Over the past few years I have heard one phrase a lot It is a phrase that although not unexpected, it causes me concern. This phrase is:
"Teacher's don't read research"
The obvious question then becomes "If they are not reading research, what are they reading?". For most teachers I have come across it is books of resources, articles about their content or maybe blogs such as this one that might describe activities that a teacher has done. They tend to read stuff that they can pick up and take into their class the very next day and use it.
So why is reading research important?
My simple answer to this is that reading resource books changes might change a lesson, reading research can change your outlook on education in general and can transform your classroom over a much longer period of time. Educational research is not about finding a great lesson on area of a square, it is about the big questions in education
This is only a small fraction of the questions that researchers are attempting to answer. They spend years investigating even investigating a small part of one of these questions with the aim of shedding some further light on the rest of the story. The answers they come up with are important, they describe how the outcomes changed not just for a few, but for hundreds or thousands of kids. The answers are important as they force us to examine what is currently happening in our schools, and in our classroom. They get us to judge our own day to day practice against the research piece we are looking at and look for commonalities or differences. It forces us to fundamentally examine what we believe about our profession and the way we approach it. It has the potential to change every part of our day to day practice. This same level of scrutiny is not put on individual lessons.
Research is also incredibly important as there are a lot of practices that are prevalent in many schools that have been disproven strongly by research. This means that there are a number of practices occuring in schools around the world that have been shown to have a negative impact on student outcomes. Some examples of this that I hear a lot when talking to teachers are:
Why don't teachers read research?
I think there are a number of reasons don't read research, I think some of the reason are based on the teachers and some are based on the researchers.
- What hand you write with might influence how good you are at maths
- Maths ability is 75% genetic
I am not disputing the results of their research, I haven't read it. I haven't read it because as a teacher this research doesn't help me. If I start making instruction decisions in my class based on their genetics and what hand they write with then I feel I would have to answer some pretty serious questions. The findings might be statistically valid but they don't help me to be a better teacher it is not within my realm of influence. I think it is dangerous to start making judgements and instructional decisions based on what hand someone writes with.
In conclusion if we are going to continue to grow as a teacher as we expect our students to continue to grow then looking for lessons just won't do it, we need to really pay close attention to the research so that evidence-informed practices can better influence our teaching. I see it as my role as an instructional coach and a faculty leader to digest this research for and with teacher so that it may better inform our practice.
.There are times when you are teaching that you realise you are looking outwards when you should be looking inwards. When looking through many of the tweets I read about teaching I came across one that seemed particularly appealing and that I wanted to know more about.
The reason I found it to be so appealling is that it seemed to take something that I have used with students for years and instead of turning the spotlight on what they choose to spend their time on in class, it was putting the spotlight on what choose to spend my time on in class.
Typically I have used this idea of time to give students a sense for how much of their school year the may be wasting by some of the choices they make in regards to being slow to start and in attempting to pack up early. The idea I look at with them is quite simple. There are 40 mins in a lesson and 40 weeks in a school year. Therefore if they choose to waste 1 min every lesson then over 1 year this will equate to 1 week of schooling, Therefore it they take 5 mins to get to class and get ready to start and then try to pack up 5 mins early then that is 10 mins each lesson and 10 weeks or 1 term of schooling missed each year.
I was really excited to see that the talk was posted online (see below). The way Andrew Stadel looked at this in his talk was in ensuring that we look at ourselves and the way we choose to spend class time with the same level of scrutiny. He advocated the idea that we need to use the lack of time our advantage to really focus on those practices that are most effective, to squeeze as much learning out of that time rather than focussing on ineffective practices. I would take that one step further, but along similar lines and say that I should not be spending 1 minute on something that I am not prepared for students to spend 1 week on.
There have been a lot of books previously that I have got a lot out of, normally it is a chapter or a passage or a series of activities, but none that I have felt compelled to write about, this book was an exception to me. Although I feel that I was still engaging with many of the ideas I learnt though the course I wanted to be refreshed, re=invigorated and re-inspired, I wanted to that burst of enthusiasm that I got when I was doing the course. I wanted that renewed sense of purpose, to look critically at what I am doing to see if I am on the right track and to look for what the next challenge is. With a project that I am working on already at scale within our local area (http://www.empoweringlocallearners.weebly.com) I wanted to really look at how it was travelling and despite the success, where the current issues may be
I wasn't disappointed.
I guess the first thing to say about this book is that it doesn't feel like a book, it feels like you are having a conversation with a mentor. It feels like you are sitting down with someone who believes in you, believes in what you are trying to do and believes that you are the person to be leading it, they are just there to give you what you need, when you need it. Sometimes it is that dose of inspiration such as a story from their own or someone else's desire to innovate, sometimes it is a supportive word to help pick you up when things might not be going well. Other times it is is a tool to help you move forward when you may have hit a wall. Sometimes it is about giving you the kick up the backside and the reality check you need to make sure you keep your ego and potentially your tunnel vision in check and to keep you focused on who you are really trying to make this change for.
As I moved though the book I realised that it doesn't necessarily frame this type of innovation and leadership as all puppy dogs, rainbows and unicorns. The book is all about "unleashing teacher led innovation in schools" so they talk a lot about leading change when you don't necessarily have a "leadership role" in the school. It talks about the people who will keep telling you no, that you can't do it, that they don't want to do it, that it is too much work, but it also gives you ways to work with these people to try and get them on side or to make sure they don't impact on what you are trying to do. It talks about how you will fail over and over again, that some of your ideas will be awful and that people you respect may also tell you that ideas you like are a bad idea, but it also talks about how this is an important and necessary part of the process. It talks about how you will probably put more of your physical and emotional time into this than you ever have with anything also before in your working life, but it also shows you what the rewards of it can be. In implementing this myself from the course back in 2012 I can see that it paints a realistic picture of what to expect. What I like is that they not only tell you what to expect in terms of the challenges, but they also tell you at what point in the process you can expect to come across those challenges.
The first section of the book really gets you think a lot about what you are passionate about changing, not just what annoys you, but what keeps you awake at night, what you lose sleep over, what you see day after day that you know would make all the difference if you could just change that one thing. However it also gets you thinking about what their world would look like if that did change, how it would be different. This focus on narrowing you down to what you are deeply passionate about changing really sets the scene for the rest of the journey though the book.
As you get into the second section of book the really get you drilling down in understanding the problem you are trying to solve. They are very clear and deliberate in slowing you down so that you don't jump to implementing something to solve the problem when you really don't understand the problem enough. They work with the premise that the better you understand the problem, the better you can design a effective solution as you are getting to the root of the problem.
The third section moves into how you create, test, reflect and refine effective solutions to your problem. But it is more than that, it is really about how you do these things in short cycles, how you can get a quick idea for how effective your solution will be before you pour too much of your time and effort into a larger scale test of concept that may or may not work. Finally the book looks at how you share your success and how you can scale it to involve more classes, more schools, more communities, states or countries and ultimately have a positive effect on more children.
I would recommend this book to anyone who is passionate about creating change and working towards something better for your students. The simple idea of working towards solving a problem that you are absolutely passionate about means that you are much more heavily invested in it, but also more likely to succeed if you stick with it, this book seeks to keep that journey on track, to keep it progressing and to building it in a sustainable way. With that focus in mind I think if every teacher in Australia read this book and took on the ideas seriously then a lot of the current problems in education would be moving towards being solved by the end of the year. However in saying this not everyone is at a point in their life where they can commit to a project of this kind and a book such as this may be too daunting for them.
This is the sort of book I would give to those teachers that I have really strong, thought provoking conversations about education with. I would give it to those who identify problems in their classroom or school but don't place the responsibility for fixing that onto others, they strive to be the change that they want to see in the school I would give it to those who speak with a great deal of positivity and optimism about where their students will end up given the right opportunities. I would give this book to them because they are the ones I want on my team when I start to implement this more formally again, I want their ideas, their insights and their criticisms. Though giving them this book I would also hope that they would keep me honest to the process. I also hope that if they found inspiration from this book for their own change project then I hope they would bring me along to do the same.
I can see myself picking this book up again and again, In fact I have already gone back and revisited some stuff based on my current thoughts and I have only had it for a week (it is looking a bit worse for wear already). The thing is for me, is that they get you thinking different and working differently to what you have ever done previously, Never before have I written in or highlighed a book, but I have done both these things with this book (although my OCD made me use an orange highlighter because it kinda matches the front cover.). It feels like a working document that I can continue to come back to because it has been set up that way
If you can ever manage to get into a course with these guys, don't hesitate, just do it. If you don't get that opportunity then this book is a great start for you.
There is a bit of everything here, some measurement, algebra, arithmetic and some random problem solving tasks. None of the problems on here were particularly big problems, they were in fact quite small, none of them were also particularly important, but they were just questions that had my interest at the time. None of the stuff on the paper is particularly neat or well set out, but it served its purpose, it allowed me to organise and test my thinking at the time, it help me to process the question I was working on, That is the point of messy thinking and I think that this type of thinking is under-represented in most classes.
Most people's view of doing mathematics is looking at a question and carefully setting out a well articulated set of steps to solve the problem and being able to do that straight away. Yes of course it is possible to do this, but only when the question you are doing is well known to you and well practiced. It does not happen in this way when the problem is unfamiliar or challenging. on these questions you have to try your ideas somewhere, you are going to make mistakes, you are going to have several shots at it, it is only when you have tried and made sense of the problem that you can begin to see how to turn it into that nice neatly articulated solution that so many are used to.
The problem with this is that most students do not want that messy thinking in their books, they don't want any mistakes in there, they only want those perfect solutions. If they make a mistake quite often they will rip the page out to make sure that no-one can ever know that the mistake was made. This year I wanted students to feel safe to do the messy thinking. This has been achieved in two ways.
These are two things I have tried this year with some success, but I am always on the look out for further ways for students to be more comfortable with making and learning from mistakes and from showing their messy thinking because as my blog title suggests I value this messy thinking myself.
in looking at all of the aspects of maths that are expected to be covered over the course of a year I feel that statistics offers some really great opportunities. It allows a really authentic way for students to get into some real maths with data that matters to them and to others. It is not that there is not authentic ways to engage with the other aspects of the course and get into some real maths, it just sometimes seems like it doesn't seem like an authentic situation for them, there is not the emotional buy in. With statistics you have the opportunity to introduce some very provocative data sets or ones that directly speak about them. You can have some really great discussions about how statistics are used to make decisions, how others use them to make decisions that effect you, to look at how you or other people can use them to build convincing arguments (even if the stats are quite deceiving).
I am at the very start of my unit on statistics, but I wanted to start it with them having a discussion about some data, their own diagnostic testing data. I chose to use this data for a because sometimes I feel they don't see the use of doing the testing, they don't always treat it properly and that skews our data. I also chose it as I feel that they do not always understand the results of the data, I wanted them to have much more awareness of what the data tells them and of how we use the data as eduators.
The last person to talk picks the next person to talk (from those with a counter out) by throwing them a ball or similar, only the one with the ball can talk. Once a person has used all of their counters they then cannot contribute any more to the discussion, they can sit and listen, but that is it. The teacher in this process is a facilitator, but tries to stay out of the discussion as much as possible. They provide the provocation to start off with, they pick the first person to talk and they will ask questions to stimulate the discussion if it dies off completely. In this role you need to avoid jumping in to help with that I tend to give myself the same number of talking stones that everyone else gets, if they only have three opportunities to add to the discussion then I only have three to stimulate it, it forces me to be strategic as well. This is hard when you completely disagree with what is being said, but you need to let students be the ones to respond them and to challenge that thinking.
I gave them two prompts to start their contribution with they could start with
Viral videos online attract a lot of attention and normally I don't buy into the hype, the video below is not one I had seen before until I saw it in another teachers blog. However with over 20 million views in less than a year it was clear to me that a lot of people had seen it. It was video I came across in a link in Dan Meyer's blog. The link was a link to another blog that contained the video below, watch the video before you read their post or mine. I would encourage you to support the people that led me to this post by following the links in orange to their blogs.
I really like how the teacher used this video..... I really like it a lot, why I said to watch the video first is what that teacher got out of it when they saw it was not what I initially got out of it, but after reading their post I also realise that there is a whole lot more that this can be used for. In the post the author writes
After we watch this, I like to make the connection to the classroom.
I think that this video works so well as almost every student can relate to two people in the video, the lady trying to fill up and the person watching the monitor.
When you first watch the video you find yourself as the person watching the monitor, you find it hard to put yourself in the place of the lady trying to fill up because you don't really understand why she is finding it difficult to figure out, why she is continuing to make the same error over and over without seeming to learn from it
But after reading that post I started to see both myself and some of my students in the role of the lady trying to fill up because to be honest there are times in our schooling and our lives where we feel like (and we are not) making any progress, we seem to be making the same mistakes over and over and we just can't seem to break the cycle. Quite often I feel that kids won't share their thoughts about the work we are doing or they won't ask for help because they don't want others to know that they are finding it difficult, they don't want to be the only one who asks a question because they feel that others are laughing at them. For some reason they have this reaction to maths more than any other subject. However it also made me think of a few other questions that I may ask such as.
What really struck home though is the last question that this teacher asked about what would happen if the lady gave up and just drove away. It got me thinking about what are the short term consequences and what are the long term consequences on giving up on it. Does she just fill up tomorrow? Does she run out of petrol on the way home? If she does run out of petrol what does she miss, is she late for work, does she miss something really important.
It got me thinking about both the short and long term consequences of giving up in the classroom, I had obviously thought about this before, but this got me thinking about it in a new way. In the short term it might mean they don't understand that concept, they might not be able to do that work over the next lesson or two but from that point it begins to snowball. The course is hopefully built in a way that one idea helps to build on the next, so if you don't understand the concept from this week maybe you also won't be able to follow the ones next week and the week after. Maybe this will mean you can't do the assessment task and that you get a failing grade. But a failing grade again is not the end of the world, but since your program is structured in a way that the ideas build then not understanding that topic may also mean that you don't understand the next topic and the next. Since the work in a year of school builds upon the previous year then maybe you don't understand next year either. Maybe after all this you give up on maths completely and maybe when you have kids yourself you pass that onto them, and they pass it onto their kids.
The account above is a bit dramatic I know but over the days, weeks months and years this builds into a self-concept of yourself as a mathematics learner. Your experiences shape you as a person, you make a decision as to whether maths is something you can do or you can't do. Your self-concept towards a subject effects how you approach it and how you talk about it. How you talk about it can influence how others see you as a learner of a subject and can also effect how others see themselves. If they feel they are doing as well as you and you start saying that you are really bad at maths then they may start to feel that they are not doing as well as they think. This self-concept is something you can break by doing something different, you just need to stop doing the same laps of the same petrol pump.
When students think about presenting their solution to a mathematical problem visually I get very excited because I find those visual solutions hard to generate myself, I am getting better it, but I don't see the mathematics in that way when I am solving a problem generally, I get too wrapped up in the equations in the formal mathematical notation. The reason I get excited about those visual representations for a problem is that they often are much easier than the formal mathematics and they lead to some great mathematics.
The other day I did a task with my class that I got from Professor Peter Sullivan from Monash University who I had the pleasure of working with once per term for three previous years in my work as a numeracy coach. The question is as follow
I like this question on a range of levels
One of the groups working on this task came up with the solution shown below, it has been altered from the original (which was just dots showing the same information) but the same thinking was there. They first started by looking at the 0.7 and 0.6 and converting them to 70% and 60% which they then turned into 70/100 and 60/100 which simplified to 7/10 and 6/10. From this they reasoned that ten was the minimum number that could be on the train. From here they attacked the main part of the problem by first assuming that there was as much sharing as possible, making sure everyone with a computer also has a backpack. This gives six people having both items, this is shown by the image below on the left. They next thought about orgainsing the same but with as little sharing as possible, by making sure everyone who didn't have a backpack needed to have a computer. This scenario gave the image on the right below, an overlap of three. Hence they gave a range of answers as being between three and six out of ten people.
The animation below shows they range of answers with more clarity
What occurred to me as I was documenting their thinking on the board is how nicely this representation led into the intended purpose of the lesson, Venn diagrams and two-way tables. Simply by circling the laptops in one colour and circling the laptops in another I had generated a fairly accurate Venn diagram as shown below. You could clearly see in each case how many were in the intersection of the two sets, how many belonged to only one of the two sets and how many were outside of those two sets.
What I really liked about this is now easily it made the transition to Venn diagrams and two-way tables. from our initial starting point of probability of simple events.
A few weeks ago I came across an article on my Twitter feed that I thought was really good, it was not a long read but it was one that really challenged me to think deeply about my practice and what constitutes a good day of teaching, I would strongly suggest that you give it a read at some point. The article is 'When is a Good Day Teaching a Bad Thing' by Timothy F Slater (click the link to open the article). The article starts with a description of most teachers idea of an ideal day. Limited behaviour issues, got through the work you planned, students seemed to engage by both answering questions correctly and asking questions that you could answer. It goes on to say one particularly important point
"I submit to you that when everything seems fine, it s probably the perfect time to carefully find out exactly what depth of learning is actually occurring in your class."
The article goes on to talk about a hidden contract between students and their teachers which is an unspoken set of rules that both parties follow. Students agree to behave, do their work, ask and answer questions if the teacher agrees to organise well detailed lessons and work, try to make it interesting, assign work that is very similar to that clearly gone through in class and show them exactly what they need to do to achieve a high grade.
No one ever speaks to each other about these contractual agreements, but you notice it in a class if someone breaks them. If the teacher breaks it by assigning a question that has not been specifically covered as an example in class then the off task behaviors and the cries of "this is unfair, you haven't shown us how to do it" ring out. If a student breaks the contract by not behaving then they are often removed from the class.
When I read through this I went back and re-read the first part and could clearly see that hidden contract at play and the greater importance of that quote. It was seen as a good day teaching because everyone was meeting their part of the hidden contract. However one of the fundamental parts of that contract is that there is little emphasis from the student or the teacher on having to truly think for themselves, they just need to reproduce the work the teacher has already done for them. Students could easily answer the questions as the teacher had already given them the answers, they had written them on their page, they didn't have to synthesise a response, they just had to find it. The teacher could easily answer the questions from the student because the student was only engaging with the work on a superficial level, the work they had gone through, and the questions they had been asked didn't challenge their thinking, didn't target their possible misconceptions, didn't deepen their understanding or draw connections to previous work, it was more than likely just a slight extension on the previous lesson. There was no way of them thinking deeply enough about the work to ask a really good thoughtful question.
Those days where there are tasks given to students or questions asked of them that target some deeper thinking are often not associated with quiet classrooms, Students are challenged and sometimes this means they are frustrated that they are making some mistakes or that their approach just doesn't seem to be working as they thought it would, they might be frustrated that the are not sure where to start. This may be coming out of them thinking they should already have the answer somewhere in their book, it might be coming out of the idea that they have to think about things differently to they ever have before.
What ever that reason for the frustration it can be a powerful motivator for learning and a powerful tool for improvement, but the key is just keeping them frustrated enough to keep trying rather than so frustrated that they simply give up. That frustration of knowing you can do something, but you just don't know how to yet is a frustration I know well, but it is one I have had to learn to become comfortable with. The idea of knowing there is just something small you are missing, someone you need to talk to, a different way of looking at it, something that is just outside your reach is one that is important in not only building conceptual understanding but students who know how to learn and have resilience in the face of setbacks.
In any classroom and any learning situation it is important to have an idea of what students are bringing to the learning. Having a sense for what they already solidly grasp, what they find difficult, and what their misconceptions are all help you to better target your teaching.
In looking at what students bring to the learning it is often the diagnostic testing or a pre-test on the particular content that may form the basis of knowing what they bring. However I think that this only looks at a very narrow band of understanding, what formal mathematical tools they have or remember. This is approaching it from a basis of procedural fluency rather than conceptual understanding. In looking at what they bring to the learning it is very important to me to know if they have a feel for the concept, do they have a sense of what it is before I start to apply too much formal mathematics to it. Can they intuitively determine a way to do the problem without knowing the formal mathematics and if they can, can I use this intuitive understanding as a base for building further understanding.
An activity that we did in class other day really brought that into clear focus for me as it does most years. The problem and the specifications for the task are shown below.
Obviously with this task the food helps, there is some competition here to help maximise the number. It is clear that this becomes a problem on volume, but this was not something students were told, a few came to that conclusion as they completed the task and it was good for me to know that some had a sense of volume, but it was not necessary to complete the task.
The intention behind the task was to see if they could connect their idea of area to that of volume of shapes with uniform cross sections. How that intention was set up was by limiting the number of cheese balls they were given. By limiting the materials you force them into thinking about the problem in more depth they need to think flexibly about how they can use the resources they have to solve the problem they had been given. The most common approach to solving this problem was the one shown below
Using this method students created a layer of cheese balls on the bottom and multiplied it by how many of those layers could fit in the container, they determined this by measuring the side in cheese balls. In this case the student would have found that they could fill it with 80 balls (10x8). What is interesting about this approach is that it is the exact method they would be taught to calculate the volume of these shapes, multiplying the area of the end by the length of the shape and they had got to the point where they had generalised the solution. Many had started with rectangular prisms and determined the area of the base by multiplying the length in cheese balls by the width in cheese balls but then ran into difficulty when looking at a cylinder, they had to come up with a way to approach that and realised that area was the link that generalised for any shape.
It was a situation where they did not need to be taught it, they had a sense for it already, my role was then to formalise the thinking at the end of the task or
Sometimes ideas for lessons get away from me and take me to some unexpected places, and sometimes the reaction of classes to those lessons are also unexpected. I was thinking about a lesson idea for circumference and I thought about a lesson I saw once from Andrew Stadel (lesson link here). Where he wanted students to determine how many rolls of tyre it would be for a tyre to hit a target, I liked to lesson but was not sure how my students would "buy in" to the task. I wanted to redesign the task a little to give students a greater reason for getting into the maths.
Like with many of my ideas I ran it past a teacher at the school that I often collaborate with on tasks such as this and we came up with what I think is an interesting alternative to that original task.
Students had to determine where on the ground they were going to put a chocolate frog so that it met two criteria:
The twist with this task was that they were only allowed to use 1 item from their bag to measure both the tyre and the distance on the ground.
In relation to this task I think there are three incredibly important aspects to it. Firstly is that they really have to think about the positives and negatives of anything that might be in there bag in relation to it's use as a measuring device, there was nothing in anyone's bag that could accurately measure the circumference of the circle in one measurement so they had to think about aspects such length, flexibility and having actual measurements on the device. Secondly was the idea that the criteria and the restrictions I provided made the task of achieving it quite difficult, Using something that was not ideal as a measuring device meant that there was going to be inherent errors in the way they could possibly measure the tyre. They had to be very accurate in what they used as the measuring errors could compound quickly as they measured both the tyre and the ground.Finally there was a high degree of ownership over the task as they seemed to really want to be able to not have a squashed frog. That little element of competition was very valuable in this task, That element of competition I have found to be very useful in a range of tasks I have done previously.
The Approaches and Challenges
The range of measuring devices people used to measure the tyre was quite interesting. Most chose their ruler from their bag to measure it. However since the ruler was only 30 cm and the tyre was significantly bigger than that both in circumference and diameter they needed to make lots of measurements and therefore compounding any measurement errors. Most were also using a rigid wooden ruler to measure a curved surface which made the measuring more difficult again, some had a more flexible ruler that they could wrap around, but some of the compounding errors remained. Many of these students decided to use a ruler as they could then stick within their comfort area of standard units of measurement.
Others chose to use headphone cables as measuring devices, they found them to be much more flexible and longer than the rulers, therefore they could accurately follow the contours of the tyre and it was long enough that the measurement errors were not as significant. However they seemed to encounter difficulty when dealing with lengths that were not quite a full headphone cable length. They were not sure how to figure out what fraction or proportion of the headphone cable was left over. When Introduced to the idea of folding the headphone cable to figure out how many parts were used they found this area. For example in the image below if they measured the tyre and got a total diameter of the blue part of the line below, they could fold it as shown to give an approximate length of just over 3/4.
The other part of this that students seemed to find challenging is using headphone cables as a unit of measurement in a mathematical formula. The seemed to have this impression that the formula for circumference of a circle would only work if you were working in standard units of measurement. They didn't realise that If you said that the diameter was 3/4 headphone cables then the diameter would be 3.14 x 3/4 = 2.36 headphone cables. This however was not unexpected, in mathematics we get so used to dealing with measuring devices with standard units of measurement that we do not often realise that sometimes the non-standard units of measurement can be just as valid and just as accurate.
Some of the students who engaged in the task a little more strategically came up with multiple ways to measure the tyre using the same device. The measured the circumference directly, but then they also measured the diameter and used to formula to determine the circumference, where there was significant differences between the two values they took measurements again to verify their results and if they were accurate then they had some discussion about which of their measurements they felt was more accurate. They realised that a discrepancy of 3 cm was not much but when you multiply it over 10 rolls you have just potentially lost a third of your target area.
The final challenge most of them faced was where to place the frog because that question is not as simple as it seems. If you put it too close to where you think the tyre will finish and your measurements are off then your frog will get squashed. Conversely if you put it close to 1 m away from where you think the tyre will finish and your measurements are off then you could be outside the target range. Most people put it closer to the tyre and a few put it closer to the end of the 1 m, very few considered putting it where they thought of the middle of the range may be which in my humble opinion is where I would be aiming.
Overall when we rolled the tyre the level of excitement was high, they were all keen to see how their calculations faired. Of the 8 groups that placed frogs down 1 group was more than 10 rolls away but outside the 1 m target range, four groups had their frog squashed (but by less than 15 cm) and 3 groups met both criteria. They seemed to really enjoy the activity and everyone got to eat the frogs at the end.
Senior Leader of Pedagogical Innovation and Mathematics Coordinator in Regional South Australia.
Opinions in this blog are my own and do not necessarily represent the views of my employer.