Surviving and Thriving in High School Mathematics

High School can be just as daunting for the parents as for the students. Will my son or daughter fit in? Will they be successful? Has their primary school prepared them well enough?

There are many sites that can give advice about many of the general areas of the transition to high school. This article is to help you specifically with Mathematics but will also give you some general ideas regarding homework, working with your child’s teacher and the school, and helping your child to be organised and ready for each class.

Firstly some ideas about Mathematics and learning Mathematics. Many people say to me, “Oh, I was never any good at Maths at school.” Please do not use this as a reason why your son or daughter should not be good at Maths. Things have certainly changed since I was at high school in the 1970s and I am sure that they have changed since you were at school. There are many different ways in which students can be taught Mathematics and I believe that every child can be successful at Mathematics.

Elements affecting Success in Mathematics

Preparedness Developmentally

Every child develops at a different rate. In addition, children have spurts and plateaus of development through their childhood and adolescence. There are so many factors that impact on this. Unfortunately, the Australian Curriculum, or any Curriculum for that matter, is written for specific year levels. This means that because a percentage of children are developmentally ahead or behind the average for their age, they are potentially either bored or struggle to keep up. Over time, most children catch up but this may not happen until as late as Year 9 or 10. By this time, many advanced students have become so bored that they have switched off and coasted, meaning they do not develop the skills in persistence needed for the advanced study of which they are capable, and many struggling students have gaps in their knowledge that leads to further struggles and to them becoming further behind, thinking that they are too dumb and will never catch up, and so they too switch off and stop trying.

Preparedness Emotionally

Childhood and Adolescence is fraught. In today’s society there are so many impacts on the emotional development and state of children. Social media, family issues, health, changes in hormones, friends, school – these all have an impact on the emotional state of children. Learning is dependent on being in a good emotional state. If there are stresses in a child’s life, then these impact on the child’s ability to take up and remember the material at school and on their willingness and ability to do any homework.

Engagement

Since every child is different, they also have different areas of interest and strength. Different children will naturally be more interested and therefore more engaged in different classes. If a child is not at least moderately engaged in class, then they have little hope of interacting positively with the material and therefore little hope of understanding, remembering or building on this information. A lot of parents (and teachers for that matter) think that because children are attending school regularly that they will be learning, but there is a lot more to the learning process than just turning up to class.

Understanding

All of the previous areas of impact on learning apply equally to any subject. Because Mathematics is such a technical subject, understanding is critical for learning. This might seem self-explanatory but in fact there is more to it. In Mathematics, there are four ‘proficiencies’ – understanding, fluency, problem solving and reasoning. A working definition of these would be: understanding means that you can complete basic questions using a particular strategy, following a prescribed format. Fluency means that you can apply this concept quickly, efficiently and across a broader range of questions. Problem solving usually requires the application of the concept and sometimes incorporating other ideas from other concepts as well as good mathematical communication. Reasoning is much broader and involves looking for patterns and making connections with other concepts and areas of mathematics, as well as communicating effectively about these connections. Many students don’t master understanding and most don’t go beyond that to build fluency, problem solving and reasoning.

Practice

Now we get to the crux of the matter when learning Mathematics. Practice. This is the key to both building the proficiencies – understanding, fluency, problem solving and reasoning, but also what can overcome all the other roadblocks to learning in Mathematics.

The Zone of Proximal Development

The What??? This term (coined by Vygotsky, a renowned child and adolescent psychologist) is used by educators and psychologists to describe the balance point for learning. It is the point at which there is a good balance between something being challenging enough to feel like bothering, and easy enough to have the courage to try. If a student is trying to problem solve before they have understanding, they are not in the zone of proximal development. If a student is trying to learn to add fractions but has no real understanding of the concept of fractions and the relationship between the numerator and the denominator (top and bottom number), then they are                     certainly not in the zone of proximal development. In order for students to succeed, ideally, they should be learning in their own zone of proximal development. In any one class, particularly in high school, there could be a variation of up to 5 years or more in the preparedness of the students. All good teachers do their very best to cater for the needs of each student in the class by what we call differentiation – pre-testing the students and then pitching the practice at the appropriate place. Unfortunately, we are still required to present all of the content of the Australian Curriculum (or whatever curriculum is being taught in a particular school) and so what is presented to the students may not meet their exact needs (sometimes not even close).

So what can you do?

There are several things.

Contact School

Firstly, be proactive in being in touch with your child’s teacher. While most teachers would dearly love to be able to ring every student’s parents on a regular basis, the truth is that we already work between 50 and 80 hours a week during term time and some of us work for 20 to 30 or more during much of our holidays. It helps us enormously if you contact us. The best way is usually email. And to be honest, you might have to send a couple. Not only do we work long hours but the pace is also more hectic than most people can imagine. (I am not complaining – I absolutely love my job – but I have done a variety of other jobs and none compares even close to the pace, except for perhaps being during an emergency exercise). So, be in touch with the teacher and see what he or she says about where your child is situated with respect to the achievement standards of the year level. If you have no joy here, send me an email and I can provide you with a quick diagnostic that will give you an idea. Also, ask for a copy of the list of topics being covered in the semester if that is not already available to you. Most schools will have this on their websites in some form or other.

Good habits

Secondly, help your child develop good homework habits. This does not have to be hours and hours unless they are in Years  9-12 and doing the top levels of Maths. The best way to do this is to have them do a manageable amount (see table below) at least 4 nights out of 7. What they do is important. Ideally, they should be doing practice of questions that are easy for them but are reinforcing the concepts taught recently in class. This is provided there are few gaps. We will come to “gap filling” shortly. Most teachers should be able to tell you what this should be. Usually it will be a question from the textbook or online list depending what is being covered.

Again, if you are struggling here, send me an email with the topic and year level and I will send you some starting material.

Guidance

Thirdly, be firm. (This is a bit of the pot calling the kettle black here but…). In Year 7, establish good practices such as:

  • No mobile phones or television while doing homework.
  • If computers must be used, try using software that only allows access to certain sites.
  • The child needs to show you their homework before and after it is finished. This might seem like you don’t trust them but you would not believe the number of parents who report their children stating that they have no homework when in fact they do, or that they have finished when in fact they were “surfing” the whole time.

How long should students be spending on homework?

Year Times per week All subjects homework
per night
Maths homework
per night
Total homework for a week Total Maths homework for a week
7 4 30 minutes 10 minutes 2 hours 40 minutes
8 4 45 minutes 15 minutes 3 hours 60 minutes
9 4-5 1-1 ½ hours 20 minutes 4 to 7 ½ hours 80 to 100 minutes
10 5 1 ½ to 2 hours 20 to 30 minutes 7 ½ to 10 hours 100 to 150 minutes
11 5-6 2 to 3 hours 30 to 60 minutes 10 to 18 hours 150 min to 6 hours
12 5-6 3 to 4 hours 30 to 75 minutes 18 to 24 hours 150 min to 7 ½ hours

Notes: The times listed above are a guide only. Factors that will influence the amount of time are efficiency, personal goals and academic preferences, and in senior years, the type of package (the times above relate mainly to tertiary packages – requiring an ATAR to enter university).

Finishing homework is as important as starting.

When homework time is finished, help your child to check the next day’s classes and ensure they have packed everything they need. Teach them the routine of checking their equipment (textbooks, exercise books, pencil case, calculator etc). This will help to ensure that their learning at school is also productive.

Wrap up

Year 7 is the best time to start getting homework routines going but it is not too late even in Year 12. I am not saying it will be easy but with the guidelines above, at least you have a starting point.

Do you have any questions? Email them to admin@missenlinks.com.au

Next time: Helping students establish homework routines for Maths.

NEXT NEXT TIME

Why is homework necessary for effective learning in Mathematics? It may be up to 4 or more days between lessons. Drop off occurs so that by the time they return to the classroom, there is nothing left in the short term memory and if there has been no practice, then there is nothing in long term memory either. We are effectively starting from scratch. The more practice, the deeper into long term memory the learning goes.