The Titcombe Maths Test

rogertitcombe's picture
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Many years ago, when I was a physics teacher, I gave a test like this to my top set Y11 GCSE students. The results were very poor. I have since shared this test with some current maths teachers. They have told me that their GCSE maths students would struggle with it because the topics tested are not specifically on current GCSE maths syllabuses.

I was never a proper maths teacher although I was on occasion been pressed to teach maths to fill timetable slots.

I suspect that current Y11 maths students would have problems with my test. What I would really like is to give it to Y12 students including those with GCSE C+ grades. It would be interesting to see how these students fared and whether those with B+ grades can sail through it, as they should be able to.

I was reminded of my maths test by the BBC 2 series broadcast in September 2015 featuring a Hampshire school, which carried out a very brave experiment dividing a year group into equal cohorts, one of which was taught 'normally by the school's teachers. The other cohort was taught by a team of expert Chinese teachers.

This experiment deserves a post of its own as there is so much to learn from both the experiment itself, the attitudes of the Chinese and UK teachers to each other and to the students, and from the outcome. I summarise this as the Chinese teachers having enormous problems with the behaviour of the students, which they put down to the UK welfare state mitigating the deservedly harsh consequences of school failure for UK school leavers. Despite this, and some truly awful lessons shown in front of the TV cameras in all their horror, when both cohorts were given the same tests at the end of the experiment, the students that had the 'China School' experience scored higher.

There are a great many questions that need to be answered before reading too much into this outcome, however, there appeared to me to be one characteristic of the teaching approach of the Chinese teachers that may be relevant to the 'Titcombe maths test'.

It appeared that the Chinese teachers  placed great emphasis on securing the understanding of the most basic concepts, like those in my test. My test appears to reveal some very common basic weaknesses, such as students being insecure in their grasp of place value in the decimal number system (let alone with other number bases) and with performing functions involving zero and one.

I am posting this because it seems to me to raise a number of interesting questions and issues. I hope some teachers, retired and current will comment.

 

The Titcombe maths test

 NO CALCULATORS, TAKE AS LONG AS YOU LIKE BUT YOU MUST ATTEMPT EACH QUESTION – IF NECESSARY GUESS

 Use a paper and pencil for working out if you wish

 

Part 1 Numbers

 In this section you are asked questions in words but you must write your answer as a number (not words)

Add one and one

Multiply one by one

Divide one by one

Divide nought by one

Write the number, one hundred thousand and eighty seven

Add fourteen to one hundred thousand and eighty seven

Take away fifteen from ten thousand and twelve

Multiply one hundred by one hundred

 Score = ______ / 8

 

Part 2 Fractions

In this section you are asked questions in words but you must write your answer as a fraction, a whole number or a whole number and a fraction (not words)

Add a half and a half

Take away a half from a half

Multiply a half by a half

Divide a half by a half

Add a half and one

Take away a half from one

Divide one by a half

Multiply a half by a quarter

Multiply a half by three quarters

How many quarter-tablespoonfuls of syrup would make

two tablespoonfuls?

 Score = ______ / 10

 

 Part 3 Decimals

In this section you are asked questions in words but you must write your answer as a decimal number (not words)

Add nought point one to nought point one

Take away nought point one from nought point one

Multiply nought point one by nought point one

Divide nought point one by nought point one

Add nought point one to one

Take away nought point one from one

Divide nought point one by one

Divide one by nought point one

Multiply nought point nought one by

nought point nought one

Divide ten by nought point nought one

Score = ______ / 10

 

 Section 4 Percentages

 In this section you are asked questions in words but you must write your answer as  numbers, pounds or pence (not words)

What is one hundred percent of one pound?

What is one percent of one pound?

What is one percent of ten thousand pounds?

A shop has a sign, ‘30 percent off everything’

How much must you pay for an item whose previous

price was twelve pounds?

A shop has a sign, ‘30 percent off everything’

How much must you pay for an item whose previous

price was nine pounds?

A shop has a sign, ‘buy one get one free’

What percent reduction is this?

A shop has a sign, ‘buy two get one free’

What percent reduction is this?

A savings account has an annual rate of interest of

two percent.  If you deposit ten thousand pounds

how much interest will you earn after one year?

 Score = ______ / 8

 

Section 5 Area

Write your answer as a number

 A person can mow a square lawn whose sides are 20m in 10 minutes. Estimate how many minutes it would take the same person to mow another square lawn whose sides are 40m.

A person can mow a circular lawn whose diameter is 20m in 8 minutes. Estimate how many minutes it would take the same person to mow a circular lawn whose diameter was 40m.

A sheet of A3 paper has each side twice as long as the sides of a sheet of A5 paper. A printer can print on either size of paper. If an ink cartridge will print 40 sheets of A3 paper before running out, estimate how many sheets of A5 paper it would print.

A4 paper is the same shape as A3 paper but its height is the same as the width of an A3 sheet. Estimate how many sheets of A4 paper could be printed before the cartridge ran out.

 Score = ______ / 4

 

Section 6 Volume

Answer as a number

A child has a set of cubic wooden building blocks whose sides are one inch long. An inch is an old fashioned unit of length about equal to the distance from the top of your thumb to the knuckle. How many blocks does the child need to build a cube whose sides are 3 inches?

How many blocks are needed to build a cube whose sides are 10 inches?

A rectangular wooden block weighs 1 kilogram. Another rectangular block made of the same wood is the same shape but all its sides are twice as long. Estimate how many kilograms this larger block would weigh.

A tiny metal ball weighs 10 grams. Another ball made of the same metal has twice the diameter. Estimate how many grams this larger ball would weigh.

 Score = ______ / 4

 

Do I need to post the answers?!

 

 

 

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