A Young Teacher’s Guide To Using Textbooks As Teaching/Learning Tools

At the outset, let me say that teaching from a textbook is a ‘no-no’. It would almost always give the impression to students that you don’t know your ‘stuff’ or you are not confident. Here, you need to remember that you will always know or understand more than the vast majority of your students with the topic you are teaching. There will occasionally be gifted students in your class who will understand it all. Use them as tutors/mentors for fellow students. They will often express difficult ideas in ways better understood by their classmates.

However, since textbooks can be expensive, it is important that they be used often and effectively. A good textbook can be a real asset to you as well as for the student. The author was, most likely, a teacher who has written the book on the basis of their own experience.

A good textbook is an essential tool in learning, helping with consolidation and practice of skills. Therefore, take a great deal of time researching various choices to find the one that best suits your needs. A bad choice becomes an expensive mistake.

The writer spent most of his career teaching Mathematics where a textbook is essential. During his years as Head of Mathematics, he introduced several new syllabuses into his school. Consequently, he and his staff needed to research carefully to find the best available textbooks. Sometimes it took up to two years to test out the available text books. His experience in using textbooks and selecting new ones provided the information for this article.

A good textbook is a:

• Reference guide;

• Source of the basics to learn and/or practice;

• Source of rules or procedures to be learnt;

• Source of exercises used to consolidate new learning and ideas on how to practice new skills; (These need to be carefully graded to allow students enough practice to consolidate the basics and then allow them easy movement forward to the more challenging tasks.)

• Source of revision exercises;

• Source of worked examples; and

• As a backup when you teach new and challenging topics.

It should contain the following:

• Chapter summary of ideas to be remembered;

• Chapter review/test;

• Answers;

• Easy to understand diagrams, graphs, pictures and other illustrations; and

• It may also contain a suggested work program as a guide to the time you need to spend on each topic.

Teach your students how to use the textbook effectively as it can be an efficient learning tool at home. Spend a lesson looking at the following list of sections in the textbook, explaining how to use each part.

(a) Contents page

(b) Index

(c) Explanations of new work

(d) Worked examples

(e) Learning work

(f) Exercises to do

(g) Skill practice

(h) Chapter review

(I) Chapter test/diagnosis

(j) Problem solving

(k) Extension work

(l) BOB, back of book – answers

Work Program and Your Textbook

Give students a work outline to go with the textbook. In it, detail the basic exercises the students need to do to gain an understanding of the subject. This is the minimum requirement only. However, specify what needs to be done to extend this understanding to gain the best marks possible.

Some final advice:

Insist that students have their textbook with them every day in class. If you know that you will definitely not be using it next lesson, tell the class not to bring it. (Students appreciate not having to carry heavy books unnecessarily.) However, don’t forget to remind the class to bring it to the next lesson. You need to be careful with this process in lower level classes especially in junior high school classes.

When you know that you will use a textbook in a lesson, insist it remains closed until you have finished the teaching part of the lesson unless you plan to refer to it as part of your teaching strategy. It is important to write the number/s of the page/s you intend to use on the board. Then, don’t start referring to what the students must do until you are sure everyone is on the same page. This is also true when you set work from a textbook for the students to do.

Some teachers, particularly, in lower high school classes with less able students, have extra textbooks with them or photocopies of the relevant pages to ensure all students will be able to do the planned work.

In the end, your text must be:

• Teaching tool;

• Teaching aid; and a

• Learning tool

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.

A Young Teacher’s Guide To Homework In Mathematics In High School

Most of what appears below was the advice that I wrote for teachers who taught Mathematics in my department when I was its head. It appeared in my department’s handbook.

Homework was an accepted part of what we did as Mathematics teachers for all classes except those with special needs students.

How And When To Set Homework

• It should be set daily or after each lesson.

• Write the assigned homework on the board.

• Ensure the students write it in their school diaries at the end of the lesson. In junior classes, you may stand at the door checking the homework is written in their diary as they leave.

• Discuss how long the work should take and any necessary advice.

• Lastly, early in the school year, teach your students how to use their textbook to help them do their homework.

What Homework Should You Set?

For students to achieve their full potential in Mathematics at high school, homework must be done on a regular basis. Homework, based on current class work, is meant to be an extension of the lesson and is needed for the re-enforcement of concepts.

In high schools, homework in Mathematics may consist of:

• Written exercises set for practice of skills and concepts. These are based on classwork.

• Learning work, e.g. rules, vocabulary and theorems.

• Assessment tasks – these usually count towards Semester reports.

What About Students Who Don’t Do Their Homework?

Teachers should record in their diaries the names of defaulters. Parents must be advised when a pattern of missing homework becomes evident.

Teachers should develop a process for dealing with homework defaulters.

What If Students Can’t Do Their Homework?

As most homework is based on the work done in class that day, this is not usually a problem for most students. However, if a student has difficulty in beginning homework, teach these strategies:

• The student should look for a similar problem in the work done in class. This is usually all that is needed to jog the memory.

• The student should look for an example in the textbook prior to the exercise. Each different type is usually done in full with an explanation.

• If students still have difficulty, they should see their teacher the next day BEFORE CLASS and arrange a time for individual help. Most teachers are available for a “homework help” time at lunch time or before and after school. Your teacher will tell you when he/she is available.

What If A Student Tells His/Her Parents That They Never Have Homework?

Often, there are complaints from parents who tell us that their students never have homework. This is clearly not the case! If a student has no written homework, (which is unlikely) then we would suggest that the parents set one of the following to be done:

• Ask the student to write a summary of the rules for the current unit and to work an example of each type of problem. The textbook will be useful here. Look for chapter summaries.

• Look at the student’s exercise book and find an exercise that caused difficulty. Set this exercise to be done.

• In each textbook, there are chapters on basic skills. Students can do any of the exercises from this chapter.

• Often there are chapter reviews and practice tests. These can be done.

The Review Process

Homework should, wherever possible, be reviewed during the next lesson for the greatest impact on learning to occur. This learning may, in fact, be the basis of the next lesson. A full description of a review practice can be found in the Article “Reviewing Homework in High School Classes” to be found on this website.

Even though there is a continuing debate as to the merits of homework, the advice here will help the young Mathematics teacher deal with homework successfully.