Whether you are a teacher, student or parent, you are likely to have your own opinions about the benefits and purpose of homework. Many educators believe that homework is essential since it bridges the gap between children’s learning at home and school. The theory is that homework will enable students to manage their time wisely and plan out their study schedules.
Time management is a useful skill to have, especially when they reach their senior high school years, university, or employment within the corporate world. Therefore, completing homework early in your child’s schooling years ensures that this task becomes a habit rather than being seen as an inconvenience.
Many teachers find it useful to track students’ progress via their homework submissions, making it easier to notice if a child is falling behind or lacking in understanding. Submitting homework will also develop a student’s character since it’s a good lesson in diligence and responsibility.
Disadvantages of homework
One of the most common arguments against homework is that it takes up rest and recovery time. School is an emotionally, socially, intellectually, and physically enduring daily task, and many students are exhausted in the afterhours. Many children who spend a lot of time with their homework miss out on family bonding time, socialising, chores and extracurricular activities which are also important for real life lessons.
For students in Years 11 and 12, it can be difficult to manage homework especially if they have part-time or casual work. Also, homework assigned during the holidays may cause severe stress for some students and may even lead to sleep deprivation issues.
How much is too much?
Homework can be categorised as a burden and no longer benefit students when it is not carefully planned and implemented. This usually happens when the homework is too challenging or overdone, causing many students to become frustrated and give up.
Teachers can customise a homework based on the age of their students. For ages 10, it is advisable to use other forms of media like a video reference of the topics included in the homework. This will make it more engaging to the students since they will be watching a video rather than just reading a book.
For students ages 13, teachers must provide focused assignments since it is easier for their students to understand and complete. Homework should not reinforce or introduce too many ideas, because it is less likely to contribute to their learning. Not to mention that 13 years old kids haven’t developed their abstract thinking yet, so they cannot handle too many concepts at once. This is particularly true for some maths concepts, which are difficult to teach, let alone learn on your own.
Lastly, 16 year old students often get bored if all their homework is similar. Therefore, teachers must try mixing styles and approaches. This makes each assignment unique, engaging, and enjoyable.
How to motivate students both in class and at home
Teachers must design a balanced homework schedule and figure out ways to give students immediate feedback. This is relatively applicable for preschool and elementary students.
Teachers who are working with high school students must leverage homework to require students to read a chapter of a book at home, watch a video, create a second draft of an essay, or reflect on a topic recently tackled in the classroom. Homework tasks should be created in such a way that students can work through them without support.
Teachers can make homework less overwhelming when they give students flexibility on when they can submit their assignment. This will be beneficial for students in Years 11 and 12 since they can work around other commitments before completing their homework.
Some teachers choose to overextend students during class time, setting high volumes of work which, if not completed in class, must be completed for homework. This will motivate students to knuckle down during class time, so they have less homework. It sometimes helps to set fun and engaging practical tasks based on the topics already discussed.
Lastly, teachers should communicate with parents of students who are not completing their homework, so they can trouble shoot and problem solve ways to motivate and assist this student.
Overall, homework that is age-appropriate, relevant, and engaging can enhance learning and instil good study habits.
Probability is an important topic in mathematics since it explores collecting, describing, organising, and analysing numerical data. So, whether you’re trying to make sense of a weather report, election results, or product reference surveys, you’ll need a basic understanding of probability and statistics. In fact, students need to understand these concepts to help them judge the validity of an argument which is commonly supported by persuasive data.
High school probability requires students to learn and work with fractions and decimals, as well as developing an understand of various terminology and symbols. They must be able to apply the sum of probabilities to solve problems, while also identifying complimentary events. Students use and create graphical displays including venn diagrams, arrays and tree diagrams to solve various problems.
In addition, they must construct sample spaces for single-step experiments to get the ideal outcome. This means they must assign probabilities to the outcomes of events and determine their probabilities.
Lastly, students must learn how to compare and construct a range of data displays, including steam-and-leaf plots and dot plots. This will help them identify and investigate issues that involve numerical data.
Issues around the teaching of probability
Probability is often the last topic of the year, so many students are tired without the focus they had earlier in the year. Teachers often rush through this topic as time is running out and students are losing interest. Not to mention that students find it daunting to learn new symbols and terminologies.
Another issue is that most of the topics in probability are not linked or integrated, so it’s harder for students to retain the information.
How to help students learn and retain concepts within probability
Maths is definitely a tough subject to teach, but probability is one of the easier topics to make fun and engaging. Teachers can introduce games for the students to practice and apply their learning. This hands on approach will help students retain the skills and understanding required for successful completion of the game.
It is also advisable to group students together during games and problem solving tasks. Students can often learn more by actively working through problems with their peers. However, it is important to watch out for students who are not participating in the group. This situation can sometimes be avoided by assigning roles to each student in the group.
Following games, investigations and problem solving tasks, students can complete reflections or discussion questions. This will help consolidate their knowledge and give the teacher insight into their level of understanding.
Traditionally, maths had been taught in a conventional setting where teachers lecture the topic while students passively copy notes, and complete related exercises. They usually use short lessons with explanations and examples, followed by a request for students to read the textbook and answer problems. Teachers track their students' progress through quizzes and tests, which can easily be assessed.
It seems to be easier to teach maths to primary school students since teachers relate mathematical topics and concepts to real-life applications. They also give practical tasks which are more engaging and memorable, helping students have fun, while developing more understanding of the concepts being presented.
Maths in high school is different
Mathematics is a fundamental part of the school curriculum, especially in Australia, but it's also a unique subject since it's associated with other sciences. In fact, mathematics is used in every facet of life, but many high school students often dislike it because they believe that it's a complicated subject to learn, with of a lot of the concepts taught being useless.
We need to understand that learning maths is influenced by many factors, both cognitive and affective. Teachers also find it much harder to teach maths in high schools, as the real life applications of complex mathematics takes a long time to explore. Classes are simply not given enough time to develop in depth understanding through practical exploration. Therefore, students cannot see the connection of specific math topics to their daily lives.
Students find it difficult to consolidate their knowledge when they are taught skills as individual entities, never being shown how the individual parts work together in a meaningful way. In other words, maths is taught as a skills-based subject, without enough opportunities for integration or application. High school teachers are hard-pressed due to their constricted schedules, and they often rush through their lessons without checking if their students have grasped the concepts and understanding, not just the skills. This situation often leads to frustration and some students, especially those left behind, will not be achieve the results they are looking for.
How to make teaching maths easier
It is essential for teachers to collaborate with their colleagues and devise a better approach that they can utilise in their classroom. Something worth trying is called "inquiry-based learning," in which students are required to actively engage in problem-solving and discussion with their peers. This makes the process more interesting and practical for students, thus providing better learning gains.
Teachers must also be able to summarise and conceptualise the skills and knowledge required to tackle certain topics or concepts. Students can then be given problem solving application questions which incorporate a range of skills and concepts to practice integration and consolidate their understanding. It is advisable for teachers to give tests or assessments more often since this can gauge their students' progress and learning.
Overall, teaching maths can be quite challenging, but teachers can use creative and unconventional methods to make learning more engaging, especially if they're teaching high school students who struggle with mathematics. Alongside the difficulty of teaching maths comes the arduous task of learning it. If your child is struggling, it could be a good idea to get in touch with Maths Tutors Melbourne to learn about tuition options.
Making errors and trying new strategies are a natural part of the learning process in maths. However, if kids have an underdeveloped understanding of a certain concept in maths, like those in fractions, this may impede their progress.
Usually, misconceptions will not be corrected unless teachers and parents explicitly address them by instruction. Teachers need to be aware of misconceptions of their classes and individuals and then find an effective way to address them. Identifying misconceptions will require a purposeful diagnostic assessment and careful observation of what their students are thinking.
Common maths misconceptions in fractions
We understand that most kids find fractions particularly challenging. The main reason for this is that they compare fractions from the common kinds of numbers they often worked with. They often forget how fractions work and how to work with them effectively.
In fact, most misconceptions in fractions come from the fact that kids try to draw associations with natural numbers. Natural numbers are those positive whole numbers like 1,2,4,12,110,255,670 etc. These are the kinds of numbers that most of our kids encountered from a young age and they spend a significant amount of time in early education learning about these numbers.
Students often forget how to add, subtract, multiply and divide fractions. There could be a few solutions to this dilemma:
Misconceptions in adding or subtraction fractions
A common mistake that kids often make is that they forget to find a common denominator before adding or subtracting fractions. In fact, they tend to treat the numerators and denominators as whole numbers.
Misconception: 2/3 + 5/6 = 7/9
The correct way is to add fractions by creating a common denominator and then adding the numerators. The right way of adding these fractions is written below.
Correct working: 2/3 + 5/6 = 4/6 + 5/6 with a total of 9/6 = 3/2 or 1 and 1/2
The same method applies to subtracting fractions. Many children make the mistake of subtracting the denominator as they would the numerators just like the example below:
Misconception: 5/7 – 1/4 = 4/3
You could address this misconception by finding the common denominator before subtracting the numerators, then just copying the common denominator to arrive at a solution just like below:
Correct Working: 5/7 - 1/4 = 20/28 - 7/28 to arrive at the solution of 13/28
Overall, this misconception needs to be continuously addressed and practiced so kids will know how to correctly add and subtract fractions. Now that school is running as normal in Victoria again, teachers will be able to more accurately address misconceptions within their classrooms.
In maths, an equation is a representation of two things which are equal, so it’s generally two expressions related by an equals sign. Equations can be solved using both symbols and numbers. When solving numerically, then only numbers are admitted as solutions. However, if you are solving equation symbolically then expressions can be used to represent the solutions.
What is the importance of math equations and why do kids need to learn it?
Equations are useful in daily life since various disciplines in the real world depend on maths and equations. Electricians, builders and engineers all use equations as part of their daily activities. Even every day tasks like doing the shopping require simple solving skills.
Computer chips and other modern gadgets/machines we use in our daily lives are based on mathematical equations and algorithms. Therefore, it is essential for kids to properly learn the concepts of solving equations.
Usually, math teachers instruct students to solve equations at grade school but even kindergartens can learn a bit of simple equation solving using basic arithmetic. The most important thing is for them to develop the skills they need to solve numerical problems using computational methods.
Kids are often given equational problems with a number missing, for example 50 + ___ = 90 – 2. Students need to be aware of the process involve in solving this problem and they must know how to use inverse. In fact, they must know what they should add to 50 to come up with 88.
Learning basic concepts is essential for students so they will be able to solve more complex quadratic equations as well as understand several topics like curve sketching and finding the maximum and minimum values of an equation.
Why do basic concepts get lost when more complex concepts are learnt?
Some students forget basic concepts when they are tackling more complex equations like quadratics. They often forget to use to use the both sides method as they are bombarded with the null factor law and the quadratic equation, along with various methods of factorisation.
We need to help student integrate what they learn from the past with the new methods they recently acquired. Therefore, teachers must be able to assess the current method they are using and remind them that they must also apply some basic concepts to solve difficult equations. I like to create a flow chart for my students so that they can learn when to use each method of solving depending on the question type. To simplify, I tell students that if only one term has the unknown, then the both sides method is the most simple and practiced method to use. If multiple terms have an unknown (for example; 5x and 2x2) the equation must first be made equal to zero, then factorised or put into the quadratic formula.
Students will master these methods through constant practice, so teachers must provide them with lots of opportunities to practice their skills conceptually.
Overall, students must understand the importance of basic concepts in solving equations. Maths continuously builds to new levels of difficultly but basic concepts are always still important to remember when learning more advanced solving techniques. Given that students have only just started learning in schools again, it is even more important to revisit the basics
Some parents experience an uphill battle when it comes to encouraging their child to improve their maths skills and understanding. You may need to engage your children at home by playing some active maths games, and I don’t mean apps or games on their mobile devices.
In fact, your kids will enjoy these games without even realising that they are learning some important concepts along the way. You may also customise most of these games based on what skills you want your kids to learn, so it wouldn’t hurt to pick a few to try. Your kids will beg for more once they try some of these maths games.
Overall, these games are engaging and fun and will teach your children some valuable maths concepts that they can use to improve their skills. Even though onsite learning has now resumed, experts are predicting that many students may have fallen behind with the events of 2020 lockdowns in Victoria, so extra practice at home will surely help your children get to the expected level.
Square roots are found in many science and maths problems, and students must know the basics of square roots to tackle many questions. Square roots are indispensable in various fields like calculus, engineering and virtually every career path of the modern world. Solving equations involving square roots is an important skill in algebra, so kids must understand the simple square root concept.
Basically, the square root is a number that when multiplied by itself provides the original number. For example, the square root of 100 is 10 and the square root of 0 is 0. Also, every root has a positive and a negative answer, so the square root of 4 = 2 and also -2. This is because 2 squared is four and -2 squared is also 4. But most kids tend to remember the positive answer only. So, √4 = ±2, with the ± standing in for “plus or minus.” Although answering just 2 is acceptable in many cases, particularly when a negative answer does not make sense for the intended application. For example, if the solution to the square root is the answer to a question involving dimensions of a prism, only the positive solution is applicable.
Why is this simple concept so often forgotten?
A lot of kids forget this concept since they are introduced to negative numbers later on in their schooling and different topics are segregated in primary school and early high school. This makes it hard for students to integrate topics as they progress to more advanced levels of mathematics. My theory is, students learning about surds will no doubt be explicitly taught about the plus/minus answer and remember to apply it, but then set that knowledge aside when learning about polynomials or algebra.
How to help students remember this outside of its direct teaching?
It is essential for us to remind our kids that the answer to a positive number's square root will always have both a positive and negative solution.
As students tackle problems independently, they are likely to make mistakes by omitting neative solutions. As they study, they are likely to learn from these mistakes and begin to make them less often. This is why it is so essential for students to learn and practice a variety of study techniques as part of their homework routine from a young age. With the recent return to school, teachers can begin introducing positive study techniques and habits into their daily classroom routine.
Similarly, we should emphasise that negative number do not have real square roots, because a real number cannot yield a negative value when multiplied by itself. Therefore, a negative square root of a positive number is often ignored. For example, they will give an answer for the square root of 361 as 19 rather than -19 and 19.
It is important for students to understand that the negative root exists, but the positive answer is often the preferred choice.
Overall, kids often forget this concept, so parents and teachers must make an extra effort to remind that every number will always have two roots – a positive and negative. It is then up to them to answer the question with consideration to the practical application.
Education Minister James Merlino announced the reopening of schools on Monday 12th of October. The decision to return to onsite learning was based on the updated public health advice and the current situation in Victoria, where experts see the region’s progress in defeating the second wave of Covid-19.
Since October 5th, students in specific year levels begun the transition to onsite learning. Yesterday, all primary students in years P-6 returned to school. Students in years 7,11 and 12 arer also returning to school this week, though schools have the option to stagger the return depending on local circumstances.
However, based on Victoria’s reopening roadmap, it is expected that all students in Prep to 6, Year 7, 11, and 12 will be back onsite by Friday 16th of October.
How to help your child transition back to school
Due to the coronavirus, returning to school this October feels very different. In fact, parents and children are expected to feel overwhelmed with greater levels of stress and anxiety, especially when there’s a threat of contracting and spreading Covid-19 at school.
While stress and anxiety levels may be high, it’s essential for parents to help their children cope with this transition and reduce their worries. There are several ways to encourage a positive back-to-school transition, and these will include the following:
What differences to expect in schools
All students will now be required to wear masks and do frequent hand washing when inside the school premises. Some schools might also limit the number of students per classroom, so this means that they might re-arrange the sections or extend school hours in order to implement the social distancing rules set by the government.
What to do if you or your child feel unwell
The first thing to do if you or your child feel unwell is to call your healthcare provider in your area as soon as possible. It’s also recommended that you organise a test for Covid-19 and quarantine your child and yourself inside your home while you wait on results. This will prevent any possible transmission and determine the cause of your child’s illness.
You or your child may also get a flu vaccine which can reduce the likelihood of being sick or hospitalised.
Overall, it’s essential to help your child to cope with the challenges brought upon by this pandemic. Therefore, you’ll need to have a proactive mindset as you support them though the return to onsite learning. If your child is in need of a tutor for Maths in Melbourne, contact us today!
If you’re preparing for VCE, it’s essential to know which maths subject to select. In fact, the subjects you’ll be choosing may influence your options beyond high school. You’ll need to set your goal, and what knowledge and key skills a particular subject can provide, especially if it’s required in the career you are pursuing.
You must also know if the maths subject you’re taking will be relevant to the areas or fields within your career path.
Here are some of the things you’ll need to know when choosing maths subjects within the VCE curriculum:
Another thing to remember about Foundation Maths is its strong emphasis on areas that include shape, space, design, patterns and numbers, measurement, and data. Students will tackle various techniques, processes, and routines involving real and rational arithmetic, lists and tables, diagrams, geometric constructions, equations and graphs.
Therefore, by undertaking these units, students are expected to use by-hand and mental approaches to computation and estimation. They should also have developed graphical, numerical, symbolic, and statistical functionality of technology for learning and teaching mathematics.
In addition, content covered in this subject is a clear progression of knowledge and skills from Unit 1 and Unit 2. So, students are expected to be able to use estimation, computation, by-hand, and mental approaches to solving problems.
In units 2, the focus is more on simple transcendental functions and calculus of simple algebraic functions. At the end of units 2, students are expected to have learned the content outlined in these units, and they must be able to apply the techniques, routines as well as processes they have covered in this subject.
So, if you have an interest in the discipline of mathematics and to have a sound background for further studies in maths and its related fields, then you should take this subject.
Overall, be sure to choose the subject(s) that interest and challenge you, but are not so difficult that they consume all of your study time, causing anxiety over poor grades or failure.
Do you need to know when to start preparing for exams? Click the link to learn more
Maths and science are frequently associated with each other because mathematics assists in our understanding of biology, chemistry, geology, astronomy, physics, and psychology. In fact, students are required to master foundational mathematics in order to read scientific charts and graphs.
More complex maths like algebra, geometry, and calculus can help students solve problems in chemistry and understand planets' behaviour in astronomy. Mathematics is also important in practical sciences such as computer and engineering science since students will be required to solve equations when developing algorithms and writing intricate computer programs.
Even medical subjects require mathematics like how to precisely calculate dosages or create medical charts that record an individual’s clinical status, history, and caregiver involvement.
How maths comes into play when learning science
Physics and maths are closely connected subjects, and mathematics, particularly calculus, is commonly used to solve scientific problems. In fact, electromagnetism and classical mechanics are all related through calculus. The movement of objects and its inertia, including the total energy of objects can be found using several concepts in calculus.
In chemistry, math can be used for a variety of tasks like balancing the equation of a chemical reaction. Mathematical calculations are also essential to explore concepts in chemistry like utilising the dimensional analysis to get the reactions of various elements and the concentration of chemicals in a solution.
Chemistry also required calculations for the compression of a gas, energy released in reactions, or the amount of chemicals needed to reach the desired concentration, and quantities of reactants to added.
In addition, mathematics also plays a key role in biology, especially in the creation of mathematical models. These are mathematical equations and formulas that can describe or predict natural events. A good example is the behaviour of a particular organism or the changes in their population over time.
These mathematical models can be utilised in a variety of ways, but the main goal is to effectively measure a phenomenon without relying too much on raw, numerical data. Even the spreading rates of diseases and frequencies of gene expression can be calculated using mathematical models.
Psychology is another subject that needs mathematics, especially statistics since students must interpret tables, graphs, and statistical analyses. They also need to design quantitative research studies as well as reporting results. Statistical knowledge is also vital for critical and analytical skills that psychologists need to understand and study complex human behaviour.
Overall, students must learn and understand several maths concepts since these are essential in learning science. Therefore, one must complete several learning activities in each subject so they can develop a better understanding of both subjects.
If they pursue a career in science, they will eventually use mathematics in real-world practices, especially in their work.
If your child is looking for guidance in either maths or science, check out our online tutoring options.