Preparing Students For High School Maths

A Guide For Primary School Teachers

A High School Maths Teacher’s Wish List

What has occurred in recent years as many more students complete high school and seek a tertiary education, is a growth in parents wanting their children to do Mathematics at a higher level. They see Mathematics as a key to tertiary entry and insist that their children be given the opportunity to do the subject at the highest level possible even going against the school’s advice on the matter.

Therefore, high school Maths’ teachers must teach almost all students for all their years at high school irrespective of their innate ability in the subject.

This trend will not go away and high school teachers need the help of primary teachers to prepare their students to enter the rigours of high school Mathematics.

This article is written based on my experience as both a high school Maths teacher and as a Head of Mathematics who often had to advise parents on what was best for their students in the subject. Much of what I write here was presented to primary school teachers in a workshop on the topic.

Most, if not all of the points I make in this article, will be known to experienced primary school teachers so it is aimed more at those new to the profession.

Mathematics is a subject discipline where the student must develop his/her understanding of Mathematics. Learning rules and procedures can take the student only so far. It will not help in the modern world of real life Maths problems in unfamiliar contexts.

To help prepare students for high school Maths, upper primary school teachers need to attempt to develop the following within their students.

  1. A work ethic and one which is self-motivating. Often, students in Mathematics will need to work alone and unaided.
  2. A homework ethic. The speed of teaching the syllabus requirements in high school is dictated by outside authorities. This means that the teacher must cover a mandated syllabus in a specific time. For the student, this means that homework is an essential part of the learning process if he/she is to keep up with the pace of teaching.
  3. A study ethic. It is important that students learn that homework does not equal study.
  4. A belief that all students can do some Maths.
  5. An understanding that Maths is an essential part of everyday life and we all do Mathematical things successfully every day, often automatically.
  6. A belief in students that asking questions in Maths is a ‘cool’ thing to do.
  7. A belief in students that Maths is unisexual, not just for the boys.

Below is a list of what I call essential preparation that is not directly Mathematical but will assist students greatly in their study of Mathematics as well as other subjects.

Students should be taught:

  • Study skills
  • How to be powerful listeners
  • How to ask questions
  • Checking procedures
  • Estimation as a checking device
  • Various problem solving techniques
  • An effective setting out procedure
  • That the answer only is not enough. The students must explain in written Mathematical form how they achieved their answer.
  • That there is often more than one way to solve a problem
  • An understanding of order convention
  • Examination technique

Communicating mathematically is a skill that needs to be taught. It involves students being taught the following:

  1. The correct use of Mathematical terms including their spelling;
  2. Correct use of all Mathematical symbols;
  3. Logical setting out;
  4. Justification of each step where necessary;
  5. Logical reasoning;
  6. The use of neat and clear figures, accurate and appropriate diagrams;
  7. To work vertically down the page to allow ease of checking and the elimination of errors in copying;
  8. The translation from one form of expression to another, e.g. numerical/verbal data to diagrams/tables/graphs/equations, and
  9. Correct and appropriate use of units, e.g. in area, volume and so on.

Lastly, you can give your students a taste of high school classes by doing the following. (You might call these suggestions an Action Plan).

  • Set your classroom up with desks in rows and teach a number of “Chalk and Talk” lessons.
  • Insist that students work on their own while doing Maths exercises in a quiet environment.
  • Use textbook exercises.
  • Run some formal, timed examinations in a formal classroom setting.
  • Do regular problem solving exercises. Ones in unfamiliar contexts so they get accustomed to the idea that problem solving is an everyday event, not just one that comes up in assessment.

As I alluded to in the title of this article, this is a high school Maths teacher’s wish list. Whatever you can do as a primary teacher to help develop this wish list would be greatly appreciated by Maths teachers but more importantly will help students to step into the rigours of high school Maths more confidently.

Strategies For ‘Attacking’ Maths Problems, A Guide For Students And Teachers

In an earlier article, “How to Answer Questions in a Formal Examination-A Student’s Guide”, I discussed how to answer questions to gain the best possible results in an examination. This article continues that theme but this time in relation to answering questions in a formal Mathematics examination. The strategies mentioned in the previous article should be applied to the Mathematics examination as well as the ones discussed below.

It is important to define what I mean by a problem in Mathematics before you start to study the strategies to solve them.

These problems are almost entirely ‘word’ problems. More often than not, the student needs to use a variety of Mathematical skills or ideas to gain a solution. Often, particularly in the senior years of high school, there will be an unfamiliar context in which to use your Mathematical knowledge. Alternatively, there may be a series of sometimes complex steps necessary to achieve a result. Finally, the answer is not one which is obvious.

Below are a list of strategies, if used together, will help you gain greater success in solving real problems in Mathematics not just ones you have practised. However, remember, if you don’t know your basics in Mathematics then no set of strategies will help you solve the problems.

So strategy Number 1 is and will always be:

“Know all your learning work and procedures as well as you can.”

The remaining strategies are as follows:

2. Remember, everything that you need to solve the problem is in the question itself. (So list what data the problem gives you as your starting point).

3. Checking is a compulsory part of every problem you are to solve. Here is a checking procedure to use:

• It is best to check as you do each step in the problem as this saves time often preventing unnecessary extra work.

• Ensure you have done only what you have been asked to do. Check, in fact, that you have actually answered the question fully.

• Check you have copied down all the data for the question correctly.

• Check that your answer (its size, etc.) fits, in a practical sense, into the scenario/context of the question.

4. Make sure you have been neat, tidy, organised, logical, clear, and concise. This will help you with your checking and allow the examiner/teacher to follow your logic easily.

5. This strategy was mentioned in the first article. It is part and parcel of answering any examination problem, especially in Mathematics. It is: List the steps you need to take, in order, to gain a solution.

Below is an example of what I mean by this strategy in Mathematics.

The Swimming Pool Problem

“How long does it take to fill a swimming pool with a bucket?”

Here is how I teach this strategy:

Step 1: I write the above problem on the board.

When I do this, I ask the students for their reaction:

It will be: “We can’t do it”

You ask: “Why?”

Their reply: “There are no dimensions”

Your reply: “You don’t need them. If I gave you them to you what would you do?”

Step 2: Now I have the students write down the steps they would use.

Step 3: Then I discuss the steps the class select and list the steps on the board.

e. g. Find the volume of the pool.

Find the volume of the bucket.

How long does it take to fill the bucket and pour into the pool?

How many buckets of water do I need to fill the pool?

Find total time to fill the pool.

Step 4: Now, I make the point that the above steps do not mention the dimensions of the pool. It doesn’t matter what it measures you still follow the same process.

Step 5: Lastly, I emphasise that a correct answer depends upon the correct steps, i.e. method of solution.

As a student, you can’t learn these strategies overnight and expect that they will ‘come to you’ easily in a formal examination situation. You must practice using them. Make a list of the strategies and have them with you as you try each new problem. Evaluate how well you use them and work to improve those you find hardest to use or are easily forgotten. Look to your teacher for help with this process. Remember, in an examination, be disciplined, write out the list of strategies you will use before you start and use them to solve the problems.