2 ObjectivesTo consider the data handling cycle and the effective teaching of data handlingTo clarify the terminology and conventions used for different tables, charts, graphs and diagrams.Data handling is often an area that is not covered to the best advantage because teachers are not clear about what they should be teaching when, and also about what they should be repeating from what has been taught at an earlier stage. (e.g. Carrolls on Y6 tests)- objectives from framework are not very helpful as they put all data handling together rather than separating out.Considerable time is spent on the collecting of data (primary data) and far less time on interpreting the findings. At KS2 more secondary data needs to be used and where data is collected it needs to be collected speedily.
3 Key terms Primary data Secondary data Discrete data Categoric data Continuous dataGrouped dataACTIVITY - categories of dataData sort handout, identify which data is categoric, which is discrete and which is continuous. (Use key terms handout to support with this).One of the examples in continuous is slightly different. Can you tell me which one? The conversion graph. WHY? It is still continuous data but the conversion is not variable so each value is exact so every bit is accurate, whereas the other conversion data shows trends. The bits between the actual measurements are guesses between the accurate bits.ANSWERSCategoric dataFlavours of crisps we like to eatType of PetsVehicles Which Pass Our School in One HourColour of EyesOur Favourite ComicsDiscrete dataShoe sizes of children in Y1Number of slides on our plane shapesCoins in people’s pocketsMarks out of 10 in the spelling testContinuous dataDaily temperature taken at noon during the month of SeptemberThe weight of Sean’s baby sister during her first yearVolume of water in a water butt throughout a dayDistance covered in a sponsored bike rideConversion chart for miles and kilometres
4 The data handling cycle Posing thequestionInterpreting and discussing the dataCollecting the dataThe data handling cycleIdentify a problem and pose a questionPlan what information to collect and how to go about it. Decide where the information can be obtained and what results may be expected.Collect data from various sourcesprimary and secondary. How large should the sample be and what range should beincluded?Organise, analyse and present the data in an appropriate form.Is it appropriate to calculate an average? (mean, mode, median)Interpret the results to answer the initial problem or question.What can be gained from the results? How does the interpretation of data relateto the question? Can the results be interpreted in more than one way? What hasbeen learned bout the problem or question?Posing the question is the important introduction so that we can solve a problem or test a hypothesis.It is important not just to say “we are learning about bar charts today” but to actually pose a question without mentioning data.Page 4 in handout pack – starting points for handling dataFor these types of questions:Children need practice in considering the questions posed so they can begin to identify what they actually want to find out.To answer any questions, data has to be collected and the way it is to be collected needs to be decided.This raw data then needs to be summarised in some way so that analysis can take place.Analysing the data
5 Types of graphical representation Mapping or arrow diagramTally chart / frequency chartPictogramBar chart Bar linePie chartTree diagramVenn diagramCarroll diagramLine graphFor each of these can ask for suggestions as to how they can be used if desired.MappingStarts in KS1. Linking numbers to their doubles etc. It links to x and y axis later on in KS3.Tally charts and frequency tablesWhen collecting data from the class on ‘ who likes which drinks’, you can ask the children in turn and tally, or, you can ask hands up who likes cola and write the number straight into a frequency chart.Pictogram (Activity 3 from Using ICT booklet) A picture or symbol is used to represent items or groups of them. Initially one symbol will refer to one item but gradually this should be increased so that the symbol could refer to 2, 5, 10, etc. The difficulty here is showing 1 when the symbol represents 2, 3, 5, etc. E.g. J (draw on board) if this represents 5, how do you show 1? So designing the symbol is important.Bar chartColumns or rows of shaded bars can be used to represent numbers of items in different categories. What is important here is whether the bars should or should not have a space between them - When bar charts are used for discrete or categoric data the bars SHOULD have a space between them.By the time children are in Year 5 children should be starting to use bar lines to represent the bar rather than a thick block.Pie Chart (Activity 7 from Using ICT booklet) A frequency diagram where the angles of the sectors correspond to the frequency. (Interpretation only in Y6, not construction)Tree diagram/Branching database (Activity 4 from Using ICT booklet) Early years call it sorting tracks. It is how you sort something e.g. a shape has 4 sides yes/no etcVenn diagram (Activity 1 from Using ICT booklet) A method of sorting items where they can belong to more than one set. The rectangle around the outside provides a place for items that have none of the specified criteria.Carroll diagrams (Activity 2 from Using ICT booklet) A way of sorting, by one, two or three criteria. The items are sorted by having the criteria stated or not. e.g. ‘multiple of three’ or ‘not multiple of three’Bar line (Activity 6 from Using ICT booklet) as bar chart but in lines instead to make drawing less time consuming.Line graph (Activity 6 from Using ICT booklet) This can only be used for continuous data as points are plotted and then joined.Activity 8 from Using ICT bookletWork in pairs, look at sample sets of data and decide which method of presenting the data would be best and why.Take feedback with reasons and discussion.Trends between each point can be discussed. (use Archimedes program)Very often in the classroom much time is taken up by the children spending a long time collecting data.This has its place especially in the early stages but often means that not enough time is spent on interpreting data.It is also not enough when interpreting data to simply ask closed questions that can be read directly off a graph. Questions need to be probing and open.‘How many’ questions usually tend to be closed whereas ‘why’ questions usually tend to be open.
6 Probing questions What questions could you ask about this data? If not covered, ensure these are demonstrated as they are more open.Why do you think so few cold drinks were sold on Friday?How many more drinks were sold on Monday than on Wednesday?How many cold drinks were sold during the week?Do you think we would have the same graph if we took the results from a different week? Why?Talk me through the story of the graph – (on Monday there were ___ sold and then etc)
7 125102410203615304820405102550612306071440708165080This can be made to support with target getting.Piece of paper or card with axis on (as on rhs of slide).Slots cut in axis with thin paper strips pulled through (border roll is quite good for this).Separate sheet of paper with post it note scales on, counting in 1s, 2s 5s, 10s, further through school will also use 20s, 50s, 100s, 1000s etc.Children can be given data, encouraged to choose an appropriate scale and this can be shown using the paper strips.For mental oral starters, a set of data could be shown easily on this and then adjusted by simply altering the height of the paper strips.Can also do for bar line chart with wool instead of paper strips.9185590102060100
8 This activity can be reinforced in the plenary, by creating a human bar chart. Two children hold the axis and other children then crouch behind the horizontal axis and rise to the point their classmates tell them to.Activity - Creating a human block graph and changing to pie chart.Give out post-its. Everyone draw favourite fruit from a selection of 4, e.g. grapes, apple, banana, plum.Put pictures of fruit down and make lines of people behind the fruit.Ensure that the people are lined properly, e.g. 1st in each line all level, 2nd in each line all level etc.To create pie chart. Make a circle of people with all grapes standing side by side, all apples, bananas, cherries etc. Where there are two people with differing fruit standing side by side, they should hold one end of a piece of rope which goes to the middle of the circle.
9 Using ICT in data handling Links to ITPs – and other programs in ICT folder
10 Issues from QCAChildren not given opportunity to decide on increment ofscale for axis;Children told today we are going to draw a bar chart toshow rather than introducing through a problem to besolved. They are not encouraged to think about the bestway of representing the different data;Children only see bar charts where the bars are shownvertically and not horizontally;Children in Y6 required to consolidate previous knowledgebut children aren’t always consolidating understanding ofpictograms – even though they appear in the SATs.Children not given opportunity to decide on increment of scale for axis.Children told today we are going to draw a bar chart to show rather than introducing through a problem to be solved. They are not encouraged to think about the best way of representing the different data.Children only see bar charts where the bars are shown vertically and not horizontally.Children in Y6 required to consolidate previous knowledge but children aren’t always consolidating e.g. understanding of pictograms.
11 Planning for handling data across the curriculum Look at the different topics you will be teaching this term in all subjects.Identify opportunities for data handling in different units of work.Think about the range of graphs and charts the children will need to be familiar with.Consider moving the data handling unit of work to ensure children have been taught the skills to apply to different subjects.Look at the different topics you will be teaching this term in all subjects.Identify opportunities for data handling in different units of work.Think about the range of graphs and charts the children will need to be familiar with.Consider moving the data handling unit of work to ensure children have been taught the skills to apply to different subjects.The more we can incorporate using and applying skills of data handling, the more effective children will be.Go through rest of materials in pack (ideas and progression).
12 Key messages Ensure progression and variety of presentation. Use different sources of data so that children at KS2 don’t only use primary data.Ensure there is enough time given to interpretation of data.Use the knowledge and skills taught in Maths and apply them through different subjects.Opportunities for data handling occur in most subjects. Make links explicit for the children.Ensure progression and variety of presentation.Use different sources of data so that children at KS2 don’t only use primary data.Ensure there is enough time given to interpretation of data.Use the knowledge and skills taught in maths and apply them through different subjects.Opportunities for data handling occur in most subjects. Make links explicit for the children.