a beetroot unpackaged and untouched is far better than a jar of sliced beetroot. You get the idea. If you can do a bit of cooking for yourself, you will never go hungry. Minor improvements to the quality of food you consume will help improve your concentration and focus going forward. Indeed, we all could do with that. More importantly for you, this will allow you to make a fast start for Term 1 in September.

You won’t go to far wrong by increasing your intake of fruit and vegetables for the remainder of the holidays. This will help you build up resistance to any bugs flying around come autumn time. Eating as many different coloured vegetables as you can is the secret to providing plenty of nutrients for your body. If you do opt for a takeaway (as is ok at times of course), cook some homemade vegetables to eat on the side. This balances the books a little and ensures you are still getting important vitamins and minerals.

Hydrate as Best You Can

Firstly, it’s important to know that your weight affects your fluid needs. You should drink 35ml of fluid daily for every kilogramme you weigh. For example, a 70kg (11 stone approx.) person should drink 2.45 litres per day. The recommended daily amount of water for a teenager is two litres, which works out at around at eight to ten glasses. The recommendation is to drink more than this if the day is particularly hot or if you are exercising. Research on athletes has shown that a two percent drop in hydration can lead to thirty percent drop in performance. This applies to any activity requiring a certain level of focus. It is also worth noting that a person’s body is made up of 50-60% water.

Water is the best form of hydration, and the benefits of water are well documented. Water increases energy, flushes out toxins, improves skin complexion, boosts the immune system, prevents cramps, balances the body’s fluids, promotes digestion, and eliminates waste products. Having all these benefits working in your favour is only going to help you maintain better health. Some low sugar fruit juices, like cranberry, blueberry and apple are also good for hydration and contain enzymes and vitamins. Fizzy drinks will also increase hydration, but again are to be avoided due to their high sugar content. Other foods to improve hydration include Cucumbers, Watermelon, Pineapple, Tomatoes, Blueberries, Pear, Lettuce, and Melon. Ultimately, sipping on water throughout the day is the best way to keep your body properly hydrated.

If you get dehydrated, your concentration for revision at home or performance on the sports field will be affected. Here are four tell-tale signs that your body is dehydrated and that you need to drink more fluids:

  • Dry mouth and skin: If you are dehydrated, you may not be producing enough saliva, which will lead to a build-up of bacteria in the mouth. Acne may also occur.
  • Food cravings: The body confuses thirst for hunger sometimes. Drinking water will reduce these cravings, as it is water your body often requires not food.
  • Headaches, tiredness, and confusion: A lack of water can lead to headaches during the day. This makes it very difficult to operate to your maximum capacity. Ask yourself the question, “Am I constantly tired?” If the answer is yes, you might just be lacking water in your diet. The process of learning and retaining information has been proven to be more difficult if your body lacks fluid.
  • Urine colour: The colour of urine should be light if you are well hydrated. The average hydrated person goes to the toilet to excrete urine six to eight times daily.

To combat dehydration, bring a bottle of water with you wherever you go. Keeping bottles of cold water in the fridge at home will make it easy to ‘grab and go’ and you can sip away on it as the day progresses. It is important to note that if you feel some of the above listed symptoms, your body may already be dehydrated. Prevention is better than cure in this case. Building good hydration into your everyday routine is a great habit to implement before Septembers’ resumption in school. Summertime presents an ideal opportunity to form this important habit. Joe

**Spend Time, Energy and Effort well over the next four weeks.**

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2023) and his Award Winning ACE Maths Solution Books can be found via the links below.

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

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

*****

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Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2022

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Leaving Higher Maths Paper 2 usually contains Probability and Stats, Trig, Geometry, Inferential Statistics and Co-ordinate Geometry, Area and Volume.

  • Your Paper 2 is on the Monday so you will have some time to look over. Again watch out for topics appearing here that should appear on Paper 2.
  • Paper 2 is more about the formula’s so use them if you are stuck
  • Label your diagrams and Label co-ordinates (x1, y1)
  • Do not get caught up in one or two topics – cover all your topics
  • Note that Financial Maths came up on P2 2018 – Be careful..
  • Proofs can be mixed between the two papers

What do you need to learn off for Paper 2?

  • Constructions Numbered 1-22
  • JCH Theorems 4, 6, 9, 14 and 19
  • LCH Theorems 11-13
  • Eight Trigonometric Identities 1-7 and 9
  • Some Statistics Terms (explain the words….‘population’, ‘sample’ etc)
  • Some Geometry Terms (explain the words…‘axiom’, ‘theorem’ etc )

See your textbook for all of these

Geometry

  • Geometry and Trigonometry often come up together
  • This idea of Similar Triangles is quite popular lately
  • There’s a bit of learning here:
  • Students need to Learn Constructions and Learn Theorems off by heart
  • Practice these and know all the steps
  • The best way to learn your proofs and constructions is to keep writing them out. Pin the ones you find difficult to remember up onto your wall. Repeat this process.
  • This could well be mixed with Trigonometry or Area and Volume
  • This is usually one short question on the paper (Section A)
  • In order to learn your proofs and constructions, keep writing them out. Pin the ones you find difficult to remember up onto your wall. Repeat this process.

Trigonometry

  • 3d Shapes are popular. The advice here is to break the shape into 2/3 triangles and solve using SOH/CAH/TOA, Pythagoras, Sin or Cosine Rule.

[Sin and Cosine Rule is in the Log Tables]

  • Be able to read the period and the range from a Periodic graph or a Periodic function
  • Be able to solve Trig Equations (this also may appear on P1 also)
  • You need to be able to prove 8 trig identities – these are listed in your textbook
  • The advice here is go over the questions from 2014-2019 as practice
  • This can be mixed with an Area and Volume Diagram or Co-ordinate Geometry
  • Triangles and Circles linked
  • Understand Trigonometric graphs including Periodic functions (period. Range etc)
  • Go over the past exam questions from 2014-2019 as practice here

Area and Volume

  • Started to get popular from 2017 onwards
  • We sometimes see combined shapes here so it’s a good idea to redraw diagrams
  • Have a look at Q7 2018 and Q7 2017 as practice
  • Can appear on Paper 1

Co-ordinate Geometry of the Line and the Circle

  • They can come up together or on their own
  • They tend to be more in Section A and could be two short questions
  • All the Important formula for these topics is on Page 18 and 19 of the log tables
  • I feel the ‘Big 3 formulas’ are Important (always have a great chance of appearing)
  1. Perpendicular distance between a point and a line
  2. Dividing a line in a given ratio
  3. Finding the angle between two lines using the Tan Formula

[ALL THREE OF THESE ARE IN THE LT]

  • Know the idea of slopes well. Slope formula (LT), m = -x/y & rise/run
  • Know the method for finding the equation of a tangent to the circle. This will involve the slope and maybe the radius of a circle
  • Be able to find the centre and radius of any circle given its equation..

Note that the equation can appear in different formats….

  • This tends to be more in Section A of Paper 2
  • Mixed with Geometry

Probability

100% chance of probability appearing…

  • Know the following three formula’s off by heart (Not in LT)…………… There is a great chance one of these will appear…..
    1. Formula for Conditional Probability – Probability of an event A occurring given that event B occurs.
    2. Formula to show that two events are independent
    3. Formula to show that two events are mutually exclusive
  • One of the following topics usually comes up every year:
    1. Bernoulli Trials (Know how to spot this & apply formula)

or

  1. Expected value of an event
    • e.g. Expected profit from A GAA club lottery
  • It doesn’t tend to be a long question (Section B) except in 2015 when it was mixed with patterns. It could be too short questions on Section A however
  • There isn’t really any help from Log Tables here so learn the above

Statistics

  • Be able to understand z scores for the normal curve
  • The Empirical rule can also appear. Symmetry is the secret to solving. Learn and practice this:
  1. 98% of the population falls within one standard deviation of the mean
  2. 95% of the population is within two standard deviations of the mean
  3. 68% of the population is within three standard deviations of the mean
  • Inferential Statistics. This is where we use the data from a small sample to assume something is true or not for the full population
  1. Know Confidence Intervals for a Sample Proportion
  2. And Know Hypothesis Testing

Both could well appear on Section A but more likely on Section B. Try and understand these as opposed to just learning off the methods like a robot

  • Know how to analyse data by measuring its middle – Mean, Median and Mode. Know about data spread – range, inter-quartile range and standard deviation.
  • Know how to analyse data by measuring its middle – Mean, Median and Mode, as well as its spread – range, inter-quartile range and standard deviation.
  • Correlation and correlation co-efficient does pop up the odd time
  • The Empirical rule does also appear every so often. See the diagram in the Log tables on Page 36. Symmetry is the secret here. Learn and practice this:
  1. 98% of the population falls within one standard deviation of the mean
  2. 95% of the population is within two standard deviations of the mean
  3. 68% of the population is within three standard deviations of the mean
  • Inferential Statistics. This is where we use the data from a small sample to assume something is true or not for the full population
  1. This is a mix of Probability and Stats
  2. This has a good chance of appearing
  3. Confidence Intervals/Hypothesis Testing or both could well appear
  4. It could appear on Section A but more likely on Section B
  • Try and understand confidence interval and hypothesis testing as best you can as opposed to just learning off the methods like a robot.

To view my recent feature article on ‘Best Practice for LC Higher Maths Paper 1’, click here.

More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022) and his Award Winning ACE Maths Solution Books can be found via the links below.

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

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

*****

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

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Surprisingly, thousands of top Maths 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 their 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). Joe

To view last weeks article on ‘The ACE Guide to Exam Prep from Home”, click here.

More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022) and his Award Winning ACE Maths Solution Books can be found via the links below.

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

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

*****

*****

Photo:@ZhangChaosheng

Joe’s Jotter: How to become more Successful in Maths (2021)

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Grasping a subject of difficulty is always a big challenge for even the best students. One of those subjects is too often Mathematics. Maths seems to have developed a ‘bad boy cred’ over the last twenty years, but I feel things are getting better slowly and I know students feel more positive about it since the introduction of Project Maths in 2008. In general, I think students are enjoying the more practical approach in the subject since the changes. The existing course is however still quite long, and you need to box clever in order to pin it down. Many students are still trying to come to terms with the amount of words on Maths exam papers and indeed how they link to the concepts. I totally get this. However, I still believe you can learn to grasp key concepts without being born a Maths genius.

Can Anyone Be Successful at Maths?

People regularly ask me about this hypothesis, and I believe Maths is a subject everyone can do well in by being more open minded and willing to try different methods. For sure, your parents have a role to play here, so make sure and get them involved. Parents can get involved in homework from an early age and should be encouraged to send notes to the teacher if there is a particular area their child is struggling with. Above all, it is imperative that Parents pass on a positive attitude about Maths early in their child’s development. A ‘can do’ attitude gives the student belief that they can face problems in the subject and come through them. Encouragement and positivity are the most constructive way any parent can help boost their child’s ‘Maths conviction’.

Maths is Learning by Doing

To me, Maths is a subject where you need to be continuously ‘learning by doing’ and the importance of attempting exam style questions cannot be underestimated. Reading through questions and text like you do in other subjects will not work in Maths and having access to a structured solution book for exam questions is important. Inevitably with some challenging questions in the subject, you will run into difficulties getting started and this is where having the first line or two of the solution can be extremely helpful; a detailed solutions book is ideal for this. I believe that referring to the first part of a solution and then revisiting the question yourself is a very efficient way of developing key Maths skills. This technique isn’t one much practiced in other subjects.

Skills That will Improve Your Maths

You must adopt different approaches in Maths; it is unique. A genuine attempt to start a question in Maths will allow you to gain momentum and progress to apply the concepts you have learned in class. In my experience, the biggest stumbling block to achievement in Maths is getting the question started; but a single grain of rice can tip the scales. In general, if you are finding it difficult to get started and feel lost in Maths, start by practicing the part (a) questions in your past exam papers and work your way upwards to part (b) and so on. If you are an exam student, go back on your 2nd or 5th year notes to refresh those key basics. The majority of students just fire notes from previous years in a corner. Past notes should be stored carefully for easy access later. It’s amazing how much you will recall about what you wrote down and what advice your teacher gave you back then. Re-do some questions from then to start a Maths revision session. As you always hear me say, Algebra is jewel in the crown at all levels. Maths is about having a go, knowing the tricks, when to use formulae, consistent practice and really believing in your ability and the work you have done.

More Interesting and Informative Maths feature articles will follow as we lead up to the Junior and Leaving Cert 2022.

More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022), ACE Maths Assessments, and his Award winning ACE Maths Solution Books can be found via the links below.

W: acesolutionbooks.com/ace-maths-tuition

FB: facebook.com/JoeMcCormackEducationalExpert/

 

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Joe’s Jotter: Secondary Maths – Some Useful Insights for Parents

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I think it may be interesting for both students and parents to consider the following observations I have become aware of in Maths over the last number of years. Maths is a very emotive subject, and everyone has their own way of understanding and practicing it. This presents its own set of difficulties. The below insights and observations may help you as a parent to reach out and help your child with Maths in a more positive way.

The Second Year Dip

Firstly, in general, I have noticed that some of my students (and those of my colleagues) experience a slight dip in performance in Maths during their second year in secondary school. This is partly due to workload and the fact that the first-year common course is quite basic. This dip for girls is not as pronounced as for boys. There is also a drop off in fifth year, but it isn’t as extreme as the second year one. If your child is heading into second year, you need to be aware that this could be the case for them. I believe that working diligently on their algebra, fractions and general numeracy would be a big help in overcoming any barriers that block their path. These topics are the three main pillars of Junior Cycle Maths and underpin and are linked to many other topics on the course.

We all need to keep in mind that online learning has not suited some students and that they have missed out on that key face-to-face contact with teachers, especially in Maths. As a parent, it is important that you encourage positivity around this subject and remind them that every student in the country is in the same boat. From a personal point of view, I noticed that last year’s Junior Cycle class did struggle (more than usual) with some topics, but it did eventually come together for them in the end. I expect that the incoming third year cohort will take a while to settle back (through no fault of their own) this year. In fairness, it may take many of them until after Christmas before they settle down into a pattern of revision and work across all subjects. It is understandable that they may not hit the ground running this year and we all need to be cognisant of this.

Girls – Go for it!

From the students I have taught since Project Maths was introduced, I have noticed another trend in my classes. I have spotted that female students are less likely to take risks when attempting past exam questions. The new phrasing of questions on Maths papers suit boys better, as they are less conscious of what they are writing down and are less afraid of being wrong. In my opinion, it is important for girls to express their opinions freely and openly and we, as teachers, need to help them develop this skill. I think it is important for all students not to get unduly perturbed if they cannot get a certain part of a question out perfectly. In Maths now, it is more important to go onto another question (within the allotted time), instead of looking to complete every single question part absolutely perfect.  I feel that Churchill’s (not the dog) quote is quite apt for our modern day Maths syllabus.

“Perfection is the enemy of Progress”.

Winston Churchill (Former Prime Minister of the UK)

One does not really have time for absolute perfection on a Maths paper as they tend to be quite long, and unlike other subjects, there isn’t as much time for admiring your work. Students should apply this principle across the board to all their Maths tests in 2021/22.

The New Practical Style Questions

Thirdly, girls especially need to practice more exam questions involving engineering and mechanical parts. My reasoning for this is that, in general, most of the student cohort studying Engineering, Construction studies and Design/Communication Graphics (DCG) at Leaving Certificate are boys, and girls are not being exposed to this specific type of learning. With more everyday life practical questions being the order of the day in Maths, it is inevitable that more technical and mechanical questions will appear in years to come, and girls and parents of girls need to be aware of this. This trend will slowly become more pronounced if the Governments’ promotion and focus on the Science, Technology, Engineering and Maths (STEM) subjects continues and I expect it will.

Follow Your Passion

Lastly, in a recent survey, twenty-nine percent of Irish parents surveyed thought that technology subjects weren’t suitable for girls and fifty-three percent of girls in secondary school dropped STEM subjects due to pressure from their parents. These statistics may be contributing to the lack of representation of females working in STEM. Students and parents need to be aware of the excellent third level courses and future career opportunities available in these areas for both genders. Students need to be encouraged to explore all avenues of interest and follow their career path of choice. Pursuing some spinoff of the subjects that a student enjoys each day in school wont set them too far wrong. Joe

To view last weeks feature article on ‘ACE Tips for Transitioning into 1st Year (Part 1)’, click here.

More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022), ACE Maths Assessments, and his Award winning ACE Maths Solution Books can be found via the links below.

W: acesolutionbooks.com/ace-maths-tuition
FB: facebook.com/JoeMcCormackEducationalExpert/

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Project maths-the silver bullet or a step in the right direction?

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Project Maths –the silver bullet or a step in the right direction?

Maths teacher and ASTI member Joe McCormack looks at the impact and challenges of Project Maths The new Project Maths course is well and truly upon us now at this stage. This new way of teaching and learning maths will be given a fair shot to see if it can raise maths competency and increase the cohort of students who take higher level maths. Last June, Strands One and Two of the Project Maths syllabus were examined in the Leaving Cert with students studying the new course on Probability/Statistics and Geometry/Trigonometry, alongside other topics from the ‘old’ maths syllabus. This cohort only began to study the new syllabus in Fifth Year and so the students were in the precarious position of having to try to understand the “Project Maths way” in just two years. While, in general, the “old” course saw the above topics examined as separate questions with little linkage between them, June’s exam paper, in some places, linked topics together. I welcome this new association since we now live in an integrated world where problems, both academic and real life, need to be solved using a mutli-pronged approach. The Leaving Cert class of 2013 will need to need to be even more competent in dealing with the new concepts as they take on Strands Three and Four of Project Maths. Like the 2012 students, this year’s class will have studied the old syllabus at Junior Cycle, which means they have to work hard to adjust to the new course. Most teachers would agree that it would have been more beneficial for Project Maths to be introduced to only First Year students initially, with these students working their way up through the system, building on the concepts from the foundation up. Leaving Cert 2012 The results are now out for the class of 2012, so what are their implications and what kind of reaction have they got thus far? Firstly, an increase in the numbers opting for the Higher Level maths paper was anticipated, but the surge of 35 percent on last year’s numbers exceeded expectations. In actual terms, the uptake on this paper increased from 16pc to 22pc. This year 11,100 candidates sat the higher level paper, up from 8,235 in 2011. Almost all of them (98pc) were eligible for the additional 25 bonus CAO points because they achieved a D3 or higher in the subject. This should give great encouragement and reassurance to students in two minds whether to take this level. The bonus points inevitably contributed to higher CAO cut-off points in areas such as science and technology. Points for such courses were expected to rise anyway, driven by the increase in demand from students heeding the advice of Government and employers in relation to jobs. However, this initiative does not seem to have distorted the points system as much as was expected with only approximately 3,000 students using maths as one of their six CAO subjects and thereby benefiting from the bonus points. This would indicate that different or additional measures may be needed. Employers have welcomed the results but warned there was no room for complacency. Student feedback Students’ experiences and feedback on Projects Maths, in general, are mixed. From my experience, the First Years are enjoying the common introductory course. For example, the new Probability section allows them to get involved in more practical maths in the classroom, enhancing their learning on the primary school topic ‘chance’. I believe the more practical questions will increase students’ interest in the subject because they relate more to student’s everyday experiences. The teacher will have more opportunities for open discussions on topics in class and allowing students to back up their answers with relevant information should also allow them to express themselves more, leading to them developing a deeper knowledge of topics. In parallel with this, if a student can argue their case properly in the context of what they are being asked, they could be in line for very high marks. I see this as a positive development as it will foster creativity and promote independent thinking. However, in my opinion, there needs to be a more balanced paper set at all levels. Some elements of the papers were marked too easy while topics in other areas were too difficult. I would be more in favour of questions that are fair with a more rigorous marking scheme applied, if necessary. It would be nice if students finished their Post Primary Maths experience satisfied that they did their best and that the rewards reflect their efforts. They shouldn’t feel traumatised to a point that preparation for other exams might be compromised. This year, most students got the result they deserved anyway so why should we put our students through this? We, as teachers, want to see our students given a genuine opportunity to show what they have learned. I feel that they cannot do this with complicated over wordy questioning aligned with some abstract university type problems. Surely every student deserves simple language and somewhat relevant questions on their paper? Social media has allowed students to feedback openly on the new course. The idea of being able to write on the paper is clearly one they welcome. However, practical issues must also be considered: will the length of a student’s answer be influenced by the amount of space allocated for each sub question? Unfortunately, I think a weaker student could be drawn into the idea that a small amount of space for a question might mean a very short solution is required. Also, students must be given enough room to write their answers to a particular part of a question on the same or next page. Teaching challenges There is no doubt that teachers will need to adjust to this new practical way of teaching their subject. They will need to choose their books carefully and use a wider range of resources outside these books. They will need to think outside the box and try to bring some of these new topics to life using practical examples and real life demonstrations. They will need to be more ICT proficient; I believe the Department may need to look at some more Continuous Professional Development in maths specific ICT. One of the biggest challenges for the classroom maths teacher is time. At the moment, it is hard to gauge how much time to spend on each topic and sub topic. Teachers will learn, as each year passes, to structure the course better, including the topic order and timeline. They will learn to choose the best paths through each topic while keeping a closer eye on the syllabus than ever before. However, I believe the Leaving Certificate courses at both Higher and Ordinary Level in their current format may now be too long. Looking through the available exam papers, the length of some of the questions has increased significantly. Those schools that haven’t done so already may need to introduce a double maths class on their senior cycle timetable. In parallel, I envisage a situation where schools may start investing Transition Year maths time to teach some of the Project Maths syllabus and concepts. The marking scheme will be interesting too with the new credit system seeing students being marked from zero up. At present there are a number of graded versions inside the marking scheme. After seeing how this year’s papers were marked, many teachers I spoke to felt the Department hasn’t yet hit the target with the weighting of marks. Students and teachers need to be given more concrete information on how the exam is being assessed. I welcome the Department’s Initiative to create a “Professional Diploma in Mathematics” course. This is a free two year course to upskill maths teachers and to support the implementation of Project Maths. There is an incentive there for many maths teachers to improve their skills and the Department has, in fairness, improved the resources available to teachers via the Project Maths team. In general, we as maths teachers are still a little sceptical about Project Maths. There is also a concern about some topics that have been removed from the syllabus that may be necessary for some mathematically related university courses. In a survey of 253 members of the Irish Maths Teachers Association (IMTA), over 77 percent thought students would benefit if maths teaching in schools was combined with industrial visits to view real-life application of maths. The Government has little money to spend; industry must be encouraged to support the work of maths teachers as much as possible to bolster the effectiveness of Project Maths.

Project maths-the silver bullet or a step in the right direction?

Project maths-the silver bullet or a step in the right direction?
Project maths-the silver bullet or a step in the right direction?More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022), ACE Maths Assessments and Solution Books via the links below.