This post is based on a plenary I did for the Christchurch Mathematical Association (CMA) Statistics Day in November 2015 where I presented 10 ways to embrace the awesomeness that is our statistics curriculum. You can find all the posts related to this plenary in one place here as they are written.

## What are our awesome messages?

This post is based on a plenary I did for the Christchurch Mathematical Association (CMA) Statistics Day in November 2015 where I presented 10 ways to embrace the awesomeness that is our statistics curriculum. You can find all the posts related to this plenary in one place here as they are written.

## Not so awesome interpretations …

Being able to communicate an interpretation of a confidence interval is important. The reason why we care so much about students writing good investigative questions is so that when they come to answer these questions as a result of their exploration and analysis of the data, they are clear about what they were trying to find out and who they were trying to find it out about (in the case of sample-to-population inference). I will discuss in a later post (“Believing assessment is awesome”) more about using the written interpretation only as a measure of understanding of confidence intervals. What I am focusing on in this post is how we need to encourage students to go beyond the words or the procedure of writing the interpretation of the confidence intervals and to think about what they are really saying. |

So, it appears that Auckland runners with names that start with J run faster on average than those with names that start with P. But why would that even make sense? It is common practice to encourage students to write about their expectations for an investigation at the beginning of the process and then to reflect on the findings in respect to their expectations. In this situation, given students know about the differences between males and females in terms of physical performance, students may be able to consider that perhaps there is something else going on here…. |

…. which could be that names that start with J may be dominated by male names and names that start with P may be dominated by female names. We need to be careful that in focusing on the investigative question variables and the necessary interpretation of the confidence interval that we do not forget that we are dealing with multivariate data. When we observe a tendency for one group to be higher than another group in these sampling situations we need to be careful that we also discuss and dispel implications of causality. An effective way to minimise ideas of causality is to show students other groups to compare the numerical variable on, like we have here (letter of first name, gender). If we don’t demonstrate these other relationships and just say “don’t make a casual claim” it may be hard for the students to really understand why we need to be careful with causal attribution. |

Returning to the practice of getting students to reflect on whether the findings of their investigation make sense – which is a great thing to get students to do! However, we need to be careful here that we don’t promote causal attribution unintentionally. In this example, two different students investigated intelligence self-ratings, with one student comparing whether someone was in a sports team or not, and the other comparing gender. Both students can “make a call” and both students can align this result with what they think is going on (see the slide above for examples). But it is important with “sense making” that we don’t encourage students to consider this as evidence of a causal link – just because something makes sense to you doesn’t mean that it is true. Ideally, you would want these two students to look at each other’s results and discuss what they both found – including looking at the relationship between sports team and gender (two categorical variables). |

This post is based on a plenary I did for the Christchurch Mathematical Association (CMA) Statistics Day in November 2015 where I presented 10 ways to embrace the awesomeness that is our statistics curriculum. You can find all the posts related to this plenary in one place here as they are written.

## Using awesome real data …

There is a lot of real data out there that can be used for learning about statistics. It’s important, though, to choose data with variables students can understand and can connect with. I was really inspired by a talk Rob Gould gave at the NZAMT conference in July 2015 about professional versus modern data (you can read more in Rob’s paper |

The Auckland marathon is held each year and nearly 12 000 people enter the different events of the marathon. The reason that the Auckland marathon appeals to me as an example is how some of the data is collected for each runner: through a chip interfacing with different sensors placed at different points in the running courses. So we have “modern” data in terms of using sensors but it is intentionally collected so that runners can be awarded prizes. In this case, because of technology, we can get accurate data on quite a large number of runners. This data is combined with data that runners would have provided when entering the competition through an entry form, which is more like “professional” data in that this entry form was designed. This is also an example of a well-defined population (all the runners entered in the Auckland marathon) which we could use to learn about sample to population inference. Before anybody starts to worry about the fact that we do have all the data so why would we take a sample, you should note that in the previous sentence I used the word “learn” – that is the important word here. For students to learn about sample to population inference, we need to be able to demonstrate the relationship(s) between a population and samples from this population, and to do this you need to have all of the “data” for a population. The most important thing about setting up students to sample from a population is that students get they are learning about sample-to-population inference: that they learn about what they can and can’t say about a population (parameter) when they only have some of the data from that population. If the focus is on this aspect of learning, then students do get why they are only using sample of the population data for their investigation. |

So, when I first started teaching we got students to use a random number generator on their calculator to select members of a population list (and so their data) for a sample. There is no reason why students still couldn’t do this – procedurally it is no different from using a population bag…… |

…. or using an application/script to select a random sample from a hidden population (database). |

Whether students see all the data in a spreadsheet, see all the data cards in a population bag, or use a population database, students know that in this learning environment all of the data exists (in that the variables have already been defined and measured for each member of the population) and that they are only going to have access to some of the data. Students should be learning about what is involved in creating data through sampling – not just the difficulties of defining sampling frames and minimising non-sampling errors like non-response bias etc. but also about defining variables to be measured. However, we also need to balance different priorities for learning in statistics – we want to make connections between understandings but we also need to focus on some ideas more than others at different points in students’ learning progression – so there should be no issue with using “ready made” population data for learning about sample-to-population inference. Although the data is in the database sitting behind the tiktok.biz website, if you really want students to experience the “pain” of sampling, you could give students the range of bib numbers for the 2015 Auckland marathon (20 to 35951 although not all numbers are used in this range) and get them to generate random numbers using their calculator to select members of their sample. They can then go to the race results website http://tiktok.biz/aucklandmarathon/2015/ to look up each of these runners in their sample and record the information needed for an investigation. If you would like the whole population data set for the Auckland marathon 2015 you can access that here. |

## Using awesome contexts … and questions!

The New Zealand Income Survey SURF data set from Statistics New Zealand is a great resource (as are the many other awesome things available from Statistics New Zealand). I used this context and data set initially with a group of Year 13 students who had come through our “applied” pathway (see an earlier post on how we got students to write first before looking more specifically at the variables). The questions that we ask are as important as the context that we use for an investigation. I know many of us have developed generic questions we ask students for each stage of the inquiry cycle, but have you modelled asking these questions in context? When working with this particular group of students I found it really effective to ask “feature spotting” questions in context so that students could see what writing specifically about data looked like, and then had guidance to write their answer (basically to recycle the words used in the question in their answer). This approach for students took away some of the initial barriers to getting into writing. Using contextualised questions also gives the opportunity to model deeper thinking for that specific context and set of data. We want students to see how the chain of questions we follow changes depending on what we see and explore in the data and we need to model this for different contexts and data. |

This example of a wide range of questions used to start investigations is not just about using funny hooks to engage students but also comes from questions the students themselves were interested in finding out answers to – why not ask your students what they would like to investigate? I would also encourage as much as possible to get students simultaneously investigating different variables and situations rather than the whole class doing the same thing. At the heart of learning about statistics is to recognise “What is staying the same(ish)?” and “What is changing?”, and this can be strengthened when four students working beside each other investigating completely different questions/data can compare what was similar and different about their investigations.. There also something about students getting to choose what they want to investigate in terms of ownership and buy-in. The data used to explore these questions came from a “Ratings survey” which we developed and got students from our school to complete. |

Going further with the idea of using survey to get data and set up a context that students will find interesting, we also used this “Super survey” with all our senior students at the school to get reasonable sized population data set from which we could then sample (if you are uncomfortable about this practice, read more in the post “Using awesome real data …“). There are so many ways that this data can be used and it gives a fresh take on the data students are familiar with from the awesome Census at School. Two of these questions were inspired by Neville Davies (the ones based on the distance from home to school) and the plenary he gave at the 2013 AMA Statistics Teacher’s Day. We used Google forms to set up the survey and many of the questions require students to use various web-based resources to get answers. The survey itself would not necessarily pass a questionnaire design assessment as it really was a jumble of questions but it did give us a really rich data set to explore with students. |

A few other things that we did to make sure the students had a good connection to the context, variables and so the data was to ask them to review each question used in the super survey by classifying the variables as categorical or numerical (with the possible groups and likely numerical values) and also considering how the variable was measured. This stuff is important for all investigations even if the focus is on one aspect of the curriculum (e.g. sample-to-population inference). I also selected some of the numerical variables and some of the categorical variables and |

## Making awesome connections between standards …

Jelly bean sample data as a CSV file: jelly bean data

## Getting the awesome messages heard …

Learning about statistics is awesome – it helps you to make sense of the world and it helps you to make good decisions when faced with uncertainty. It shouldn’t be that difficult to get these kinds of messages across to teenagers since they are so important. But then think about what decisions teenagers actually get to make about their lives – how do we give them something where they will care about the decision being made? Teenagers do need to make decisions about things like alcohol, drugs, driving, study, sports, relationships etc., many of which we can use as contexts within a classroom learning environment, although some finer details we would definitely avoid! There is also a very strong case to use contexts to encourage students to think about more than just themselves and to think about the world and wider social and economic issues and how decisions made by others could affect their lives now and in the future. There are great examples of how statistics has been used to make important discoveries and we should share these with students. But there is also a good case to play to your audience (egocentric teenagers) and make it about them right here and now 🙂 |

Teenagers hate things that are unfair. For example, telling them to stop talking when clearly there are other students in the class talking! I think that sometimes students don’t care about whether they can make a call or not when engaging with sample-to-population inference because they don’t care about getting it wrong (or right). Why should teenagers care if the median height of boys at their school is higher than the median height of girls at their school? We, of course, want them to care about the statistical understanding required to know how to answer that question. Something we tried last year was to begin the unit of work on inference with a scenario where a Principal had made a decision that “unfairly” affected just one group of students: Year 12 students not getting to wear mufti. Note we asked students to discuss the scenario in groups and give one reason for and one reason against the decision. It is important to ask students why they think the decision could be justified so you can uncover misunderstandings as well as understandings (more about this is a related post later). What we wanted was for students to tell us that you can’t make a call based on the medians alone but they (in particular the Year 12 students) came back with other reasons, including challenging the variable being used (e.g. shouldn’t it be results in the exam?) A funny thing about using this scenario was that a few weeks later during an assembly our Principal did announce a special Year 13 only mufti day. My Year 12 students were convinced this was all my fault! |

So we want students to challenge the messages given to them, but not just out of self-interest (like the previous example) but also from a statistical point of view. We also want students to be able to explain to others (e.g. their parents) why some messages given in the media need to be challenged and so share these important messages about how to use statistics to make decisions. It is important for students to consider specific contextual reasons or explanations for differences BUT it also important that they can use general statistical ideas to discuss weaknesses in decision making. With this scenario, similar to the previous scenario, students were keen to give explanations focusing on personal contextual reasons or “stories” but did not immediately respond with challenges based on the need to take into account sampling variability. Yes, there are lots of ways in which the two schools are different, and there are potential issues with how the data was collected and what variable was used to measure performance, as well as generalisability issues (using Year 12 students credits to generalise about all students at each school), but …. |

…. we also want students to imagine the sample data not provided in the article and think about this in terms of the key message about using samples to make inferences about populations – we can’t make good calls based on the sample statistics alone without taken into account sampling variability. |

The New Zealand Income Survey SURF data set from Statistics New Zealand is a great resource (as are the many other awesome things available from Statistics New Zealand). I used this context and data set initially with a group of Year 13 students who had come through our “applied” pathway (more about this in the next related post). The idea is to get students writing initially for an investigation about what they thought about the issue and how it affects them personally. It was all part of an attempt to get students to “buy in” to the investigation so they would care about what they found out. It was also to get them writing straight away without needing to know anything statistical, to avoid turning students off at the beginning of the investigation – everyone can write about what they think and feel about something! And of course, using something where you can link going to uni with possibly earning more money can be used to encourage them to do well in their University Entrance subjects 🙂 |

## Setting up awesome investigations …

Statistical investigations are not necessarily the same thing as teaching activities. They can be pretty close but one area where I think we could do things more awesomely is spending more time pulling students into the context for the investigation. We don’t need to start with questions and problem development right at the beginning, and then look for information to build our contextual understanding (unless of course it is a context that the students are very familiar with). We can start by building contextual understanding first with fun hands-on activities that build curiosity and a desire to find out more 🙂 My example for this is focusing on the nature of speech and in particular the use of filler words such as “um”. |

When I was in Year 9, our English teacher used to make us play this “game” where one by one we would stand in front of the class and she would give us a topic to do an impromptu speech on. As soon as we said a filler word like “um” or “ah” or paused for too long, we were out. I think it was supposed to build confidence with public speaking but I always found it pretty intimidating. This activity though gives a nice introduction to this investigation. Get students to work in pairs, give them a topic to talk about, and they can time how long it takes the other person to use the word “um”. With the teachers at the plenary, our topic was “assessment”, and after a few minutes, there were still some teachers talking confidently about assessment – I guess they had a lot to say 🙂 I didn’t collect data from the teachers but you could collect data from your students and discuss the distribution of times. |

How many teachers have tried making videos for students to watch outside of class? I know many are not confident at doing this, and also are worried about how they will sound when listening to themselves talking. I have made a lot of videos for students in the past and quickly realised that I used filler words A LOT in my speaking. In fact, I took a recent video I made for this blog (the one about how to use the report comment writing tool) and recorded the “time between ums” using the lap function on a stopwatch. After making students/teachers reflect on their use of the word um in speaking, it seems only fair that I share my data. Turns out, on average, I use the word um every nine seconds. But then I am a teacher and not necessarily trained in the art of speaking…. not like actors or actresses right? |

Pop culture again! Here are three actors/actresses that have won Academy Awards? Do they use the word “um” during their acceptance speech? Which one will say this word the soonest? On what basis are you making your selection? Here are the links to each video so you can watch and time for yourself 🙂 Check the times that I recorded here – a nice example to discuss regarding measurement error! |

And now we can develop a more specific investigative question for this context, one that hopefully the students are really interested in finding out the answer to! |

Of course there are lots of investigations that could be carried out using a sample of Academy Award acceptance speeches! What about how long it takes someone to say “thank you” or to mention their mum/husband/child? What about how long they talk for? Or how fast they talk for? Do these things change when you compare gender, the year of the Academy Awards, whether someone had prepared a speech or not? Do male Academy Award winners tend to use the word “ah” and female Academy Award winners tend to use the word “um”? I would get students to list as many different things they are interested in about finding out and let them loose with the data to explore. |

This investigation is also good for making students go out and get the data themselves as it probably requires them watching a video. The good people at the Academy Awards have a database which contains information about each of the acceptance speeches (including a transcript) which you can find here. The thing is you need a sampling frame – a list of every award winner that exists in the database – and a way to select winners from this list randomly. There are 100 pages of names given in alphabetical order so perhaps a systematic sampling method might be appropriate. If I find a list of all the award winners (or someone creates one and lets me know) I will put a link to that list here later. |

Turns out, at least one other person has already investigated Academy Award acceptance speeches, but fortunately from a more qualitative perspective (and only focusing on the top five awards) so there is still a lot that students could do with this source of data even if they spend some time on this page by Rebecca Rolfe (check out the option to generate your own Oscar acceptance speech!) You can also make connections between contexts by learning about language and how people speak using the Academy Awards and then shifting to a slightly different context of the MTV VMA awards (perhaps for a follow up assessment activity). A “hook” into the MTV VMA awards could be to consider how long would Taylor Swift’s acceptance speech have been back in 2009 if she wasn’t so rudely interrupted by Kanye West? She only spoke for around 20 seconds all up which seems pretty short, considering this year when she won an award at the MTV VMA awards she spoke for around 2 minutes. |

## Working with teenagers is awesome …

Teaching teenagers statistics is such an awesome job. These 10 ways to easily engage with teenagers by Chris Hudson will not be unknown to any high school teacher and could pretty much serve the foundation of any lesson plan. I definitely have found that considering these kinds of ways to connect with teenagers in your teaching does make learning statistics (and mathematics) fun and effective. One task I tried this year uses at least four of these these ways: letting teens teach you or others, using pop culture, giving them a choice and setting them a challenge. |

Memes are pretty funny and one of the awesome things that have come out of the internet. You can check out other examples of funny memes I’ve found in my pinterest folder 🙂 Turns out, teenagers are kind of into memes as well and there are all sorts of apps online they can use to create them. So why not use memes to learn about statistics? I thought it would be cool to take something like non-sampling errors and challenge students to create memes to demonstrate these (rather than giving them text-based examples). |

After showing students my meme to demonstrate selection bias (and my dislike of beards) I challenged them to make their own more funnier versions. They could choose whatever non-sampling error they wanted and had to email them to me and I would choose a winner. I got some interesting memes – some definitely NSFW – but in the end I was really happy with what the students attempted and the level of engagement with the task. |

I have also used pop culture – this time the Academy Awards – to challenge students to think about what is being communicated and how they could go about investigating this claim. In Julianne Moore’s Academy Award acceptance speech she repeats a claim that she read in an article that winning an Oscar could lead to living five years longer. When I heard her say this during the ceremony, I remember thinking “What? Where did she get that from?” and then pulling out my laptop to do a search for this article. We want our students to also be ready to question claims made by others and know how to evaluate these claims. A good follow up article to read regarding this claim can be found here. |

## 10 ways to embrace the awesomeness that is our statistics curriculum

I’m pretty sure that none of us became teachers just so that we could teach our students to achieve assessments. We became teachers because we care about students; we care about their learning and we care about making a difference to their lives in positive and empowering ways. We also absolutely care about preparing students well for the assessment, but we also need to care about the messages that students take away from our teaching in terms of what statistics is all about.

I gave a plenary at the Christchurch Mathematical Association (CMA) Statistics Day in November 2015 where I presented 10 ways to embrace the awesomeness that is our statistics curriculum and re-focus our teaching on what we value in learning statistics. I am going to post about each way separately so I can also discuss what I had planned to talk about but didn’t end up talking about 🙂 You can find all the posts related to this plenary in one place here as they are written.

The original title for this plenary was 10 ways to show your students that you care about more than the assessment in your teaching of statistics. Assessment is an essential part of teaching – in fact I am not even sure you can call something teaching without assessment. It would be like cooking but not tasting, talking but not listening…… But I am worried that without our intention, students may be receiving less than great messages about learning or doing statistics, and may think that we care more about what they write for the assessment than what they understand about statistics. I watched an online video recently that a teacher had made for students about developing a purpose for a statistical investigation. In this video the teacher said something like “It doesn’t matter what you write as long as you link it to the data…..”. I don’t think the words “it doesn’t matter what you write” should be a message that students should be given about communicating statistics. |

Nor do I think the message “You can write anything you want in statistics as long as you justify it” is quite right either. What I think is important in our teaching of statistics is that our students are encouraged to make connections and that we focus on developing statistical thinking. We should also we care about messages that we send students about statistics because we also want students to care about the messages that others try to send them about statistics. We definitely don’t want students to accept any claim that is made using statistics just because someone has attempted a justification. We want them to be able to critically evaluate these messages. The 10 ways I will discuss I hope will show examples of these three important teaching focuses in action 🙂 |