Continuing the pattern

Many students could continue the pattern in the first question (which contained the repeating unit), and notably fewer could continue the second pattern which needed one more element to complete the whole repeating part of the pattern. Over ten percent of students did not show the shades for the shapes in question a).

For question b) students are asked to continue a repeating pattern for which the whole unit of repeat has not been shown. In this case a notable number of students assume that the pattern will simply repeat "from the start again".

Explaining their method

The most common way that students explained how they worked out the subsequent elements of the pattern was by stating that they followed or continued what the pattern looked like or simply that they "looked at the pattern". Some students gave a vague response such as "I saw the drawings and drew them", "I looked at them and drew them" or "I looked at the start and I knew". These were considered insufficient explanations as they lacked descriptive detail.

The next most common explanation was that they looked at the beginning or went back to the start (or beginning). Both these methods were more successful when all the elements of the repeating unit of the pattern were shown (question a). However, for question b) the success was significantly lower, as all the elements of the repeating unit were not shown.  This would suggest that as a method it lacks sufficient detail and relates strongly to a misconception.

More success in continuing the patterns was shown by students that described methods that involved

• looking back at the pattern and identifying specific attributes that helped them continue it;
• details about the shape and the shading;
• targeted ideas about particular shapes.

These methods could be summarised into explanations that involved recognising a unit of repeat (or the repeating nature of the pattern) or the attributes of the pattern (see below for examples of each).

One sixth of students did not explain how they worked out the next three elements in the pattern.

Examples of students' sufficient descriptions or explanations (generally with the correct order of shapes)

Question a)Explanations that involved recognising a unit of repeat or the repeating nature of the pattern

• I looked at the last shape then looked at the one at the start and it was the same as the bottom and then I copied the next three after that.
• Because the start is a striped heart and that's what we stopped on so we start again.
• I looked at the 1st one on the pattern and then I copied the ones after the heart with stripes. Because at the beginning of the pattern there's the same hart and the one that comes after that is the diamond with the dots.

Explanations that involved recognising the attributes of the pattern

• Because the pattern goes heart, diamond, heart, diamond, … and it goes striped, dotted, coloured so the next shape were dotted diamond, coloured heart and striped diamond.
• There are 2 shapes but 3 different patterns.
• It goes heart, diamond and the pattern goes stripe, dot, plain.

Question b)Explanations that involved recognising a unit of repeat or the repeating nature of the pattern

• The stripey square was last, so I did another square then I went back to doing circles.
• I used the pattern already printed to mark out that I had to put the square in then I repeated the pattern already printed.

Explanations that involved recognising a unit of repeat

• This time it was different there was two circles two triangles and two squares it was stripes and blank I done the blank I chose circles stripes and circle blank.
• The pattern goes striped, plain, striped, plain and it goes two of the same shape then two of the next shape and so on.
• 3 different shapes and they go twice but in two different patterns.
• I looked at the pattern and it went stripe circle blank circle, strip triangle blank triangle, striped square which meant it had to be blank square.

Explanations that involved one attribute*

• Because after each shape there is a blank of it.
• Because it goes lined shape then blank shape.

*These explanations might be considered insufficient in that they don't explicitly identify the second attribute (shape). However because the shape is immediately repeated this could be argued to be a sufficiently clear explanation in this instance.

Examples of students' descriptions or explanations with insufficient details

Question a)

• I saw the first pattern but it was stripes next it was spot and then it was just ordinarily blank. [almost a sufficient explanation, but they do not state or suggest how the shapes change]
• I looked at the first one and saw that it started again.
• Because the one that they did was from start to end.
• I looked at the order to see how it's done.
• By looking back at each shape and looking at the shape after it.
• I worked out the shapes by looking how to do it and how to try and copy it.
• Because it went back to striped heart at the start.

Question b)

• When the shapes stopped I went back to the start and copied them.
• Looked went back and worked it out.
• By starting at the start and guessing the square was last.
• I copied the pattern by looking at the shape.
• The square wasn’t in any of they patterns so I figured out that it might start from the beginning again.
• Cause the square was the one that it stopped on I think we redo the pattern at the start.
• Well just following in the first bit.
• The square must be the last shape.