##### the survey results

*How does the teaching time for students in different year groups compare at UK secondary schools within mathematics? And why might it matter?*

In part 1 I looked at the national and international background on teaching hours and summarised what the research said on teaching time for mathematics: studies show that increasing teaching time leads to improved results within mathematics and that this increase may be larger for disadvantaged students and for girls.

In this post I will share the results of a survey I conducted investigating how many hours students have for maths lessons per week. This survey appears to be the first attempt at an in-depth and detailed breakdown of mathematics teaching time at UK secondary schools.

A link to the questions used in the survey and a download of the full results is available at the bottom of this post.

##### summary

A survey on the teaching hours for mathematics across different year groups at UK secondary schools was shared on Twitter on July 23rd. 619 teachers responded to the survey over the course of several weeks through to the 14th of August 2020. The results indicate:

- there is fair variety but the majority of students in KS3 and KS4 have between 3 and 4.5 hours of maths lessons per week (86% in year 7 to 71% in year 11)
- 88% of A level mathematics students have between 4 and 5.5 hours of lessons per week
- there is a significant increase in lesson hours for mathematics moving up through the years of secondary school
- year 9 serves as an intermediary year fitting either within the year 7 and 8 context, or within the year 10 and 11 context depending on when schools start KS4

While the statements above may not be a surprise to most maths teachers, this survey allows for a much more detailed analysis of these facts.

##### headlines

The headline results of the teaching hours per week for different year groups are given in the table below:

year | N | mean | SD | Q1 | Q2 | Q3 |
---|---|---|---|---|---|---|

year 7 | 597 | 3.681 | 0.926 | 3 | 3.5 | 4 |

year 8 | 600 | 3.707 | 0.920 | 3 | 3.5 | 4 |

year 9 | 612 | 3.824 | 0.987 | 3.3 | 4 | 4 |

year 10 | 614 | 4.062 | 0.964 | 3.5 | 4 | 4.17 |

year 11 | 612 | 4.157 | 1.026 | 3.5 | 4 | 4.5 |

year 12^{(1)} | 381 | 4.758 | 0.945 | 4.5 | 4.75 | 5 |

year 13^{(1)} | 380 | 4.833 | 0.943 | 4.5 | 5 | 5 |

year 12^{(F)} | 316 | 4.850 | 2.536 | 4 | 4.5 | 5 |

year 13^{(F)} | 314 | 4.900 | 2.613 | 4 | 4.5 | 5.15 |

*(1) – A level mathematics only, (F) – A level further mathematics only. *

The following table gives a breakdown of the distribution. The year group is denoted at the top and the amount of lesson hours per week goes down, with all values denoting the percentage of respondents who gave an answer in that range.

*(1) – A level mathematics only, (F) – A level further mathematics only.*

Results for each year group are given in the following histograms. All graphs are to the same scale, with the x axis being hours per week and the y axis being the relative proportion.

*(1) – A level mathematics only, (F) – A level further mathematics only.*

The graphs show that year 7 and 8 are relatively evenly distributed between 3 and 4 hours with an abrupt drop off above 4 hours. Year 9, 10 and 11 have very distinct peaks at 4 hours per week, with less of a sharp drop off above 4, especially for year 11.

Year 12 and 13 A level maths have clear peaks at 5 hours per week, with a big drop off above that amount. For A level further maths the results are relatively spread out, and both years have by far the largest standard deviation of all results. This may reflect the fact that further maths is less common and that some schools have different approaches in structuring A level maths and further maths.

Each graph shows an unexpected bump between 7 and 9 hours, with about 3.5% of responses for year 7 to year 11 indicating that they have more than 6 hours a week. It is presumed that these are respondents who incorrectly gave hours per fortnight (with most secondary schools following a fortnightly timetable). Since there is no clear cut off point and no way of knowing for sure, these responses have been kept in the data but their impact is small.

Overlaying these graphs allows for a clear comparison between year groups.

*(1) – A level mathematics only, (F) – A level further mathematics only. *

There are many interesting comparisons to be made from these graphs.

- the similarity between year 7 and 8, or between year 10 and 11, is well reflected in graphs a) and e).
- the increase in hours between year 7 and 11 in well reflected in graph b).
- the increase in hours between year 11 and year 12 A level maths is well reflected in graph f).
- year 9 sitting as an intermediary between year 8 and year 10 is well reflected in graphs c) and d). This point is investigated further below.

Some interesting further insights become apparent when the interval of the histograms is decreased. For example comparing year 7 and 11 we have:

Graph d) shows the peaks more precisely for each year group, with year 11 having a pronounced peak at 4 hours and smaller peaks at 3.5 and 5 hours per week, and year 7 having peaks at 4, 3 and 3.5 hours.

##### year 9: the in-between year

Year 9 serves as a particularly interesting group to investigate closer. Of 619 total respondents, 42.3% indicated that within mathematics KS4 starts in year 10, 51.1% indicated that KS4 starts in year 9 and the remainder mostly said there was no clear difference. The impact of this on teaching hours per week is summarised in the table below.

category | N | mean | SD | Q1 | Q2 | Q3 |
---|---|---|---|---|---|---|

year 9 (all) | 612 | 3.824 | 0.987 | 3.3 | 4 | 4 |

year 9 is KS3 | 258 | 3.375 | 0.990 | 3 | 3.5 | 4 |

year 9 is KS4 | 314 | 3.927 | 1.023 | 3.5 | 4 | 4 |

Whether year 9 is treated as KS3 or KS4 has a statistically significant difference on the amount of lesson time students have in year 9 for mathematics (t = 2.98, p = 0.003). Year 9 students treated as KS4 have, on average, 15 minutes more of maths lessons per week or nearly 10 hours more over the school year. While this appears small it is a 16% increase in timetabled hours. The context in part 1 indicates that this may influence student progress within mathematics.

The following graphs represent the distributions for the categories of year 9 and give clear visual comparisons:

- graph a) shows the contrast between year 9 being treated as KS3 or KS4, with b) and c) comparing to year 9 responses overall.
- graphs d) and g) show that year 9 being KS3 gives a distribution similar to year 8, while year 9 being KS4 gives a distribution similar to year 10.

##### exam board

Data on the exam board used for GCSE was also collected in the survey. Comparing to the 2019 entries for GCSE mathematics serves as a validity check for the data. From the survey responses only AQA, Edexcel and OCR were considered, as these were the only exam boards to have more than 10 respondents.

board | N | % | real^{(2)} | % |
---|---|---|---|---|

AQA | 156 | 27 | 146,715 | 25 |

Edexcel | 382 | 66 | 387,588 | 67 |

OCR | 40 | 7 | 44,953 | 8 |

(2) – these are the 2019 entrants, considering only entrants in school year 11 or below for AQA and Edexcel. For OCR this is all entrants. Source: AQA, Edexcel, OCR.

The percentage in the third and fifth column indicates the relative percentage from the total of AQA, Edexcel and OCR, not the overall percentage of all respondents or all entries. The close relation between the survey respondents and the real values gives good indication that the data may be reliable.

Only AQA and Edexcel have sufficient responses to compare the timetabled hours data. Without performing in depth statistical tests, no significant and obvious differences were apparent.

##### school type

The type of school the respondent was employed at was also collected. Overall responses from the survey indicated:

- 57.9% – Academy
- 20.0% – Local Authority Maintained
- 8.9% – Private
- 5.2% – Grammar
- The remaining 8% – some other type of school such as Faith school, Free school, Alternative provision etc.

Only Academies and Local Authority Maintained schools had sufficient responses to compare timetabled hours. Without performing in depth statistical tests, there appeared to be no significant and obvious differences. There is some indication that private schools have *less* timetabled hours for mathematics, although the small sample makes it impossible to draw any conclusions.

The type of school can also serve as a second validity check for the data. This is given in the table below. The fourth column lists student numbers at the relevant type of school as of 2020, while the third and fifth columns list the relative percentages of the given totals.

(3) – Sources: DfE (2020) indicates that there were 3,409,227 students in secondary education in July 2020, with 77% of these students at Academies (which includes free schools) and 23% at Local Authority Maintained Schools. The number of students in private education is collected by the ISC (2020).

This is a less clear fit than the exam board data. This could be because the respondents to the survey were teachers and this is comparing to student numbers, not teacher numbers. Data comparing teacher numbers or maths teacher numbers at different types of schools could not be found. Private institutions have a higher teacher to student ratio, which may explain the relative over-representation of teachers at private schools. Although the most likely explanation is the limited sample.

##### previous surveys

A final validity check can be made by comparing this data to a previous survey by Jo Morgan (2019). Morgan’s survey had more respondents (N between 1442 and 903), but due to being conducted on Twitter did not allow any further breakdown or exploration of the data. Morgan’s survey asked only of year 7, 9 and 11. A comparison to this survey and Morgan’s is given in the table below, where all numbers are percentages.

While they are broadly similar, there are some larger differences. For example, every year group has a large difference in the 3.5 to 4 column. The reasons for this are not clear.

##### conclusion

This survey aimed to create a rich, in-depth and publicly available data set on the amount of maths lessons that students have at secondary schools in the UK. Of course, this survey is only a informal one and one with a limited sample size, but it does provide more details than previous results.

The results allow teachers and school leaders to more accurately compare the amount of hours they offer with other schools. As mentioned in part 1, research indicates that an increase in teaching time for mathematics increases outcomes especially for disadvantaged students. Schools with a relative weakness in mathematics and a low number of hours for maths may wish to consider this when structuring their timetable.

Many further questions are raised by this survey. Most of all, there is a need for a large scale survey and study on mathematics teaching hours across the UK and the impact this may have on student progress.

This survey did not include the hours for Core maths, GCSE resits or Additional maths, which would also be interesting to investigate further.

There were few responses from Northern Ireland and Scotland (judging from exam board responses and comments), and the survey did not account for the differences in school structure between the home nations. It would be interesting to compare in more depth any differences between England, Wales, Scotland and Northern Ireland on timetabled hours for mathematics.

The length of lessons was not accounted for in the survey, nor was the number of lessons or the distribution of lessons through the week. This again is of interest to teachers and school leaders and should be researched further.

##### resources

A copy of the questions used in the survey is available here.

The full results of the survey are available to download here. You are welcome to further analyse this data in anyway you please. I would love to see any further analysis or results based on this data set – please do let me know what you create by contacting me on twitter @drstonemaths. I have removed any personal information included in the responses.

All graphs were created on Demos. You are welcome to explore and interact with the graphs and data within Desmos by using this link here.

And finally, a huge thank you to everyone who responded.

It is noted that two significant outliers were removed before analysis

- responses number 373 for year 7, which was given as ‘44’ and
- response number 576 for year 8, which was given as ‘36’.

Contact me on twitter @drstonemaths.

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