# New content for GCSE Maths announced

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was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

Following the consultation discussed previously on this blog, the Department for Education has announced the revised content for GCSE Mathematics.

Compared to the current content, the most notable changes are (a) separation of probability and statistics, (b) removal of the data-cycle, (c) increased material.

The proposed content for probability is as follows:

Probability

- record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
- apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
- relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale
- apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
- understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
- enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
- construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
- calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
- calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams.

From my personal perspective, it's good to see reference to '*frequency trees*', '*expected outcomes*' and *'expected frequencies*', since hopefully this will encourage the teaching of probability through expected frequencies. It's a shame that two suggestions in the consultation were dropped: *'interpret risk through assigning values to outcomes (e.g. games, insurance)*, and *calculate the expected outcome of a decision and relate to long-run average outcomes.* But can't have everything.

For statistics it's

Statistics

- infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
- interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use
- construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use
- interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:

* appropriate graphical representation involving discrete, continuous and grouped data, including box plots

* appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)- apply statistics to describe a population
- use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing

Compared to the consultation, box-plots and unequal-interval histograms have gone in, and fitting a straight line has come out.

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