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Mathematics Subject Leader. Spring 2010. Programme. Session One Data Session Two Marking Session Three Data Handling. Session One. Data . Aims. Aims: Moving on in mathematics Gaps in children’s mathematical knowledge RAISE online An understanding of the analysis of SATs 2009.
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Mathematics Subject Leader Spring 2010
Programme Session One Data Session Two Marking Session Three Data Handling
Session One Data
Aims • Aims: • Moving on in mathematics • Gaps in children’s mathematical knowledge • RAISE online • An understanding of the analysis of SATs 2009
Five sections • Identifying children with gaps in attainment in mathematics • Pinpointing and narrowing the gaps in mathematics • Sustaining impact • Celebrating success • Supporting materials
1. Identifying children with gaps in attainment in mathematics • RAISE online • Tracking data • Assessing Pupils’ Progress (APP) • Question level analysis
2. Pinpointing and narrowing the gaps in mathematics • Attitudes, aspirations, behaviour and attendance • Mathematical knowledge and skills • Mathematical processes • Language • Fit for purpose pedagogy • Securing levels and overcoming barriers
3. Sustaining impact To know whether actions are having sustained impact and children are making the progress we expect, careful and ongoing monitoring and evaluation are required.
4. Celebrating success • Share success with: • children • parents and governors • all the school • other schools • SEF
Distribution of questions and marks by Framework core learning in mathematics by year
Implications to consider • Mental test 50% of questions relate to Year 4 objectives Timed questions are in levelled order • Test A Calculations are presented in a line to encourage pupils to choose how to set out their working A balance of calculations for children to solve mentally and written 41% of questions relate to Year 4 • Test B Pupils need to know the order of operations to use with a calculator 45% of questions are Year 4
Using and Applying This design has one large square and two identical small squares . The design measures 36 centimetres by 28 centimetres. Calculate the length of the side of the large square.
Explanation Two part question Children do not complete all the parts to the question. Children do not use the related mathematical language. Calculation Children still confused over the meaning of ‘show your method’.
Children can . . . Look at a calculation and recognise when mental methods are more appropriate. To estimate first so they can check whether their answers are sensible. To use jottings and annotations to help them to find solutions.
Session Two Why do we need to mark children’s mathematics work? Marking
Think and share your thoughts on how marking in mathematics is carried out in your school?
The purpose of marking • The purpose of returning marked work or providing oral feedback is to enable pupils to improve their learning. • Marking and feedback can be improved by the teacher considering: • how well the pupil has understood the task • what the pupil knows and does not know • what the pupil needs to do next to improve • how they can encourage pupils to review their work critically and constructively • Teachers who use a range of effective techniques for assessment, marking and feedback are most likely to be successful in raising standards.
A simple marking model Show success Indicating improvement Giving an improvement suggestion Making the improvement
A constructive sandwich Praise: That’s good work, I particularly like… Constructive educational feedback: To improve, you could work on these aspects. Praise: Well done.
Marking • Effective feedback points to success and improvement against the learning intentions and success criteria • Feedback is only given about what the children were asked to pay attention to. • Ensure effective and consistent use of whole school marking policy • Use structure for improvements : Reminder, Scaffold and Example • Inform parents and carers about your approach to marking ‘Quality’ or ‘focused’ marking makes a difference
Session Three Data Handling
Aims • To consider the range of charts and graphs used to organise and represent data • To identify where more emphasis needs to be placed in the data handling cycle, and the implications for teaching • To increase subject knowledge of handling data
Five aspects of the data handling cycle • Specify the problem Formulate questions in terms of the data needed and the type of inferences that may be made from them. • Plan • Decide what data should be collected, including sample size and data format, and what statistical analysis needs to be carried out. • Collect data • Obtain data from a variety of appropriate sources, including experiments and surveys, and primary and secondary sources. • Process and represent • Reduce the raw data into summary information, including lists, tables and charts, to provide insight into the problem. • Interpret and discuss • Relate summarised data to the initial questions.
Decisions needed • What data should we collect? • Will the data consist of measurements or opinions? • How should we collect the data – by counting or measuring? • Whose opinion should we ask – everyone with an interest or just a sample? • How do we ensure that our samples are representative? • Should the opinions of some groups have a weighting, or should all opinions have the same value? • How should the data be analysed? • How should results be presented? Does this influence how we should collect the data? • What else needs to be considered?
Data handling activity • As you look at each card consider • The type of graph or chart shown • Is the data discrete or continuous (collected by counting or measuring) • Now put the cards in order of progression considering the following • The type of graph or chart • The scales used • The use of grouped data
Progression steps 10 steps of progression
Points to note • The use of discrete data in years 1 to 4 and the introduction to continuous data in years 5 and 6. • The use of line graphs to represent trends as well as relationships. • The labelling of the axes and the titles given. • The symbols used in pictograms to represent one or more units. • The progression in the vertical scales of bar charts from ones to twos, fives to tens, and the need to keep the reading of scales in line with reading measuring scales and work on co-ordinates. • The choice and labelling of intervals when discrete data has been grouped.
Level 1-2Tables • Who picked up the most cubes in one hand? How do you know? • Who do you think has the smallest hand? Why? • What else does this table tell you?
Bar charts Robbie collected some information about the colours of some bikes. Here are his results. The bar graph shows the information from the table. Fill in all the missinglabels and numbers. ‘There are more red bikes than green and pink together.’ Is this statement true? How could you change the bar chart to show 40 green, 70 red, 120 blue and 30 pink bikes?
Level 2-3 Look at this block graph. Which way of travelling to school is used by most children? Explain how you know.Can you think of another question you could ask and answer using the data? Do you think it's true that most children in our class have packed lunches? How could we find out? Make a list or table and explain what you have found out.
Bar chart In the 2000 Olympics USA won 39 gold medals. Is that more or less than in 2004? How many more or less? What labels would you add to the axes of this graph? How would you work out how many gold medals Britain won in 2004?
Level 3-4 Carroll diagram Write one number in each white section of the diagram. Put these numbers in the correct sections: 60, 742, 1180, 390, 530 Describe the numbers that could go in each of the white sections.
Factors of 36 Odd numbers 12 15 20 Venn diagram Write these numbers in the correct places on the Venn diagram. Some numbers are already placed. 33 6 72 3 What is the largest whole number that should go in the intersection of the two sets?
