# Statistics assessment: The good, the bad, and the ugly, S McCusker, J Nicholson, J Ridgway

Tags: Nicholson, International Association of Statistical Education, pencil, Paper McCusker, IASE, Assessment tasks, exam papers, James Nicholson, Jim Ridgway, GCSE maths papers, statistical reasoning, compulsory education, GCSE Statistics, GCSE, statistics, statistics education, pencil case, probability and statistics, monthly rental, Ridgway, wingspan, McCusker, body length, scatter diagram, Edexcel GCSE Statistics Higher Tier Paper, Foundation Tier, Ridgway Real, Mathematics, European Union, 16 year olds, GCSE Mathematics, Royal Statistical Society
Content: ICOTS8 (2010) Invited Paper
McCusker, Nicholson & Ridgway
In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society. Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS8, July, 2010), Ljubljana, Slovenia. Voorburg, The Netherlands: International Statistical Institute. www.stat.auckland.ac.nz/~iase/publications.php [© 2010 ISI/IASE]
ICOTS8 (2010) Invited Paper
McCusker, Nicholson & Ridgway
Real world but not age-appropriate
The table shows the price index Numbers for the average monthly rental of twobedroomed properties in Manchester between April and August.
The base month is April.
Average monthly rental of two-bedroomed properties in Manchester
Month
April
May
June
July
August
Price
100
97
110
70
96
Index
(a) In which month was the average monthly rental higher than it was in April?
The average monthly rental was Ј720 in April.
(b) Calculate the average monthly rental in July. ... Edexcel GCSE Statistics Higher Tier Paper 1H 1389/1H June 2008
Context irrelevant Clare is reading a poetry book. (a) The shortest poem in the book has one verse and the longest poem has six verses. The poems in the book are from ten to fifteen lines in length. Design a two-way table for Clare to record the number of verses and the number of lines for the poems in the book. [3] (b) Clare counted the number of letters in each word of one poem. There were 28 words in the poem. She drew this table to show her results.
Number of letters Frequency
1
2
2
5
3
6
4
8
5
2
6
3
7
2
Total
28
Calculate the mean number of letters per word in the poem.
...
OCR GCSE Mathematics Syllabus A Paper 2 (Foundation Tier) June 2008 J512/02
Unrealistic context There are 8 pencils in a pencil case. 1 pencil is red. 4 pencils are blue. The rest are black. A pencil is taken at random from the pencil case. Write down the probability that the pencil is black.
Edexcel GCSE Mathematics B (Modular) ­ 2544 / Mathematics (Modular) ­ 2381 Foundation Tier June 2008 ­5542F/8B 5381F/5B
International Association of Statistical Education (IASE)
www.stat.auckland.ac.nz/~iase/
ICOTS8 (2010) Invited Paper
McCusker, Nicholson & Ridgway
International Association of Statistical Education (IASE)
www.stat.auckland.ac.nz/~iase/
ICOTS8 (2010) Invited Paper
McCusker, Nicholson & Ridgway
variate data was encountered, the relationships were linear. However, to imagine that most of the interesting issues in the world are uni-variate or bi-variate in nature, and can be solved by the simple statistical models encountered in the UK syllabus is to be naive. The major issues of relevance to youth today are multivariate in their nature. For example the extent to which one is exposed to a Sexually Transmitted Disease (STD) is dependent on its prevalence in the age group and socio-economic status of one's sexual partner. Any attempts to deal with STD as an issue must take into account the way in which it has changed over time. (see Nicholson, Ridgway & McCusker, 2010 for a fuller discussion). Analysis of some 2009 GCSE statistics papers is more encouraging; there are some instances of non-linear bi-variate relationships, some set in reasonably interesting contexts. Interesting context; realistic modeling The scatter diagram shows the average wingspan and the average weight of 8 British birds.
Put a cross in the box to indicate which one of the equations is the best model for these data.
The scatter diagram below shows the body lengths and wingspans of the same birds. ... The scatter diagram shows positive correlation. (b) What can you conclude about the relationship between the body length of a bird and its wingspan? A line of best fit has been drawn on the scatter diagram. The equation for this line of best fit is of the form y = ax + b (c) Work out the equation for this line of best fit. A crow has a wingspan of 100 cm. (d) Estimate the body length of this crow. Edexcel GCSE Statistics Paper 1H Higher Tier1389/1H There is much in the press which seeks to demonise youth, presenting them in a negative light, or pronouncing on issues which are relevant to them. Some recent headlines from UK mainstream media refer to Labour's maths bungling leaves kids on scrapheap; Shock hike in kid coke addicts (The Sun­Online), Alcohol and cigarettes are more harmful than Ecstasy and LSD, says drugs tsar; Booze Britain: hard evidence links alcohol and youth crime (Daily Mail ­ Online).
International Association of Statistical Education (IASE)
www.stat.auckland.ac.nz/~iase/
ICOTS8 (2010) Invited Paper
McCusker, Nicholson & Ridgway
They can't read, can't write, keep time or be tidy: Tesco director's verdict on school-leavers (Guardian - Online) Violent games `worse' than porn (BBC News Website). These headlines are illustrative of those which the pupils in the 14-16 age group might meet everyday in the mainstream press, where ill-founded speculation is presented as fact. It is possible to create curriculum activities where pupils deconstruct media myths about adolescents. This has the potential to show the power of statistics. An example is presented in Figure 1 and Figure 2, that shows a mashup (A webpage with multiple links to information sources) comprising recent survey data on alcohol use, presented in an interactive display, with links to recent Newspaper Articles on alcohol consumption by young people.
Figure 1.
Figure 2.
Students worked with the task for three separate one-hour periods, starting with an introductory piece focused on smoking, which allowed pupils to familiarise themselves with the software. The main objective was for the pupils to create a media report on the topic of Alcohol and Young People. The structure for student outputs was very open. Pupils were not given strong guidance on the content of what they were required to produce or how to analyse or interpret the data presented to them. They were encouraged to explore the domain and report on their findings, with respect to the news articles. These reports took a variety of forms such as letters to the editor, newspaper articles, interviews and TV news reports. Students were encouraged to produce a report in any format with which they felt comfortable. In total about 100 reports were produced and analysed. Student responses were categorised primarily in terms of: use of argument (the ways in which students use data to critique or create text media, and the extent to which they synthesise information from different media accounts); and use of empirical data (judgments on the extent to which students have made use of the data in the interactive displays). A high proportion (> 80%) of the children were enthusiastic about the task. Reports were well presented, with a good sense of audience and structure: only four reports failed to meet all of these criteria adequately.
· Over 80% of the reports used data, with about 60% using it accurately and appropriately to critique the media articles or in the creation of their own articles. · Just over 20% of the reports described trends in a clear and accurate manner, and a further 10% described trends with at least some degree of success. · About 15% of the reports made mention of 2-way interactions: this is interesting, because the topic of interaction is usually considered to be too complex at age 16 years. In fact such analyses are not required even within the A Level Mathematics and Statistics curricula in England, designed for mathematically able 18 year olds.
DISCUSSION Pupils' worlds are filled with complex and interesting problems. Statistical reasoning is a powerful tool which is able to help make sense of these worlds. Pupils need to see the applicability of statistical techniques and how these can relate to their environment and help them to understand the issues which engage and threaten their interests. If we lead children to believe that statistical
International Association of Statistical Education (IASE)
www.stat.auckland.ac.nz/~iase/
ICOTS8 (2010) Invited Paper
McCusker, Nicholson & Ridgway
reasoning consists of set of techniques which allow them to determine Confidence Intervals around the volume in pots of yogurt, they might struggle to see how this set of skills might reveal to them the threat of catching an STD, help them to counter the bad press which they receive or reveal to them the fact that the behaviour of their parents' generation was much worse than theirs. REFERENCES Birenbaum, M., Breuer, K., Cascallar, E., Dochy, F., Dori, Y., Ridgway, J., Wiesemes, R., & Nickmans, G. (2006). A Learning Integrated Assessment System. Educational Research Review, 1(1), pp 61-67. Burkhardt, H. (2009). On Strategic Design. Educational Designer, 1(3). Online: www.educationaldesigner.org/ed/volume1/issue3/article9/. Carlson, W. (1999). "A Case Method for Teaching Statistics". Journal of Economic Education, 30(1), 52­58. Nicholson, J., Ridgway, J., & Mccusker, S. (2010). Luring non-Quantitative Majors into Advanced Statistical Reasoning (and luring statistics educators into real statistics). Proceedings of ICOTS8. Ridgway, J, McCusker, S., & Pead, D (2004). Literature review of e-assessment, NESTA Futurelab Series Report 10, Bristol: NESTA Futurelab. Ridgway, J., Nicholson, J. R., & McCusker, S. (2007). Teaching statistics ­ despite its applications. Teaching Statistics, 29(2), 44-48. Hand, D. J. (2009). Modern statistics: the myth and the magic? Journal of the Royal Statistical Society, 172, 287-306.
International Association of Statistical Education (IASE)
www.stat.auckland.ac.nz/~iase/

S McCusker, J Nicholson, J Ridgway

### File:statistics-assessment-the-good-the-bad-and-the-ugly.pdfTitle: Microsoft Word - 5D1_Mccusker.docAuthor: S McCusker, J Nicholson, J RidgwayAuthor: u1Published: Tue May 25 23:36:11 2010Pages: 6File size: 0.15 Mb

Zack's Alligator, 7 pages, 0.14 Mb

Quiet City, 2 pages, 0.21 Mb

Cultural criminology, 2 pages, 0.01 Mb

Poems, 1799, 93 pages, 0.13 Mb