Make awesome statistical friends …

statistical-friends

 

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Welcome to the last of the 10 ways to embrace the awesomeness that is our statistics curriculum! And maybe one of the most important.

Teaching is an awesome job, made even “awesomer” by working with other teachers to get great stuff happening that benefits our students. Everyone needs friends and statistical friends are the best kind – they know how to deal with uncertainty after all! Talk lots and often about teaching statistics – this includes through email. If you can’t find enough statistical friends within your school than head online and find awesome teachers there. Statistical friends are also people that you can share geeky statistical things like in the slide above. This graph is of the number of new followers I got each day on the Future Learn course Data to Insight since it started, with a question to my statistical friend “How many followers do you think I will get tomorrow?” Her prediction was wrong but only a statistical friend will accept your mistakes, since of course we’re only ever pretty sure about things in statistics 🙂 It is also important to have a statistical best friend – someone who is an expert statistics teacher. Someone who can steer you in the right direction and get you to reflect on what matters most in teaching statistics. We are all still learning and we can all still improve in what we do as teachers. My personal development as a statistics teacher has been heavily shaped and influenced by friendships with amazing statistics teachers and statistics education researchers. Their time, advice, guidance and mentoring is a big reason why I think teaching statistics is awesome!

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.

Believing assessment is awesome :-)

formative

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Assessment is awesome. How great is it when students complete a task and feel success with applying something they have learned? Without feedback on our work, how would we know which areas we need to improve? Assessment is important as it validates and values teaching and learning. The thing about assessment is that you are not going to be able to assess everything in one task – there always needs to be a selection and ideally this selection represents what matters the most. However, we are in a great position where our current curriculum for statistics and the associated standards are closely aligned so the important things we want students doing when learning about statistics are the same things we want to see in the formal assessment.

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I think it is good to reflect on how we used to assess something like confidence intervals. This example is from the last external exam for the standard AS90642 Calculate confidence intervals for population parameters. The title of this standard sums up the focus for achieving this standard – calculating. Actually, students had access to graphics calculators so they didn’t even have to calculate by hand the confidence intervals (not that I am arguing for students to calculate confidence intervals by hand!). While teachers could place their teaching of confidence within real situations and work through statistical enquiry cycles with real data and meaningful purposes, it was harder to get teacher and student buy in when the formal assessment didn’t require these things. That is not the case anymore, where the formal assessment of confidence intervals at NCEA Level 3 requires students to work though an enquiry cycle using real data and requires the interpretation of a confidence interval (this was only required at Merit level in AS90642). However …

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… things can still go wrong if we only teach to the output required for an assessment and not to the understanding (or thinking) that this output represents. Turns out that I have been trying to give the same messages about learning about confidence intervals for a few years now – the snippet above is from a workshop I gave on confidence intervals in 2007 but I could be saying this about our current teaching of confidence intervals 🙂

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This kind of interpretation of a confidence interval has become the target for measuring understanding of confidence intervals. Each part that is bracketed could be linked to important understandings we want students to have (a good task would be to get students to explain the importance of each part) but…………. just because a student can write this or identify this interpretation does not exclude the possibility that they have misunderstandings about confidence intervals. How much you care about more than “the assessment” will influence whether you care about finding out about these misunderstandings. You won’t know unless you ask, and if you stick to only what is assessed in “the assessment” in terms of output you may never know 🙂 This is not a criticism of “the assessment” because as I said at the beginning of this post, you can’t assess everything in one task, and the current assessment is better than what we had. Communication and writing about statistics is important. But it is our responsibility as teachers to use formative assessment to check for understandings and misunderstandings throughout our teaching – this is one way we can show students we care about more than just “the assessment”.

The following slides are examples of formative assessment I have used for confidence intervals (at the plenary I showed these super fast because I completely ran out of times – whoops!)

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There are a lot of things students could discuss regarding the validity of the principal’s interpretation. Will they focus on why he used a sample in the first place rather than historic data from the student management system? What about using the next 50 days? Or treating all students absent for at least half a day as being absent for the whole day? Then there is the misunderstanding that the values around the middle of the confidence interval are more likely to be the true population parameter than those on the edge…..

 

 

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Can students connect one of the visual components of the bootstrapping process (the medians for each re-sample for each group) to a key understanding of sampling variability, that the re-sample medians for the degree group are more spaced out because there was greater variation within the weekly incomes of that sample group (both sample sizes were the same)?

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Can students make sense of confidence intervals when no graphical outputs or prompts are provided? Do they understand what things affect the width of a confidence interval within a context?

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Can students design an investigation or statistics process where sample-to-population inference is needed? How will they decide how to sample words from each book? How will they make a call about sticker colour?

 

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Do students get that the confidence interval is about plausible values for the population mean not individual weights of cereal packets? Are they just using pattern recognition or a procedure (e.g. just check whether 50 is in the interval of not!)?

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?

messages_awesome

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For different topics I teach, I try to pull out what the three key aspects are that will be connected and tested to uncover student understanding. This approach is not the same as trying to define what happens at each stage of PPDAC. Trust me, I have developed detailed rubrics for every statistics standard and while teachers/students alike really like having these I struggle with how specific and mechanistic these can become.  As teachers, we have a strong desire to take a complex topic and break it down into smaller chunks so that students can understand each part, and often we do this by creating tick lists or elaborate diagrams. The problem is that this can become really structured, really specific, and really boring (and perhaps even limit creativity). By breaking stuff down into parts we can lose sight of the whole. Ideally, what we want is a message like “Stop, drop and roll” – something that has minimal structure (just three key things to remember what to do), optimal transfer (these actions work well for different situations involving fire) and where instead we focus on getting students to experience applying these things as many times as possible across a wide variety of situations and contexts. So what could our awesome messages be? Maybe something like (1) It matters how much data you have and how you got that data (2) It matters what you are measuring and how you are measuring it (this applies not just to variables but also statistical measures or models) and (3) It matters that you are uncertain and there is variation.

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Like I said earlier, we teachers like to provide diagrams and “how to guides” for our students, and I am no different. While my messages for students throughout their learning about confidence intervals and sample-to-population inference were based on the “big ideas”, I still provided additional structure. This diagram was an attempt to provide a framework for thinking about the investigation (the stuff in rectangles in the middle) but also a way to emphasise the kinds of questions we ask ourselves as we work through the process of trying to make a sample-to-population inference (the stuff in the ellipses). This was constructed towards the end of the learning as a summary of our investigative process, not given to students at the beginning of the learning phase as the blueprint to follow – I think the time of when we use scaffolds is important. It was also an attempt to provide an exemplar of how to think during an investigation without providing a finished written up investigation which the students have a tendency to copy and paste from.

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 …

interpretation

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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.

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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….

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…. 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.

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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 …

real_data

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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 Statistics and the Modern Student) and it did make me think about how we expect students to connect with data that has come from a study. If we give data that was collected through a study that itself had a purpose for the study, why should we expect or want students to develop their own purpose for investigating this same data? I do think students can be really interested in data from studies so I am not discouraging their use but perhaps that is what the purpose should be framed around – what am I personally interested in finding out about using this data?

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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.

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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……

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

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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.

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 contexts … and questions!

contexts

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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.

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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.

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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.

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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 made asked students to develop different problems for an investigation. The condition was they had to be interested in finding out the answer to their questions – this was to avoid them just choosing the first ones on the list!

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.

Making awesome connections between standards …

jelly_beans

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Is there a way to get some great connections happening between standards that could also benefit student learning? Could we use the same set of sample data to explore relationships between different combinations of categorical and numerical variables and as a consequence get deeper statistical and contextual understanding happening? To do this requires an overall question that sits above the individual investigative questions required for each standard. For this example, the overall question is about budget brands – are they just like the real thing?

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An important note regarding using an approach like this for assessment is that both the standards for AS91581 and AS91582 require the use of a multivariate data set. The intention is that students are supplied with this data set (it is not a requirement that students collect data themselves) and that the data set has enough different variables (both numerical and categorical) so that students have a choice of which variables to use for their investigations for each standard. So if you just used the data set I have created for this example it would not be sufficient for assessment against these standards as there are only three variables (brand, width, length). So, what could you do? I see no reason why you could not involve your students in the creation of the multivariate data set and then give them this data set back for use in their learning/assessment. For this context, you would also record/measure colour, weight and volume using appropriate equipment. Note that our overall question has become a little more specific by adding on “Can you tell them apart based on length and width?”

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Throughout the measuring and recording process, I was actually not sure what I was going to find when I looked at the data. By the time I had finally finished measuring all the jelly beans and could chuck the data into iNZight to see what was going on I was fully invested in whether the data would reveal anything – I’m not sure this would have been the case if I had just been given the data (but I will give you the data at the bottom of this page!) These features are interesting because they are not necessarily ones I could detect with my eye but they do make sense in terms of manufacturing and quality control systems and processes – I really like for this context how variation is an important feature of the data to discuss. Now might be a good time to watch a video about how jelly beans are made 🙂

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The actual formal inference for this example – answering an investigative question like “Is there a difference between the median length of Pascall jelly beans and the median length of Homebrand jelly beans?” – is only interesting because of the “So what?” consideration, which leads us back to the overall questions “Budget brands – are they just like the real thing? Can you tell them apart based on length and width?”. Somehow I went through all my 12 years of classroom teaching without ever using calipers to take measurements but for this context (manufacturing) using a tool that can measure more accurately than a standard ruler is important. A question that came from the audience during the plenary was about researching context and whether I knew if the jelly beans were made by the same factory, since this teacher knew that for some products (like in the video above) those that are not good enough to go in the “branded” packages and used in the “budget” brands. These two types of jelly beans are both made in Australia but by different factories but this could be information further explored by students to make stronger connections to the context.

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Since jelly beans are supposed to look like beans we would expect there to be a relationship between the length and width – and the resulting scatter plot kind of looks like a jelly bean too 🙂 There are two pairs of values that stand out which do represent actual jelly beans (as shown in the picture above). Generally we can see a tendency for wider jelly beans to be longer, but there is a reasonable amount of scatter. Why do we have this scatter? The sources of variation again can be partly explained by how the jelly beans are made (as shown in the video) but also by higher or lower levels of quality control which leads nicely to……

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…. adding a third variable (Brand) to the plot using colour. What I really like about this particular set of data is that when we subset on Brand we are doing this for a reason aligned to our overall question about budget brands being just like the real thing, not just as a “tick box” approach or as a procedure. Decisions we make about exploring data using different techniques and approaches should have a good basis and be motivated to find something out that is related to the overall question(s) being investigated.

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Lastly, I think this analysis is a great formative assessment question to give students regarding discussing the influence of possible outliers on the model(s) they have fitted. Why would we not expect the model to change much for the Homebrand jelly beans but we would for the Pascall jelly beans? We want students to have the statistical knowledge to be able to answer this based on what they see above, not just try the model with and without the outlier as a procedure (although doing this can help with building conceptual understanding). At a minimum, I would want students to discuss that for the Homebrand jelly beans the relationship is weak (large amount of scatter) so sure if you removed the outlier the correlation coefficient would increase, but your predictions are not going to be that precise anyway, so the line (slope and/or intercept for the model) moving slightly when you exclude the outlier won’t make your predictions “better”.

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

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.

Getting the awesome messages heard …

messages

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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 🙂

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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!

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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 ….

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…. 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.

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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 🙂

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.

Setting up awesome investigations …

ummm

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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”.

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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.

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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?

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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 🙂

Jennifer Lawrence

Daniel Day-Lewis

Kate Winslet

Check the times that I recorded here – a nice example to discuss regarding measurement error!

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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!

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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.

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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.

 14Turns 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.

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.

Working with teenagers is awesome …

hipsters

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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.
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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).

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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.
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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.

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.