Welcome to the trial Sat question analysis 2003

Sample Test Questions KS1 and 2

Background information

From 2003, there will be two changes to the assessment of mathematics.

·         Key stage 1 will have a separate level 2 and level 3 tests

·         Key stage 1 and 2 tests will include questions that assess     children’s ability to use and apply their knowledge, skills and understanding of mathematics.

The inclusion of questions assessing using and applying mathematics (UAM) will have implications for teaching mathematics in key stages 1 and 2, not so much in terms of content, but in emphasis and approach. For each section in the mathematics curriculum, children will need to be able to be taught the skills contained in the three strands of UAM

·         problem solving;

·         communicating;

·         reasoning.

It was these three skills, particularly children’s ability to communicate their methods and understanding that was the focus for this work.

Details of the project.

Mathematics co-ordinators were given a sample of test questions provided by QCA.
(Oct 2002 also available
KS1  http://www.qca.org.uk/12316.html
KS2  http://www.qca.org.uk/12314.html)
There were a range of key stage 1 and 2 questions, with co-ordinators from all schools that attended the Autumn term co-ordinators update, being asked to select groups of children to complete the questions. Any completed questions were then collected at or before the Spring term co-ordinators update. The response was very good, with much co-ordinators annotating work, and commenting how useful the exercise had been.

As a maths team all the papers were the shared out with one consultant focusing on one or two specific questions. A proforma was devised with the intention of standardising how and what we focused on. i.e. what was the preferred method to solve a given question number line, partitioning, vertical method, written in words, and annotation outside the answer box. This proved time consuming to complete and actually told us very little! An added difficulty was some schools had allowed a large age range to attempt each of the questions meaning that for example some Y6 children were answering the Key stage 1 sample questions often in a different way than a Y2 child may approach the same question. It was decided to collate answers from Y1, 2 & 3 for the intended Key Stage 1 questions and similarly Y4, 5 & 6 for the Key stage 2 questions.

We then focused on whether the answers showed an ability

·         to select and apply strategies to solve problems in different contexts, checking their results;

·         to organise their work, using correct language, symbols and notation;

·         to reason logically, look for patterns, make deductions and explain them.

Using the QCA sample question analysis we compared the questions submitted with the trial analysis.

This is a summary per question including examples from individual children from Staffordshire schools.

Hill Castle tickets (assessing problem solving)

The question was successfully accessed by children whether using repeated addition or multiplication because of the simple numbers involved.

Teachers need to model children’s explanations to help overcome lengthy written scripts.

     Hill Castle 1.       Hill Castle 2.       Hill Castle 3.

Class 2’s rainfall graph. (assessing problem solving)

Part A of the question was answered successfully by the majority of questions looked at, despite the level being between two labelled divisions.

     Rainfall 1.     Rainfall 2.     Rainfall 3.     Rainfall 4.

Ben’s addition (assessing, communicating & reasoning)

The majority of children in Y2 used partitioning. Number lines tended to be used only by Y3 children.

     Ben's Add1.     Ben's Add 2.     Ben's Add 3.     Ben's Add 4.

Find the angle (assessing problem solving & reasoning)

Quite a few children did not know the size of angles in an equilateral triangle. Many of those thought that it was 45° but if the child uses the correct reasoning with the wrong angle they would still gain one mark.

Many children did not even attempt this question.

Very few children annotated the diagram and of those that did quite a few used the annotation to estimate the answer rather than calculating it.

     Angle 1.      Angle 2.      Angle 3.      Angle 4.

Sum/Difference

More children were unsuccessful than successful at attempting this question. It was mainly Y5 & Y6 who attempted the question on the samples received.

     Sum/Diff 1.      Sum/Diff 2.

Missing Number

The ‘missing number’ question was mainly answered correctly although most strategies used were inefficient using trial and improvement methods, the boxes were often left blank with children struggling to find a method to start to solve the problem.

   Missing no. 1.    Missing no. 2.    Missing no. 3.    Missing no. 4.

Subtraction.(205-143=)

Most children who subtracted correctly recorded some working to support their thinking, although vertical methods often resulted in the smaller digit being subtracted from the larger.

Some  individual children’s subtraction answers are linked to the addition question (64+85+56=) and show success in one but not the other.

    Subtract/Add

Implications for teachers.

If we take one of the three skills ‘communicating’ rather than ‘problem solving or reasoning’ this may be developed in the classroom by using activities such as those in ‘Mathematical Challenges for the More Able Key Stage 1 and 2.’ Such activities can be used to teach children how to interpret precise mathematical language, symbols, notation and diagrams and then use these to communicate their mathematics. This can be modelled for them in what teachers draw and write and in the language that they use.

Possible ways to develop children’s ability to communicate mathematically.

·         Encourage children to use suitable written methods for calculations they are not confident to solve mentally;

·         Encourage children to use jottings, including when checking answers that have been reached by mental methods;

·         Give them opportunities to discuss and work in pairs ( e.g. during the warm-up one whiteboard between two and reaching a decision about an answer);

·         Allow them to explain their thinking to a group or the class ( this could be written by the teacher as or after an explanation is given);

·         Encourage them to give a written explanation, building on the modelling done by the teacher;

·         Give them opportunities to modify, redraft, and compare explanations and methods

·         Provide opportunities for children to record in different ways, ways that they choose how to present their work;

·         Ask them to compare and contrast different forms of communicating a solution – a table, a graph or written explanation. Consider which explanation  is easier to follow and understand;

·         Use past test questions as a discussion starter and share strategies for finding the solution including annotating the diagram and working backwards to decide what information needs to be found;