## Without These 3 Components, Your Primary/Elementary Mathematics Lessons Won’t Work

As a primary or elementary teacher, you are probably not a specialist in mathematics. As the old adage goes, “high school teachers teach subjects; primary and elementary teachers teach students”.

As a result, knowing how to teach students mathematics really well may be something you find a challenge. If so, this post may help you.

1. Focus First on the Mathematics

This is the biggest, most important factor in getting mathematics teaching right. If you don’t nail the mathematics and put it at the center of all your math lessons, it will be very difficult to capture students’ interest, and impossible for them to really understand the topic. This step is needed right at the beginning, at the planning stage.

For example, if the topic is “symmetry in flat figures”, you would teach the terminology of symmetry, the two different types of symmetry, correct terminology and mathematical ways to analyse symmetry (such as the angle of rotational symmetry).

If you lack the content knowledge in a topic, I would go to Wikipedia for a quick brush-up on what the basic math is. As an encylopedia, rather than a blog or social media site, Wikipedia will have succinct summaries of all the topics you are likely to teach, and is highly likely to have the facts correct.

2. Work Out What Mental Processes Students Will Need

The second major step in planning a great math lesson is to consider the student. What processes will they need to practise for this topic?

For example, if you are teaching number facts, the standard we are aiming for is instant recall of every fact. So the mental processes needed are memorizing the facts in the first place, then recalling them from memory.

Note that with this approach, there is no argument about whether students need to remember all those facts or can “invent” ways to come up with them when they are needed. The bottom line is that number facts are needed for just about every math topic, and using up precious brain power (and time) to work them out when needed is just too inefficient.

3. Use the Best Methods to Connect Math to Mental Processes

Lastly, you need to find the best methods you can to truly connect students and their thinking to the mathematics. This has a couple of important components:

• Make the mathematics the primary focus of the lesson. In other words, it’s not about games, exercises, routines, or any other activity or behavioural focus.
• Don’t focus on making math “fun”; true mathematical activity requires attention to detail, discipline and following rules. Students will experience satisfaction from understanding the mathematics and the  processes needed to reach solutions and correct answers, but “fun” is the wrong focus.
• Doing mathematics involves a good deal of mental effort and mental processes. It is essential that your students are engaged in thinking for themselves, using a variety of mental processes including memorization, visualization, mental computation, exploring options, testing hypotheses, following logical connections, holding pieces of information in the working memory while applying mathematical processes such as operations, etc.

I have decided that I will no longer help teachers to inject fun, simplicity, tricks or cute pseudo-math processes in an attempt to buy students’ affection. (As an aside, I am working on a new product about fractions. We brainstormed titles for the series, and rejected “Fun Fractions”, “Fantastic Fractions”, “Spectacular Fractions” and the like because they send entirely the wrong message.)

What do you think? If you are a primary/elementary teacher, does this article help? Does the above advice match your own practices? Please leave a comment below!

Graphic Credits:

• Primary student group:  © iStockphoto.com/Chris Schmidt
• 5x Table:  © iStockphoto.com/Dougall Photography

## Teach the 9x Nine Times Tables

This podcast video is from my Free Math Worksheets series, which you can access here.

If the video does not display, watch on YouTube.

Multiplying by 9 raises some really simple and interesting patterns, which you can use to help children to learn this set of number facts or times tables.

Teaching the 9x Nine Times Tables

As explained in the video, if you start with the equivalent multiple of 10, you can then compensate to quickly find the 9x answer. For example, think about 8×9:

• 8 x 9 = ?
• 8 x 10 = 80
• Subtract 8 ones (one for each set of 10): 80 – 8 = 72
• 8 x 9 = 72

9x Tables: Sum of Digits Equals 9

Look at the multiples of 9 up to 90, and check out the sum of the tens digit and the ones digit in each multiple:

• 09  :  0 + 9 = 9
• 18  :  1 + 8 = 9
• 27  :  2 + 7 = 9
• 36  :  3 + 6 = 9
• 45  :  4 + 5 = 9
• 54  :  5 + 4 = 9
• 63  :  6 + 3 = 9
• 72  :  7 + 2 = 9
• 81  :  8 + 1 = 9
• 90  :  9 + 0 = 9

Students can use a two-step process which takes advantage of the above pattern:

• 6 x 9 = ?
• There must be 5 tens (because we know it is a bit less than 60)
• So, 6 x 9 = 5?
• If the digits in the answer add up to 9, what is the other digit; ie, 5 + ? = 9. The other digit must be ‘4’
• 6 x 9 = 54

9x Tables: Finger Trick

Put both hands up in front of you, palms facing away. Imagine that each finger is numbered, from left to right, from 1 to 10.

To find a multiple of 9:

• 3 x 9 = ?
• Hold up your hands, thumbs together
• Put down the finger that corresponds to the number multiplying the 9: the third finger
• Count the fingers to the left of the finger that is down: 2 – this is the number of tens
• Count the fingers to the right of the finger that is down: 7 – this is the number of ones
• 3 x 9 = 27

## Math Teachers Survey 2012

Do you teach mathematics?

Are you a teacher who teaches mathematics?

In 2011 I asked my readers what they were looking for to help them to teach mathematics, and their responseswere very helpful.

This year, my list has grown, and the number of visitors is significantly up also. I’d really like to know what you think is important in your classroom, and how I can best help you with your mathematics teaching.

Click to enter the survey: http://www.surveymonkey.com/s/W62S5NJ

Click to go to 2012 survey

The survey is completely anonymous, and should only take you a few minutes. Your time would be most appreciated – thanks in advance! So you know I take note of what my followers tell me, in a few weeks I will put up a follow-up post to let everyone know the results.